Testing equality knapsacks for feasibility

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Testing equality knapsacks for feasibility
Hansen, Paul P
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Dynamic programming ( lcsh )
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Integer programming ( fast )
bibliography ( marcgt )
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Submitted in partial fulfillment of the requirements for the degree, Master of Science, Applied Mathematics.
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Department of Mathematical and Statistical Sciences
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by Paul P. Hansen.

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A thesis submitted to the
University of Colorado at Denver
in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
Public Administration

1996 by Mary Thomas Apodaca
All rights reserved.

This Thesis for the Doctor of Philosophy
degree by
Mary Apodaca
has been approved for the
Graduate School of Public Affairs
Occ 7

Apodaca, Mary Thomas (Ph.D., Public Administration)
Problem Definition, Political Innovation, and School Reform:
The Texas Statewide Systemic Initiative
Thesis directed by Professor Peter deLeon
A Nation at Risk (1983) initiated the current era of school
reform and provoked much policy making. The goals of school
reformers has not been reached. Further, the efforts have not
garnered significant public engagement because of their
fragmented nature. This dissertation turned on the idea that
problem definition, a postmodern policy theory strand, would
provide insight. Problem definition delimits a workable concept
from an amorphous problematic situation.
The research was driven by the following questions: Was
the group that created the problem definition or the group
directing the project an outside-the-bureaucracy group or a
bureaucracy? Did the group take a problem-centered approach,
engaging in frame reflection and/or lay probing? Did it exhibit
other postmodern tendencies? Was a policy entrepreneur
involved? What part did politics play?

A case study of the Texas Statewide Systemic Initiative, a
National Science Foundation-funded project relied on
documents from Texas, Colorado, and the NSF. Interviews with
staff, plus an outside monitor, and other public officials filled in
gaps in the narration. Interviews were conducted during one
site visit and by telephone and electronic mail.
The initial Texas proposal-writing group was inside the
bureaucracy and did not use a problem-centered approach.
Funding was suspended due to inadequate progress. Politics
kept the process going until a policy entrepreneur emerged to
write a new proposal. The project is currently directed by a
third-party agency and has been called the "central systemic
initiative in the state." Problem-centeredness and frame
reflection are extremely difficult approaches for policy makers.
However, there was some of evidence of these approaches and
there were definitely other postmodern tendencies at work
during the evolution of the project. A policy entrepreneur was
integral and politics was intertwined throughout.
The implications fall along two dimensions:
1. Broad-scale policy innovation is not on the horizon;
furthermore it would not effect epic-change school reform; and

2. Third-party agencies working at the state level, in
concert with federal and state agencies, and with equal power
in their particular area, can effect changes that government
agencies alone cannot.
This abstract accurately represents the content of th
candidate's thesis. I recommend its public;
Peter deLeon

I had the distinct advantage of living policy making
during the life of this dissertation and first wish to thank the
workers behind-the-scenes, my fellow school reformers at the
Colorado Department of Education, across the state of
Colorado, and across the nation. Thanks also go to Arvin Blome,
Richard Laughlin, and Brian McNulty, Associate, Deputy, and
Assistant Colorado Commissioners of Education. Their ability
for empowering middle level people is exemplary.
Without the assistance of members of the Texas
Statewide Systemic Initiative, there would have been no case
study and no dissertation. They easily and freely shared the
documentation of the project, and even more importantly, they
spoke openly about obstacles they had encountered. They lived
Uri Treisman's assertion that "the only good dissertation is a
completed one."
Rose Acera, Karen Eikner, David Hill, and Cathy Seeley,
and Uri Treisman, among many Texas SSI staff, gave
generously of their time and thoughtful insights. I am also

grateful to Janice Earle and Peirce Hammond, among others at
the National Science Foundation, who understood the value of
different perspectives on this major effort. Wayne Welch, the
Texas Statewide Systemic Initiative's outside monitor, was
invaluable to the research through written reports, interviews,
and comments on drafts.
The Woodrow Wilson National Fellowship Foundation
where I began working at the final stages of the study, provided
not only time and financial resources, but emotional and
intellectual support and encouragement. Thanks go to Dale
Koepp and Nancy Mohr who commented on final drafts. Each
member of my dissertation committee at the University of
Colorado at Denver provided valuable insights at the
colloquium and defense. They helped me be more emphatic in
my conclusions and the dissertation would be much less
without any one of them. Linda deLeon was especially
generous of her time.
Lastly, this dissertation would not have been
accomplished without the guidance and assistance not to
mention insistence of the committee Chair, Peter deLeon. His
thorough understanding of the writing process, his writing and

editing skills, his kindness and sense of humor, his commitment
to learning and graduate students all of these alone and
together are inspiring. How do we replicate the access Peter
provides? This dissertation attempts to interest its readers in
this kind of learning for all students, not just the lucky few who
end up doctoral candidates.

This dissertation is dedicated to my daughter,
Kristen Dogan,
who began teaching in September 1996.

TABLE OF CONTENTS....................................X
1. INTRODUCTION...................................1
School Reform on the National Scene............1
The Concept of Problem Definition..............5
The Power of Problem Definition................7
Educational Reform............................11
A Plethora of Solutions.................13
Schooling Overwhelms Reformers..........16
The Current Era of Education Reform.....18
Bureaucracy and Education.....................22
Thesis Outline..........................29
2. REVIEW OF THE LITERATURE......................30
Defining Problem Definition.............31

Related Policy Strands.....................41
Changing the Equation......................46
Policy Innovation..........................50
The Policy Entrepreneur....................54
Polsby and Schattschneider as Prologue....59
Current Perceptions of Problem Definition........61
Lay Probing................................61
The Christening............................67
Framework, Weapon, and Outcome.............73
Problem Setting............................81
Instrumental versus Expressive.............85
Regime-Level Policy........................90
A Conceptual Framework...........................99

3. RESEARCH DESIGN.................................104
The Study.......................................104
Rationale for the Case Study Method......105
Integrity of a Case Study................106
The Texas Site..................................109
Specific Procedures......................112
Unsolicited Confirmation........................114
4. CASE STUDY......................................116
The National Science Foundation..........116
The Dana Center..........................117
The Texas Statewide Systemic Initiative..120
The National Science Foundation
Statewide Systemic Initiatives.....121
Stages of Evolution.............................125
Systemic Change..........................127
Stage One: The 1991 Plan.................129
Stage Two: A New Plan and
New Rejection......................138

Stage Three: The Addendum................142
The Policy Entrepreneur..................147
Stage Four: Implementation (1994-1996)...151
Early Implementation.....................152
The Texas SSI Inside the Dana Center...........158
Election Year Politics.........................162
5. CONCLUSION.......................................169
Characteristics of the Texas Groups............170
Are Non-Bureaucratic Tendencies Apparent?.....171
The Policy Entrepreneur as Liaison.............175
How Was Problem-Centeredness Evident?..........185
Frame Reflection.........................185
Experts versus the Public?...............191
The Role of Policy and Politics................195
Implications for Policy Research...............199
Even Goals Are Not Givens 203
Lessons Relearned..............................208

A. QUESTIONS FOR INFORMANTS.................211

School Reform on the National Scene
On July 23,1995, Sesno and Morton of CNN's "Late
Edition" wrapped up an hour of political give and take on
affirmative action with a short discussion of how education
figured into the debate. Any educational reformer would have
listened with enthusiasm as Morton briefly explained the
findings of the 1983 A Nation at Risk, a blistering indictment of
the education system. When he had finished talking about the
report, Sesno asked, "Has anything changed [in the past dozen
years]?" Morton's terse reply was "I don't think so."
A national political commentator knows nothing about
education reform? Clearly, current education reform efforts
to alleviate the condition characterized in A Nation at Risk
have not succeeded in becoming a national, visible innovation.
Sesno and Morton made their "awareness that things are not as
they should be" explicit (Majone 1989,57) but, contrary to
Morton's glib assessment, the 1980s through early 1990s were

characterized by an extremely high volume of educational
policy changes at all governmental levels (Fuhrman, Clime, &
Elmore 1987,1991; Fuhrman & Massell 1992; Mawhinney 1993).
As Odden (1991, 301) has observed, for example, "44 states
required student testing for minimum academic competencies,
and 38 states required new teachers to pass a state standardized
test before entering a teacher education program and/ or before
becoming certified to teach."
All this, and yet a recent report on the future of
education in Colorado states "two in three Coloradans think the
public schools aren't adequately preparing students for
tomorrow's jobs and careers" (Setting the Standard, 1994,1).
And an October 1995 (Bradley 1995) report claims almost 50% of
parents surveyed nationally did not believe that a diploma from
their local high school would guarantee that a student had
"mastered the basics."
While these statistics clearly indicate a lack of public
support for the educational status quo, few schools display a
sense of urgency for reform that includes a "number of
departures from conventional practice that fundamentally
change the roles of teachers, administrators, students and
parents working with schools" (Newmann & Clune 1992,10).

Thus, despite dozens of federal, state, and local initiatives,
hundreds of articles and books, and millions of private and
public dollars, the latest round of American school reform
touched off by A Nation at Risk has not become what I will
call, after Polsby (1984), a "political innovation," let alone is it
classified a success (Cuban 1995; Daggett 1995; Fuhrman &
Massell 1992; Newmann & Clune 1992; Rothman 1993). As
Richard Elmore (1991,6) says, there is little proof that "policy
innovations, no matter how well-intentioned, necessarily
improve the performance of public organizations." Education
policy making, although often frenzied, has failed to change
schools enough to catch the public's attention.
This may be more understandable if we heed Peterson
(1983,3-11), who lambastes studies conducted by task forces
and commissions like A Nation at Risk. He says such reports
have a function, but "fact-finding, rigorous analysis, and policy
development are usually not among them." He continues, they
are "certain to exaggerate the problem...state only broad,
general objectives... [and] recommend changes that are beyond
current technology and resources." Peterson points out that
such commissions have no authority and, more importantly, no
responsibility. This compels us to ask, How can school reform

evolve "from elite quarrel to mass movement?" (Mitchell 1981).
This question leads to the subject of this dissertation.
This dissertation is intended for researchers, students,
and practitioners of generic public policy in general, and
education policy. In particular, I propose to shed light on the
near past and future of school reform as a policy agenda issue in
its predecision stage. Students of public policy have several
excellent sources (as documented in the literature review) for
the study of problem definition; however, I have not found any
explicit histories of the development of problem definition
before a significant policy change. This dissertation helps fill
that gap.
Policy researchers have called for more stories,
narratives, and case studies of the process, especially those of
protracted policy issues (e.g., Schon & Rein 1994), and political
innovation even political innovations that do riot occur
(Polsby 1984). Meanwhile, educational reformers continue to
struggle with "scaling" reform efforts, that is, moving from
fragmented projects to nationally (or state) recognized,
sustained progress towards fundamental and lasting reform.
Reformers need a broad and long-term view of the possibilities


of success of their efforts from a policy standpoint. This
dissertation attempts to respond to these needs and requests.
The Concept of Problem Definition
Imagine a puzzle with a thousand pieces all black.
Even though fiendishly difficult, our make-believe puzzle could
be solved. If you set out to solve it, you would know that your
goal was to fit the pieces together using all of them. What is
more, once it was solved, you would know it had been solved
and you could demonstrate that the solution had been reached
before someone knocked over the card table.1 The failure of
our schools, on the other hand, is not a puzzle or a problem; it
remains what is called in public policy theory, a "problematic
situation or difficulty." According to social constructivist public
policy theory, a problematic situation or difficulty is a very
different beast from even a fiendishly difficult but
conceivably solvable puzzle.
1 A billion-piece all-black puzzle was used as a metaphor for
breaking the Soviet code, a feat almost miraculously accomplished by
American cryptographers during World War II (Weiner 1995, A10).

A "problematic situation" or "difficulty" is a conception
of, for instance, the way the education world is for the present
and foreseeable future. It is overwhelmingly (or vaguely and
naggingly) not as it should be. "That's just the way it is...
nothing can be done about it." As long as failing schools simply
exist as a part of life there can be no policy solution.
A "problem," once defined, is something else. A problem
is a contradiction, something we can get our minds around.
Social problems lend themselves to solutions, but, as Aaron
Wildavsky said, we never solve a problem "once and for all."
We tackle one problem and then move on to the next set of
problems mostly caused by our earlier attempts at resolution.
Wildavsky adds,
instead of thinking of permanent solutions we
should think of permanent problems in the
sense that one problem always succeeds and
replaces another...the capacity of policies to
generate more interesting successors and our
ability better to learn from them what we
ought to prefer, may be their most important
quality (Wildavsky 1989,5).

From this perspective, problematic situations and even
I the more manageable defined problems have always been
| and always will be with us. These less-than-ideal conditions
in our best-of-all-possible worlds include such national
dilemmas as substance abuse, societal and family violence,
i teenage pregnancy, environmental degradation, unequal access
to health care, homelessness, poverty, declining cities,
uncontrolled and perhaps uncontrollable trade and fiscal
| deficits, a low savings rate, a questionable military strategy, a
! crisis in public support for democratic institutions, and most
I critical for this dissertation what is often called "the worst
I system of primary and secondary education in the First World"
! (Lind, 1995).
| The Power of Problem Definition
| In this dissertation, I look at a situation vast numbers
! of students not performing at high enough levels to thrive in, let
| alone contribute to, our society through the conceptual lens
| of the "flourishing subfield within policy studies," called
j "problem definition" (Bosso 1994,188). In Baumgartner and
J Jones' (1993,54) description, problem definition exists partially

because "policymakers seeking particular policy outcomes
attempt to redefine issues to suit their needs, taking advantage
of circumstances as they can."
Problem definition is a relatively new, and postmodern
theoretical strand. As Rochefort and Cobb (1994a, 7) spell out,
postmodernism is "an intellectual style concerned with
examining the unquestioned value assumptions embodied in
culture and society."2 Fischer (1990,216) adds that
postmodernism (he refers to it as postpositivism) thus
"confronts positivism's most fundamental principle, namely,
the strict separation of facts and values" and thus provides "a
more comprehensive concept of rationality."
A concerted effort at school reform has persisted since
1983 and A Nation at Risk, and yet has failed to become a
national innovation schools that are somehow failing remain
a problematic situation for most citizens. That is why most are
not engaged in the educational reformers' struggle for reform.
2 Up until a few years ago, the term "postmodern" has been used
more in the arts, literature, and philosophy, while the term "postpositivism"
has been used in the social sciences. "Postmodern" is now "sweeping the
social sciences" (Rosenau 1993,1, [quoted in Rochefort & Cobb 1994a, 7]).

In this dissertation, I assert that educators are reluctant to focus
on the question "What is happening? (Dery 1984)" rather than
the more common "What should we do?" This proclivity
impedes progress towards a general agreement on how public
education could best serve its actual clients: the students (who
attend, in theory, to learn), their parents (as schools assist in
socialization), and the public (who benefit from public
education as a result of a public goods arena). I argue that the
apparent lack of significant energy and vigor of this effort can
be attributed to the nature of the reform effort itself, the failure
of education reformers to engage the public in formulating a
compelling problem definition.
Such a definition could ignite the public imagination
not to mention the imagination of other reformers and the
educational bureaucracy. It could then lead to a nationally
recognized effort understood by educators and the public alike.
Instead, educational reformers continue to head off with great
energy but in all directions at once, competing with each other,
denigrating, and sometimes even nullifying other efforts. And,
most important, they are still lacking a clear idea of a problem
that could engage the public. The research in problem definition

in this dissertation is intended to help clarify why this is so
(Majone 1989; Rothman 1993).
A more interesting problem definition has the potential
of focusing public energy. It is my assertion that more powerful
definitions at once engaging to the public and yet appealing
to school people and policy makers of all political persuasions
are key to the ultimate success of fundamental and lasting
education reform. Or, at least as Wildavsky says "a better
class of problem." Optimal definitions are necessary, if not
sufficient, for a large scale, highly visible break with current
educational practice and institutions in order to accomplish
significant, continual improvement in the level of learning for
vast numbers of currently underserved students.
The basic argument is that what stands in the way of
dynamic, compelling definitions is the approach to problem
definition by the educational bureaucracy. I will argue here for
a "problem-centered" rather than the more typical "solution-
minded" or "methods-driven" approach. A problem-centered
approach is one in which the participants focus on the
problematic situation rather than jumping to a solution (Dery
1984; cf. Cohen, March, & Olsen 1972). They then move toward
a problem definition, ideally involving the public in the

problem situation (Lindblom 1990). They frame the problem in
a way that reflects the aspirations and fears of all interested
parties (Schon & Rein 1994).
I will also propose that a problem-centered approach is
most likely to emerge through the efforts of a group outside the
educational bureaucracy. The literature review will demonstrate
that institutions, bureaucracies and thus the larger
educational community and its bureaucracies were
themselves once solutions to a problem or problems. Their
members tend to depend on ready-made (as opposed to
broader, innovative or not-yet-conceived-of) solutions, the ones
that worked in the past or that they have always believed
would work but were thwarted in attempting or truly
implementing. It is necessary, I contend, to find an organization
that has the capability of centering its work on the problem
rather than on its own continued existence.
Educational Reform
What schools look like and how they function are
considered the public's privilege to decide. Schooling, especially
secondary schooling, has been a political issue since its

inception in the nineteenth century. This politicization can be
seen throughout the twentieth century as school reformers have
taken several cuts at the definition of "failing schools." In the
1920s, schools were not "efficient" enough to please the
Progressives; that is, they were not organized like a business. In
the 1930s, teachers were unpaid. In the 1950s, scientific and
engineering training did not measure up once Sputnik was
launched. In the 1960s, "over-bureaucratization, under-
involvement by parents, and racial segregation were considered
the major problems" (Peterson 1983,29-30).
Moreover, education goals have frequently changed. In
the first decades of the twentieth century, good schooling meant
the rapid and total assimilation of waves of immigrant children.
The Progressives' goal was to use scientific management
techniques for organizing the educational system for efficiency
along with the rest of America according to the factory
model (Tyack & Cuban 1995,8).3
3 The typical American high school follows the factory model in that
students are classified according to age and ability and march in cohorts
from one classroom and subject to the next every set number of minutes,
regardless of interest or need. Individual students are allowed to slip
through the cracks as long as the administrative order remains intact.

Following the civil rights movement of the 1960s, good
schooling meant universal access to all schools for all students
(Graham 1995,43). Conversely, the mid-1970s version of school
failure identified whatever gains in equity were accomplished
in the 1960s as the source of the lack of student achievement
(Tyack & Cuban 1995,29). It seems that keeping all students in
school led to changes in schools and their curricula that were
resented by middle class families whose children once were the
only ones in the public schools (Tyack & Cuban 1995,14). For at
least the American middle class, there once was a Golden Age
of Schooling, lost when schooling became the legitimate right of
students of all social classes.
The changing political climate and world events have as
much or more to do with a specific call for reform as does the
true condition of schooling (Cremin 1989). Consensus-building
definitions and focused efforts are lacking, however, leading to
an overabundance of solutions.
A Plethora of Solutions
The end of the twentieth century has seen a call for
fundamental reform in many parts of American society.

"Restructuring" is one of the more recent code words. In
education, this translates into a concept that includes
decentralization, shared decision-making,
school choice, schools within schools, flexible
scheduling with longer classes, teacher
teaming, common academic curriculum
required for all students, reduction of tracking
and ability grouping, external standards for
school accountability, and new forms of
assessment such as portfolios (Newmann &
Wehlage 1995,2).
There is more,
site based management...empowered]
teachers ...roles and responsibilities
...personnel structures ...shared
missions.. .transforming physical space of
schools.. .flexible group learning environments
...moving away from superficially covering
facts toward substantive understanding,
problem solving, and analytical thinking
(Berends & King 1994,30).

In short, there is a long list of possible school reforms.
This list derives from a predilection of the educational
community a major assumption of this dissertation to leap
to solutions rather than to center on a problematic situation. The
predilection for quick solutions is a national trait, not simply a
failing of school people. Even educational researchers decry
"the high volume of education policy production at all
levels...and a tendency to address each problem with a distinct
special program" (Fuhrman & Massell 1992,1). These critics call
for "systemic change," that is, more coherence through national
standards and subsequent consistent changes in testing,
curriculum, and instruction. They would add more flexibility
and yet stricter accountability for individual schools.
The intent of this dissertation is to look at the whole of
school reform as a national policy issue rather than as the
property of one or another reformer or as a project. I propose a
broader longer-term and policy-oriented lens for looking at the
problematic situation of failing schools.

Schooling Overwhelms Reformers
Both insiders and outsiders have tried to change
schooling. Insiders were successful in nurturing the growth of
the common school during the nineteenth century through
"networks of professionals, centered in teachers' colleges,
cutting across states and localities" (Elmore 1984,126). Later,
insiders tried to humanize schooling with the installation of the
kindergarten and the junior high school. However, "through a
process of institutional assimilation, the kindergarten and the
junior high school ended up resembling the primary and high
school grades above them," (Tyack & Cuban 1995, 75-76). The
intended changes were trivialized and marginalized.
Outsiders have a long history of working inside schools.
Private companies provide for transportation and food services,
as well as services for special education and incarcerated youth.
They sell class rings and sports equipment, and rent graduation
gowns. When outsiders have moved to change schooling,
however, their success has proven more fleeting. In the
Texarkana scandal of 1969, teachers were required to take part
in "performance contracting," a technique in which they would
be compensated by the number of students who performed

successfully on standardized tests. The first test results seemed
to show improved student achievement. However, it was
shown that faced with this high stakes "teacher-proof"
technology, teachers had employed actual test items to prepare
students for the tests. A subsequent 1971 study by RAND
showed no significant overall difference between the
experimental and control groups (Tyack & Cuban 1995,117-
In the early 1990s, Education Alternatives, Inc. (EAI), ran
nine Baltimore public schools on a profit-making basis. In late
1995, the school district terminated its five-year contract with
EAI after three and one-half years. Prolonged negotiations
failed to convince EAI to accept a $7 million cut to help the
school district meet a shortfall. Data showed that "although
students in EAI schools posted modest gains, the company
spent about 11 percent more per student than the rest of the
city's public schools" and, as has been the case elsewhere, "EAI
suffers from overselling in the first place" (Walsh 1995). While
there have been numerous attempts at institutional school
reform by outsiders, the results have not been any more
fundamental or long-lived than those by insiders.

The Current Era of Education Reform
As noted above, in 1983, "a report to the Nation and the
Secretary of Education and an open letter to the American
people" from the National Commission on Excellence in
Education, the before-mentioned, A Nation at Risk, trumpeted
"a rising tide of mediocrity," and the first problem definition of
this generation of school reform. It stated the fundamental
mission of public education was to prepare young people for
democratic citizenship and to promote individual and national
prosperity. It also made it clear that mediocre student
achievement and poor teachers were the reasons reform was
needed. A Nation at Risk stated its solution: state level policy
requiring a core curriculum, increased high school graduation
requirements, expanded student testing, and toughening
requirements for entering the teaching profession (Odden 1991,
301; Ravitch 1995,135).
This characterization of the problem and solutions was
accepted by policy makers who produced a flood of laws and
policies of control to be carried out by bureaucrats (Fuhrman &
Massell 1992). A Nation at Risk clearly stated a simple problem
and its solution, but subsequent reformers have concluded that

it was wrong on both counts (Harris 1994,6). "Critics dubbed
this the 'more-longer-harder' strategy of education reform."
Policy as translated by the bureaucracy decreed that students
and teachers would take more courses, put in longer hours, and
work harder. "Like most command-and-control strategies, it
failed" (Osborne & Gaebler 1992,315).
Partially as a reaction to the "deskilling" of teachers and
the top-down nature of the first wave of reform plus its
failure to effect the desired improvement the second
definition of reform opposed the notion that those who educate
our children are no more than early nineteenth-century factory
workers who must be subjected to direction. The underlying
problem now was redefined as the first definition of reform,
that is, suffocating state and local education agency
bureaucracies and their stultifying effects on schools, teachers,
and students. The solution lay in granting more autonomy to
school-level practitioners (teachers and building
One branch of reformers called for the privatization of
schooling (Chubb & Moe 1988; Chubb & Moe 1990; O'Neil
1995). Another branch of reformers emphasized public school
change with heavy involvement of staff, parents, and the

community around individual school buildings. These grass-
roots efforts were supported by educational policy
entrepreneurs through projects such as James Comer's School
Development Project (Yale), John Goodlad's National Network
for Educational Renewal (University of California at Los
Angeles and University of Washington), Henry Lewin's
Accelerated Schools (Stanford), Deborah Meier's Center for
Collaborative Education (New York City), Philip Schlecty's
Center for Leadership in School Reform (Louisville, Kentucky),
Theodore Sizer's Coalition of Essential Schools (Brown
University), and William Spady's Outcome-Based Education
(Vale, Colorado). These efforts have spawned their own
considerable literature (e.g., Ascher, 1993; Comer, 1986;
Goodlad 1984; Meier 1995; Sizer, 1984;; Spady 1977).
The first and second problem definitions continue even
though their effort has already been called a failure, (Looking
Back, 1994). Privatization has also so far failed to occur. A third
definition that uses economic arguments has emerged. The new
story admits that Americans have always been a bit wary of
everyone learning. It asserts that the factory model of the
education system, adequate up through the 1970s, will not meet
the world class competition of the 1990s.

This refrain is different from A Nation at Risk's
argument because it says that student performance has not
declined, but continues to rise, only too slowly. That student
performance has not risen dramatically would not be surprising
given today's societal problems; however, even this too gradual
rise constitutes a grave problem for the United States, because
the real reason for distress is that today's world of work
requires a new kind of schooling for all students. As Linda
Darling-Hammond said, "we now have to educate every
student for a kind of 'thinking work' rather than for assembly-
line or semi-skilled work, as we did years ago" (Harris 1994,6).
We want higher achievement for all students, "much more
thoughtful, adventurous, and demanding teaching and
learning, instructional guidance to produce it"
(Cohen & Spillane 1993,37).
The new definition resists blame and blaming; it makes a
call to the nation as a whole. It is most often couched in terms of
systemic change, "increasing coherence in the system through
centralized coordination and increasing professional discretion
at the school site" (Fuhrman & Massell 1992,1). This reform is
called "standards-based education." It is an attempt to "develop
structures and practices at the top of the system that promote

and support bottom-up reform .. .neither 'top-down' or
'bottom-up' efforts are sufficient ...success in these efforts
requires 'meeting in the middle'" (Lusi 1995,1-2). However, it is
important to note that the top and bottom distrust each other.
The new definition of meshing top and bottom is seen by many
at the bottom as top-down all over again. Whether it is a new
way of tackling the problem or not, for the third time in this
latest era of school reform, by this paper's counting, we are
presented with a solution-minded problem definition.
Bureaucracy and Education
This generation and its waves of school reform have been
around for more than a decade without noticeable large scale
visibility or effect (Newmann & Wehlage 1995). Public policy
literature has highlighted a central reason this is so. The
bureaucracy is ill-equipped to take an approach to problem
definition that engages the public. Osborne and Gaebler (1992,
314) characterize public education as "a classic example of the
bureaucratic model... centralized, top-down, and rule-
driven...a system that guarantees stability, not change."

E.E. Schattschneider's (1960) insights into the value of the
scope of the conflict and the power of the audience emerge as
especially germane when related to Iaimaccone's (1967,19)
observation that the politics of the educational bureaucracy
"tends to strengthen the boundaries of its social systems,
resulting in a narrow base of support, and to perpetuate itself
and its internal power elite despite the needs of society."
Majone (1989,95) warns that the "entire machinery of
government" limits strategic thinking. Janet Weiss (1989,117)
showed that the problem definition that triumphed in the long
debate over government paperwork was analytically superior
to the old definition, but, "the losers were agency officials. Their
credibility in decisions about what information they needed
was leached away." Since public perception and support of the
government have deteriorated, it is hard to imagine that state-
level bureaucrats would be heavily invested in anything other
than what Lynn and Kowalczyk (1995,5) call "the professional
control model" of school governance, where "the interests of the
providers of educational services were weighed more heavily"
than those of parents and other citizens. "No one wants to
innovate themselves [sic] out of a job" (Osborne and Gaebler

Reformers have their critics, too, of course. The call for
"systemic change," to enlist more than just the educational
community in the problems schools face, has been called a
strategy to "avoid blame and the burdens of reform" (cf. Stone
1988,292). And there are many within the educational
establishment who argue publicly that education does not need
to change fundamentally (Berliner & Biddle 1995; Bracey 1991a;
Bracey 1991b; Bracey 1991c; Bracey 1991d; Bracey 1992; Bracey
1994; Bracey 1995; Bradley 1995; Durden 1995; Schrag 1995;
Viadero 1995). Some even blame A Nation at Risk and its call
for wholesale reforms on a right-wing plot to privatize
American education (Applebome 1995). Others are very much
against top-down systemic changes because they would rob
children and communities of what is significant to them (Apple
1990; McNeil 1995).
It is important to note that the problematic situation
could fail to be defined or be defined in such a way as to leave
schools out of the definition, or...the possibilities are endless.

i Suffice it to say that there is not agreement that there is a
problem (Shanker 1996).4
Since 1983 and A Nation at Risk, educators and policy
i makers have "tried all the conventional medicine" (Osborne
j and Gaebler 1992,315-316), while many if not most school-level
| practitioners deny there is a problem in their school. If we
| cannot look to the responsible bureaucracy for problem
j definitions for reform, where do we look? "The real question
i today is who is putting together some new understanding of the
problems, and some new ideas for action..." (Osborne &
Gaebler 1992,324). It is with this question that this dissertation
A problem definition and the solutions that flowed from
| A Nation at Risk although generating a flood of new policies
| have not yet solved the problematic situation of discomfort
j with student achievement nor have they engendered a national
4 Critiques and rebuttals are on the website of the American
Federation of Teachers as of September 1996: http: / /seamon

innovation for educational reform. Consider the changing
and ever-growing list of solutions. Our argument is that the
educational reform community could profit from a problem
definition conceived without immediate recourse to ready-
made solutions, that is, a "problem-centered" rather than a
"solution-based" or "methods-defined" approach. New ways to
approach problematic situations can be found, but perhaps in
places other than traditional bureaucratic institutions.
Most of the research on problem definition to date is
composed of theory-building case studies that (a) demonstrate
the instrumentality of problem definition in the success or
failure of a policy issue; (b) relate how various actors in the
policy scene strategize to reach a definition and maneuver their
definition onto the public agenda (although success seems often
to have been achieved serendipitously); and (c) define
characteristics and outcomes (both intended and unintended) of
successful problem definitions (e.g., Rochefort & Cobb 1994;
1994a; Sabatier & Jenkins-Smith 1993; Weiss 1989).
I will focus on a relatively small event with a definite
goal and a short timespan (four to five years) and relatively few
players (not including the broader public). I understand that I
may be studying a situation where a successful problem

definition will not occur. I will be cognizant of closely related
strands of public policy theory including the areas of political
innovation, agenda setting, and punctuated equilibria.
In 1990, the National Science Foundation (Foundation)
proposed an innovative concept, called the Statewide Systemic
Initiative. The Foundation asked Governors and the state
agencies for higher education and for kindergarten-through-
twelfth-grade education to envision a new, improved state
system for higher quality student learning in mathematics,
science, and technology for aU students, especially the
traditionally underserved. The Foundation called the solution
"systemic change," but no one knew (or perhaps even today
knows) what true, lasting systemic change looks like. Thus, the
Foundation was open to state interpretation of the problematic
Twenty-five states (as of September 1996) have received
these ten-million-dollar, five-year awards. In only three states,
Connecticut, Montana, and Texas, is the project directed by
what the Foundation calls a "third-party agency," that is, an
agency that is outside the bureaucracy. States rarely take
advantage of the many reform-minded third-party agencies

available in this arena or in other places where they could make
and implement policy (Corcoran, 1996).
The Texas education community is a huge bureaucracy
with a tradition of centralized control over all aspects of
educational policy. That Texas would allow this fairly large
Foundation project to fall under the auspices of a third-party
agency is a significant event. If allotting this kind of power and
authority to an outside-the-bureaucracy group works in Texas,
other states need to take a look at what happened, especially in
this era of unprecedented attacks on government, attacks that
are both internal and external.
I propose to document the progress of the Texas state-
level group commissioned to write a proposal to the National
Science Foundation to leam if it approached the problematic
situation in a problem-centered or solution-minded way and to
leam how the project came to be directed by an outside-the-
bureaucracy group. I will document early implementation of
the grant project by the third-party agency because, as Sabatier
and Jenkins-Smith (1993,2), among others, emphasize, public
policy is decidedly non-linear. Thus, problem definition (cf.
Majone 1989; Weiss 1989) is active not only in the predecision
phase but is at the heart, both substantively and temporally, of

the policy making process. The study will contribute to
knowledge about problem definition and how it intertwines
with knowledge in related strands of the predecision phase in
public policy theory, agenda setting and punctuated equilibria.
The research will be especially interesting because it
documents experimentation in state level initiatives and states
are often called laboratories for experimentation. What we learn
may assist in the transformation of the now-fragmented and
isolated examples of school reform into a more coherent
transitional phase. Powerful definitions are necessary, if not
sufficient, for a large scale, highly visible break with current
educational practice and institutions. At the very least, these
new definitions will scatter seeds for generating new education
reform efforts highly visible to the nation's Mortons and Sesnos.
Thesis Outline
Chapter 2 reviews the relevant literature that situates
problem definition as a policy strand with special emphasis on
public administration. Chapter 3 explains the research
methodology. Chapter 4 is the case study of the Texas Statewide
Systemic Initiative, and Chapter 5 presents the conclusions.

j Introduction
j The literature search frames and structures the
| assumptions of the research. First I define problem definition as
| a new strand of public policy research. I next define
j postmodernism to demonstrate that problem definition is part
j of postmodernism because postmodernism shares with problem
definition research the notion that "policy proposals cry out to
be deconstructed, tom apart from within" (Rosenau 1993,2;
quoted in Rochefort 1994a, 7).
Third, I highlight the salient features of any existing
bureaucracy that, I argue, preclude creative and innovative
approaches to problem definition. Fourth, a definition of
"national innovation" is necessary to clarify what it might look
like if school reform that is, a highly visible, steady progress
of widespread fundamental improvement were pervasive
throughout American society. Fifth, I describe related
predecision-phase public policy strands. Next, I touch on the

origins of policy studies in order to highlight the centrality
accorded to problems from its beginnings. Finally, the bulk of
the review will document "the importance of the problem
definition phenomenon" (Rochefort & Cobb 1994a, 4).
Defining Problem Definition
David Dery (1984) and Rochefort and Cobb (1994a, 8)
separate two understandings of problem definition in die policy
sciences. The first understanding refers to the technical, logical
step for diagnosing problems and devising solutions for a
policy making authority in policy analysis as an applied
profession (cf. Brewer & deLeon 1983). In this dissertation,
however, the meaning derives from the second understanding,
that "problem definition can never be purely a technical
exercise ...policy choices are always statements of values, even
if some value positions are so dominant that their influence
goes unexamined or so unrepresented that their neglect goes
unnoticed." It is an intellectual "contest of different
perspectives" (Rochefort & Cobb 1994a, 8).
Government action, agenda setting, institutional
structures, formal and informal institutional procedures, and

the partisan balance of power are some of the forces that shape
policy, but problems are central,
public policymaking must also be understood
as a function of the perceived nature of the
problems being dealt with, and the qualities
that define this nature are never incontestable
(even though they may sometimes be taken for
granted) (Rochefort & Cobb 1994a, 4).
Wildavsky, you recall, tells us, "instead of thinking of
permanent solutions we should think of permanent problems in
the sense that one problem always succeeds and replaces
another" (1989,5). A problem definition implies that a certain
problem exists; it also contains the optimum solution to the
perceived problem and, thus, suggests how the implementation
of this solution flows from the definition (Baumgartner 1989,
75). An example is provided by Thomas R. Dye (1975,331) who
said, "public education never faced a 'dropout' problem until
the 1960s, when, for the first time, a majority of boys and girls
were graduating from high school.
Let Janet Weiss explain, "problem definition is a package
of ideas that includes, at least implicitly, an account of the

causes and consequences of undesirable circumstances and a
theory about how to improve them" (1989,97).
Social constructionist problem defining (and setting)
began in fields such as sociology and social psychology (e.g.,
Best 1987,1989; Hilgartner & Bosk 1988; Seidman 1986; Seidman
& Rappaport 1986a; 1986b). These works add to the
understanding of the concept of problem definition in public
policy and thus to policy research, but this review will narrow
its perspective to policy studies per se, those p.-ecursors who
lead the way to problem definition, a "flourishing subfield
within policy studies" (Bosso 1994,188).
A short detour into a clarification of postmodernism
situates the dissertation and illuminates the postmodern
tendencies of the policy sciences since their origin. As Charles
Lindblom and David Cohen (1979,50) say, "we do not discover
a problem 'out there;' we make a choice about how we want to
formulate a problem." This is consistent with the social
constructionist school of thought. It reveals "public policy
making as a representation of disputable definitions over the

existence and character of social conditions" (Rochefort & Cobb
1994a, 7-8).
Best defines social constructionism,
our sense of what is or is not a social problem
is a product, something that has been
produced or constructed through social
activities. When activists hold a demonstration
to attract attention to some social condition,
when investigative reporters publish stories
that expose new aspects of the condition, or
when legislators introduce bills to do
something about the condition, they are
constructing a social problem (1989,6).
While researchers do not always comment explicitly on
their use of a certain intellectual style, some do call problem
definition "constructionist" or even postmodern. Self-admitted
social constructionist policy researchers include Stone (1988,
307), who argues, for instance, "nature doesn't have categories;
people do...categories are human mental constructs in a world
that has only continua." In Dery's Problem Definition m Policy
Analysis the first book to use "problem definition" in its title
Aaron Wildavsky's preface clearly places problem definition

in the constructionist camp. He says, "the very notion of
problem definition suggests a constructivist (rather than an
objectivist) view; that is, problems do not exist 'out there'; they
are not objective entities in their own right" (Dery 1984, ix).
I not only argue that problem definition is constructivist,
but I stretch that understanding to an acknowledgment of its
postmodern qualities. My goal is not to pigeonhole problem
definition, but to demonstrate its postmodern tendencies in
order to move past current thinking. Furthermore, Guba and
Lincoln (1995,116) say, "no inquirer, we maintain, ought to go
about the business of inquiry without being clear about just
what paradigm informs and guides his or her approach."
Frank Fischer (1990,226) says that postpositivism
(postmodernism in our terms) rejects "the concept of a value
neutral science." He adds, "a postpositivist orientation
emphasizes the presence of competing interests struggling to
interpret reality" (1990,266). Donmoyer (1995,19) agrees and
says that current policy making in education "displays a diverse
array of voices speaking from different, often contradictory
perspectives and value commitments."
Pangle (1991,245) attributes four features to the
postmodern attitude, "openness to the other; preference for

diversity, opposition to metanarratives, and opposition to the
established order." Farmer (1995) calls postmodernism "anti-
administration," a facet of Pangle's "opposition to the
established order." Kanpol (1992,37) says that postmodemity is
opposed to grand theories (metanarratives): "contrasted to the
positivistic elements of modernism, postmodernism negates a
world that is held together by absolute and universal truth and
universal reason." Farmer (1995,244) adds that postmodernism
"deterrritorializes knowledge," and regards science "as one
discourse among many." How are these tendencies reflected in
problem definition research? Can we identify problem
definition as an example of the postmodern attitude?
Links will be seen throughout this review; I mention a
few here. Deborah Stone (1988, viii) predicts that her views on
the political nature of all human actions, including policy
analysis, will cause some to put her in the "postmodern
intellectual camp." Torgerson (1986) says that postmodern
policy theory embraces creativity, eschews precise solutions,
and incorporates conflict balanced with cooperation, achieved
through reasoned discussion among all interested parties a
democratic inclusiveness (cf. Donmoyer 1995). Lindblom (1990,
270) argues that true policy analysis has always conflicted with

the "dominant style" (read modem or positivist or purely
scientific) in policy research because it is neither rational nor
value free. Schon and Rein (1994) say that their policy research
goes against the tide because it rejects the rational paradigm.
Rochefort and Cobb (1994a, 4) tell us "contemporary policy
analysis is multidisciplinary in its techniques and orientation,
and perhaps nowhere more so than in the burgeoning study of
problem definition." Elaine B. Sharp (1994,155-156) adds that
"different cultural conceptions of how a problem is formulated
provide alternative world views for participants in the policy
Janet Weiss (1989) complains that the outcome of the
battle for the definition of the problem of government
paperwork made government workers the losers and so was a
decidedly anti-bureaucratic outcome (cf. Farmer 1995). The anti-
administration tendency of postmodernism leads us to ask if the
quality of or approach to a given problem's definition
might be related to its identification with or its situation within
an organization or a bureaucracy and for the specific
purposes of this dissertation, within the educational

Full Text
Studies of governmental bureaucratic organizations
come principally from public administration research, but
political and policy researchers have also had much to say on
the subject. These include Schattschneider (1960,71) who called
organization "the mobilization of bias." Thus, an organization
may not be the optimum place for finding an innovative
problem definition. "The irony is that the analyst starts off
expecting to influence the bureaucracy, but it is the bureaucracy
that influences him," says Nagel (1980,12). As Dye (1975,21)
adds, "governmental institutions are really structured patterns
of behavior of individuals and groups... institutions may be so
structured as to facilitate certain policy outcomes and to
obstruct other policy outcomes" (1975,21).
Dery clarifies why an organization, itself the result of
creative endeavors, resists creativity:
An organization is itself a solution to a
predefined problem. The scope of "relevant"
inquiry is therefore severely restricted so as to
accommodate available resources and policy
instruments, interests, constraints, prevailing

values, and other commitments the
previous definitions of problems (1984, xii).
Thus, an organization naturally provides an environment
where policy analyses "involve taking goals as givens and
determining what policies will maximize those goals" (Nagel
1980,13). Donald Schon and Martin Rein (1994,34-35) say that
what they call "metacultural frames" shape policy. Frames are
the mindsets of "institutional actors." Frames are powerful, but
tacit, and this tacit quality makes them difficult to overcome.
Wildavksy relates this phenomenon to the recalcitrance of
organizations toward moving to new ways of thinking:
Displacement of goals becomes the norm as an
organization seeks to make the variables it can
control its own efforts and processes the
objectives against which it is measured. This is
how organizations come to justify error
instead of creating knowledge (1989,35).
Illustrating how termination is sometimes necessary in
order to break free from a given organization's constraints,
deLeon (1988,193-194) makes it clear that only determined,
even relentless, efforts will succeed in ending entrenched
policies and organizations. MacRae and Wilde concur,

the definition of a problem situation often
implies that certain goals or values are to be
sought. Thus, if the existence of an
organization is threatened, persons in the
organization may take its survival to be the
goal of analysis (1979,19).
Public administration research backs up this policy
research and theory. According to Michael Barzelay (1992, 118),
bureaucratic thinking values (a) efficiency over quality and
value; (b) control over winning adherence to norms; and
(c) following rules and procedures over identifying and solving
problems. Perrow (1986,4) says the bureaucracy eliminates "all
unwanted extraorganizational influences on the behavior of
members. Ideally members should act only in the organization's
interest." Add to these ideas Michel Crozier's (1964) elements of
a bureaucracy: ambiguous objectives, unclear norms (cf. Schon
& Rein's 1994 tacit frames), and sparse power. A bureaucracy
will tend to turn to its traditional solutions because these offer
efficiency, control, and procedural validity. An innovative
problem definition demands vigorous, sustained study of a
policy issue and the issues in which it is embedded. Change is
inherent in this kind of analysis, but insiders are compelled to

stay with the tried-and-true and lack the freedom time,
resources, imperatives for new thinking.
Related Policy Strands
Problem definition has emerged as a topic of
considerable interest from among interwoven strands of policy
research whose thrust is "how public issues are identified and
conceptualized" (Rochefort & Cobb 1994a, 27). This is the
predecision phase of public policy research (Kingdon 1984,2).
These theoretical strands, I argue, like problem definition, rely
on the "social construction of reality, and so reflect the
constructionist and postmodern style, both of which hold that
the "definition of a social problem is dependent on time, place,
and society" (Rochefort & Cobb 1994a, 5). I will limit our
discussion of related strands to agenda setting (Kingdon 1984),
and the punctuated equilibria theory of Baumgartner and Jones
(1993), which explores how new institutions emerge. I look to
Baumgartner and Jones principally because of the protracted
nature of education reform.
The agenda, as John W. Kingdon (1984,2) uses the term
in his study of national agenda setting, is "the list of subjects to

which government officials, and people, outside of government
closely associated with those officials, are paying serious
attention at any given time." How these topics "came to be
issues in the first place" is the question. Kingdon asks, "Why
does an idea's time come when it does? (1984, vii).
Polsby (1984) found two processes inherent in political
innovation: the creation of policy options and the utilization of
these options. Kingdon found three: problems, policies, and
politics. He observed that "people recognize problems; they
generate proposals for public policy changes; and they engage
in such political activities as election campaigns and pressure
group lobbying" (206). Kingdon refers to the problem stream as
"problem recognition," (1984 206). As his choice of the word,
"recognition" demonstrates, Kingdon acknowledges the
existence of a problem rather than focusing on how a problem is
socially constructed. This differs markedly from the core of
problem definition research in that Kingdon perceives problems
as realities "out there." Problem definition research stresses the
fact (e.g. Weiss 1989) that problem definition is found in all
parts of any policy process rather than being confined to the
opening stages. This also conflicts with Kingdon's placing it

firmly in the predecision phase. In spite of these differences,
Kingdon's findings provide a context for problem definition.
Baumgartner and Jones (1993) synthesize
implementation and agenda-setting research, arguing that
although the agenda-setting model underlies the American
political system and shows consistency in the way it processes
issues, the system also naturally exhibits periods of volatile
change. This is an evolutionary view of policy change, an
alternative model paleontologists developed to account for
evolution. It is not a cycle-model that exhibits regular spurts of
energy interspersed with regular periods of calm. Instead,
political change can be described as unpredictably episodic. The
American government can best be understood, Baumgartner
and Jones (1993,251) say, as a series of institutionally enforced
stabilities (equilibria), periodically punctuated by dramatic
change. Effective issue redefinition and the resulting
institutional instability create new institutions. These new
institutions then provide another era of stability.
Punctuated equilibria research shares with problem
definition theory a respect for the power of redefinition: large-
scale change and the resulting tendency to enforce the new
order of things, (cf. Dery 1984; Dye 1975; Majone 1989; Schon &

Rein 1994; Wildavsky 1989). That these punctuations of volatile
change happen unpredictably is also in concert with problem
definition revealing the messiness and non-linearity of policy
making (Kingdon 1984; Polsby 1984; Weiss 1989; Bosso 1994). It
is important to keep in mind that what seems evolutionary to
those involved may seem revolutionary to later observers.
The policy sciences have always had three principal
attributes that call to mind social constructionism and
postmodern ideas. Lasswell explains it this way,
the first [principle] is contextualitv: decisions
are part of a larger process. The second is
problem orientation: policy scientists are at
home with the intellectual activities involved
in clarifying goals, trends, conditions,
projection, and alternatives. The third is
diversity: the methods employed are not
limited to a narrow range (Lasswell 1971,4;
emphases added).

Charles Lindblom (1968,13; emphasis original) says
"policy makers are not faced with a given problem.. .they have
to identify and formulate their problem." He provides an
example from the 1960s:
Rioting breaks out in dozens of American
cities. What is the problem? Maintaining law
and order? Racial discrimination? Impatience
... with the pace of reform now that reform has
gone far enough to give them hope? Incipient
revolution? Black power? Low income?
Lawlessness at the fringe of an otherwise
relatively peaceful reform movement? Urban
disorganization? Alienation (1968,13)?
Yehezkel Dror (1968,170) stresses the importance of
context and values rather than the rational approach to policy
analysis. Dye offers a different perspective on why we have to
pluck problems out of the kaleidoscope of reality,
most of society's problems are shaped by so
many variables that a simple explanation of
them, or remedy for them, is rarely possible...a
detailed understanding of such a complex

system as human society is beyond our present
capabilities (1975,16).
This brief foray into its history shows that problems and
the values that form them have been central to the study of
policy analysis since its beginnings. Early theories and research
like that of Schattschneider and Nelson Polsby provide a base
on which to build problem definition theory.
Changing the Equation
E.E. Schattschneider says in his ground-breaking book,
The Semi-Sovereign People, "it cannot really be said that we
have seen a subject until we have seen its outer limit and thus
are able to draw a line between one subject and another"(1960,
22). He adds, "the definition of the alternatives is the supreme
instrument of power" (1960,68). Schattschneider further
counsels, "in political conflict every change in scope changes the
equation" (1960,5), that is, every fight consists of two parts:
"the few individuals who are actively engaged... and...the
audience.. .as likely as not, the audience determines the
outcome" (1960,2; emphasis original). Schattschneider says
definition is key because it sets the boundaries. How a problem

is conceived can enlist support or make enemies (cf. Rochefort
& Cobb 1994). Along with Stone (1988,309), he stresses the idea
that we constantly deal with unstable boundaries "in a world of
continua." Delimiting the scope of the conflict and the power of
the audience emerge as germane to problem definition in
general, and especially in educational reform, when compared
to Iannaccone's observation that the politics of the educational
community "tends to strengthen the boundaries of its social
systems" (Iannaccone 1967,19). Another major theme of
problem definition research is found in Schattschneider's (1960,
71) insight that organization is "the mobilization of bias."
Problem definitions create organizations that embody the
solution implied in the definition. The institutions then carry on
the bias of the definition. Rochefort and Cobb (1994a, 27) agree
with other researchers that Schattschneider (1960) was the first
to offer "a systematic way to unveil interrelationships and their
significance," the interdependence of actions and words.
Schattschneider points out (with irony), "somewhere
along the line the owners of the government decided to read the
constitution as if it were a democratic document" (1960,116). As
Cass R. Sunstein (1996,29) in a review of Jurgen Habermas'
Between Facts and Norms." puts it, "the first [United States]

Congress rejected "the right on the part of constituents 'to
instruct' their representatives how to vote," favoring instead "a
deliberative democracy in which representatives would be
accountable to the people but also operate as part of a process
that prized discussion and reflection about potential courses of
action." Many people in the twentieth century, according to
Schattschneider, would, in contrast with the Founding Fathers,
prefer to "instruct." As early as 1960, Schattschneider provided
great insight into the difficulties the bureaucracy would
encounter in the last decades of the twentieth century.
Along the same train of thought, Schattschneider (1960,
138) asks how "leadership, organization, alternatives, and a
system of responsibility and confidence" can be organized to
remain sensitive to the needs of a political community of
hundreds of millions of ordinary people. The idea that such a
large democracy as today's United States may not be
democratically governable challenges the reality, the power,
and even the value of the modem conception of the nation-state.
These insights become important as we study a possible
national educational innovation. Even in the Constitution, the
control of education is given to the states.

Schattschneider's insights also bring to mind Habermas'
conception of majority rule,
not as a mere statistical affair, an effort to tally
up votes, but instead as large social process by
which people discuss matters, try to persuade
each other and modify their views to meet
counter-arguments. In this way we form our
beliefs and even our desires (Sunstein 1996,
From Schattschneider we leam that to be viable, what I
now call problem definition must (a) limit the scope of an
otherwise borderless situation; (b) yield an explanation that
engages those not specifically engaged in a way that supports
those who seek to define the problem; (c) expand regular
Americans' awareness of their power and promote the concept
of discursive democracy, not only among the elite of the House
or Senate, but among citizens; and (d) overcome the difficulty of
reaching vast numbers of citizens.

Policy Innovation
In Political Innovation in America (1984), Nelson Polsby
studies conspicuous national policies to learn about the pre-
decision-making process. The characteristics of the innovations
he considers assist in defining "political innovation." In this
dissertation, I will use the related term "policy innovation" to
spell out what significant change and improvement in
education would look like and to contrast that notion with what
has been achieved up to the present.
I contrast the terms "policy innovation" and "political
innovation." For instance, the privatization of schooling would
be a purely political innovation, one that would change the
locus of authority, but that would not necessarily improve
learning for currently underserved students. If schooling were
to change suddenly and dramatically, the change would most
probably be the privatization of public schooling. However,
privatization (currently defined as educational vouchers) would
not be the same as fundamentally different schooling that uses
cognitive research-based theories of teaching and learning to
ensure that all children reach ever higher levels of thinking and

learning. This is policy innovation, an innovation that brings a
"new thing" rather than merely a new' seat of authority.
While privatization would exhibit Polsby's three criteria
for political innovation, it would not be the type of innovation
investigated here. It could, however, be the prelude to more
fundamental change. On the other hand, such a huge political
innovation might satisfy the public's desire for change in
education while obfuscating the fact that all that changed was
the politics of schooling and funding, not the philosophy of
Polsby (1984,100) says, "to the extent that a common
definition of a 'need' can be created among decision-makers,
innovation is possible." According to Polsby (1984,8), political
innovations: "(a) are relatively large scale phenomena, highly
visible to political actors and observers; (b) embody from at
least one point of view a break with preceding governmental
responses to the range of problems to which they are addressed;
and (c) unlike major crises, with which they share the preceding
traits, have institutional or societal effects that are in sense
lasting." Polsby deals with national policies while this study
embraces the possibility that educational reform may not be
effected through national policy alone.

I incorporate the ideas of Mary Sanger and Martin Levin
(1992) of a more evolutionary, emergent or grassroots
(postmodern) innovation with Polsby's purposefully top-
down approach. Polsby's observations are insightful and
relevant to our study because national cognizance, in our
definition, would bring with it support both by government
institutions and the public.
Although Polsby warns that his findings are preliminary,
the seven dimensions he teased out from the "extraordinarily
messy" facts of his case studies assist us in understanding the
intransigence of the school reform problem. The most important
for us can be summarized as follows. When a problem is
protracted, (a) specialists have little influence; (b) there is great
political conflict, and (c) possible solutions are widely
publicized (Polsby 1984,148-149). These are all attributes of the
protracted struggle for education reform. Polsby adds that
innovations arise from the interworkings of (a) interest groups,
(b) "the intellectual convictions of experts and policy makers,"
and (c) solutions, along with the "certain knowledge that in
some form or another they could work" (1984,166; cf. Kingdon

Polsby (1984,173) notes that the study of political
innovation must adopt "very generous time perspectives." He
(1984,11) adds that his study looks only at policy initiations that
occurred, and "takes no account, even as a control, of those
dozens or hundreds of nonevents which might have happened,
but did not." This dissertation might well be a study of one such
nonevent, as we shall see in subsequent chapters.
Quiet, persistent workers are the backbone of the
innovative nature of American society, according to Polsby.
They invent and subsequently sustain policy options. Important
for this dissertation is Polsby's contention that among their
ranks are what he calls "policy entrepreneurs.. .whose careers
and ambitions are focused on the employment of their expertise
and on the elaboration and adaptation of knowledge to
problems" (1984,173). He contrasts these entrepreneurs with
nonspecialist politicians in the sense that the entrepreneurs "are
focused upon the substance of policy and on the consequences
of different arrangements for outcomes in the policy area..."
(1984,55). Who are these entrepreneurs that Polsby finds so
vital to policy innovation?

The Policy Entrepreneur
Polsby identifies policy entrepreneurs as "persons with
special interests, competence, or expertise, who have a great
deal to do with the alternatives considered and debated by
more prominent figures" (1984,55). Polsby's conception of the
policy entrepreneur involved in the initiation or problem-
definition phase of policy contrasts with Kingdon's (1984)
entrepreneur who can play a role in any part of the innovation
process. Kingdon also provides a definition of policy
They could be in or out of government, in
elected or appointed positions, in interest
groups or research organizations. But their
defining characteristic, much as in the case of a
business entrepreneur, is their willingness to
invest their resources time, energy,
reputation, and sometimes money in the
hope of a future return (1984,129).
Kingdon (1984,188) also tells us where to find a policy
entrepreneur. He or she might be a cabinet secretary, a senator
or member of the House, a lobbyist, an academic, a lawyer, or

career bureaucrat. He describes the qualities of an entrepreneur,
saying he or she must
have some claim to a hearing. ...expertise, an
ability to speak for others...or an authoritative
decision-making position ... [be] known for his
political connections or negotiating skill...and
probably most important, successful
entrepreneurs are persistent (1984,190).
Kingdon insists on the entrepreneur's persistence rather
than his or her technical skill in policy analysis (cf. Cohen &
March, 1972). Policy entrepreneurs "lie in wait" for a window of
opportunity to open:
Some portion of the time.. .problem solving
does take place, but people in and around
government not solve problems. Instead,
they become advocates for solutions and look
for current problems to which to attach their
pet solution (1984,190).
Polsby's emphasis on the entrepreneurs' quiet, persistent
work contrasts with Kingdon's depiction of their more
influential status (they have to have some "claim of to a
hearing" and their hope of a future return) and his assertion

that their success is often a result of "dumb luck" (1984,188,
192). Polsby stresses the interdependence of policy
entrepreneurs and elected and appointed officials: officeholders
and candidates need policy entrepreneurs, who "specialize in
identifying problems and finding solutions." He quotes an
election analyst, who says "entrepreneurs need politicians, too"
(1984,171). Polsby has faith in technocrats and in ready-made
solutions. This confidence contrasts with a major theme of this
dissertation that ideal policy making starts with the problem
not a ready-made solution.
This high regard for government workers and ready-
made solutions places Polsby with Sanger and Levin (1992,88)
who say that innovation depends on "evolutionary tinkering."
Polsby (1984,171) calls this "dusting off old ideas." Sanger and
Levin also argue that "innovation does not spring from
systematic policy analysis." Polsby (1984,171) says real-life
policy making is a process of opening a drawer, finding a
previous analysis, revising it and presenting it again.
Alternatives to rational, systematic policy analysis are another
recurring theme in problem definition theory and research
(Wildavsky 1989; Lindblom 1990; Schon & Rein 1994).

David Price (1971) finds policy entrepreneurs on Senate
committees while Michael Duffy (1992) describes the rise of a
member of President Clinton's 1992-1993 transition team who
co-created the Progressive Policy Institute as an example of the
entrepreneur. Paul Krugman (1994,10) holds what he calls
(largely economic) policy entrepreneurs, in low esteem. They
are part of "a new class, neither professors nor politicians, that
has come to play a key role in the interplay between ideas and
policies." Krugman's complaint is "they offer unambiguous
diagnoses, even where the professors are uncertain; they offer
easy answers, even where the professors doubt that any easy
answer can be found" (1994,11). Krugman names such high-
profile types as President Clinton, Labor Secretary Robert Reich,
and MIT professor Lester Thurow as policy entrepreneurs.
Sanger and Levin (1992, 109-111) disagree with
Krugman. They argue that public sector entrepreneur-
executives are not only indispensable, but socially desirable.
According to their findings, these entrepreneurs (a) created
"new and personal missions for their agencies"; (b) took
advantage of opportunities, making "virtue out of necessity";
(c) were risk-takers, especially in the area of "taking on too

much"; (d) "had a bias towards action"; and (e) consciously
underestimated "bureaucratic and political obstacles."
Educational entrepreneurs are an important presence in
the current reform era. They would probably disagree, but, in
the large view, each began his or her work focused on a school-
based solution rather than thorough research into a broader
problem. They are not as cautious as the bulk of their colleagues
(Krugman 1994), and they are ambitious and persistent
(Kingdon 1984). However, the best-known educational policy
entrepreneurs have worked in and with schools and thus are
not approaching the problem from the superficial stance that
Krugman criticizes (1994). Although they might have entered
the policy arena with a naive view about the possibility of
change, the difficulty schools faced in implementing their
original ideas has made it clear to them that there are no easy
answers (Stringfield, 1994).
Drawing on all of these policy research sources Price,
Polsby, Kingdon, Duffy, Krugman, and Sanger and Levin the
ideal policy entrepreneur for the purpose of political innovation
in the name of fundamental school reform would have the ear
of policy makers and be steeped in the complexities of school
reform. In general, theory says the policy entrepreneur has his

or her pet solutions, has at least a modicum of self-interest, is
grounded through work "in the trenches," can conceptualize
grand schemes, is often, but not always, a leader, and
understands policy making.
Polsbv and Schattschneider as Prologue
Schattschneider outlined the basic tenets of problem
definition theory without giving it a name decades before it
became a policy theory strand. Defining a problem provides the
ability to get things done. It provides an advantage to those
who share the definition by giving the problem a name,
stabilizing, crystallizing, delineating it from the shifting
kaleidoscope of the problematic situation, rendering it
understandable and workable. The more manageable segment
can engage the audience, enlisting its assistance. In other words,
problem definition organizes, and organization is the
"mobilization of bias" (Schattschneider, 1960). A dilemma is
how to include the vast public of today's United States.
Polsby's research brings out several important ideas for
this foray into problem definition theory. For instance, there is
general agreement that policy making is much messier than

theory has heretofore depicted and thus more difficult to
analyze (cf. Weiss 1989; Bosso 1994 et al.). For Polsby, political
innovation is the interaction of a process of invention with
another "that senses and responds to problems, that harvests
policy options" (1984,173). He does not subscribe to an
approach that focuses on the problem.
Polsby shows that a new problem definition redefines
not only an issue but also the government. Innovation in most
of his cases amounted to new governmental organizations as
the solution to the problem (cf. Dery 1984; Majone 1989; Weiss
1989; Bosso 1994). The events Polsby calls political innovations
have an imposing quality while Sanger and Levin (1992, 88)
consider innovation a process of "evolutionary tinkering with
existing practices." Polsby also accords a great deal of respect
for this kind of change. He considers quiet, slow change the
rule, but quiet slow change sometimes bursts onto the national
scene with a major innovation what Baumgartner and Jones
(1993) call punctuated equilibrium.

Current Perceptions of Problem Definition
We now enter into a discussion of policy research
focused on the concept of problem definition, although not all
the researchers use the term.
Lay Probing
Lindblom (1990,223) contrasts two models of social
problem solving, carrying his conception of "muddling
through" to the whole of society, beyond policy analysis. His
two models are the science-guided society and the self-guiding
society. Lindblom finds that democracy came loose from its
close association with science very early in modem thought,
largely due to the outrages of the Terror of the French
Revolution. He provides the example of moving from the divine
right of kings to the rotation of leaders through elections to
demonstrate that great changes can occur, even those
antithetical to the current regime (Bosso 1994; Kuhn 1962;
Polsby 1984).
Lindblom looks to lay people rather than professional
analysts, the technicians to probe issues because it is
important to him that the exploration of policy issues be

grounded in a certain time and place, and thus, certain values. It
is also essential that probing be action-oriented (1990,216,224).
Lindblom's ideal society does not include a search for a grand
conceptualization since it holds little faith in pure reason
divorced from action to solve social problems (cf. Dery 1984;
deLeon 1992; Fischer 1990; Schon & Rein 1994; Torgerson 1986;
Wildavsky 1989).
Lindblom (1990,36), who does not use the term, explains
why problem definition is more than a technical exercise,
"formulating a problem calls for inquiry no less than does
formulating a solution to a formulated problem. The origin of a
social problem lies in the probes that declare it to be a problem."
It is naive, he says, to think that one has found the best solution;
it is significant that an issue has been well-probed (cf. Rochefort
& Cobb 1994a; Wildavsky 1989). I call this probing problem-
centeredness (cf. Dery 1984; Weiss 1989; and Wildavsky 1989; cf.
Schon & Rein 1994).
Lindblom (1990,270) maintains that policy analysts
engage not in the rational model, as the dominant theory
dictates, but in "trial and error, Simon's satisficing, disjointed
incrementalism, Etzioni's mixed scanning, and the like." He

questions the ability of policy analysts to engage in the rational
exercise policy analysis is conceived to be:
The do-it-all model assumes a single problem
to be defined, then solved, a task with a well-
marked beginning and end. In fact, problems,
year after year, require reexamination and
redefinition (1990,266,274; cf. Dye 1975;
Wildavsky 1989).
Problem definition research not only consciously rejects
the idea of value-free policy making, but one of its main
purposes is to investigate the role values play in policy making
(Wildavsky 1989; Dery 1984; Fischer 1990; Weiss 1989; Schon
and Rein 1994). Stone (1988, viii) wants "a kind of analysis that
recognizes analytical concepts themselves as political claims
instead of granting them privileged status as universal truths."
Wildavsky (1989,124) argues there has to be a balance between
the purely intellectual and the purely interactive, and good
policy analysis provides this "hybrid," using "intellect to help
guide rather than replace social interaction."
Lindblom says that often in the self-guiding society there
is no practical solution to huge predicaments, until, he adds,
society is ready to "bear the costs of the remedy," that is,

"reconsider the institutions, social processes, or behavioral
patterns up to that moment regarded as parameters" (1990,217;
cf. Schattschneider 1960; Wildavsky 1989). Large changes are
difficult if not impossible; redefinitions must struggle against
the recalcitrance of institutions the outcomes of previous
solutions. Ideal problem solvers understand that they are just
taking a step toward betterment, not reaching a solution, what
Wildavsky calls "problem succession."
Aaron Wildavsky (1989,8) is also skeptical about the
possibility of the rational paradigm ("order objectives, compare
alternatives, choose the highest ranking") and argues, instead,
that "problems are man-made" (1989,57). Wildavsky does not
use the term, "problem definition," but in his writing, he
constantly skirts the concept. Policy analysts, he claimed, ought
to work backwards. Instead of beginning with a problem, they
should "formulate a problem at the very end" (1989,3).
Wildavsky's backwards framework calls to mind Elmore's
(1982) "backward mapping." In backward mapping, one first
decides what the preferred outcome looks like and then plans

backwards to the present. This contrasts with starting with the
present situation (however defined) and taking steps to reach a
future desired point.
Wildavsky opposes the rational model of policy analysis
because it "accepts as immutable the very order of preferences it
is our purpose to change, and it regards as perfectly plastic the
recalcitrant resources that always limit their realization" (1989,
404; cf. Peterson 1983 on task forces). He says that policy
analysis is linked to culture because solutions to problems are
first limited by "values and beliefs that support the social
structure" (1989,396; cf. Bosso 1994; Stone 1988). The solutions
to policy problems change those very values and beliefs what
Wildavsky calls the modification of public preferences. He
considers improving preferences the highest calling of policy
analysis (cf. Stone 1988; Majone 1989; Lindblom 1990; Bosso
Wildavsky warns that a powerful definition must
involve the public in its formulation and definition (cf.
Schattschneider 1960; Lindblom 1990). According to Wildavsky
(1989,13) "through interaction, common understandings
(though not necessarily, common positions) grow." He sees the
"purely intellectual mode" of policy analysis as divorced from

reality and thus reaching trivial conclusions. In this way,
"thought," says Wildavsky, "is made supreme at the expense of
having anything worth thinking about" (1989,125). Because of
his desire for a change in preferences, Wildavsky (1989,404)
says he values error in the policy process: "Error must be the
engine of change. Without error there would be one best way to
achieve our objectives which would themselves remain
unaltered and unalterable." Here, Wildavsky seems to
contradict himself because elsewhere he states that it is
imperative to relate "resources to objectives so that the promise
of public policy can be kept" (1989,397). If error is essential to
change, how can keeping promises also be paramount?
He says "problem-finding is analogous to inventing or
theorizing" (1989,3). Unlike Dery (1984), Majone (1989), and
Schon and Rein (1994), Wildavsky claims that if there is no
solution, there is no problem. A solution, a goal (but not
necessarily a method for reaching that goal) must be at hand
before a problem can be conceptualized or defined. Again this
seems contradictory because elsewhere (1989,397) he says that
changing our preferences is the finest quality of policy analysis.
Dery, Wildavsky's student, has different views on the subject.

The Christening
In Problem Definition in Policy Analysis. David Dery
(1984,4-5) says problems as defined in social research are "the
product of imposing certain frames of reference on reality...a
framework within which certain interventions are considered
and indeed defined as solutions." Rather than emphasizing
the solution, Dery maintains that dissatisfaction coupled with
aspiration for better conditions leads us to define problems
(1984,17). "The task is to outline an approach to problems in
general rather than to presume an 'ownership' of solutions to
each particular problem" (1984,113).
Dery insists we cannot resolve all dissatisfaction,
alluding to Wildavsky's problem succession. Contrary to
Wildavsky's insistence on the necessity of solution before there
can be a problem, Dery emphasizes the central character of the
problem with a definite slant toward the innovation that can
result from a focus on the problem. "The definition of a problem
as a discrepancy between a given and a desired state implies
that the latter is to be treated as constant. In fact, only present,
undesirable conditions call for manipulation and change" (Dery

Problems should not be seen as the gap "between 'what
is' and a fixed 'what ought to be'" (1984,7). The desired state is
neither a given nor fixed. The facile "Does it work?" is replaced
with the more complex and open "What does it do?" (1984,42).
Dery does not deny that thinking about possible solutions is
part of the process of examining the problem, but he maintains
that problems are "better treated as opportunities for
improvement" (1984,5). This leads to constant problem
redefinition or Wildavsky's problem succession.
Dery suggests "problem-mindedness" (which I join with
other theories, especially Lindblom's [1990] lay probing and
Schon and Rein's [1994] problem setting and call "problem-
centeredness"). By this he means exploring the nature of the
problematic situation rather than simply choosing among given
solutions. Choosing among givens preserves or at least can
favor the status quo. If we choose among the easy givens,
"the scope of 'relevant' inquiry is therefore severely restricted
so as to accommodate available resources and policy
instruments, interests, constraints, prevailing values, and other
commitments the previous definitions of problems" (1984,
xii). Wildavsky argued that our preferences would change even
though he insisted that a solution was necessary.

Dery says that the world is a complex system because
nothing can be changed without winners and losers. He calls
this a restatement of the Pareto optimum in objective terms
(1984,64). This is a resurgence of values, that constant theme in
problem definition research. Values render objectivity and place
the rational paradigm out of the reach of even positivist policy
practitioners (cf. Stone 1988; Lindblom 1990; Schon & Rein
1994). Dery stresses the inventiveness of problem definition, the
constant search for a better way or the imaginative end of what
we are now doing. He provides further insight into the
obstacles to defining a problem situation while supporting and
enhancing Wildavsky's earlier contentions about the necessity
and desirability of creativity and the ability to learn. Unlike
Wildavsky, he does not believe that a possible solution is a
necessary prerequisite. Yet, like Wildavsky (e.g., 1989,60), Dery
wants us to move beyond today's mindset to "opportunities for
improvement" (1984,116). Majone concurs.
Majone (1989,1) views policy analysis as conversation,
that is, persuasive arguments that rely upon data, models,

metaphors, and stories. He agrees that analysis begins with a
problem situation,
an awareness that things are not as they
should be, but without a clear idea of how they
might be corrected. Problem setting is the
process of translating a problem situation into
an actual policy problem stating the goals to be
achieved and a strategy for accomplishing
them (1989,57).
Majone (1989,5) sees institutions as the "entire
machinery of government... laws, regulations, norms,
organizations, decision-making procedures." These constitute
the outcome of previously successful problem definitions (cf.
Dery 1984; Polsby 1984; Weiss 1989). Majone agrees with
Wildavsky (1989), Lindblom (1990), and Schon and Rein (1994),
among others, that policy analysis cannot be purely intellectual
(1989,146). He calls the belief that it can, the "rationalist
fallacy," and adds, "imagination, judgment, and analogical and
associative thinking play a bigger role in problem setting than
rigor and technical skills" (1989,57). Here, Majone seems to
stress different kinds of thinking rather than a grounding in

action, the importance of values, and involving the public (cf.
Wildavsky 1989; Lindblom 1990; Schon & Rein 1994).
According to Majone, the aim in problem definition
should be neither to mask assumptions nor to attack the
opposition, so much as it should be explicit about our
assumptions and values so that we can find a basis for
education and common understanding among people with
different values. Schon and Rein (1994) call a process similar to
this "frame reflection." At one point, Majone (1989,71) puts a
mathematical spin on approaching a problem's definition. In
mathematics, he says, it is often productive to ask what cannot
be done and why in order to find what does not "fit into
current conceptions ... to open the door to radically new
configurations of policy."
Majone later backs up the importance of values. In
organizations with transparent principles, proposals are judged
by "how they contribute to the ongoing debate" (1989,152).
Thus, sharply defined core principles "may facilitate...
adaptation to new situations by providing clear criteria...."
Conversely, selection of goals and activities will not be effective
"where the community is too open...if each and every proposal
were taken seriously, the burden for the selection mechanisms

would soon become unbearable, leading to a breakdown of
evaluative criteria" (1989,163). Majone is not arguing for
restriction; he favors openness in discussing conflicting values.
In an earlier work, Majone (1981/2,12; quoted in Browne
& Wildavsky 1983,246-8) discusses the relationship between the
structure of an organization (whether it is a bureaucracy or not)
and its task environment (whether it has well-understood or
ambiguous goals [ends] and ways to meet the goals [means]). If
ambiguity is present in ends and means, a bureaucracy tends to
control inputs through budgets and accountability. The non-
bureaucratic professional organization, on the other hand,
promotes collegial control, "mutual adjustment...learning and
effective cooperation...peer review" without recourse to explicit
rules of behavior because it is based on its members having a
clear and common understanding of their values (cf. Schon &
Rein 1994).
Majone calls for a grounding philosophy for a group, an
idea that resonates when we think about a bureaucracy's
difficulty in engaging in the work of change due to ambiguous
objectives and unclear norms (Crozier 1964). Focus and
persistence allow for successful advocacy as we see in Janet
Weiss' (1989,99) analysis of the redefinition of federal

paperwork, the conflict between "the government's need for
information and the resistance to collecting it."
Framework. Weapon, and Outcome
Janet Weiss finds great power in problem definition. It
creates language for talking about problems
and non-problems that draws attention to
some features of social life at the expense of
others; locates responsibility for problems,
putting some groups on the defensive and
others on the offensive; widens and deepens
public or elite interest in particular social
phenomena; and mobilizes political
participation around issues or symbols
highlighted by the problem definition (1989,
Problem definition lies at "the heart of the action"
according to Weiss (1989,98) and "heart" in this instance
implies importance and power but also the center, conceptually
and temporally. In this interpretation, problem definition is a

tool found inside a given policy's history as well as in the theme
for both its initiation and outcome.
She calls problem definition elusive because it is
embedded in both the decision ("an intellectual framework for
further action") and the implementation ("a weapon of
advocacy and consensus") phases of the policy cycle. It can also
be a new institutional mindset, that is, an outcome of the cycle.
It can change language and responsibilities. Weiss says "much
policy making is preoccupied with whose definitions shall
prevail" because the intellectual framework brings with it the
power to shape what happens by justifying only some solutions
and actors as well as focusing attention on only certain
outcomes, certain ways of evaluating success or failure (1989,
98-99; cf. Schattschneider 1960; Stone 1988). Weiss
deconstructed the paperwork policy process, exemplifying the
postmodern approach.
Like others (e.g., Majone 1989; Dery 1984; Rein & Schon,
1994), Weiss says a policy sets up new structures that reflect the
problem's definition, "problem definitions must accommodate
political realities, but they also help to create those realities...
problem definitions carve new channels in institutional
arrangements" (1989,114). Skocpol (1992,58; quoted in Bosso

1994,200) agrees, "as politics creates policies, policies also
remake politics." Although case studies shed light on certain
processes that make redefinition more probable, they cannot
predict what will happen, she adds (1989,103). One must
always be open to unintended consequences. There is an
interplay, "a dynamic process in which intellectual
understanding and institutional behavior guide one another
over time" (113). Like Kingdon (1984; cf. Polsby 1984), Weiss
sees at least three influences, "the objective features of the
problem, the emergence of policy entrepreneurs, and
fluctuations in the appeal of political symbols and language"
Problem definition can never be locked in and often
remains an open and messy question, leaving room not only for
"multiple options for addressing a given problem, but multiple
definitions each implying its own family of solutions" (1989,
98). Furthermore, political events can reinforce or thwart the
power of the symbols invoked in the definition or the coalitions
gathered. These political events can be, but do not have to be,
crises. Her study, for instance, shows that the collection of
information by the federal government "had probably been a
problem of about the same magnitude for many years" (1989,

109). Conversely, Kingdon (1984) places emphasis on the
severity of a problem, as do Rochefort and Cobb (1994). Far
from merely setting the process in motion, problem definition
and redefinition follow the process all the way through (cf.
Brewer & deLeon, 1983). Creativity is valuable because it
attracts like-minded thinkers and assists in reaching common
ground among diverse coalitions. A process gathers momentum
as it reaches a critical mass. Consensus is usually too much to
ask, but "modest interdependence" creates new channels for
shared political realities.
Policy entrepreneurs play a pivotal role (cf. Polsby 1984;
Kingdon 1984). At the auspicious moment, they move quickly
toward "concrete legislative and administrative proposals" says
Weiss (1989, 111). In turn, recalcitrant organizations and
bureaucracies that generally constrain innovative definitions of
problems finally respond to new ways of thinking when the
pressure is strong enough. Problem definition can then be seen
as an outcome, that is, newly configured governmental
institutions. Weiss sees a policy as setting up new structures
that reflect the new problem definition, in Schattschneider's
words, the "mobilization of bias" (cf. Baumgartner & Jones

1993; Dery 1984; Polsby 1984; Schon & Rein 1994; Bosso 1994;
Skoqpol 1992).
Weiss' (1989,99) history of the government paperwork
question demonstrates how "policy actors struggle over
problem definition throughout the policy process, how political
context shapes problem definition, and how consensus on
problem definition influences successive rounds of policy
making." As mentioned in Chapter 1, Weiss points out that
agency officials were the losers in the paperwork story, "their
credibility in decisions about what information they needed
was leached away.... Their participation in information policy
was reduced by the assumptions and theories of the new
regime" (1989,117). The redefinition of the problem was anti-
administration, a postmodern attitude (Farmer 1995).
Weiss stresses problem definition's power. She makes it
clear that advocates need a rationale behind a definition, a
creative interpretation of a problematic situation a new story
in order to be successful.

Deborah A. Stone (1988,282) takes a "social
constructionist view of policy problems. ..our understanding of
real situations is always mediated by ideas; those ideas in turn
are created, changed and fought over in politics." Stone
describes what she calls "causal stories." Stories are analogous
to a problem's definition. Like problem definition, these stories,
challenge or protect an existing order.. .assign
responsibility to particular political actors so
that someone will have to stop an activity, do
it differently, compensate its victims, or
possibly face punishment...[ they] can create
new political alliances (1988,160-161).
Adamant about the purposeful intent in problem
definition, like Weiss (1989) and others, Stone says problem
definition is a strategy "created in the minds of citizens by other
citizens, leaders, organizations, and government agencies, as an
essential part of political maneuvering" (1988,122). She argues
that there is "a systemic process with fairly clear rules of the
game by which political actors struggle to control
interpretations and images of difficulties" (1988,282).

Stone places great value on what she calls political
reasoning the strategic use of stories. She sees political
reasoning as an outlet and impetus for human imagination. In
her respect for this process and her refusal to rely on traditional
problem solving and the rational approach, she agrees with
other problem definition scholars (cf. Polsby 1984; Dery 1984;
Wildavsky 1989; Lindblom 1990; Schon & Rein 1994), and
expresses her ideas in the postmodern style.
Like Weiss, Stone sees problem definition or political
metaphors as a strategic part of "a contest over
policy...addressed to a hostile audience" (1988,309). However,
for Stone (1988,306), contrary to Lindblom (1968; 1990), there is
no middle ground nor is there a dichotomy between analysis
and politics: "reasoned analysis is necessarily political. It always
involves choices to view the world in a particular way when
other visions are possible. Policy analysis is political argument
and vice versa." Stone clarifies how large societal myths help
determine how a society defines problems (cf. Bosso 1994;
Rochefort & Cobb 1994a). Stone says
assertions of a causal theory are more likely to
be successful if its proponents have visibility,
access to media, and prominent positions; if it

accords with widespread and deeply held
cultural values; if it somehow captures or
responds to a "national mood"; and if its
implicit prescription entails no radical
redistribution of power or wealth (1988,159-
Stone's comments about rules, games, and political
maneuvering call to mind Bosso's (1994,200) ideas on "a polity-
centered approach to problem definition," the convergence of
"existing structural and political conditions to create the
contexts within which political actors jockey to promote
competing problem definitions and formulate public policy."
On the other hand, Stone says, our aspirations for equity,
efficiency, liberty, security, democracy, and justice unite us even
as contradictory interpretations divide us. The pressure to
communicate our preferences and visions makes us a
community. She sees debates over a problem's boundaries as a
privilege; it encourages the use of our imaginations (1988,310).
She holds in high esteem the acts of arguing for one's values
and convincing others or changing one's mind. Changing
minds is what the democratic life is all about. Like Stone (cf.
Wildavsky 1989), Schon and Rein (1994,20) say that "change in

the way participants look at and understand the world" is a
desirable consequence of reaching a problem definition.
Problem Setting
As they consider and critique the policy world, Rein and
Schon5 (1977,238-9) use the term "problem setting" to describe
a process that can develop "new purposes and interpretations."
They say, "the questions we ask shape the answers we get....
Whatever is said of a thing, denies something else of it." They
agree with Schattschneider's idea of "boundary-setting."
Frames, they say, (a) highlight some features of the situation;
(b) ignore other features; and (c) bind the remaining features
into a pattern (1990,238-9).
They question working backwards from a desired state
because, instead, they want to ask the unaskable, subject values
to inquiry, and question what is most desired (Rein & Schon
1977,248; cf. Dery 1984; Wildavsky 1989). This brings to mind
Dery's (1984) problem-mindedness and Majone's (1989)
5 Schon changed the spelling of his name from Schon to Schon. We
will use the new spelling in the text, but both spellings in citations and the

mathematical spin. Wildavsky finds a desired outcome
indispensable to policy analysis. Schon and Rein want
organizational players to learn new ways to question their
values and desired outcomes.
Schon insists on problem setting rather than problem
I have become persuaded that the essential
difficulties in social policy have more to do
with problem setting than with problem
solving, more to do with ways in which we
frame the purposes to be achieved than with
the selection of optimal means for achieving
them (1986, 255; cf. Lindblom 1990; Schon
Schon says we need to recognize one person or one
organization's description of a problem as that entity's
description rather than reality. In this way we are led to
understand that this description is not everyone's "reality." This
is one of the facets to how we succeed at looking at the same
situation through different organizational lenses. Again, values
and the elusiveness of the problem's definition are brought to
the fore. Schon also suggests that immersing oneself in practice

rather than remaining cerebral allows us to "capture the
experienced richness of the situation (its phenomenology)
without forcing it into existing formal categories" (1986,279).
Schon (1986,279) adds that through research of practice in this
vein we can "inquire into the processes by which we are able to
construct new category-schemes, new models, from the
information-rich stories we tell."
Like Lindblom (1990), Schon and Rein (1994,10) divide
policy making into three traditions rational actor, politics,
and negotiation all three of which they reject because they all
share the central idea of instrumental
rationality: that policy makers are rational
actors who choose the means policy
positions, strategies of political action or
negotiating ploys that they believe to be
best suited to the achievement of their ends,
which are rooted in their interests (cf. Dryzek
& Torgerson 1993,214; Elder & Cobb 1983,1-
They say their 1994 book "swims against the prevailing
tide." Schon and Rein thus place themselves with problem
definition researchers. However, they say that, unlike

Lindblom, they do not see practitioners as "muddling through."
Nor do they see a need to leave policy making or probing to lay
persons (cf. Lindblom 1990). Instead, they see "a kind of
reflective practice, which we call design rationality" (1994, xi).
Schon and Rein also offer the idea that "the parties to
policy controversies see issues, policies, and policy situations in
different and conflicting ways that embody different systems of
belief and related prescriptions for action..." (1994, xvii; cf.
Majone 1989). They continue (1994,29) "frames are not free-
floating but are grounded in the institutions that sponsor them,
and policy controversies are disputes among institutional actors
who sponsor conflicting frames." Again we find the marrying of
a solution and an organization (cf. Dery 1984; Majone 1989;
Schattschneider 1960; Weiss 1989). Schon and Rein assist us in
thinking through how institutions work together. They make it
clear why there are difficulties inherent in collaboration among
agencies. This reinforces the idea of organization as the
"mobilization of bias" (Schattschneider 1960). Rochefort and
Cobb provide a different perspective on the "why" of these

Instrumental versus Expressive
Rochefort and Cobb (1994a, vii) edited a collection of
studies that integrated Rochefort's background as a researcher
in the "social images of problems and their impact on policy
design" with Cobb's earlier studies of agenda building and
symbolic politics. A dominant theme of their book, as expressed
in the final section (Bosso 1994,200), is an approach to problem
definition that focuses on "culture, socioeconomic conditions,
institutions, and history." Like Weiss' (1989) article on
government paperwork, these studies demonstrate that a
successful problem definition is an outcome as well as a
prologue to policy change. New definitions create new
problems, which, in turn, create new structures. The studies also
depict policy making as seen through the lens of problem
definition as disorganized and decidedly non-linear, in fact,
"sloppy and complicated" (Bosso 1994,201).
They subscribe to the "social construction of reality, the
idea that the definition of a social problem is dependent on
time, place, and society (1994,5). As you might recall, they
explicitly attribute problem definition's surge in importance to
postmodernism "an intellectual style concerned with examining

the unquestioned value assumptions embodied in culture and
society" (1994, 7). Of paramount interest for our purposes is
their slant on why so many policy makers and authors talk past
each other. They call it the "instrumental versus expressive"
orientation (1994; 1994a). In the expressive mode, the end does
not justify the means. The process embodies one's values and
beliefs. In the opposing instrumental orientation, action is
undertaken for the purposes of promoting or achieving some
larger goal. It is a means to an end, and is subject to assessment
of success or failure and relative efficiency.
The instrumental > expressive continuum constitutes a
trap for opposing problem definers, a subtle way to disagree.
An apparently easy consensus on a universally desired outcome
can be devilishly difficult to attain because, while the problem
definers may agree on the ultimate goal, the obvious or
proposed path there may be unacceptable to one faction (1994a,
23-24). Yet the two sides often do not perceive that they are
talking past each other. One focuses on the means (expressive)
and the other on the end (instrumental) because for them, this
time at least, the means are amenable or even innocuous. Clean
needle distribution to curb the spread of AIDS among drug
users, condom distribution to prevent the spread of AIDS

among high schoolers, and a balanced federal budget that
requires cutting entitlements are examples of easily agreed-
upon goals with differing means that can pit one faction against
the other.
This dimension can be seen in the contrast between two
opposing visions of how children attain literacy. The "Great
Reading Debate" rages
between advocates of two main philosophies
of reading instruction: the whole-language
method, which emphasizes reading for
meaning, the use of children's literature
instead of basal readers and worksheets, and
the teaching of skills in the context of reading;
versus the phonics or code-oriented approach,
which emphasizes direct instruction in letter-
sound relationships and patterns (Matson
If we look through the expressive lens, we see that for
some, good schooling cannot be children learning spelling and
vocabulary without ever reading anything but stories
constructed only for school. For others, the vision of good
schooling is not children pursuing their own interests, never

learning the basics. Even if one way were demonstrated as
unquestionably more efficacious for better student learning, it
could not or would not be accepted as the answer by the
opposing side.6
A new problem definition in education reform
standards-based education purports to embody an
instrumentalist perspective. It allows flexibility on how to
educate coupled with accountability for results; each faction can
align its school with its vision of good schooling. The problem is
reaching agreement on measuring results.
Rochefort and Cobb (1994,176-178) observe that
adoption of one mode or the other cannot be predicted for
certain populations or aligned with liberalism or conservatism,
for instance. In addition, advocates of a given policy often mix
the two ends of the continuum; the dynamic is more complex
than it seems,
those who object to the impropriety of
premarital sex sometimes offer instrumental
counterarguments (such as, "condoms are
6 The evidence "increasingly points to the conclusion that neither
method by itself is as effective as a balanced approach that combines the
two" (Matson 1996,1).

unreliable") as a way of attacking the condom
distribution program. And instrumentalists are
invoking moral values, not cost-benefit
analysis, when they plead the sanctity of
saving "even one life" (Rochefort & Cobb 1994,
These divisions are convoluted because they become
"entangled with, and influenced by, preexisting social and
ideological cleavages" (1994,177). In general, the closer one is to
a problem, the more drastic steps one will take to combat it, but
the struggle gets even more complicated when, for instance,
racial tensions enter the picture. Rochefort and Cobb add that
even when there is strong public support, the policy is at the
mercy of individual decision makers' value systems, as well as
turns in public attitudes and political contexts. Echoing a
recurring theme of problem definition research, Rochefort and
Cobb (1994,178) conclude that this is an area where values
clash, and that "only those policies that are widely perceived as
doing both 'what's right' and 'what will work' will cross
untroubled political waters."
The instrumental > expressive dimension is another a
way of looking at organizational structure and how it might

influence the creation of a problem definition. Bosso provides
several insights along these lines in his macro perspective on
organizational structures.
Regime-Level Policy
In line with Stone's (1988) ideas of societal catalysts and
constraints that favor or disfavor a certain problem definition,
Bosso (1994,183) tells us "problem definition illuminates how a
society solves problems." He calls these constraining influences
"societal value systems," or "culture." These forces are not
easily changed, but Bosso (1994,190) believes they can change
and that this type of huge cultural change might be the most
interesting aspect for scholars of problem definition. Wildavsky
(1989) would call this changing our preferences, Polsby,
political innovation. Lindblom (1990) reminded us of the end of
the concept of the divine right of kings to persuade us to believe
that enormous changes are possible. It would take epic change
for American schools to reach significantly higher quality
learning for all students.
According to Bosso, problem definition research
questions the modem nation-state, or statism, i.e., faith in the

power of technical experts or public administration. This
skepticism has already been seen, for instance, in
Schattschneider's (1960) perception of people's expanded sense
of their power and the difficulty of governing such a vast
democratic nation (which is much larger in 1996 than it was in
1960). Bosso's ideas are also related to Stone's (1988)
explanation of policy solutions as modes of constructing and
maintaining political boundaries, and Lindblom's questioning
of faith in science and reason for governing society (1990). Dery
(1984), Weiss (1989), and Majone (1989) say that problem
redefinitions discredit or redirect old (current) ways of thinking
as they create new institutions.
On the other hand, Polsby (1984) and Sanger and Levin
(1992) profess faith in technocrats. Polsby (1984,165) claims the
United States political system "favors the application of rational
thought to problems" and has "incentives to search for
innovations." Weaving these ideas together new definitions
discredit the old but the system is designed to redesign itself
brings to mind the punctuated equilibrium theory
(Baumgartner & Jones 1993). Polsby and Baumgartner and Jones
have more faith than, for instance, Bosso or Stone, in the
system's ability to effect large changes that go against the grain.

Bosso maintains that overt conflict over problem definition
often does not occur because the prevailing culture and
institutions "simply screen out most (and sometimes all)
alternative definitions of a problem" (1994,199). While the
"received culture," that is, governmental structures, and
institutions, can and do change, some parts are more resistant
than others (1994,193). Stone (1988, e.g., 300-310) agrees.
Reminiscent of Schattschneider's sense of the public's
heightened perception of its power, Bosso also talks about how
sometimes the general public gets control of an issue, "its
influence [is] felt through electoral returns or other mechanisms
that tell policy elites just how far they can go" (1994,199). Bosso
says elite arguments can simmer for decades, which is why "so
many public debates about institutional reforms really have
substantive policy impacts in mind" (1994,200). These debates
are concerned not only with surface issues, but also long-
standing struggles for problem definition and for a redefinition
of institutions.
Bosso cites Baumgartner and Jones (1993), but not Weiss
(1989), who stresses that the question of government paperwork
had been debated for years before 1972 when the problem was
effectively defined and the Paperwork Reduction Act was

passed. Nor does Bosso mention Polsby (1984) who divided his
cases of political innovations into those that were quickly
enacted and those that took decades or even longer. School
reform resembles the paperwork debate because it, too, is a
protracted struggle. Further, it may well be that school reform
will not become pervasive and so will join what Polsby calls
Bosso stresses the "sheer complexity of law in the
American context," (1994,196) especially local and state control
and the ensuing effects on policy. He points out that localities
have considerably more flexibility than the federal government.
States are often called "laboratories," (or "natural experiments"
in the policy evaluation literature). He adds that state or local
control is certainly of importance when talking about education:
"the result is a patchwork quilt of debates and policies, with
local conditions playing central roles" (1994,196). This
patchwork calls to mind Schattschneider's (1960) ideas of
enlarging or reducing the size of the conflict to gain or leave out
bystanders. It also recalls Wildavsky's (1989) contention that
one-size-does-not-fit-all, as well as the overtly postmodern idea
of inclusiveness in policy analysis (Torgerson 1986).

Further, Bosso discusses the "unique periodicity of the
American system to its issue dynamics" (197; emphasis
original), due to differing electoral timetables. For instance, in
the 1996 election campaign, a long-simmering debate over the
privatization of public schooling, one that has raged since the
beginning of public schooling, came to the fore. This high
profile of the debate may portend change in the next
administration, no matter which candidate wins.
Bosso contends that even policy entrepreneurs (cf.
Kingdon 1984; Polsby 1984; Stone 1988), along with virtually
everyone else, of course, are channeled by institutions.
Problems often depend on these entrepreneurs to get them on
the public agenda, but even the relatively powerful
entrepreneurs are not free of cultural or institutional constraints
(197-199). Bosso's perspective on problem definition as a
regime-level concept provides us with a broad context for this
policy strand and brings us to the end of the literature review.
Problem definition is a political process; education and
education reform are also political (deLeon 1988; Wildavsky

1989). Problem definition may help to clarify the reasons behind
the lack of success of the many attempts at fundamental school
reform that have come and gone throughout this century.
The goal of educational reformers is argued to be no less
than a national innovation, whether it is imposed from the top
(Polsby 1984) or is bottom-up and evolutionary in nature
(Sanger & Levin 1992). The political nature of educational
politics can be seen as working against an easy, early, or
universal solution. Styles of public policy theory, such as social
conflict and politics, social constructionism, or postmodernism
may come together to provide a novel and productive approach
to problem definition (Rochefort & Cobb 1994a; Bosso 1994;
Sunstein 1996).
Through the lens of problem definition, public policy
making appears messy, non-linear, grounded in action, and
inclusive of many players (Torgerson 1986; Stone 1988; Weiss
1989; Wildavksy 1989; Lindblom 1990; Bosso 1994). Among the
many facets of the complex policy puzzle of problem definition,
we focus on "problem-centeredness" exploring the nature of
the problem and the generation of alternatives from the
problem's many ramifications, probing a problematic situation
with lay persons and being mindful of the bias of our

organization. Problem-centeredness is opposed to "solution-
mindedness" jumping to a solution without mucking around
in the problem. Problem-centeredness may have the power to
move us to radically new configurations of policy and thus
more powerful problem definitions (Dery 1984; Lindblom 1990;
Schon & Rein 1994).
Organizations in general, and "the educational
bureaucracy" specifically (Osborne & Gaebler 1992), seem ill-
suited to problem-centeredness rather than solution-
mindedness because organization is "the mobilization of bias."
A given definition is a weapon for advocacy and consensus for
breaking down the status quo, just as, contrarily, it can be a
bulwark for the same status quo (Weiss 1989). Institutions are
the instruments of stability of their definition (or bias)
(Schattschneider 1960; cf. Baumgartner & Jones 1993; Bosso
1994; deLeon 1988; Majone 1989; Schon & Rein 1994; Stone 1988;
Weiss 1989).
Members of organizations have a tendency to see the
agency's continued existence and success as their major goal
(Nagel 1980). Although they were once the solution to a
problem as were bureaucracy and the educational
bureaucracy such organizations now contribute to a period

of stability or rigidity (Baumgartner & Jones 1993). Effective
issue redefinition creates new procedures and institutions
(Baumgartner & Jones 1993; Bosso 1994; Stone 1988; Weiss 1989;
Skocpol 1992), which can result in administrative intransigence
rather than innovation.
An outside-the-bureaucracy group with a definite focus
might be more capable of dealing with the ambiguity inherent
in creating a dynamic problem definition. Such an organization
would be freer to take a more problem-centered approach.
However, it, too, would be constrained by the larger culture
(Bosso 1994; Stone 1988). An outside-the-bureaucracy group is
defined as a group whose leaders are not employees of the
kindergarten-through-twelfth-grade educational bureaucracy or
a school of education in a state university, or the Governor's
Office. This group is not estranged from bureaucratic groups.
On the contrary, such a group, if it is to be effective, must work
well with them. "Working well with" does not necessarily mean
not effecting change on the bureaucracy itself.
For an outside-the-bureaucracy group to gain power, a
policy entrepreneur is necessary (Bosso 1994; Duffy 1992;
Polsby 1984; Price 1971; Sanger & Levin 1992; Weiss 1989). Even
though he or she would also be constrained by the rules of the

game, institutional constraints, and the "received culture"
(Bosso 1994; Stone 1988), the entrepreneur would skillfully and
purposefully ignore these constraints whenever possible. He or
she would also exhibit other traits like risk-taking, a bias
towards action, the ability to impose a personal mission on a
new organization, and opportunism (Sanger & Levin 1992).
Problem definitions of public policy issues spring from
networks of like-believers who sometimes succeed in pushing
their issue onto the public agenda (Kingdon 1984; Weiss 1989;
Rochefort & Cobb 1994; 1994a). Existing institutions, devolution
to the states, periodicity, and other national characteristics of
the United States inhibit or facilitate certain definitions
(Baumgartner & Jones 1993; Bosso 1994; Polsby 1984; Stone
1988). This is partially because effective issue redefinition
creates new procedures and institutions (Skocpol 1992; Stone
1988; Weiss 1989). In areas as patently political as school reform,
a definition may succeed or fail depending on whether the
outcome is embodied within the method (the instrumental/
expressive dimension). It has to be perceived as workable but it
also has to do "the right thing" (Rochefort & Cobb 1994).

A Conceptual Framework
My model of the process of reaching a problem definition
relies on Polsby's (1984) three criteria for large scale, national
innovation: (a) wide visibility, (b) break with preceding habit,
and (c) lasting consequences. I use Polsby's concept of large
scale, national innovation to contrast what has happened so far
in the area of school reform with what school reformers desire.
School reform, although a robust industry within the education
community, has not reached the status of a political innovation,
still less that of a policy innovation, and has little hope of doing
so without a more powerful problem definition. Unlike the
implications of Polsby's (1984) study, however, I do not believe
the innovation must be federal or national. It could emerge in a
postmodern fashion, that is, from schools, localities, states, or
even school reform efforts, that is, it could emerge from the
grassroots and be incremental (Sanger & Levin 1992). The
innovation I target a fundamental transformation in the
philosophy of schooling to include high quality learning for all
students may take a generation or more (Polsby 1984;
Sabatier & Jenkins-Smith 1993). I have acknowledged that this
huge shift may be overtaken by privatization of public

schooling, another innovation to be sure, but purely political in
I propose five assumptions about the process of reaching
a problem definition:
1. A problem-centered approach to problem definition is
desirable but rare (Dery 1984). There is a greater likelihood of
finding the focus and, at the same time, the representative
participation to allow for a problem-centered approach in a
group that remains outside the bureaucracy. Again, an outside-
the-bureaucracy group is defined as a group whose leaders are
not employees of the kindergarten-through-twelfth-grade
educational bureaucracv or a school of education in a state
university, or the Governor's Office.
2. An outside-the-bureaucracy group would need to have
some sort of powerful person attached to it: a policy
entrepreneur (Polsby 1984; Kingdon's 1984; Weiss 1989; Sanger
& Levin 1992; Bosso 1994). The ideal entrepreneur is
characterized by at least five traits, as outlined by Sanger and
Levin (1992): the entrepreneur (a) created a new and personal
mission for the agency; (b) took advantage of opportunities;
(c) was a risk-taker, especially in the area of "taking on too

i much"; (d) "had a bias towards action"; and (e) consciously
J underestimated "bureaucratic and political obstacles."
| 3.1 expect to find a problem-centered approach to
J problem definition in this outside-the-bureaucracy group. Part
| of our definition of problem-centeredness is the type of
| interactions Schon and Rein (1994) call "design rationality/' and
| Lindblom (1990) calls "lay probing." Design rationality is in the
! realm of the technician while lay probing includes the public,
j 4. We will see postmodern ideas emerge from problem
| definition research. They include questioning values and an
j anti-administration perspective (Torgerson 1986; Majone 1989;
| Weiss 1989; Schon & Rein 1994; Farmer 1995), the importance of
context and action (Dery 1984; Lindblom 1990; Schon & Rein
1994), avoidance of precise definitions (Torgerson 1986),
| reasoned discussion among all interested parties, reflected in an
| openness and a preference for diversity (Torgerson 1986;
Majone 1989; Lindblom 1990), and an aversion to the idea of
absolute truth (Weiss 1989; Pangle 1991; Kanpol 1992; Lindblom
| 1990; Fanner 1995).
j 5. Politics will be of crucial importance in the rise of the
policy entrepreneur, the feasibility of implementing a program,

and the viability and power of the resulting problem definition
(Bosso 1994; Rochefort & Cobb 1994; 1994a; Stone 1988).
This dissertation is based on a case study. I will explore
how an outside-the-bureaucracy group approaches a
problematic situation or difficulty. I see the need for a policy
entrepreneur who champions this group. I argue that political
conditions will be conducive to the rise of the entrepreneur and
the group's influence.
The questions that define the case study are
1. Was the group that created the problem definition an
outside-the-bureaucracy group? Is the group directing the
project an outside-the-bureaucracy group? Is it a bureaucracy
(Barzelay 1992; Crozier 1964; Osborne & Gaebler 1992)?
2. Was a policy entrepreneur connected with the project
and/ or its creation? What qualities did he or she display
(Kingdon 1984; Polsby 1984; Sanger & Levin 1992)?

3. How did the process of reaching the problem
definition reflect problem-centeredness, frame reflection, and/
or lay probing (Dery 1984; Lindblom 1990; Schon & Rein; 1994)?
4. Did the process exhibit postmodern tendencies such as
questioning accepted values (and public administration), and
the importance of context and action (Dery 1984; Majone 1989;
Lindblom 1990; Rochefort & Cobb 1994a; Schon & Rein 1994;
Torgerson 1986; Weiss 1989)?
5. What role did politics play in the evolution of the
problem definition (Kingdon 1984; Polsby 1984; Rochefort &
Cobb 1994; 1994a; Stone 1988; Weiss 1989)?
These questions define the research and form the basis of
the exploratory nature of its design, setting the stage for the case

This dissertation focuses on the predecision phase of
policy making, specifically, the approach that organizations in
the public sector take in reaching a powerful problem definition
when confronted with a problematic situation. I have posited
several assumptions of the problem definition strand of public
policy theory. These assumptions deem it possible as well as
desirable to establish a problem definition without deciding
first on a solution.
The Study
The research design is a case study. Copies of documents
provided by the National Science Foundation (Foundation), the
Texas Statewide Systemic Initiative (Texas SSI), plus interviews
with various staff will be the main sources.

Rationale for the Case Study Method
This dissertation proposes to explore the theories of other
policy researchers. It is in line with Rein and Schon's (1994,114)
contention that "a study of rare events...holds the potential for
illuminating the careers of stubborn policy controversies." I
wish to provide "explanatory clues" (Komarovsky 1967,349;
quoted by Peshkin 1993,25). The case study method is
proposed because (a) I want to explore how a group outside the
traditional educational bureaucracy approached a problematic
situation; (b) the case constitutes an event that started in the
recent past and continues in the present and (c) a major focus is
the boundary between studied phenomenon (the group and its
process) and the overall context (the state educational
bureaucracy); and (d) the process was complex and could not be
captured by surveys (Yin 1994,9,10,13,22,39).
I consciously chose a case study methodology because I
am working with the postmodern and social constructionist
theoretical strand of problem definition which is focused on
human interaction. I want to maintain coherence between
theory and method, and, as Schon and Rein say (1994,145), a
frame, such as postmodernism or social constructionism,

determines "what counts as evidence and how evidence is
interpreted." I attempt, however, to step "far enough outside"
my frame to see that my "position is not self-evident and that
other ways of framing the issue are possible" (Schon and Rein
1994,44). As I search for reason in the policy give and take of
the Texas Statewide Systemic Initiative and its relations with the
National Science Foundation, I strive to understand the point of
view of both entities as well as their interactive dynamic,
keeping in mind the difficulty of remaining neutral and fair-
Integrity of a Case Study
It is appropriate in studying a postmodern theoretical
issue to employ a qualitative case study approach, thereby
assuming the responsibility of dealing with reality, that ever-
changing, amorphous entity and flirting with a lack of
positivist dependability, which depends on an unchanging
universe for replicability.
Every attempt will be made to establish and maintain the
credibility, that is, the internal validity of the case study. The
ability to be neutral and fair-minded and thus enhance the

internal validity of the study will be ensured by soliciting
comments from study participants as the work progresses
(Marshall & Rossman 1989, pp. 144-149). I also attempt to assess
participants' truthfulness through my knowledge of group
processes and understanding of roles in the educational
hierarchy. Analysis of documents and interviews will be used in
a "triangulating fashion" (Yin 1994,13) in order to check the
reliability of individual sources and to add to the robustness of
the study. "Triangulation" is defined in this study as purposeful
redundancy (asking the same questions of several informants in
different roles and organizations in order to compare their
versions), overlapping methods (multi-interviews and
successive perusal of documents), and "thick notes" (Denzin &
Lincoln 1994). Although Yin (1994) makes it clear that a case
study of a rare event does not need a comparison, I will study
the same sorts of documents and conduct interviews with a few
staff members from the Colorado Statewide Systemic Initiative
because it is more traditional in its relation to the education
bureaucracy and its approach to a problem definition. The
purpose of this line of research is to assist in confirming that the
Texas effort's evolution and its final problem definition were

not commonplace in this national Foundation effort, and
constitute another attempt at triangulation.
Similarly, to control for bias in interpretation and thus
assure confirmability. I will use a combination of the following
tactics: (a) reliance on the dissertation committee, the outside
SSI monitor, and Texas SSI and Foundation staff as "devil's
advocates"; (b) a constant search for negative instances; and
(c) value-conscious note taking and interpretation (taking
everything down as each subject talks and submitting
information to triangulation).
The lack of external validity is typically seen as a
weakness in the case study approach, but I assert that the
findings will be theoretically (versus statistically) generalizable
because of the ubiquity of the problem of problem definition in
the policy process and policy design. Government agencies are
currently under attack internally as Congress and state
legislatures cut back on federal and state resources and
authority because of a lack of faith in the bureaucracy's ability
to get things done. The government is also under external attack
as the public perception of its efficacy is at an extremely low
point. This study of educational problem definition could lead

to a more desirable status where the public and government
agencies work together.
All records and documentation will be kept in
chronological order in files in the researcher's possession.
The Texas Site
The National Science Foundation's Statewide Systemic
Initiative Request for Proposals and grant process offer an
opportunity to explore how one state group approached the
problem of systemic school reform in the area covering science,
mathematics, and technology. The site chosen is the Texas SSI.
The Texas site is unusual among the 25 states that have received
these ten-million-dollar, five-year grants because the
organization that houses the Texas project, even though situated
within a part of the huge Texas educational bureaucracy (i.e.,
the University of Texas at Austin [UTA]), it is not directly in line
with the Regents or the state higher education agency.
In most states, official parts of the state educational
bureaucracy, typically the state kindergarten-through-twelfth-
grade or higher education agency, were the responding agents
to the Foundation SSI request, although many state agencies set

up other agencies to house the SSI once the grant was won.
Among the 25 states awarded the grants, only Connecticut
(from the outset), Texas (because of a break in implementation)
and Montana (during implementation) housed the
implementation in third-party, outside-the-bureaucracy
The Texas SSI is housed and directed from the Dana
Center for Mathematics and Science Education at UTA. The
Dana Center was not created for the Texas SSI project, as were
many of the other state organizations connected with Statewide
Systemic Initiatives. The Dana Center existed before the
initiative, has vast resources outside the Foundation grant, both
separate from and connected with it, and will continue to exist
after the Texas SSI project has been completed. More
conventional agencies for the implementation of the initiatives
include the state kindergarten-through-twelfth-grade agency or
state higher education agency.
Texas was selected because of the unusual character of
this situation. It is surprising that such a large and centralized
state would empower a third-party agency for a large project.
Connecticut is a small state (although it has a sizable
population) and Montana, while large geographically, has a

small population. Both tend to be discounted as valid venues
for generalizable research (it is not true, however, that systemic
change is easier there; it is just different). Texas and the Texas
Education Agency (TEA), on the other hand, are extremely
large, as is the whole Texas educational bureaucracy. The very
size of the Texas educational bureaucracy makes highly
conspicuous the empowerment of an outside-the-bureaucracy
group, especially to manage a multimillion dollar project. There
are enough agencies inside the bureaucracy; it does not seem
necessary to look outside. Thus, Texas is considered a good
laboratory for other states because of its size, the size of the
bureaucracy, the diversity of its population, and the power
vested at the state level.
Third-party agencies exist in all states. If the case study
shows the Texas third-party agency to be less cumbersome and
more able to create a viable and engaging problem definition
and/or if it is more agile in implementing its plan, this event
would definitely add to policy theory. This dynamic could then
be expanded outside educational policy making. If Texas can
move outside the bureaucracy to effect statewide policy, other
states can too. Since, however, as Yin (1994, 26) notes, "there is
no precise way of setting the criteria for interpreting" the type

of findings that this case study will yield, the work of
explicating the findings that actually emerge from the case
study will be left for the conclusion.
Specific Procedures
Uri Treisman (Executive Director), David Hill (Assistant
Director), and Rose Acera (Coordinator of Research and
Evaluation) have granted permission to study the Texas SSI and
the Dana Center. Texas SSI documents will be the main source.
These include publicly available documents: successive
iterations of grant proposals, evaluations from outside
monitors, responses to Foundation questions, letters to and
from outside monitors and program officers, Foundation
regulations, and instructions, personal notes, and memos. These
documents are to be examined in order to understand (a) the
context of the national Foundation effort, (b) the Texas SSI's
evolution, and (c) the relationship between the Texas group and
the Foundation.
I will visit Austin once, arriving on Sunday, May 5, and
departing on Wednesday, May 8,1996. The Foundation audit is
planned for that Monday and Tuesday. Hill requested that my

visit coincide with a Foundation peer audit visit, so many
people I want to interview will be close at hand. In addition, the
first two days of interviews will be enhanced by observing the
Texas SSI presentation to the visiting Foundation team and the
auditing team's responses. I have been assured the Texas SSI
presentations will be highly interactive so I will witness the
level of satisfaction and hear the concerns of the visiting team. I
plan to take detailed notes on the computer and by hand as the
subjects speak, both to the group and in interviews.
The Executive Director of the Texas SSI has discussed the
dissertation research with the Texas SSI group and has agreed
to be interviewed and has suggested other interviewees. He will
introduce me at the May meeting with a short explanation of
the context of the research. As I approach each subject, I will
explain that the interview will take approximately one to one
and one half hours and ask if follow-up questions can be
pursued by telephone or electronic mail.
I plan to cite selections from the interviews and
documents. In a relatively small organization like the Texas SSI
(approximately thirty people), anonymity on the inside is
probably not possible and it has not been requested (except for
specific statements). However, to insure wide participation in

the interviews, informants will be assured that reference will
not be made to interviewees' identities, except where it is either
obvious and/ or deemed necessary for explanatory purposes.
To balance the information gleaned from Texas SSI staff
(triangulation and thick notes), I will also interview the outside
monitor7 as well as Foundation officials in Washington DC, and
people associated with other SSIs.
Unsolicited Confirmation
In the late stages of the writing of the dissertation, I
encountered unsolicited backing for information gathered
during the study. One non-Texas SSI participant volunteered
praise for Treisman's ideas via electronic mail. One non-SSI-
participant in yet another state told me of the visionary and
inspiring quality of Treisman's ideas once she learned he was
the subject of my dissertation. A third-party agency CEO in
New Jersey said that Treisman was the person in mathematics
and science education that he most admired. A third person
7 To provide formative evaluation, the Foundation hired outside
monitors who visit the project four days each year and spend four additional
days writing reports. These reports are sent to the NSF and the state.

with no ties to Texas, the Foundation or the SSI asked me if I
knew that Treisman had "saved the Texas SSI."

The assumptions from the literature review form the
underlying structure of this case study as they were the basis of
the questions that drove the research. The case study begins
with an explanation of the institutions involved.
The National Science Foundation
A recent brochure identifies The National Science
Foundation (Foundation) as an independent federal agency
established by Congress in 1950 to promote and advance
scientific progress in the United States.8 The brochure states,
"the Foundation accomplishes its mission primarily by
awarding competitive grants to educational institutions for
8 The establishment of the National Science Foundation is one of the
case studies in Nelson Polsby's (1984)!

research and education in the sciences, mathematics, and
The annual budget exceeded three billion dollars and
represented three percent of the total federal research and
development budget. It also represented thirty percent of
federal support for math and science education. Over ninety-
six percent of the Foundation's budget went directly to
institutions and individuals for research and education
programs. The agency collaborates with universities, state
governments, other federal agencies, and others on a broad
range of projects in science, mathematics, engineering,
technology, and education. (Forms and Publications, [n.d.]).
The Dana Center
The 1995-1996 mission statement of the Dana Center
the Charles A. Dana Center at the University
of Texas works in Texas and nationally to
achieve equity and excellence at all levels of
public education. A catalyst and incubator for
educational innovation, the Dana Center is
engaged in research, program development,

and dissemination, advocacy and equity in
j mathematics and science education, and
j promotion of educational policy that supports
j useful change. While recognized as a leader in
| strengthening mathematics, science, and
! technology education, the Dana Center also
| operates programs in literacy and public
| engagement" (Rose Acera, personal
i communication, October 1996).
The Dana Center is supported by the Charles A. Dana
Foundation, several federal grants, and on-going grants from an
anonymous donor (Welch 1995,5). Rose Acera, Coordinator for
Research and Evaluation wrote:
Uri Treisman received the Charles A. Dana
Award for Pioneering Achievements in
American Higher Education in 1987 for work
that led to higher minority student
achievement in freshman calculus at the
University of California at Berkeley. The
Foundation's first support was for national
dissemination of that work in the higher
education sector; that dissemination was the

beginning of the Dana Center. The grant
accompanied him when he was recruited to
and subsequently moved to the University of
Texas at Austin in 1991.
Present programs at the Dana Center include the Texas
SSI (with all of its extensions); the telecommunications network;
state technical assistance for federal programs; plus other
smaller state projects (Rose Acera, personal communication,
October 1996). Acera continues,
the intent is not only that the Dana Center be a
place for dissemination, but a place where
these programs can interact...and help
audience schools (with particular attention to
high poverty schools), understand, choose and
craft programs to their needs. The vision of the
entire Dana Center is systemic...we need to
connect the different components
professional development, curriculum
development, telecommunications, federal
programs, and so on which are usually
located in and report to different

bureaucracies, and usually do not talk with
one another (October 1996).
There are currently over eighty Dana Center employees
(Karen Eikner, personal communication, 1996).
The Texas Statewide Systemic Initiative
The Texas SSI is one of three National Science
Foundation Statewide Systemic Initiatives not directly
connected with a state department of education or Board of
Regents. As part of the Dana Center and as a result of the Dana
Center's third-party status, the Texas SSI operates outside the
official state of Texas educational bureaucracy and hierarchy.
The Texas SSI is not staffed or directed by current employees of
the state education agency or the Governor's Office, nor is it
directed by the University Regents or housed in a school of
education of a state university.
The Texas SSI started out like most other state programs,
that is, as a proposal written by a consortium of state agencies,
including the Governor's Office, the K-12 and higher education
state agencies, and one or more departments of education at
state universities. Initially, it was to be housed in the School of
Education at UTA. This case study lays out the Texas SSI's

evolution from a project situated well within the educational
bureaucracy into a project situated, if not completely outside the
bureaucracy, at least in a third-party agency on its edge (as
contrasted with other SSIs), yet focused "on improving the
[whole] infrastructure" (Welch 1995,18).
The National Science Foundation Statewide Systemic Initiatives
The National Science Foundation's Statewide Systemic
Initiative Program was an innovation, said Janice Earle, the first
Texas SSI program officer. Earle said that before the 1990s,
although they had funded kindergarten-through-twelfth-grade
(K-12) education through curriculum development and teacher
enhancement projects since the Sputnik era, K-12 education was
considered "precollegiate," that is, the Foundation was only
interested in those students going on to college. In the 1990s its
focus changed.
Working with state education agencies on state-level
policy was a major shift. The Statewide Systemic Initiative was
an effort to serve not only non-majors in college, but even
middle school and high school students at risk of dropping out
from high level mathematics and science education if not
from school altogether.

In its original 1990 Request for Proposal (RFP), the
Foundation introduced the Statewide Systemic Initiative
program as a solicitation for
proposals intended to broaden the impact,
accelerate the pace, and increase the
effectiveness of improvements in science,
mathematics, and engineering education in
both K-12 and post-secondary levels (Request
The statewide initiatives were to "encourage statewide systemic
initiatives designed to overcome such systemic barriers as may
exist" (1990,2). The RFP required that a state proposal be
submitted through the "Office of the Governor or another office
or organization designated by the governor and also have the
signature of the chief state school officer and/or the commission
of higher education" (1990,4).
The RFP said the Foundation would award four to eight
grants of from one to two million dollars per year, totaling from
five to ten million dollars to each successful state over the life of
the project. The RFP also called for integration of significant
state and local funds, private sector funds, and funds received
from the federal Department of Education. The RFP provided

examples of the possible focus of the effort, including various
combinations of mathematics and science in kindergarten
through community (junior) college (Request 1990,2).
According to Peirce Hammond, a Foundation official, the
RFP reflected the fact that the Foundation was attempting to
"ride several waves" of school reform begun in the late 1980s,
waves of change initiated by the 1983 publication of A Nation at
Risk. For Governors, being an "education Governor" had
become a real plus. After all, said Peirce, "education constitutes
about one-half of each state's budget." The business community
"had moved from thinking of cheap labor as the name of the
education game" because it had become apparent to many
business leaders that the new technologically-driven global
economy would need workers who could think and who knew
how to leam. On another front, constructivist learning theory,
based on cognitive research, was shifting people's thinking to
the idea that virtually everyone can engage in high levels of
learning. All of these groups were realizing that school
structures and the traditional way of delivering curriculum
(different curricula for different students) were not serving all

As mentioned above, Foundation mathematics and
science initiatives were not new to K-12 education. But, while
single intervention strategies like curriculum reform were doing
no harm, they were not accomplishing widespread change. The
tendency to believe either that small efforts will make a big
difference or that there is a "silver bullet" that will lead all other
efforts to higher quality student learning was prevalent and
needed to change. States seemed the appropriate level to begin
a new, broader intervention strategy to change the face of K-12
mathematics and science and technology education. By
definition, all "systemic" (classroom, school, district, state)
efforts had to work together. Top-down had failed and bottom
up strategies, alone, Hamilton claimed, would become
"formless." The Foundation could not fund all fifty states, but it
intended to start a trend that other states would choose to
The Foundation's definition of systemic was described in
ten "elements of systemic change" (see Appendix B). State
proposals were to be rated partially on addressing as many of
these components as they could in an "integrated and well-
coordinated" fashion (Request, 1990, 3). The elements were not

prescriptions, but "suggestions of issues relating to many of the
factors essential to systemic change" (Request, 1990,3).
The RFP also described a likely study or planning group
composition as "leaders essential to the process of bringing
about changes in the educational system of the state" (Request,
1990,4). Cohort 1 RFPs were due at the Foundation by October
15,1990. Texas submitted a proposal but it was not funded.
Stages of Evolution
In October 1991, a Texas group, much like analogous
groups who did parallel work in other states, completed the
final Texas proposal to the National Science Foundation for the
second (1991) cohort of the Statewide Systemic Initiative
program. The proposal, entitled "The Texas Science and
Mathematics Renaissance," was submitted by the Director of
Education Policy for the Office of the Governor, the Dean of the
College of Education at UTA, the Commissioner of Education,
and the Commissioner of the Texas Higher Education
Coordinating Board. These people, according to the proposal,
formed "the key liaison," charged with guiding "the
development of policy to reform science, mathematics, and

engineering education at the preservice and inservice levels"
(Final proposal, 1991,17).
Texas followed the conventional procedure with the
requisite players for states applying to the Foundation for this
sizable amount of money for statewide school reform. The
coalition of state-level agencies well within the educational
bureaucracy made good, bureaucratic sense. If a state system
promised to change the ways it established and then
implemented science, mathematics, and technology education
from pre-kindergarten through four years of college, it was
entirely appropriate that the major state education agencies,
those closely linked to the legislature, would lead the effort. In
this customary way, Texas began an interesting journey, the
case studied for this dissertation. The study of the evolution of
the Texas SSI will be divided into four stages.
Stage One is the first funded Texas plan (1991) and its
implementation (1992-1993). Stage Two includes the
Foundation's suspension of funding for the original Texas plan,
after it demonstrated "inadequate progress," and its subsequent
redesign period. Stage Three is the Texas SSI's move to the
Dana Center and its subsequent refunding (1994). Stage Four is
a snapshot of the early implementation of the Texas SSI (1995-

1996). As a prelude, we look at the Foundation's definition of
systemic change.
Systemic Change
The RFP listed ten elements of systemic change (see
Appendix B). In elaborated fashion, they are
1. The organizational structure of the educational
bureaucracy and the locus of decision making must change.
States should set the vision and keep the record. Schools should
have more flexibility coupled with heightened accountability.
Schedules and calendars should be derived from research-based
theories of teaching and learning instead of the Taylor "factory
2. Schools and districts must be provided with resources
based on the needs of students and teachers for teaching and
learning, not on the varying amounts of money gathered
through the property tax. State funding models should be used
to equalize these differences.
3. States must better prepare those who would teach and
must be sure that more women and minorities succeed in
science and mathematics education and then enter the teaching

4. We must improve the ways we keep good teachers and
encourage and support them in learning more about their
subject matter and how to teach it.
5. States need to set goals for subject matter learning for
all students and provide curriculum frameworks that provide a
broad outline for reaching those goals.
6. States must continually update the delivery of
instruction, including the intelligent integration of technology.
7. States must also find new ways for more open-ended
(as opposed to multiple-choice or one right answer) assessments
of student achievement, including problem solving and higher
order thinking.
8. Facilities and equipment need to be continually
updated and equitably provided.
9. There must be coherence within the system, among
levels of schools elementary, middle, high school, and higher
education as well as among reform efforts.
10. State systems must make it clear to their customers
basically the whole of society, focusing on students and parents
how students are doing and why and what all parts of the
system are doing to ensure improvement in student

Latitude to reach these goals was allotted to state
proposal-writing teams.
Stage One: The 1991 Plan
The first Texas plan proposed using the new money the
SSI would bring into the state (two million dollars a year for
five years) and state matching funds (one million dollars a year)
to buttress reforms that had already begun. This consortium
proposal was a case, according to one informant, of "Look what
we're doing! Aren't we great?"
The stated goal of the 1991 Texas Science and
Mathematics Renaissance (TSMR SSI) proposal was "to improve
science and mathematics education for all Texas students." The
proposal identified the major barrier to this goal as "the scarcity
of adequately prepared science and mathematics teachers in the
state." The project was focused on "providing comprehensive
and ongoing inservice training for teachers now in the
classroom, as well as excellent preservice preparation for those
students who will become mathematics and science
teachers"(Final proposal 1991, 7). The proposal was for funding
an ongoing middle school teacher professional development
project created by the UTA School of Education.

The 1991TSMR SSI focused on five Education Service
Centers (ESC) and eight middle school campuses.9 ESCs are
regional consortia of local school districts that cooperate to
procure materials, supplies, and expertise for regional
workshops and other resources for member-districts. There are
twenty ESC regions in Texas; one is the size of the state of
The stated 1991 objectives were to
1. Develop TSMR Centers for the professional
development of both inservice and
preservice teachers of science and
2. Coordinate and enhance effective science
and mathematics inservice programs and
other exemplary outreach programs...10
3. Establish a means for the business and
industry community to collaborate...
4. Establish a means to integrate technology...
9 What many states would call schools, Texas calls campuses.
Inservice programs are for teachers currently teaching; outreach
programs are those not held on a certain university campus. They may be
held on linked university campuses or at other sites.

5. Establish aggressive recruitment and
retention programs to increase the numbers
of women, minorities, and individuals with
disabilities who enter the science and
mathematics teaching professions...
6. Encourage the dissemination of information
to parents and the general public about the
importance of mathematics and science
literacy in today's world (Final proposal
Earle said that Texas is so large that it cannot be expected
to tackle everything at once. The middle school strategy,
entering through "one slice of the education pie," seemed a
good idea. California, another huge state, had a similar strategy.
The Foundation was interested in the state-level policy
potential of the project. The then-commissioner had indicated
he wanted to transform what he (and the Foundation)
considered "underutilized ESCs" into true regional educational
centers. The transformed centers would have adequate staff and
funding for high quality teacher development and be a
mechanism for decentralizing the system. Foundation staff saw
this policy transformation in the TSMR SSI proposal.

In addition, the Foundation saw Texas as a good site for
an SSI because of the early 1990 changes in Texas laws that
dovetailed with the intent of the Foundation program. In 1990,
Texas Senate Bill 1 had mandated accountability for student
performance and the creation of district committees to establish
and review local district educational goals. In 1991, Texas
House Bill 285 mandated site-based decision making for all
campuses in the areas of goal setting, curriculum, budgeting,
staffing patterns, and school organization (Strategic Plan 1993,
1). Foundation sources confirmed that these moves in the
direction of "standards-based education" (not called that in the
early 1990s), were integral to what "systemic change" meant in
the original Foundation SSI program.
According to Earle, the 1991 Texas plan made the first cut
followed by a site visit. The site visit team members liked what
they saw and heard from the Texas group. The Foundation
agreed to fund the project with one change a request that
fiscal responsibility and the "Principal Investigator" of the
project be shifted from UTA to the Texas Education Agency
(TEA). This request was made, according to Earle, because,
although the UTA School of Education had been important in
the writing of the proposal as conceived as a project for teacher

development, it was the state-level policy aspect of TSMR that
most interested the Foundation. The authority for the desired
policy changes lay in the TEA.
The Foundation had the money and the state group then
working on the project proposal had committed to seeking this
money to improve education. So, at the request of the
Foundation, the Texas SSI moved even more solidly into the
state K-12 bureaucracy and into TEA. In September 1992,
roughly a year after it had been submitted, the 1991 Texas
proposal began implementation with the fiscal year. Sources
both in Texas and at the Foundation say the TSMR SSI struggled
in its first year (1992-1993). As an example of the disarray,
several new Texas TSMR SSI directors were appointed between
1991 and 1993. According to both sets of sources, some of these
directors suffered from lack of content knowledge in science
and mathematics; most did not have the experience for such a
high profile job (a policy position at the state level), while others
were victims of the evolution of the project and the ensuing
politics. As one person put it, all of these changes including
moving the project to TEA caused some people to "get their
noses out of joint."

In June 1993, a strategic plan required by the Foundation
for the second year of the TSMR SSI was submitted over the
signature of yet another new project director in TEA. The letter
mentioned several weaknesses per the elements of systemic
change in the first year of implementation. These included that
they had not (a) expanded recruiting efforts for minorities and
underrepresented groups; (b) formed a sufficient number of
business and community partnerships; (c) engaged the public;
or (d) communicated sufficiently with schools about
The TSMR SSI was credited by its implementers with
(a) continued support from its original backers plus other
professional organizations; (b) finding good regional sites; and
(c) staffing the sites with "exceptional people, both
knowledgeable and enthusiastic" (Strategic Plan 1993, ii). As is
evident in their report, TSMR SSI people understood that
execution of their plan had not met their goals or the
expectations of the Foundation. None of the new, ambitious
undertakings under the rubric of "systemic change" was
As a consequence of this disappointment, the project's
description changed. It more closely mirrored systemic

concerns, first mentioning that Texas had many reform efforts
If TSMR is to have a systemic impact, it must
play a sometimes larger, and different role
from these other initiatives. It must enhance
and support local, regional, and state-level
programs already in place, provide a conduit
between programs and funding sources, and
initiate a select number of large-scale
programs that will result in far-reaching
impact through local implementation
(Strategic Plan 1993,1).
The second year's objectives also reflected steps, albeit
mincing, toward a more systemic view:
1. Strengthen the coordination of state
2. Develop state level professional
development programs in middle school
mathematics and science (Strategic Plan 1993,
The wording in the first objective, "coordination of state
initiatives," was not used in the 1991 TSMR SSI proposal, nor

was "state-level" mentioned. However, the writers of the plan
stuck to the idea that the TSMR SSI would "continue to target
middle school mathematics and science" (1993,1).
This "subtle shift," as the Texas writing group called the
reworking of the original proposal, was evidently too subtle to
convince the Foundation of the continuing value of the Texas
TSMR. In July 1993, in a discussion between the commission
and the Foundation program officer, the commissioner
requested that a hold be placed on the project. In August 1993,
the Foundation suspended Texas SSI funds and called for a
"redesign period." Texas could use the leftover funds from the
first year for the redesign.
Earle was sure that the Texas group had been surprised
at the large amount of attention the Foundation paid to the
early implementation because she did not visit the state very
often. Each program officer had several SSIs to monitor and
only $2000 per year in travel funds. However, outside monitors,
technical assistance by the Education Development Center, and
SSI representative meetings in Washington ("reverse site
visits.") bolstered Earle's information. However, even though
the Foundation employed outside monitors, no one, Earle
contended, could appreciate Congressional pressures on

Foundation staff because they did not interact personally with
legislators. Members of Congress were constantly asking what
they were getting for their money.
What Earle learned about Texas was that none of what
she considered the plan's promised potential had been
accomplished. Foundation complaints included the fact that it
was months after the November 1992 start-up before the first
director was named. Once named, the director did not measure
up to the Foundation's requirements for the position; nor did
her successors. Furthermore, little of the money had been spent
a sure sign that they were not working at the systemic level,
Earle added. "Nothing happened."
Another new director was chosen for the redesign period
and a team of writers, including old and new players, was
formed. Among the new names on the roster of the "broad
based group of people" working towards the redefinition of the
Texas effort was Uri Treisman, mathematics professor at UTA
and Executive Director of the Dana Center for Science and
Mathematics Education also at UTA (Strategic Plan 1993, i).
Significantly, during the rewriting, the policy context was
changing. State-level policy changes were following each other
in rapid succession, moving faster than the TSMR SSI. In 1993,

the Texas Legislature consolidated the educational
accountability system around student performance, setting
district and school campus criteria and mandating public
disclosure with prescribed state sanctions for low school
performance (Strategic Plan 1993,1). These policy changes were
evidence of "standards-based education," and elements of
systemic change as spelled out in the RFP. The project
implementation might not have been pleasing to the
Foundation, but the policy environment was certainly to their
Stage Two: A New Plan and New Rejection
During the suspension period, the Texas writing team
questioned each other as to why the TSMR SSI proposal had
been funded in the first place given its subsequent suspension.
As one Texas informant has it, Foundation funding was
awarded partially because of
the diversity of the Texas school population
in terms of ethnicity, gender, socioeconomic
level, languages spoken, rural/ urban/
suburban location, size of district, and

previous academic experiences (Seeley 1993,
They understood they did not have a common
understanding of what systemic change meant even among
themselves, and they did not know what the Foundation
wanted. There were at least three versions of the new proposal.
In an early draft of the revised plan, the mission and objectives
had changed. There was an explicit mention of systems:
Given that the goal of the SSI effort is the
implementation of systemic reform in
mathematics and science education, the
mission of the Texas SSI is to develop the
constituencies necessary for the
implementation of mathematics and science
education reform (Strategic Plan, August, 1993,
In a later draft, the objectives had evolved:
1. The Texas SSI must develop the necessary
constituencies to educate the public...
2. The Texas SSI must develop the necessary
constituencies to seed innovation...

3. The Texas SSI must develop the necessary
constituencies to monitor the implementation
of reform (Strategic Plan, October 1993,6;
emphases original).
Wording such as "develop the necessary constituencies"
responded more directly to the Foundation's originally posed
systemic elements. The group was not so subtly using the
Foundation's words. Yet, according to Earle, she and others at
the Foundation saw these drafts and found them all "flawed." It
is no wonder the plan kept changing.
In the proposal actually submitted, the objectives had
changed yet again:
1. The work of Texas SSI will serve as a model
to complement, facilitate, and augment the
alignment of policies and structures with the
state's vision for reform.
2. Texas SSI will create an environment that
supports the implementation of the state's
vision for mathematics and science teaching
and learning.
3. Texas SSI will establish lasting vehicles for
networking and for building the capacity of

various constituencies, particularly that of
mathematicians, scientists, and engineers, to
implement standards-based mathematics
and science reform, and will seed innovation
in meeting the challenges of implementing
this vision of mathematics and science
(Annual Progress Report 1994,30-31).
The second and third objectives supported a statewide
vision, but only as a "model," not as a link to state policy
change. "Establish lasting vehicles... is a hint of new ideas
fleshed out later. This annual progress report, outlining the
early implementation of the somewhat redesigned TSMR was
sent to the Foundation in May 1994. At the heart of the new
plan were three ideas: "Policy Alignment, Creating an
Environment for Change, and Building Capacity" (Annual
Progress Report, 1994,3). Its desired outcomes included models
of professional development. The TSMR SSI test sites would
continue as part of the project.
Nothing much happened between the January
submission of the redesigned proposal and the progress report.
None of the revised goals had yet been attempted. This was
understandable since Texas had not been funded beyond the

first year (1992-1993). The Foundation continued to refuse
refunding and in May demanded an acceptable revision be
submitted by June 30,1994. The Foundation even stipulated
who was to write the new revision: Treisman. The result was
the famous in Texas SSI circles "Addendum."
Why Treisman at this point? Treisman emerges as critical
to the state and Foundation turning to a third-party agency. He
was esteemed by Foundation staff (one called him a "genius")
and highly regarded inside Texas. He was called upon not only
to write the proposal but also to direct the project if the
proposal was accepted.
Stage Three: The Addendum
In the overview of the June 1994 "Proposal Addendum"
Treisman stated,
we now present new programmatic strategies
and a powerful and fundamentally new model
for developing a broad-based indigenous
leadership that can bring about the envisioned
structural reform of Texas mathematics,
science, and technology (M, S & T) education

The plan claimed to address "the concerns raised by NSF
staff members and outside reviewers" (1994,1). It described "a
complex of SSI working groups [now called Action Teams] each
charged with designing and putting in place a fundamental
building block of the new system." The topics the groups would
tackle included new curricula, new models of large-scale
teacher development, and new mathematics and science
frameworks. The "working groups" were described as follows:
These inter-institutional teams will be
composed of college and university faculty
members, teacher leaders and school
administrators, private sector scientists and
engineers, state and local education leaders,
representatives of other relevant groups of
stakeholders (Treisman 1994,1; emphases
Similar groups had been mentioned in the January 1994
proposal; however, the Addendum was much more explicit.
Empowering these Action Teams,
with a clear mandate and with adequate
resources to tackle important educational
problems, a grassroots state leadership will

emerge that is accustomed to cooperative
action, consensus building, and priority setting
a new feature of the Texas landscape (1994,
Here was the problem definition. Texas needed to grow a
new kind of leadership in the middle of the bureaucratic
hierarchy. It was not to be situated in schools or models, but in
a quasi-public forum. The emphasis was on the groups'
(a) broad-based, cross-role, grass-roots composition, (b) their
ability to make decisions and (c) take action for the whole state.
Action Teams were promised a budget, "approximately
$100,000/ year" (Treisman 1994,8). Money and the ability to
direct the money toward reform according to what the Action
Team members decided made them very different from the
usual bureaucratic "task force." The Addendum (Treisman
1994,9) emphasized the possibility that these groups would
"create a tradition of cooperative action Treisman said that
what was available was not doing the job. A "network of
distributed leadership" could change the infrastructure and
move the system to new levels of student learning. The
Addendum clearly decentralized the Texas SSI decision-

The Addendum promised a partnership between the
Dana Center and TEA, linkages with other Foundation
programs for mathematics, science, and technology, as well
with Goals 2000.11 It pledged close ties with the Texas
Education Network, the Internet link for Texas educators, as
well as other state telecommunications efforts (Treisman 1994,
3-4). Treisman (1994, 3) called the links "streamlining" to bring
"greater coherence to a chaotic landscape."
He claimed a role for the Texas SSI (1994,6), through an
"SSI policy team" that would work to align such state system
products as end-of-course examinations, teacher licensing
examinations, instructional materials, textbook adoption
guidelines, school accreditation criteria, school finance
structures, school desegregation law, and teacher compensation.
To further support this systemic work, the new SSI would use
its resources to entice districts to "redeploy their., .entitlement
monies" (1994,11). The proposal provided particulars on a
planned public relations campaign, a partnership with business,
and pledged the SSI would work with other subject areas (1994,
6). The ability to align all critical policy areas was seen as a
Goals 2000 is federal money granted to states that present a plan
for instituting standards.

source of the new Texas SSI's potential authority (1994,5-6). A
form of the word "system" was used at least six times in the
twelve pages that described the program. There was a definite
(not subtle) change from previous proposals. The desired
changes responded directly to eight of the ten elements of
systemic change in the RFP.
Treisman set up imposing challenges for the new Texas
SSI and the Addendum exuded a sense of power and urgency
as he asserted (1994,5), "in a marked deviation from the earlier
SSI plan, the framework alignment process will begin
immediately." It also stated that
as of July 1,1994, Philip Uri Treisman,
Professor of Mathematics, University of Texas
at Austin, and Director, The Charles A. Dana
Center for Mathematics and Science
Education, will become the SSI's Principal
Investigator and Executive Director...The
University of Texas at Austin will serve as the
Initiative's fiscal agent (1994,4).
Treisman said he was the principal author of the
Addendum with a little help from a few people. Others
supported his claim to principal authorship.

The Policy Entrepreneur
According to sources within the Texas SSI, the head of
the Foundation's education sector required that Treisman
become the Principal Investigator and Executive Director of the
project for the Foundation to continue consideration of funding.
Some informants insist that Treisman's taking the reins of the
project was absolutely crucial to the Foundation, thereby
rendering the actual revision of the plan secondary. Some Texas
SSI staff explained that while sometimes a plan is submitted
and accepted as a blueprint for the implementation of a project,
this time a plan was required to be submitted and accepted
(regardless of the plan's contents) just so the project could
happen. Thus, these staff members contend that Treisman's
intellectual and political presence in Texas, plus his ties to the
Foundation (he serves on the Advisory Board of the National
Science Foundation's Education and Human Resources sector,
for instance) constituted the actual reason for the refunding of
the Texas SSI, rather than its intrinsic value or substance.
The whole process was political, these sources said.
Furthermore, these same people (and others) are certain the
current Texas SSI is not implementing the Addendum plan.
These people held Treisman in awe for what they called his

brilliance; they were cynical about the bureaucracy and its
relation to politics. If true, this would certainly indicate that it
was the presence of a policy entrepreneur, not his ideas, that
was essential to the refunding.
Foundation sources tell a different story. They say that
one of the problems with mutual understanding between the
Foundation and the Texas education bureaucracy was that the
former Commissioner of Education had not "bought into" the
Texas SSI. It was pressure from Texas Governor, Ann Richards,
to get the grant refunded (after her opponent criticized her
administration during 1994 gubernatorial campaign for the
defunding) that kept the Texas players in the game. Yet the
plans remained "flawed," because of the lack of ownership by
the Commissioner.
The subsequent entry of Treisman, according to
Foundation sources, "gave us hope" an acceptable plan could
be created and implemented. Foundation sources insisted that
Treisman's performance in front of a Foundation panel in
Washington DC, where he explained and defended the new
plan, enhanced that hope. They maintained that the Addendum
plan went through regular processes and only the new promise

of real systemic change in the plan allowed the Foundation to
refund the Texas SSI under Treisman's direction.
Furthermore, in an interview, Treisman did not agree
with descriptions of the change that suggested the Addendum's
contents did not matter to the Foundation. According to
Treisman, whom a source calls "relatively humble," he had ten
days to create the new proposal. He spent "fifty non-stop
hours" writing it. In other words, he vouched for its high
quality and maintained that everything in the Addendum was
currently being implemented. In his words, "It's all there."
Treisman added that the first thing he did when he set the
refunded project in motion in November 1994 was to convince
David Hill, a former Austin area superintendent, to become
Deputy Director. He needed someone to carry out day-to-day
management, a good leader who was also well connected in
Texas education circles. Hill's job was to implement the ideas of
the Addendum. As the Texas SSI outside monitor, Welch, (1995,
14,15) reports, "David Hill has been invaluable." "Uri is not a
detail guy" said one source, referring to his management style.
Study of SSI documents demonstrated that, as Treisman
had contended, the Addendum presented new content and
dynamics and these were being implemented in 1996. Elements

of these ideas had, of course, been discussed during the
redesign year, at least when Treisman joined the 1993-1994
writing team, if not before.
One long-involved informant called the winding path of
the Texas SSI "an evolution." Others might be more apt to call it
a maze since not everyone among those involved along the way
was following the same path.12. As a result of Treisman and
Hill's leadership, several people who had been involved in
various stages of the TSMR SSI and had been pushed or
dropped out were later invited back in to fill roles that better
suited their talents and expertise. This effort at reconciliation
had caused some healing as exemplified by David Molina, a
former director of the TSMR SSI, now involved in what has
been described as a Texas SSI concrete success. He candidly
discussed his involvement and frustration with the Foundation
and, without prompting, added "there really is a vision [now]."
Molina was not alone; Texas SSI staff (including all the
people working on its many projects in and outside the Dana
Center, many of whom are only part-time SSI employees) and
Foundation officials were adamant that Treisman was an
12 Not everyone would talk to the researcher about the history of
the Texas SSI, despite numerous requests.

excellent person for the position because of his commitment to
student "access,"13 as well as his many good ideas, strategic
thinking, distinction as a mathematician, prestige among
mathematicians and scientists, and political savvy.
Stage Four: Implementation (1994-19961
A comparison of previous versions of a revised plan and
the Addendum revealed, as Treisman insisted, that the
Addendum presented new and ambitious ideas, (a) the Action
Teams and their grass-roots and cross-role characteristics,
(b) linkages with other federal programs, and (c) a far-reaching
vision of alignment of all parts of the state educational system.
The Addendum (1994,5) also differed from earlier versions by
conveying a sense of urgency. A glance at what was happening
in 1995-1996 indicates the basic concepts of the Addendum were
being carried out in the implementation of the Texas SSI.
13 "Access," as defined in education reform, says true equity
provides underprivileged students with resources, and removes barriers to
their academic preparation. See, for example, (Treisman 1992).

Early Implementation
The Texas SSI was being implemented "in the midst of a
rapidly accelerating deregulation of school governance, a
downsizing of its central education agency, and a possible
transformation of its accountability and curricular guidance
systems" (Welch 1994,1). Action Teams were given a mandate
to thoroughly investigate given issues and ultimately fashion
policy both within the project and throughout the state through
the many programs the SSI and the Dana Center administer.
However, Action Teams do not just go off on their own but are
closely tied to Texas SSI philosophy through staff who serve as
facilitators and support people to the teams.
Using the Action Teams across the conceptual "middle"
of Texas, the SSI set up a process that allowed for input from all
political camps, all educational and community roles, and all
regions of Texas. It reached out across Texas and around and
down the educational system in a three-pronged approach that
fit with the push for decentralization by the new Republican
Governor (George W. Bush) and the State Board of Education.
The three prongs are top-down, bottom-up, and "across the
middle." Treisman considered the third dynamic, "across the

middle," of major importance and the true innovation inherent
in the problem definition.
The Texas SSI "created neutral venues across the middle
of Texas" where issues could be kicked around and consensus
reached. "These fora included people from all regions of Texas
and from roles besides just education professionals: the middle.
All were concerned with education, even though the
consciousness of some had to be raised. In this heretofore
missing space, participants worked with people who viewed
education from distinctly different perspectives. Treisman
stressed the idea that mathematicians and scientists were
working with educators, and teachers were working with state
directors of mathematics and science educational reform. State
directors of government programs targeted to minorities and
the disadvantaged were also working alongside content area
specialists and school-and district level practitioners. In one
Action Team, educators from all subject areas worked together
for coherence among the state content standards.
The vision is one of a protean structure that, according to
Treisman, could ultimately become a new educational
"institution." "Protean institution" may seem to be an
oxymoron, but in Treisman's plan, this postmodern institution

would visit and revisit all parts of Texas in a rolling fashion.
Individual Action Teams would disappear once they
accomplished their task. They resembled a network rather than
an institution, and a constantly changing network, at that.
As the May 1995 progress report says (Annual Progress
Report 1995, 7), the Action Team concept is "a unique meeting
ground for activist leadership, where ideas and good local
practices can spread easily." As Welch (1995, i-ii) said, "their
action plans have the potential to reshape educational policy,
improve the science and mathematics education infrastructure,
change the way that teachers are prepared, link the SSI to the
large Title I program in the state, and change the science and
math curriculum and the way it is taught." SSI staff said they
wanted to "give local control a chance" by equipping local
administrators with decision-making tools and other tactics to
take wise advantage of their new authority so they would not,
for example, "use modem technology to deliver bad instruction
Everything is organized around state content standards.
In his comprehensive report, Welch (1995, i-ii) described the
work of the current Texas SSI as "the professional development
of team members, the creation of networks of reform-oriented

professionals, and the identification of a pool of potential
recipients for SSI incentive grants planned for the future."
There were thirteen Action Teams with 220 people
working on them during the summer of 1996. Over the life of
the project, the numbers have changed as new issues emerged.
The teams have taken on new forms as their products were
completed or missions fulfilled. The Texas SSI provided the
public space, the topics to ponder, facilitation, and the
intellectual tools to negotiate the issues. Local decision-makers
and stakeholders were invited to reach consensus on the work
that needed to be done. They were provided the time and
money to do their work. Teams shared approximately one
million dollars a year for incentive grants to schools and
districts (Welch 1994,14). The Action Teams decided how they
wanted the incentive grants constructed while Texas SSI staff
implemented the Action Team plans and administered the
As an example, the "Pre-service Mathematics Team" was
provided with a $200,000 Fund for the Improvement of Post-
Secondary Education grant for elementary teacher preparation
in mathematics. It subsequently wrote and published a
document that outlined how elementary school teachers should

be prepared to teach science. The Action Team then funded
faculty members at fourteen Texas institutions of higher
education to develop courses following the document's
It was evident that all of this was carried out in
coordination with the existing powerful segments of the
educational bureaucracy. TEA, for instance, despite all its
downsizing, still held a great deal of power, including control
over the accountability system, textbook selection, and state-
mandated curriculum. The Texas SSI maintained many linkages
with TEA. Welch elaborates,
the project has been given the authority
[through TEA] to administer the Eisenhower
mathematics program and the Goals 2000
money; TEA and SSI are working together on
the Title I action plan; the project is working
with a TEA-supported center whose mission is
the development and study of effective
practice for African-American learners, among
other things (1995, vii).
The SSI worked closely with TEA, all of the regional
service centers (no longer just one quarter of them), school

principals, and major new statewide reform initiatives, that is,
other third-party agencies. In his version of the Texas SSI,
Treisman focused on policy, and his definition of policy
included the provision that money be attached.
Money was pivotal. Rather than relying on the mere (for
Texas) two million dollars a year the Foundation SSI program
provided, the Texas SSI was using 12 million dollars and
working up to a goal of $20 million a year, said Treisman. Title
I, Eisenhower, and Goals 2000 brought in the bulk of federal
money to the state and the Texas SSI had a hand in all of them.
In addition to Foundation SSI funds, the Texas SSI used (in
1995-1996) approximately $500,000 of Eisenhower funds14 and
$360,000 of Goals 2000 resources for its Action Teams. TEA
provided one million dollars a year and TEA and the Dana
Center provided in-kind support totaling approximately $70,000
a year (Welch 1995,18).
The Texas SSI is the main contractor in developing the
state science and mathematics standards and also is assisting
the state in connecting mathematics with other subject areas
14 The SSI operated the K-12 Eisenhower program for TEA in 1995-
1996. It had close ties with the higher education part of the Eisenhower
program, but did not operate it.

such as science, social studies, and language arts as well as
career and vocational technical fields (Welch 1995,3). A real
coup was the SSI's link with the massive Title I project for
underprivileged children. The SSI also linked up with the
AmeriCorps grant which targets literacy for kindergarten-
through-second-grade children (Welch 1995,18). Before the SSI,
Treisman said, there was no real connection between efforts to
serve underprivileged students and efforts at curriculum
modernization in Texas. The Texas SSI tightly bound
Eisenhower, Technology, Title I, and Title VII programs. This
was their greatest accomplishment, Treisman said.
These accomplishments and ongoing initiatives seemed
to call for a large organization, but the Texas SSI employed only
about thirty people in 1995-1996. Its location was inside the
Dana Center although it was not synonymous with the Dana
The Texas SSI Inside the Dana Center
There was no formal entryway into the Dana Center, the
home of the Texas SSI into 1996. Once you entered, you were
surrounded by people working. And there was no physical
division between the Center and Texas SSI. They blended into

each other. The SSI section was a bunch of crowded rooms, up a
steep staircase in the back of the small building. Supplies were
stacked up everywhere, including in what was once a shower
stall. SSI staff seemed proud of the lack of formal organization;
they bragged about sharing desks and computers.
Texas SSI staff were scattered around the state. Some
worked full-time at the Dana Center location (although they
spent much of their time in the field). Others worked part-time
for the Texas SSI and part-time for universities other than UTA.
Hiring university people part-time was a strategy for bringing
more institutions into the project and broadening the SSI's base
of committed people.
Welch (1995, iv-v) commented on the Texas SSI's culture
and lack of organization: "there has been a constant explosion
of new projects and responsibilities... there is a chaotic aura that
surrounds the project...some people share the same desk."
When he asked for a copy of an organizational chart he found
"hand-written additions..." (1995, vi). Welch (1995, v) added, in
the project's defense, "despite the bustle, there is a conspicuous
liveliness about the project, especially at the Dana Center."
Welch attributed the lack of order to the number of ideas
generated. Treisman's ideas were definitely part of the culture,

considered both a true asset and also an ongoing concern. As
Hill, the person whose job was to pull all this together put it,
"not all of his ideas work, you know."
A Texas SSI staff member wrote,
I don't think of the Texas SSI as a bureaucracy
it's too ad hoc building temporary
structures to address issues and lacking in
such things as rigidity and protocols. People
who have worked for real Byzantine
bureaucracies (like [TEA]) might laugh at the
idea of SSI as a bureaucracy.
Another wrote,
I see the SSI as a team more than a
bureaucracy, almost a living organism. I've
never worked in the university before, but
have had contact with other departments since
taking this job. From what I've seen, we don't
even make the bureaucracy scales quiver by
UTA standards. Our bureaucracy is imposed
from without, by the University and
[Foundation]. It does not impact the internal
culture of our organization.

Another, more concrete assessment by a staff member is
that there is, "unquestionably, a university bureaucracy that
touches us on administrative matters (travel, reimbursement,
accounting, and accountability) but it does not drive our work
strategies or decisions."
The program monitor was not willing to say that the
Dana Center was not a bureaucracy. He found that idea
"problematic," but he did say the Texas SSI, was "a bunch of
interested, committed people trying to do a job." Welch (1995,
15) also wrote, "the management style of the project involves
getting people to work together on problems of mutual
Welch (1995,15) was certain, however, that the Texas SSI
was "entwined in the bureaucracies" and, what is more, he
emphasized that it had to take on more bureaucratic procedures
to meet its many obligations. Consequently, the non-
bureaucratic characteristics of the Texas SSI were being
challenged even as it was acknowledged to be accomplishing its
mission. Nor did its location inside the Dana Center keep it
from being knocked around by internal and external forces,
including state politics.

Election Year Politics
In August 1994, the Foundation agreed to refund the
project scheduled to run until 1998, with the new funding
starting in October 1994. Contrary to the call for urgency in the
Addendum, activities were put on hold from early October
until after the November 1994 elections. A change was possible
in the state administration, a change in parties and educational
philosophy. And the Republicans did win; the sea change
Foundation sources agreed that it had been a dangerous
time for the project. As Welch wrote (1995, viii), "another key
issue is whether [the SSI] can successfully navigate through a
changed (and increasingly politically conservative) state
government." There were legitimate reasons to be
apprehensive. For one, the SSI had earlier become a political
issue in Texas. Republican candidate George W. Bush had
criticized Democratic Governor Ann Richards when the project
was defunded by the Foundation (Welch 1995,16). Governor
Richards laid down the law, said Welch. Texas would recapture
this funding. Would newly-elected Governor Bush take on a
project that had been funded under his predecessor?

On the national level, conservative state administrations
had turned down federal education money in the last few years,
ostensibly fearing the control that comes with that money
(Pitsch 1995). The Statewide Systemic Initiative program was
focused on assuring "equity and access" to underserved
populations, a strategy found by many conservatives parallel
to affirmative action in the larger society as "dumbing
down." A Foundation source said if certain children are
succeeding under current conditions, their parents find real
value in the ways things are now. Changing the system that
decides what is taught and how those things are taught to allow
more children to succeed is perceived as "lowering the bar."
The new Republican Governor appointed a
superintendent from Lubbock, Texas, as the new Commissioner
of Education and "summarily dismissed" the former
commissioner who hailed from New York City. The State
School Board changed from a ten to five Democratic majority to
an eight to seven Republican majority. In addition, authority
was continuing to move from the state department of education
to the Governor's Office (Welch 1995,1). TEA was "severely
downsized," said Foundation sources, and much weaker than it

had been in the early 1990s. The fear among Foundation sources
was that mathematics and science would be forgotten.
Treisman left the newly funded project in limbo for a few
weeks because of the election. After the election, Treisman said
he worked with the new-Govemor's staff who were
communicating with representatives of the religious right and
the business community to decide how the SSI would mesh
with the decidedly more conservative administration and
school board. Governor Bush ultimately decided to tighten state
accountability systems while providing more local flexibility
rather than eschewing all state control and thereby
relinquishing complete control to districts. Foundation sources
said, "you have to give Uri credit for that." Bush's decision put
the SSI in a favorable position, according to Treisman, Welch,
and Foundation sources. As the monitoring report explains:
The changes at TEA and in the governor's
office have turned out to be advantageous for
the SSI. The down-sizing of TEA staff has
caused them to look outside the agency for
help. The new commissioner of education sees
the SSI as a valuable resource and has given
them funding and the responsibility for

mathematics and science reform in the state
(Welch, 1995, viii).
Welch, both in his report and interviews, attributed this
rapport to Treisman, who developed friendships in the
Governor's Office and among other policy makers. "The
Governor's office and TEA continue to seek assistance from Uri
Treisman and the Dana Center...he seems much in demand"
(Welch 1995, viii, 18). Welch added that the Governor and
Commissioner found themselves relying on Treisman almost
too much (politically speaking) and thus decided they had to
award some programs to other entities.
Texas was known in educational policy circles as the
quintessential top-down state, that is, it "has had a history of
passing legislation to address its educational problems" (Welch
1995,18). The top-down ethic says good teaching and thus
learning will occur because the legislature legislates and TEA
dictates what teachers have to do. However, earlier in 1994,
TEA had been mandated to cut its staff by 20 percent during the
period of 1995-1997, to become a service (rather than a
monitoring) agency, and to move many of its functions to the
twenty regional Educational Service Centers. Texas Senate Bill
No. 1 had set up a new, decentralized education code that

states, "The [Texas] State Board of Education by rule shall
establish the essential skills and knowledge that all students
should learn..." Such legislation and its products are nationally
known as "standards" (cited in Welch 1995).
The Texas SSI worked well with the new Republican
Administration in its stress on local control within a top-down
accountability system, said Texas sources. The new philosophy
provided much more freedom to building administrators and,
in some cases, to teachers, but it held them all more accountable
for results in student achievement.
The Texas SSI's "across the middle" capacity for realizing
important initiatives and the resulting power to fashion new
documents (such as curriculum frameworks tied to standards)
and align all of these documents (for example, standards with
teacher licensing and, eventually, teacher rewards and
compensation) gave the SSI "teeth," Treisman said. In essence,
the Texas SSI was, in tandem with other agencies, implementing
the state standards policy. The Texas SSI's ability to win new
power was attributed to (a) the policy environment within the
state, (b) strong linkages with other agencies, including TEA,
(c) its strategic position (attributed both to the Dana Center's

third-party status and the policy entrepreneur), and (d) its
momentum as it continued to win control of such endeavors.
Texas institutions and agencies (and their
representatives) who won Foundation support for a systemic
initiative in 1991 wandered through a maze. Texas participants
were spurred on at various times by Foundation questions and
criticisms. Differences in interpretation, suspension of funding,
state politics, formative learning during early implementation,
monitoring reports, and self questioning and reflection shaped
subsequent plans. State and Foundation ideas of what
constituted systemic reform differed. The difference in
interpretations remained tacit which made it difficult for them
to reach agreement. Politics kept the bargaining process going.
In the midst of a near breakdown in negotiations between state
and Foundation officials, a policy entrepreneur, highly-admired
by state officials as well as Foundation staff, emerged. Almost
single-handedly, he wrote a new proposal subsequently
accepted by the Foundation.
The new proposal embodied a systemic vision although
it is not clear whether in its subsequent refunding of the Texas

proposal, the Foundation relied on the actual ideas presented in
the proposal or on its confidence in the perceived brilliance of
the policy entrepreneur. Politics then slowed the beginning of
the new project as the election changed the Texas state
administration from Democrat to Republican. The project is
now implementing the ideas of the Addendum. What are the
implications of the case study for problem definition research
and school reform?

I will first discuss the findings related to each of the
questions that drove the research and then speak to the
implications for public policy in general and education reform
specifically. The questions were
1. Was the group that created the problem definition or
the group directing the project an outside-the-bureaucracy
group or a bureaucracy?
2. Did the group take a problem-centered approach,
engaging in frame reflection and/or lay probing?
3. Did the approach exhibit other postmodern
4. Was a policy entrepreneur involved?
5. What part did politics play?

Characteristics of the Texas Groups
Those charged with writing the original 1991 proposal
and its subsequent iterations were educators and policy makers
well inside the Texas educational bureaucracy. They came to the
table with a predetermined solution; they had structures
already in place that met the specifications of the Foundation's
Request for Proposals (RFP)'. After a shaky startup caused by
the difference in interpretation of the original Texas proposal by
its state creators and Foundation officials, a near breakdown in
negotiations occurred. The final, successful version was written,
not by a group, but by a single education policy entrepreneur in
whom the Foundation had "hope." Foundation officials
believed that Uri Treisman would create a system approach that
would fulfill their requirements. He was presented with the
unenviable task of resolving the impasse.
Treisman wrote the successful Addendum virtually
alone, so the ultimate proposal was written by a very small
group whose principal member was a professor of mathematics
at the University of Texas at Austin (UTA) and certainly part of
the education bureaucracy, but more important in terms of
my first question he is also Executive Director of The Dana

Center at UTA, a "third-party agency" and an outside-the-
bureaucracy organization by this dissertation's definition.
The findings are very messy. The first group was inside;
the second group was outside. So new questions arise: How
does the Texas process of getting to the third-party agency
compare to other states in which a third-party agency is
directing the SSI? How are the other third-party-agency-SSIs
faring? Are they as intertwined in the bureaucracies? Are they
as successful in redirecting large blocks of money? How do
these third-party SSIs compare to traditional SSIs?15
Are Non-Bureaucratic Tendencies Apparent?
Outside the bureaucracy in its location within the Dana
Center, the Texas SSI also exhibits other non- or post-
bureaucratic behaviors. First and foremost is its focus on the
customer as evidenced in the Action Team's inclusion of street-
level bureaucrats, educators who are not mathematics or science
teachers, plus non-educators. Second, the Texas SSI members
were described as people who knew what their work was and
15 The Consortium for Policy Research in Education will publish a
two-year study on standards reform in all fifty states in late 1996.

what drove it. They worked cooperatively under difficult
circumstances, some even without their own desks. So they
have a mission, clear goals, and clear norms features often
missing in bureaucracies that depend on rules and procedures.
The surprising influence of the Texas SSI also distinguishes it
from bureaucracies and their "sparse power."
Welch also commented on the Texas SSI's apparent lack
of (bureaucratic) inside evaluation processes. Texas SSI staff
expressed their need and appreciation of the Foundation's
prodding for evaluation. Yet, even though Welch had requested
in November 1995 that they hire someone to do an inside
evaluation (not taking staff away from the Action Teams), in
May 1996 no one had yet been hired. Texas SSI staff said they
understood the necessity of the requested strategic plans, but
they had trouble finding the time to think together about long-
term plans let alone write them. They were too busy doing
their work in the field. They preferred what they call "working
plans," that is, flexible one-year plans rather than three to five-
year plans. As David Hill, who was credited with bringing
order to the day-to-day management of the Texas SSI, said to
his staff, "we don't know what it looks like; we're cutting the

SSI personnel defended their non-bureaucratic ways and
claimed that in the Dana Center they had the best of both
worlds. They had the insider's ability to communicate with like-
minded souls and the prestige of UTA. They had the outsider's
flexibility, outreach capability, and respect that came with the
Dana Center and Treisman, a renowned mathematician. They
also had the Dana Center's small and elusive but useful
distance from the bureaucracy. A Texas source called it "inside
support and outside influence."
"Inside support" can be seen in the close ties the Texas
SSI maintained with the traditional Texas educational
bureaucracy. The new Commissioner of Education was co-
Principal Investigator along with Treisman. The Texas SSI was
staffed by people who still or once served within the
bureaucracy. More important, as Rose Acera, the Texas SSI's
Coordinator of Research and Evaluation, made very clear,
neither the SSI nor the Dana Center was estranged from the
bureaucracy nor did either have any desire to be. These links
were considered a major strength not only by Texas SSI
insiders, but also by Welch.
Cathy Seeley, Director of Policy and one-time TEA
employee, was incensed by the research assumption that one

needed to look outside the bureaucracy for projects that moved
radically beyond the status quo (even though I attempted to
explain that this assumption was not a disparagement of people
but of a system). However, Seeley did admit that TEA could not
legally engage in public outreach since it was seen by Texas
legislators as tantamount to lobbying by a state agency. The
Texas SSI was not constrained by state laws such as this, and
public outreach was one of its major strategies, a strategy that
would have had to be finessed differently by TEA if it had
ever been seriously contemplated.
Respect for good people and ideas inside the educational
community was important not only for the Texas SSI's
relationship within Texas, but also for its relations and
credibility with the Foundation. Janice Earle, the original
program officer said the Texas SSI fell into the role of writing
the state standards for mathematics and science because TEA
had effectively been taken out of this arena during the transition
between the two Governors. In the same vein, a current high-
ranking TEA official remarked that in order to leap ahead, the
SSI leadership needed to be outside the state agency, referring
to Treisman's ability to attract large projects as well as his good
relations with the new Governor's Office and State Board.

This third-party agency exhibiting non-bureaucratic
behaviors worked well both inside and outside the bureaucracy.
Here, in the implementation as opposed to the predecision
phase the outside-the-bureaucracy status paid off. The Texas
SSI garnered large blocks of federal and state money and
directed it all to building coherence around state standards.
How did the Texas SSI gain and maintain this ability? Again,
the policy entrepreneur is central to the mission and success of
the program.
The Policy Entrepreneur as Liaison
A recipient of the MacArthur "genius" award, Treisman
was known for "developing programs to enhance the success of
minorities in college-level mathematics." His award-winning
minority program is succeeding at UTA after being imported
from Berkeley where he created it. Although he served on the
Texas SSI redesign committee and the SSI Executive Committee
in 1993-1994, and had been extensively involved in
kindergarten-through-twelfth grade (K-12) school improvement
in Berkeley, his domain in Austin was higher education before

he agreed to take over the SSI. Is he an opportunist in the
Kingdon mode, waiting to be tapped?
He claimed he was reluctant to take on the large task of
directing the Texas SSI. He said his decision to direct the SSI
was a wrenching one, especially because of the time he would
have to devote to it. He added that he had seen the potential of
systemic change in his work with the writing committee and
stressed that he knew his new plan could be radical on the state
level since the "whole state education code was about to be
rewritten." When he agreed to tackle the rewriting, he insisted
that the Foundation pledge that whatever he created could be a
complete and fundamental break with the old SSI and old ways
of doing things.
Treisman falls far in the direction of the Sanger-Levin
(1992) end of a Krugman (1994) (destructive dilettante) ->
Polsby (quiet worker) > Sanger and Levin (indispensable
executive) continuum. But there is more. Treisman is a
conscientious practitioner who carries his classroom and
institutional experiences to the policy area. Looking down from
the top of the educational hierarchy, Treisman is adviser to staff
close to policy makers in the Governor's Office and other
agencies. From the other end of the top-down > bottom-up

continuum, Treisman is doing the work he envisions
improving, that is, practicing what he preaches. In 1996, he
taught a pre-calculus course in mathematics, facilitated his
student-access workshops, co-taught a course on mathematics
education with an Education School faculty member, and ran
several independent graduate studies and reading courses.
Further, as evidenced in his ground-breaking work in
enhancing opportunities for minorities and women at Berkeley,
and the "fifty hours" it took him to write the Addendum, he
takes a problem-centered approach to policy rather than pulling
out a ready-made plan from a "dusty drawer" (Polsby 1984). He
also took advantage of the proverbial "windows of
opportunity" (Kingdon 1984; Polsby 1984) by being available
when TEA could not carry out certain tasks. In so doing, he
paved the way for a large federal program, similar to others
turned down by conservative Governors and state legislatures,
to thrive in a conservative political environment. He bowed to
what he perceived as overwhelming obstacles by slowing
implementation of the new SSI until after the November 1994
elections and the possibility of change in the state
administration. Then he exhibited an understanding that with

would-be opponents one has to find "what's right," not just
"what works" (Rochefort & Cobb 1994).
Treisman said that unilaterally imposing one's model on
others was arrogant. It could be said, however, that he imposed
his model of lay probing on the reform of science and
mathematics education. But can inviting people to think about
issues that are going to be resolved in one way or another in any
case and giving them intellectual tools to do so be considered
imposing a model? Even if one calls it a model, it is a more
professional as opposed to bureaucratic model. It depends
on learning and cooperation based on common understanding
of values and goals (Majone 1981/2). Treisman uses his problem
definition problem-centeredness as a weapon for
advocacy and consensus (Weiss 1989).
Interestingly, the Action Team strategy resembles the
strategies of other educational policy entrepreneurs like James
Comer, John Goodlad, Henry Levin, Deborah Meier, Theodore
Sizer, Philip Schlechty and William Spady to effect bottom-up
change starting at the school level. They all profess to scorn
models, but they, too, are accused of imposing one. They have
formed networks like Treisman's "protean institution" that
moves across the middle of Texas.

The other entrepreneurs advocate that people consider
issues, talk things over, involve all school staff plus parents and
the community, consider issues, make decisions, and take
action. True, each holds up his or her own vision of schooling as
the preferred goal, but schools and communities are free to
decline that vision. One difference between Treisman and the
others is that Treisman's goal is defined by state law: coherence
driven by state content standards. Another crucial difference
between the Texas SSI Action Teams and the bottom-up efforts
is the governmental aspect of the Treisman enterprise and the
vast sums of federal and state money it has attracted over a
short time span. His SSI work is centered in one state while the
others have branched out into several states. Treisman works
within the state university system while most of the others (not
Goodlad or Meier) are in private institutions. Another
difference is that Action Teams are implementing (state) policy
that would have been implemented, however well or poorly, in
any case, whereas the other entrepreneurs are attempting to
cause change. Individual entrepreneurs would argue with each
of the above differences which only calls for more research in
this area.

What are the similarities and differences among
Treisman's strategies and scope and those of other educational
policy entrepreneurs? How do the Action Teams that
network whose individual points in the web disappear as their
work is completed resemble and contrast with such national
networks as the Accelerated Schools (Levin), the Coalition of
Essential Schools (Sizer), the Partnership for Educational
Renewal (Goodlad), and the School Development Model
schools (Comer), to name but a few?
Is Treisman influencing the bureaucracy instead of the
other way around (Nagel 1980)? The other educational policy
entrepreneurs also head third-party agencies, How have they
taken advantage of large federal and state grants? How are they
collaborating with state bureaucracies? Are their agencies
intertwined with the bureaucracies? If so, how? If not, would
they attain more power by working more closely with
government agencies? And, most important for this
dissertation, Would government agencies be more able to
implement policy that actually changes teaching and learning
with their help?
Treisman exhibited the qualities of Sanger and Levin's
(1992) entrepreneur in his work with the Texas SSI (and the

Dana Center) by (a) creating a personal mission based on access
for the Texas SSI; (b) taking advantage of opportunities;
(c) (reportedly) attempting to take on too much and taking risks;
(d) showing a bias towards action; and (e) consciously
underestimating "bureaucratic obstacles," for instance, by
melding mathematics and science reform with literacy for
underprivileged children two huge programs that do not
often work together at the state policy level.
Treisman partially attributed acquiring the Eisenhower
program, the telecommunications network, and the Title I
technical assistance contract to "luck." It would be difficult to
attribute such acquisitions of power to strategic planning; the
education environment is too unpredictable. While admitting
that luck had something to do with it, Treisman added that
these sorts of opportunities occur because of another of his
strategies, "following the money." This is because he considers
"policy" only those government actions tied to money. The
ability to "follow the money" is certainly not an innovative

concept, but is an indication of Treisman's reputed ability to
think on multiple levels.16
He provides a model of the education policy
entrepreneur. He is not a dilettante or a publicity seeker.
Instead, he is a "quiet worker." He works within the system
while exploiting the third-party-agency status of his
organization to move quickly and decisively when he sees an
opening. He finds these openings by following the money. He
understands state policy and values good relations with his
colleagues inside the bureaucracy. He is politically astute on
several levels, from using discretion when it is called for at the
top policy levels to being inclusive of those outside educational
circles. His preferred model for change is, in essence, no model,
but is guided by analysis and openness. He uses money to lend
authority and efficacy to projects and people.
More research is needed in the area of the personal
attributes of educational policy entrepreneurs as well as their
agencies. The experimentation going in education reform at the
16 He is what Jeffrey Goldberg, in his description of a 1994 Freshman
House of Representatives member, calls "the unthinkable a math teacher
with actual power" (1996,42).

federal, state, and local levels provides many likely subjects
against which to compare Treisman.
How Was Problem-Centeredness Evident?
The problem-centered approach was shown to be a
difficult stance for groups to take, as predicted by Dery (1984).
The first version of the 1991 Texas plan and several later
iterations of the Texas problem definition were solution-minded
and solution-driven. According to a long-involved Texas SSI
source, the first successful proposal was thoroughly grounded
in what was already happening. The solution was already being
implemented; the new part was the federal money the
Foundation could contribute.
It is tempting, but it would be wrong-minded to belittle
the ideas of the original group and its proposal simply because
they were not problem-centered or of the systemic magnitude
called for in the RFP. One of the myriad pressures on
bureaucrats is to refrain from constantly reinventing everything
to secure new grant money. Building on what is already in place
is a legitimate (and often rewarded) move to coherence in state
systems teeming with ideas for reform.

Unfortunately, this dynamic works against a problem-
centered approach as it builds on old solutions without
providing the intellectual space to remain immersed in the
problematic situation long enough to reconceptualize the
amorphous uncertainty. This is not to say that a problem-
centered approach necessarily calls for revolutionary or even
new solutions, only that old solutions should not be imposed on
current (or never really defined) problematic situations without
a thorough examination of the problem.
The final push for funding was solution-minded as well.
The Foundation had faith in one person to solve the Texas
dilemma. When this policy entrepreneur was finally given the
task of rewriting the proposal as requested by the funding
agency he, too, used a favored solution he had learned from
his mother.17 His solution was to take a problem-centered
approach to the implementation of the project. In a more linear,
bureaucratic, traditional, and modem track, implementation
follows selection, but Treisman postponed the definition of the
problem by dividing it into smaller components or issues and
devolving these to decentralized Action Teams, people closer to
17 His mother was a Communist union organizer.

the work. The problem definition reached by the entrepreneur
and the strategy to reach its goals were, consequently, problem-
centered. The genesis and success of the final Texas SSI were in
the realm of problem setting (Rein & Schon 1990) and a
combination of lay and expert probing (Lindblom 1990).
Frame Reflection
In one sense, the original Foundation Request for
Proposal had provided a ready-made solution called "systemic
change." That the problem was already defined and the solution
decided on in the original Request for Proposal is true in one
sense, but one hears from many states involved that the
Foundation did not have just one definition. It had multiple
definitions. Each official brought a new definition as program
officers, and subtly (as well as not-so-subtly) different
definitions quickly succeeded one another. As one of the
principal Texas players maintained, the Foundation "could not
articulate what it wanted."
From another perspective it could be said the Foundation
took a problem-centered approach in allowing states to define
what systemic change looked like. According to Foundation

sources, they were absolutely opposed to telling states what to
do. Foundation officials said, in essence, "We want a better
system, that is, one that exhibits many of these characteristics.
Tell us how you will get there and what it will look like when
you do." Foundation officials said the changes could only be
real and lasting if "owned" by the states. The states had to
define their own particular version. Foundation staff further
maintained that states wanted the Foundation to tell them what
to do because that was what they were used to and this time,
the Foundation refused.
Another explanation is that systemic change was an
elusive concept in the early 1990s. There was great frustration at
the state level (not only in Texas) with early Foundation
attempts to clarify what was wanted when state plans were
judged "flawed." According to Texas SSI sources, Foundation
staff seemed not so much to recognize systemic change "when
they saw it" (pace Mr. Justice Stewart) as to recognize faulty
plans when they saw them. However, Hamilton Peirce, a
Foundation official, objected to State officials calling early
Foundation notions of systemic change "ill-defined"; he insisted
they were purposefully vague in order for states to create their
own plans.

It would be easy to blame the lack of sustained frame
reflection among the players on budget constraints. After all,
Foundation program officers only had $2000/ year for travel to
several states. However, they were backed by monitors and
evaluators and reverse site-visits. There is evidence that the
various players tried to understand each other's point of view.
Earle obviously understood the immensity of Texas and the
particular challenges it presented for systemic change. When
the suspension of funding occurred, Earle said she had no
desire to say, "You blew it; we're cutting you off." Instead, she
sat down with those concerned and said, in essence, "what
you've done so far hasn't gotten far enough; take this money
and use it to plan anew what best strategies you might
accomplish here; submit a plan; we'll review it." Earle took the
states' side, "from my point of view, this stuff is hard to do;
nobody knows how to do it."
Yet the Foundation did tell states what to do, or more
precisely, what they could not do, that is, what was somehow
inconsistent with the Foundation's definition of systemic
reform. Foundation staff used the bureaucratic approach,
controlling inputs through budgets and accounting (Majone
1981/2). The Foundation laid out an invitation to come up with

a "state-owned" plan, but then reserved the right to decide
whether or not the state plan fit their unarticulated conception
of systemic change. Top-down control like this renders the
Foundation's approach as something different from a problem-
centered approach or frame reflection. Only the state group had
to reflect; the Foundation held all the cards and close to the
The 1993 Texas group redesigning the project (which
included Treisman, you will recall) and submitting its "flawed
plans" tried to understand why they were not more successful.
Cathy Seeley, then of the TEA, wrote,
systemic reform is something we can all agree
is necessary and appropriate, but defining
what each individual means by systemic
reform will continue to evolve over the next
five years, and beyond. Even the guidelines of
the National Science Foundation describing
systemic reform continue to change with each
new publication or call for proposals (1993,4).
Yet "project mentality" is evident in Seeley's memo to
Texas colleagues in the days leading up to the January 1994
proposal redesign about how "daunting" it would be to add

five ESCs each subsequent year of funding. Systemic rather
than project reasoning would have envisioned the Texas SSI
not as the funder or agent for this "scaling," but as the catalyst
for a leap to include all ECSs a leap effected by changes in
state policy and subsequent redirected state funding. Earle had
inferred just such a promise for state policy changes in the 1991
plan. The state group who wrote it evidently saw it in a
different light. And to take the state's perspective, Foundation
staff may not have realized the enormity of the task of "simply"
changing state policy. It appeared that the process was close to
breaking down in May 1994 when the Foundation insisted the
state group turn to Treisman. Earle considered it "fascinating"
for an outside entity to be working in Texas, "one of the most
centralized states in the country." She was surprised and
pleased that Texas agreed to attempt something new and
This frustrating experience vaguely resembles what
Schon and Rein (1994) call "reflective practice." It cannot be
said, however, that the State groups and the Foundation
reached that level of mutual understanding only that they
tried and then settled on a mutual escape hatch. Further
research could tease out valuable information both for the

Foundation, those it funds, and those it refuses to fund.18 From
a broader perspective, these interactions could inform many
areas of policy research. Where is there evidence of frame
reflection among state and federal agencies? What are the
constraints that render a meeting of the minds difficult? How
do the two types of entities view policy and the possibility of
making good policy differently? What is the role of federal
entities as the power of state agencies waxes and wanes? And in
the area of third-party agencies, What are their less-visible (than
the Texas SSI's) effects on state and national policy? How are
third party agencies and/or policy entrepreneurs influencing
the interactions of federal and state agencies?
While frame reflection remained elusive to the original
state groups and the Foundation, a relative, lay-probing, is an
integral part of the ultimate Texas problem definition.
18 Foundation grants amount to 30% of federal funding for math and
science education. The federal government supplies approximately 6% of
educational funding.

Experts versus the Public?
In the Action Team process, the "indigenous leadership"
called for in the Addendum, there is evidence of "lay probing"
(Lindblom 1990). Besides teachers,
the roster of those at the summer workshop
also included a parent, several science
directors or supervisors, professors, school
administrators, two business people, and two
consultants. They come from all parts of Texas.
A large share of them are women (about 75%)
and there are several minorities on the team
(Welch 1995,11).
The Texas SSI problem definition fixed the limits of the
system outside the mathematics and science sectors to include
elementary teachers, teachers of other subject areas,
administrators, and even the public. While inclusion along these
lines was a professed goal of "systemic change," it seemed to
trouble Foundation officials and their peer evaluators once it
became a reality.
There are several possible reasons for this. A Texas SSI
staff member hypothesized that the Foundation thinks its

education programs can be run like its other more experimental,
laboratory-based projects carried out in sterile, controlled
environments. Another possible reason is its outsider status. As
the program officer at the Texas SSI audit in May 1996 said,
"this SSI is subtle; the last visiting team [and a different
program officer] missed the point; that's why this visiting team
is here." The previous visiting team, composed of Texas SSI
peers educators from other states had not considered the
Texas SSI Action Team concept of its mission or even its
accomplishments as systemic change. They sensed its outsider
(and anti-administration) status and consequently did not see
how it could be possibly be a force inside the system.
Conversely, Welch (1995,17), who is a former Foundation
official and who spent considerably more time studying the
Action Team strategy, found the Texas SSI "the central systemic
initiative in the state." These two interpretations contrast
markedly, a contrast that demonstrates the educational
establishment's reluctance to include outsiders in its policy
making (Iannacone 1967). In this case, the outside is seen as
lacking the authority to get things done; other times the outside
or the public is seen as lacking the expertise to be part of an
envisioned enterprise.

A related concern was the Texas SSI's strategy of
"percolation." Percolation meant the project was not solely
expert-driven; it was, instead, an incremental grass-roots (in the
sense of street-level practitioners [Lipsky 1992] and citizens)
process to reach consensus and take action. In contrast to
percolation, which certainly resembles lay probing, the
Foundation is top-down and expert-driven. During the May
1996 audit visit, the Foundation program officer asked SSI staff
if Action Teams would be allowed to decide what was good
science or mathematics education. The visiting team was
evidently concerned that teachers and administrators of varying
disciplines along with regular citizens would have some
authority over Texas education. The Texas SSI staff quickly
attempted to reassure him that the definition of good science
would not be left strictly to public opinion. Action Team
meetings were facilitated by SSI staff; the experts would make
sure what sorts of answers would be answered through lay
opinion rather than scientific knowledge. "Good science and
mathematics" would prevail even in an open process. There
was no resolution of this issue the fear of public intervention
at the May 1996 meeting.

The Action Teams could be a way for bureaucrats and
the public to communicate with each other, a new way to solve
problems. However, in the implementation of this problem-
centered, lay probing, problem setting approach, we see the
postmodern involvement of the non-scientific public
vying with the modem, the received culture, the experts, the
formal. We need to know more about the Action Teams to be
sure of what is happening "across the middle of Texas."
What is the Action Team process? Are Action Teams
truly engaging street-level practitioners and the public in policy
making or is this lay probing concept already being assimilated,
trivialized, and marginalized by the institution of schooling
(Tyack & Cuban 1995; cf. Dery 1996)? Treisman's Action Team
strategy holds the promise of authentic grassroots change. You
will recall the fate of the concepts of the kindergarten and
middle school, insider attempts to change schooling to better
serve certain age groups. Both originally-envisioned
fundamental changes were trivialized and marginalized.
Kindergarten ended up looking more like first grade than a
"child's garden," and most middle schools still more closely
resemble high schools than places where pre-adolescent

intellectual needs are met. Are the Action Teams fulfilling their
Has the Texas SSI succeeded (or will it succeed) in
creating a new story in Stone's (1988) sense? If Action Teams are
vibrant prototypes of a possible protean institution, what needs
to be done to keep them authentic? What is the Texas SSI (or the
Texas educational bureaucracy) doing to be sure they fulfill
their promise?
The Role of Policy and Politics
Politics played an unquestionably large role in the
evolution of the problem definition in several ways. The
interplay of the political and policy streams was evident first in
the way state level policy changes in the Texas education scene
of the early 1990s attracted Foundation funding. Second, The
Foundation interpreted the 1991 plan as the precursor to further
major state-level policy changes. Next, Foundation policy
ultimately motivated the group creating the definition to a more
systemic view. Then gubernatorial politics forced the Texas
players to continue searching for a definition in order to secure
funding. Democratic Governor Ann Richards insisted they

continue after her 1994 Republican gubernatorial opponent,
George W. Bush, criticized her office for losing the funding in
1993. Politics kept the 1994 version from implementation until
after the election results were known. Finally Treisman worked
closely with the new Governor's Office and made the project
viable again. All of this fully supports the problem definition
research (e.g., Rochefort & Cobb 1994; Weiss 1989), as well as
Kingdon (1984) and Polsby's (1984) theories on the importance
of policies, politics, and people.
I argued that American education is political. The
Foundation Statewide Systemic Initiative program is likewise
political; it espouses not only state-level rather than federal
implementation (a conservative notion), but a concept of good
schooling based on contemporary cognitive research (an often
controversial notion that pits both liberal and conservative
reformers against those who would not change the status quo).
Treisman depicted the battle after the 1994 elections as between
the religious right and the also-conservative Texas business
community. The religious right wanted virtually no state
interference, while the business community still wanted a
modicum of top-down control with a great deal of local

Experience has shown that liberals and conservatives can
find common ground when educational reform calls for control
at the top through new, stricter accountability systems and yet
more flexibility in the areas of curriculum, school structure, and
public involvement at the school level. Liberals see social justice
in the fact that local school communities have the right and
obligation to decide how best to educate the children in their
neighborhood, while conservatives see civic virtue in strong
local control with relief from the authority of the state and its
bureaucracy (McDonald 1991). Not only policy, but also values,
twist and turn through the history of the Texas SSI, while
politics remains an insistent and yet legitimate intruder at each
The case study served up several matters of interest for
the educational and generic policy maker. I examined theories
relating to the predecision process in public policy making with
an emphasis on problem definition. Theories were supported
and negated.

The saga started in a traditional bureaucracy-centered
way. Only because of obstacles did the project devolve to a
third-party agency. The policy making process was non-linear
and complex (Stone 1988; Weiss 1989; Bosso 1994), and
displayed postmodern tendencies including an anti-
administration bias and an openness to public participation
(Farmer 1995; Lindblom 1990; Rochefort & Cobb 1994; Schon &
Rein, 1994; Stone 1988; Torgerson 1986; Weiss, 1989). Solution-
mindedness was the (bureaucratic) rule; problem-centeredness
the (third-party) exception (Dery 1984). Ironically, the solution-
mindedness of the Foundation (trusting Treisman) led to the
problem-centeredness of his third-party agency. The process
did not exemplify the rational method, but was steeped in
practice and action (Wildavsky 1989; Lindblom 1990). Frame
reflection, even reduced to the idea of good communication,
eluded the players (Schon & Rein 1994). A non-bureaucratic
organization (Barzelay 1992; Crozier 1964) played a major role
and a policy entrepreneur was integral (Duffy 1992; Kingdon
1984; Polsby 1984; Price 1971; Sanger & Levin 1992).
The viable problem definition with potential for systemic
change appealed to different groups who all seemed to have the
same ultimate goal but did not agree on how to get there

(Rochefort & Cobb 1994). So the new definition posed its own
dilemmas for public officials, administrators, policy makers,
and street level practitioners (Torgerson 1986; Lindblom 1990;
Weiss 1989). The problem definition brought the possibility of a
new, flexible institution (network) for the Texas educational
community (Majone 1984; Schattschneider 1960; Weiss 1984).
The whole was draped in politics (Kingdon 1984; Polsby 1984;
Schattschneider 1960; Stone 1988; Weiss 1989; Rochefort & Cobb
1994; 1994a).
As the theories were tested, new knowledge emerged. I
was surprised by the centrality of the policy entrepreneur and
his ability to work the system for the system's own goals.
What was learned has implications for generic public policy
makers, educational policy makers, and educational reformers.
Implications for Policy Research
The implications fall under two dimensions.
1. Policy innovation for fundamental school reform is not
on the horizon. Furthermore, I am convinced that policy in the
classical sense could not effect fundamental school reform of the
epic dimensions envisioned. Policy innovation, by definition,

would create new institutions. New institutions are not what is
needed. "Protean institutions" constantly changing networks
might provide the flexibility required for radical change in
the late 1990s. Networks created and nurtured common schools
in the nineteenth century; they are called upon again to provide
a policy environment that allows needed change to occur at the
school and community levels.
Initiating, nurturing, encouraging, and supporting lay
probing with time and money is problem definition as
implementation, even if the initial, formal "policy" is instituted
by the top of the hierarchy. If we do not have lay probing tied to
resources and action, we will not achieve system as opposed
to systemic change. The policy the Action Teams are making
has the potential to improve the performance of public schools
because it is fashioned so close to where the work is done (cf.
Elmore 1991). Of utmost importance is to distinguish the Action
Teams from task forces (Peterson 1983). Action Teams have the
power (and the money and because of the money, the clout) to
envision progress and take action. Task forces, as you will
recall, often exaggerate problems and recommend changes that
cannot be effected. Task forces have no responsibility and no

resources to carry out what they tell others they should do
(Peterson 1983).
I depicted the current era of school reform as embracing
first a top-down, then a bottom-up strategy, followed by
coherence between the two ends: systemic change. You will
recall, that in opposition to my admittedly policy-level analysis,
many street-level practitioners, my friends and fellow school
reformers, find the third strategy, systemic change, an alias for
"top-down." They see increased top-down accountability as
systemic change's dominant characteristic and maintain that
any promised enhanced flexibility at the school level is illusory
because old kinds of accountability procedures and tests will be
used to measure supposedly desired new ways of doing things.
The educational system is being set up for failure, they
maintain. They sense a "power over" rather than "power with"
relationship (Nancy Mohr, personal communication, December
October 1996).
The only hope of moving to a change in mindset and
new ways of doing things is for the two ends of the spectrum to
take the space, tools, and resources (time and money) to talk
things over, plan, and take action. "Across the middle" is an
efficacious education problem definition because including

street-level practitioners and the public is necessary to
implement the ideas of the standards movement: truly higher
quality learning for all students. Still, the Action Teams cannot
do it alone. The process, intellectual tools, and resources have to
be carried out closer to the classroom simultaneously. They
need to be carried down to the individual school-community
level and right into the schools in order to effect fundamental
change where it counts. Resources should be channeled to new
places where this can happen and to places where this kind of
problem-centered approach at the school level has already
begun. Treisman called for an "indigenous leadership." The
replication of the Action Teams on a smaller scale and at the
local level must find as well as create this leadership.
Are the the Action Teams really examples of lay probing?
What does "facilitation" by Texas SSI staff mean a process to
get things done or control of the question and so, accepted
answer? Who is included or excluded? Are the Action Teams
providing for significant change to continue and evolve? Do
university professors, administrators, teachers, and members of
the public see the opportunities as top-down or do they sense
their power at the middle? Are they merely serving as a
"telephone" between the top and the bottom or shaping policy

through their unique perspective? What is the Texas SSI doing
to ensure the efficacy of the Action Teams? How is their work
(the outcomes of the grants provided) being evaluated? How
are lessons learned being disseminated?
Even Goals are Not Givens
There is evidence in the case study of the value of
research into the evolution of problem definitions without the
benefit or drawback of knowing the outcome of that
evolution. Dery (1984) advised us to resist taking even goals as
given. I looked first at national political innovation as a
preferred outcome and then moved to policy innovation, a
"new thing," as opposed to a different locus of authority. I now
see school reform as a necessarily emergent as opposed to
large scale policy event (signaling a postmodern aversion to
the modem nation-state and to mega-narratives). This
postmodern aversion to large-scale solutions is in keeping with
the current national climate. Ralph Nader, a quintessential and
often highly visible policy entrepreneur (although not in his
1996 presidential campaign) said recently, "doing it quietly is
the way to get things done now" (Durkin 1996,51). Even with

all its large programs, outside of educational circles, the Texas
SSI has not yet registered on the national or even the state
It may be that what was happening in Texas from 1991-
1996 was the equivalent of the predecision activities Janet Weiss
describes in her 1989 study of the government paperwork
situation as she looked back at what happened after what she
deemed a definitive change in policy, a breaking away from the
professional control model and the established order, in 1972.
She would, however, be the first to admit that what she
described as a revolution in the description of government
paperwork policy was not the end of the diminution of
administrative authority. Instead, it was part of a long-term
trend linked, for example, with the later struggle for term limits
and, a year or two later, the call for campaign finance reform.
The diminution of administrative authority is a trend that has
not run its course and school restructuring can be seen as part of
it. Some of what Polsby (1984) calls nonevents may be
incremental steps toward a grander change, for which the end is
not clearly seen, let alone articulated.
Each time a significant shift in policy occurs, supporters
(and researchers think) "This is it!" but later the shifts will be

seen as part of a more massive whole, just a point on a
continuum (Stone 1988), due, in part, to the "sloppy and
complex" nature of policy change. I am not arguing for
predestination, or even progress, a modem notion, after all.
What I do argue is that what seems evolutionary to those in the
midst of the event may seem revolutionary to those who follow.
It is beyond human capability to envision epic change.
But it is important to chronicle and analyze the steps that
are part of a formless problematic situation to those in the
middle of it. Abundant policy research in the educational arena,
for example, would assure that even if later researchers declare
that a major transformation of schooling did not occur, they will
not be able to say, "Nothing happened." Much research is being
done in the school reform arena, but mostly by educational
policy researchers not always familiar with problem definition
or social construction research. A wealth of stories like the
Texas one lies inside the flurry of current school reform policy
making; interdisciplinary collaboration among general and
education policy researchers is imperative.
2. Third-party agencies working in concert with federal
and state agencies and with equal power in their particular area
can effect changes that government agencies alone cannot.

Collaboration among state agencies and third-party agencies,
similar to what is happening in Texas, is rare (Corcoran 1996).
Yet, in Texas a third-party agency succeeded in bringing
together many fragmented reform efforts under a state-level
umbrella. It garnered considerable policy (and financial) clout
and was influential in furthering an ongoing national and state
policy thrust: the content standards. If school reform is to
"scale," become pervasive rather than exceptional it needs
all the help it can get. The success in Texas should alert states to
an largely untapped resource, the third-party agency.
In Texas, the SSI sometimes filled a void when something
else had already driven administration out of the arena: state
policy in one instance, politics in another. Its third-party status
gave the Texas SSI the opportunity to try new things while
maintaining close relations with the state bureaucracies and
with the Foundation. There was no estrangement from
particular people, only from certain aspects of the bureaucracy:
rules, procedures, and the institutional bias of the educational

The "era of big government is over."19 Anti-
administration can be interpreted to mean "beyond" rather than
"against" government administrators. There is strength and
sanctuary in working inside the government while
maintaining an outside presence as well. One does not need to
be either inside or outside the bureaucracy; one can work in two
worlds, the "and...and" mindset. More research into the styles
of the educational policy entrepreneurs and their agencies
would add to our understanding of the policy changes taking
place or not taking place in the educational arena.
Also important, the success of Treisman's third-party
agency because it is part of a web with the bureaucracies
could instruct those educational policy entrepreneurs who
disdain or fear close interaction with governmental agencies.
Treisman's role as a policy entrepreneur could serve as a
starting point for research contrasting the different stances. His
perspective on systemic change would enrich the (education)
policy world's understanding of this concept. It is important
that the work of the Texas SSI in the context of its location
19 President Clinton's 1996 State of the Union address.

inside the Dana Center be better known and understood among
policy theorists and educators alike.
The Texas Model of an open, problem-centered, lay-
probing process could be a prototype of a new way for
American society to solve its problems (Bosso 1994), a stance
that emphasizes the dissatisfaction with the current state of
affairs coupled with aspiration for something better (Dery 1984).
Action Teams that work "across the middle" can change how
state-level agencies work with colleges and universities,
schools, districts, other third-party agencies, and the public to
collaborate and reach consensus and, most importantly, take
action on school reform as well as other policy areas. This
dynamic is supported by the postmodern literature that argues
in favor of wider inclusion, both in terms of good policy and a
greater sense of community (Torgerson 1986; deLeon 1992;
Fischer 1990).
Lessons Relearned
This study can be said to have advanced problem
definition and school reform research by providing a
postmodern perspective on that "slippery notion" (Peshkin

1993) we call reality. I started with five questions and ended
with many more, as posed above. To paraphrase Wildavsky, I
hope those generated belong to a better class of questions.
Learning from what I wrote, emerging as a different
policy person after this endeavor, I was also reminded that
"post" is a prefix used to mean that we could not have
postmodernism, for instance, unless we passed through
modernism, however short or long a period of time that takes.
My point was not to bash the educational bureaucracy. Rather it
was to warn of the tacit and powerful influence of any
institution on the imagination of its members. I also wanted to
demonstrate to educators and administrators in general new
ways they can overcome their insularity, their inability to
deeply involve the public.
I am now sure that a problem definition as a catalyst for a
national innovation that leads to higher quality student
learning, as I had first envisioned it, will continue to elude
reformers. I see the value of successive definitions. I am
convinced more than ever of the importance of problem
definition, that a problem-centered approach, frame reflection,
and lay probing are crucial. The question this dissertation
addressed was, How can school reform move from elite quarrel

to mass movement? How can we inform the Sesnos and
Mortons representatives of the larger public that
something of great value is happening?
Now I ask another question, Would national public
engagement hurry real reform? The answer depends on how
the public's fury or benign interest was visited on the schools.
What is happening be it defined as civic virtue or social
justice at the bottom and across the middle must be allowed
to grow and take on momentum. Top-down, policy-induced
public engagement could provide the climate and space for it.

Questions for Texas SSI Staff
The research questions are grounded in the concepts and
theories brought forth in the introduction and literature review
and generally follow Kingdon's (1984) ideas for interviews on
the predecision phase of public policy making. Different
questions were asked officials from different agencies.
1. How did you become aware of the opportunity of
Foundation funding for Texas math and science education?
Where were you working at the time? How did you become
involved? What sorts of efforts were made to be inclusive in the
process, that is, include practitioners, citizens, parents, and/ or
2. How was the writing group formed? Who were others
involved at the first? Who came on board later? Did you have
operating norms? What were they?
3. What were the affiliations of people chosen to write the
grant or expected to join the project team? What were reasons

for choosing (or not choosing) people from certain
organizations? How did you and do you interact with these
other agencies? What sort of information-gathering did the
group carry out in preparation for writing the grant proposal?
Are there records of interest in this regard?
5. What were some educational, political or cultural
events happening at approximately the time that influenced the
group's thinking? In what other sorts of information-gathering
activities did you engage? How long did the grant-writing
process take?
6. Did the Foundation award the Texas proposal as
written the first time? What were their concerns? How did your
group respond to those concerns? Did the changes the
Foundation required add to the quality of the grant?
7. What are the purpose and goals of the implementation
8. You're a mathematician (evaluator, principal,
superintendent, state agency official), how do you usually go
about conceptualizing problems and their solutions? Did you
use some of those techniques in this process?
9. What is your personal philosophy of education? How
did philosophies of education fit into the grant-writing process?

What evidence do you have that the conceptualization of the
problem honors different philosophies? What do you expect
math and science teaching to look like at the end of the project?
What else will have to change?
10. Can you give me a nutshell version of what the
project is all about? What is happening systemically because of
your strategies? How widespread is its influence? Will the
ordinary citizen know about it? The classroom teacher? What
other influences has the project had? What would you do
differently next time?
11. I'd like to ask you some specifics (items gleaned from
previous interviews).
12. What else do you think I might be interested in?
13. What records/ documents do you think I should
14. Who else can help me?
Questions for Peirce Hammond
These questions were sent by electronic mail. One to two
hour-long telephone interviews followed.

1. What was the original impetus for the SSI program?
For instance, what is its relation to the standards movement?
Why do some states have the impression that the Foundation
"wants" to fund them?
2. How many states are involved? How many cohorts?
Will all states be funded? Why or why not?
3. Have any states been de-funded? Why (short answer)?
4. How has the SSI program evolved? Why? For
5. How do you answer states' impression that the
definition of "systemic change" was ill-defined when the
program began? How has that definition evolved? (drivers then
and now) plus processes: network meetings, Foundation
questions, and state responses, other stuff?
6. What role do the site visits play? Reverse site visits?
7. How would you respond to the critique that the
Foundation expects its evaluations of SSIs to look like
evaluations of laboratory experiments?
8. Is the Texas plan unique in any way(s)? How about the
Texas SSI's ties with Title I, Reading Recovery are those
unique? Is the Texas SSI's location in the Dana Center unique?

9. Are there real qualms that the Foundation has with a
grass-roots approach? Is it inside the bureaucracy? Is it a
10. The outside-evaluator seems impressed with the
Texas SSI; yet it conflicts with some Foundation ideas. Is the
Foundation impressed?
11. If not, what is the relationship with the outside
evaluators? What is your vision of how the Foundation works
with the SSIs? How is this an interactive process? How is the
Foundation evaluation system evolving?
12. What has been learned in dealing with "systemic
change" What does the Foundation really want? That is, what
does systemic change mean? How big is the system? Does it
include parents, students, other teachers, and so on?
13. How/why would you say that the Foundation
"throws its weight around," especially in the area of, for
instance, demanding that Treisman be Principal Investigator,
Executive Director, other instances of the Foundation
demanding who would be PI in other states?
14. From what I hear, there are frequent changes in
Foundation officials who deal with a program. A lack of

continuity that otherwise could provide understanding of what
a state is about? Would you agree that is a problem?
15. Are there other people I should talk to?
16. Are there documents, especially Foundation
questions to Texas in 1992 and 1993, that you could provide?
17. What have I forgottenor not known enough to ask
that could provide insight into how policy is made in this
Questions for Tanice Earle
In general, in this part of the interview, I'm interested in
how different organizations communicate with each other to
reach a common goal, a type of organizational learning. There
are several stages:
1. I'm interested in the interaction between the
Foundation and the Texas SSI in its first year of operation. How
did the Foundation and the SSI communicate? Did you send
them questions? Did someone visit?
2. The first successful proposal strikes me as weak
systemically (8 sites, all middle schools, for instance), but it was

funded. Any insights on that? How did it then fail to show
significant progress?
3. After Texas was defunded/suspended (what's the
language?), how did the Foundation stay in contact? How did
Uri Treisman get involved? Who/what brought him in?
4. What was wrong with the 1994 Directions for Action
proposal? I haven't found any of the documents that explain
what its failings were. Did the Foundation see drafts that led up
to the 1994 submission?
5. What happened in Texas after it was refunded (right
language?)? Can you give me any insights on Uri's work with
the new governor and others?
6. Also, as I mentioned, you had confirmed at one point
that the Texas SSI was outside the bureaucracy. I'd like to talk to
you about that. How is it outside the bureaucracy? How would
you define the bureaucracy, etc.? Is it unique or rare in that
regard? Are there some statistics on states represented by third
parties not K-12 or Higher Ed among the SSIs? Other
7. Do you know about the Texas SSI's current progress?
Are you impressed by aspects of it? Which? Is it unique in some
ways? What do you think about the possibility of evaluating a

changing the infrastructure type SSI (like Texas) through higher
student achievement?
Questions for Wayne Welch
These questions were used in two telephone interviews
for a total time of approximately two hours.
I am looking for the National and regional context; the
Texas SSI's evolution; the Texas SSI as contrasted with other
1. How long have you been evaluating SSIs? Which SSIs
are you evaluating now?
2. Did you have any background on Texas?
3. Why was it unfunded?
4. Is the Texas SSI unique in any way? How about its
location in the Dana Center?
5. Do you see the Texas SSI as a bureaucracy?
6. Do you see it as powerful in the state? Why?
7. How do you see the Foundation working with the
states? Do the networks of SSIs work? Do you see an interactive
process? What does the Foundation really want?

8. Where does it throw its weight around? (replacing
directors, etc.)

Ten Elements for Systemic Change
The kinds of statewide initiatives that may win support
under this solicitation are those that will analyze, review, and
improve all or some of the systemic components of education in
the proposing state in a coordinated way. States will be
expected to integrate into plans for science, mathematics, and
engineering education initiatives such components of systemic
change as:
1. Organizational structure and decision making;
2. Provision and allocation of resources;
3. Recruitment and preparation of teachers and college
4. Retention and continuing professional development of
teaching and non-teaching personnel;
5. Curriculum content and learning goals;
6. Delivery of instruction, including the use of educational

7. Assessment of student achievement;
8. Facilities and equipment;
9. Articulation within the system; and
10. Accountability systems (Request 1990,1)

Annual Progress Report Texas Statewide Systemic
Initiative. (1994, May). Austin, TX: Texas Statewide Systemic
Annual Progress Report The Texas Statewide Systemic
Initiative for Reform in Mathematics. Science, and Technology.
(1995). Austin, TX: Texas Statewide Systemic Initiative.
Apple, M. W. (1990). Ideology and curriculum. (2nd ed.).
New York NY: Routledge.
Applebome, P. (1995). Have schools failed? Revisionists
use army of statistics to argue no. The New York Times, p. A18.
Ascher, C. (1993). Changing Schools for Urban Students.
(Vol. 18). New York NY: ERIC Clearinghouse of Urban
Barzelay, M. (1992). Breaking through bureaucracy.
Berkeley CA: University of California Press.
Baumgartner, F. R. (1989). Conflict and rhetoric in
French policymaking. Pittsburgh PA: University of Pittsburgh
Baumgartner, F. R., & Jones, B. D. (1993). Agendas and
instability in American politics. Chicago and London:
University of Chicago Press.
Berends, M., & King, B. M. (1994). A description of
restructuring in nationally nominated schools: Legacy of the
iron cage? Educational Policy. 8 (1), 28-50.
Berliner, D. C., & Biddle, B. J. (1995). The manufactured
crisis: Reading, MA: Addison-Wesley Publishing Company.

Bernstein, R. (1992, June 14,1992). The Yale Schmidt
Leaves Behind. The New York Times, pp. 32-33,46,48,58,64,
Best, J. (1987). Rhetoric in claims-making. Social
Problems. 34,101-121.
Best, J. (1989). Images of issues: Typifying contemporary
social problems. New York NY: Aldine de Bruyter.
Bosso, C. (1994). The contextual bases of problem
definition. In D. A. Rochefort & R. W. Cobb (Eds.), The politics
of problem definition: Sharing the policy agenda, (pp. 182-203).
Lawrence KS: University of Kansas Press.
Bracey, G. (1991a). Why can't they be like we were? Phi
Delta Kappan. 73,104-117.
Bracey, G. W. (1991b, April 14). Good news about our
schools. The Denver Post, pp. 1,51.
Bracey, G. W. (1991c). Outlook, commentary and
opinion: The greatly exaggerated death of our schools. The
Washington Post.
Bracey, G. W. (1991d). Research: Culture, class
management, and math achievement. Phi Delta Kappan. 73,86-
Bracey, G. W. (1992). The Second Bracey Report on the
Condition of Public Education. Phi Delta Kappan. 74 (2), 104-
Bracey, G. W. (1994). What if education broke out all
over? Education Week. 76,44,33.
Bracey, G. (1995, February). Backtalk. Phi Delta Kappan.

Bradley, A. (1995, September 6). AFT project to push
order and the basics: Teachers, parents agree on needs, Shanker
says. Education Week, pp. 1,20.
Brewer, G. D., & deLeon, P. (1983). The foundations of
policy analysis. Chicago, IL: The Dorsey Press.
Browne, A., & Wildavsky, A. (1983). Implementation as
mutual adaptation. In A. Wildavsky (Ed.), Implementation.
(Vol. 3, pp. 206-231). Berkeley: University of California Press.
Chubb, J. E., & Moe, T. M. (1988). Politics, markets, and
the organization of schools. American Political Science Review.
82 (4), 1065-1087.
Chubb, J. E., & Moe, T. M. (1990). Politics, markets, and
America's schools. Washington DC: Brookings Institution.
Cohen, D. K., & Spillane, J. P. (1993). Policy and practice:
The relations between governance and instruction. In S. H.
Fuhrman (Ed.), Designing coherent education policy:
Improving the system, (pp. 35-96). San Francisco CA: Jossey-
Cohen, M. D., March, J. G., & Olsen, J. P. (1972, March).
A garbage-can model of organizational choice. Administrative
Science Quarterly. 17,1-25.
Comer, J. P. (1986). Parent participation in the schools.
Phi Delta Kappan. 67(6), 442-446.
Corcoran, Thomas. (1996, November). Teacher
Professional Development. Speech delivered at the November
Roundtable Meeting of the Public Education Institute of New
Jersey. New Brunswick, NJ.
Cremin, L. (1989). Popular education and its discontents.
New York: Harper & Row, Publishers.

Crozier, M. (1964). The bureaucratic phenomenon.
Chicago IL: University of Chicago Press.
Cuban, L. (1995, November 1). The myth of failed school
reform. Education Week. 56,41.
Daggett, W. (1995). Ready for takeoff? The American
School Board Toumal. 182 (8), 20-24.
deLeon, P. (1988). Advice and consent. New York NY:
Russell Sage Foundation.
deLeon, P. (1992). The democratization of the policy
sciences. Public Administration Review, 52(2), 125-129.
Denzin, N. K., & Lincoln, Y. S. (1994). Introduction:
Entering the field of qualitative research. In N. K. Denzin & Y. S.
Lincoln (Eds.). Handbook of qualitative research, (pp. 1-18).
Thousand Oaks CA: Sage Publications.
Dery, D. (1984). Problem definition in policy analysis.
Lawrence KS: University of Kansas Press.
Directions for Action: A Proposal for Redesign. (1994).
[Proposal to National Science Foundation]. Austin TX: Texas
Education Agency.
Donmoyer, R. (1995). Educational research in an era of
paradigm proliferation; What's a journal editor to do?
Educational Researcher. 25 (2), 19-25.
Dror, Y. (1968). Public policymaking reexamined.
Scranton PA: Chandler Publishing Company.
Dryzek, J. S., & Torgerson, D. (1993). Democracy and the
policy sciences: A progress report. Policy Sciences. 26 (3), 127-
Duffy, M. (1992, December 14). A public policy
entrepreneur. Time. 140,51.

Durden, W. G. (1995). The swing to the right in
America's views on education. Education Week. 47.
Durkin, T. (1996, October 20,1996). The Un-Candidate.
The New York Times Magazine. 48-51.
Dye, T. R. (1975). Understanding public policy. (2nd ed.).
Englewood Cliffs NJ: Prentice-Hall.
Elder, C. D., & Cobb, R. W. (1983). The political uses of
symbols. New York and London: Longman.
Elmore, R. F. (1984). The political economy of state
influence. Education and Urban Society. 16(2). 125-144.(Elmore,
Elmore, R. F. (1991). Innovation in education policy.
[Paper presented at the Conference on Fundamental Questions
of Innovation]. Governors Center at Duke University.
Farmer, D. J. (1995). The language of public
administration: Bureaucracy, modernity, and postmodemitv.
Tuscaloosa AL: University of Alabama Press.
Final Proposal: National Science Foundation Statewide
Systemic Initiative: State of Texas. (1991, October). Austin TX:
Governor's Office, Texas Education Agency, Texas Higher
Education coordinating Board, The University of Texas at
Fischer, F. (1990). Technocracy and the politics of
expertise. Newbury Park CA: Sage Publications.
Forms & Publications, National Science Foundation,
(n.d.) The National Science Foundation. [Brochure]. Washington
DC: National Science Foundation.
Fuhrman, S., Clune, W., & Elmore, R. (1987). Research on
education reform. In A. R. Odden (Ed.), Education policy

implementation, (pp. 197-218). Albany NY: State University of
New York Press.
Fuhrman, S., Clune, W., & Elmore, R. (1991). Research on
education reform: Lessons on the implementation of policy. In
A. R. Odden (Ed.), Education policy implementation, (pp. 197-
218). Albany NY: State University of New York Press.
Fuhrman, S., & Massell, D. (1992). Issues and strategics
in systemic reform (Research Report Series RR-025): New
Brunswick NJ: Consortium for Policy Research in Education.
Goldberg, J. (1996, November 3) Adventures of a
Republican revolutionary. The New York Times Magazine. 42-
49,64-65, 81,88-89.
Goodlad, J. I. (1984). A place called school: Prospects for
the future. New York NY: McGraw Hill.
Graham, P. A. (1995). Battleships and schools. Daedalus:
Toumal of the American Academy of Arts and Sciences. 124 (4),
Guba, E. G., & Lincoln, Y. S. (1994). Competing
paradigms in qualitative research. In N. K. Denzin & Y. S.
Lincoln (Eds.), Handbook of qualitative research, (pp. 105-117).
Thousand Oaks CA: Sage Publishers.
Harris, P. (1994). Technos Interview: Linda Darling
Hammond. Technos. 3 (2), 6-9.
Hilgartner, S., & Bosk, C. L. (1988). The rise and fall of
social problems: A public arenas model. American Toumal of
Sociology. 94,53-78.
Iannaccone. (1967). Politics in education. New York NY:
The Center for Applied Research in Education.

Kanpol, B. (1992). Towards a theory and practice of
teacher cultural politics: Continuing the postmodern debate.
Norwood NJ: Ablex Publishing Corporation.
Kingdon, J. W. (1984). Agendas, alternatives, and public
policies. USA: Harper Collins Publishers.
Komarovsky, M. (1967). Blue collar marriage. New York
NY: Vintage Books.
Krugman, P. (1994). Peddling prosperity. New York NY:
WW Norton & Company.
Kuhn, T. (1962). The structure of scientific revolutions.
Chicago IL: University of Chicago Press.
Lasswell, H. D. (1971). A pre-view of the policy sciences.
New York NY: American Elsevier.
Lind, M. (1995, June). To have and have not: Notes on
the progress of the American class war. Harpers Magazine. 290,
Lindblom, C. E. (1968). The policy-making process.
Englewood Cliffs NJ: Prentice-Hall.
Lindblom, C. E. (1990). Inquiry and change: The
troubled attempt to understand and shape society. New Haven
CT: Yale University Press.
Lindblom, C. E., & Cohen, D. K. (1979). Usable
knowledge. New Haven CT: Yale University Press.
Looking back, thinking ahead. (1994). Educational
Excellence Network. Indianapolis IN: Hudson Institute.
Lipsky, M. (1992). Street level bureaucracy (1980). In J. M.
Shafritz & A. C. Hyde (Eds.), Classics of Public Administration.
(3rd ed., Vol. 3, pp. 476-484). Pacific Grove, CA: Brooks/Cole
Publishing Company.

Lusi, S. F. (1995). Meeting in the middle. [Draft].
Providence RI: Brown University Annenberg Institute for
School Reform.
Lynn, L. E., Jr., & Kowalczyk, T. R. (1995). Governing
public schools: The role of formal authority in school
improvement. Chicago IL: University of Chicago Graduate
School of Public Policy Studies.
MacRae, D., & Wilde, J. A. (1979). Policy analysis for
public decisions. North Situate MA: Duxbury Press.
Majone, G. (1981/82). Modes of control and institutional
learning. (Vol. 17). Laxenburg, Austria: Research Group, Center
for Interdisciplinary Research, University of Bielefeld.
Majone, G. (1989). Evidence, argument, and persuasion
in the policy process. New Haven and London: Yale University
Marshall, C., & Rossman, G. (1989). Designing
Qualitative Research. Newbury Park CA: Sage Publications.
Mawhinney, H. B. (1993). An advocacy coalition
approach to change in Canadian education. In P. A. Sabatier &
H. C. Jenkins-Smith (Eds.), Policy change and learning: An
advocacy coalition approach (pp. 59-82). Boulder, San Francisco,
& Oxford: Westview Press.
McDonald, J. P., Rogers, B., & Sizer, T. R. (1993).
Standards and School Reform Providence RI: Coalition of
Essential Schools.
McNeil, L. M. (1995). Local reform initiatives and a
national curriculum: Where are the children? The hidden
consequences of a national curriculum, (pp. 13-46). Washington
DC.: American Educational Research Association.

Meier, D. (1995). The power of their ideas: Lessons for
America from a small school in Harlem. Boston MA: Beacon
Mitchell, R. C. (1981, July/August). From elite quarrel to
mass movement. Society? Transaction. 76-84.
Nagel, S. (1980). The policy-studies handbook. Lexington
MA: Lexington Books.
A nation at risk: The imperative for educational reform:
A report to the nation and the Secretary of Education. (1983).
Washington DC: United States Department of Education.
Newmann, F., & Clune, W. H. (1992). When school
restructuring meets systemic curriculum reform. Brief to
policymakers (3), 1-4.
Newmann, F. M., & Wehlage, G. G. (1995). Successful
school restructuring: A report to the public and educators.
Madison WI: Center on Organization and Restructuring of
Odden, A. R. (1991). New patterns of education policy
implementation and challenges for the 1990s. In A. R. Odden
(Ed.), Education policy implementation, (pp. 297-327). Albany
NY: State University of New York Press.
O'Neil, J. (1995). On lasting school reform: A
conversation with Ted Sizer. Educational Leadership (6), 4-9.
Osborne, D., & Gaebler, T. (1992). Reinventing
government: How the entrepreneurial spirit is transforming the
public sector. Reading MA: Addison-Wesley Publishing
Company, Inc.
Pangle, T. L. (1991). The ennobling of democracy: The
challenge of the Postmodern. Baltimore MD: The Johns-Hopkins
University Press.

Perrow, C. (1986). Complex organizations: A critical
essay. (3rd ed.). New York, NY: Random House.
Peshkin, A. (1993). The goodness of qualitative research.
Educational Researcher. 22 (2), 24-30.
Peterson, P. E. (1983, Winter). Did the education
commissions say anything? The Brookings Review. 2,3-11.
Pitsch, M. (1995, April 19,1995). Mont, lawmakers reject
Goals 2000 as other states sign on. Education Week, pp. 19.
Polsby, N. W. (1984). Political innovation in America: The
politics of policy initiation. New Haven and London: Yale
University Press.
Price, D. (1971, May). Professionals and entrepreneurs:
Staff orientation and policymaking on three senate committees.
Toumal of Politics. 2,316-336.
Ravitch, D. (1995). National standards in American
education: A citizen's guide. Washington DC: The Brookings
Rein, M., & Schon, [sic] D. (1977). Problem setting in
social policy research. In C. Weiss (Ed.), Using social research in
public policy making. Lexington MA: Heath.
Request for Proposal. (1990). [Statewide Systemic
Initiative Request for Proposal]. Washington DC: National
Science Foundation.
Rochefort, D. A. (1994). Instrumental versus expressive
definitions of AIDS policymaking. In D. A. Rochefort & R. W.
Cobb (Eds.), The politics of problem definition, (pp. 159-181).
Lawrence KS: University of Kansas Press.
Rochefort, D. A., & Cobb, R. W. (1994a). Problem
definition: an emerging perspective. In D. A. Rochefort & R. W.
Cobb (Eds.), The politics of problem definition: Shaping the

policy agenda, (pp. 1-31). Lawrence KS: University of Kansas
Rosenau, P. (1993). Anticipating a Post-Modem policy
current? Policy Currents (3), 1-4.
Rothman, R. (1993). Obstacle Course. In: From risk to
renewal: Charting a course for reform, (pp. 11-24). Washington
DC: Education Week.
Sabatier, P. A., & Jenkins-Smith, H. (1993). The advocacy
coalition framework; Assessment, revisions, and implications
for scholars and practitioners. In P. A. Sabatier & H. Jenkins-
Smith (Eds.), Policy change and learning: An advocacy coalition
approach, (pp. 211-236). Boulder, CO: Westview Press.
Sanger, M. B., & Levin, M. A. (1992). Using old stuff in
new ways: Innovation as a case of evolutionary tinkering.
Toumal of Policy Analysis and Management. 11 (1), 88-115.
Schattschneider, E. (1960). The semisovereign people: A
realist's view of democracy in America. Hinsdale IL: The
Dryden Press.
Schon, D. (1986). Generative metaphor: A perspective on
problem setting in social policy. In A. Ortony (Ed.), Metaphor
and thought. Cambridge MA: Cambridge University Press.
Schon, D. A. (1983). The Reflective Practitioner: How
Professionals Think in Action. New York NY: Basic Books.
Schon, D. A., & Rein, M. (1994). Frame reflection: Toward
the resolution of intractable policy controversies. New York NY:
Schrag, P. (1995, October 9). Reform school politics. The
Nation. 397-399.

Seeley, C. (1993). Texas science and mathematics
Renaissance Project state-level management/action plan.
[Memo]. Austin TX: Texas Education Agency.
Seidman, E. (1986). Justice, values, and social science:
Unexamined premises. In E. Seidman & J. Rappaport (Eds.),
Redefining social problems, (pp. 235-258). New York NY:
Plenum Press.
Seidman, E., & Rappaport, J. (1986a). Framing the issues.
In E. Seidman & J. Rappaport (Eds.), Redefining social
problems, (pp. 1-8). New York NY: Plenum Press.
Seidman, E., & Rappaport, J. (1986b). Redefining social
problems. New York NY: Plenum Press.
Setting the standard: (1994). Agenda 21.
Shanker, A. (1996, July 7). Debunking the debunkers. The
New York Times, p. E7.
Sharp, E. B. (1994). National antidrug policymaking. In
D. A. Rochefort & R. W. Cobb (Eds.), The politics of problem
definition, (pp. 98-116). Lawrence KS: University of Kansas.
Simon, H. A. (1957). A behavioral model of rational
choice. Models of man: social and rational, (pp. 241-260). New
York NY: John Wiley and Sons.
Sizer, T. R. (1984). Horace's compromise. Boston MA:
Houghton Mifflin Co.
Skocpol, T. (1992). Protecting soldiers and mothers: The
political origins of social policy in the United States. Cambridge
MA: Harvard University Press.
Spady, W. G., & Mitchell, D. E. (1977). Competency-
based education: Organizational issues and implications.
Educational Toumal. 6 (2), 9-155.

Strategic Plan: Statewide Systemic Initiative fSSD: Texas
Science and Mathematics Renaissance (TSMR'). (1993, August).
Austin TX: Texas SSI.
Stone, D. A. (1988). Policy paradox and political reason.
Scranton PA: Harper Collins Publishers.
Strategic Plan for Texas Statewide Systemic Initiative
(SSI). (1993, October). Austin TX: Texas Education Agency.
Stringfield, S., & Winfield, L. (1994). Special strategies for
educating disadvantaged children (Research): Johns-Hopkins
Sunstein, C. R. (1996, August 18). Democracy isn't what
you think. New York Times Book Review. 29.
Torgerson, D. (1986). Between knowledge and politics:
Three faces of policy analysis. Policy Sciences. 19 (1), 33-60.
Treisman, U. (1992). Studying students studying
calculus: A look at the lives of minority mathematics students in
college. The College Mathematics Toumal. 23 (5), 362-372.
Treisman, U.. (1994). The Texas Statewide Systemic
Initiative for Reform in Mathematics and Science Education:
Directions for Action: A Proposal Addendum: Austin TX: Texas
Statewide Systemic Initiative.
Tyack, D., & Cuban, L. (1995). Tinkering toward utopia:
A century of public school reform. Cambridge MA: Harvard
University Press.
Viadero, D. (1995, July 12). New assessments have little
effect on content, study shows. Education Week. XV, 6.
Walsh, M. (1995). Sylvan makes quiet inroads into public
schools. Education Week. XV (13), 3,12.

Weiss, J. A. (1989). The powers of problem definition;
The case of government paperwork. Policy sciences. 22 (2), 97-
Welch, W. (1994). Texas Statewide Systemic Initiative
monitoring report. Newton MA: Abt Associates, Inc.
Welch, W. (1995). Texas Statewide Systemic Initiative
monitoring report. Newton MA: Abt Associates, Inc.
Wildavsky, A. (1989). Speaking truth to power: The art
and craft of policy analysis. (2nd ed.). New Brunswick NJ:
Transaction Publishers.
Yin, R. K. (1994). Case study research: Design and
methods. (2nd ed.). (Vol. 5). Thousand Oaks CA: Sage


TESTING EQUALITY KNAPSACKS FOR FEASIBILITY by Paul P. Hansen B.S., South Dakota State University, 1983 A thesis submitted to the Faculty of the Graduate School of the University of Colorado at Denver in partial fulfillment of the requirements for the degree of Master of Science Applied Mathematics 1992


This thesis for the Master of Science degree by Paul P. Hansen has been approved for the Department of Mathematics by i DEc 6'1? Date


Hansen, Paul P. (M.S., Applied Mathematics) Testing Equality Knapsacks for Feasibility Thesis directed by Assistant Professor Jennifer Ryan Consider the following problem where c, a E Z't and bE Z. max cro such that aro b ro E zn + This is an equality Knapsack Problem which can be solved using Dynamic Pro-gramming algorithms. This thesis investigates the solution of feasibility problems of this sort, and improves upon the efficiency of standard Dynamic Programming algorithms with new methods for testing the feasibility of an Integer Knapsack problem for multiple right hand sides. The form and content of this abstract are approved. I recommend its publication. 111


ACKNOWLEDGEMENTS I would like to thank my graduate committee for their help, questions, and insight: Dr. Lundgren, who motivated me to a mathematical degree; Dr. Green berg, for his insight and perceptive questions; and Dr. Ryan, for her many hours of tutoring, coaching, and patience. She has been extremely generous with her time and knowledge, and I will always be grateful for her help. I would also like to acknowledge my parents, Swede and Josephine, who have always provided emotional support and encouragement. Finally, much of my thanks goes to my wife Barbara, whose support, understanding, and patience have been invaluable. iv


Contents 1 Introduction 1 2 Historical Solutions 4 3 Alternative Approaches 9 4 Dijkstra's Algorithm 17 5 Results 21 6 References 25 A Batch Process Controlling Source Code 26 B Dynamic Programming Check Algorithm 35 C Dynamic Programming Algorithm Computing the t's 38 D Dijkstra's Algorithm 42 E Algorithm Checking the t's 46 v


Chapter 1 Introduction Consider the following problem: such that (K S(b)) where a;, i = 1, 2, ... n, c;, i = 1, 2, ... nand bare non-negative integers, and This is a single constraint Integer Programming problem known as the Knap sack problem. A solution ( :v1 :v2 :v3 :vn) to this problem such that K S( b) is satisfied is known as a feasible solution. Non-feasible solutions to the equality can frequently occur, such as negative solutions, or, in this case, non-integer so lutions. There can be many feasible solutions to this problem. If the solution is both feasible and maximizes the objective function, then it is considered an optimal solution. Note that in more general settings, the objective function could be maximize or minimize, and the problem could be made up of inequalities as 1


well as strict equalities. If we were now to remove the objective function and only test for feasibility, we would then have the Knapsack Feasibility Problem: Let a,, 1 < ::; n, b E Z+. Does there exist a feasible solution (:n1 x2 :n3 :n,.) E Zn? +" This problem manifests itself in many real-world examples, for example: 1. Suppose you have a Knapsack (hence the name), and this Knapsack has a certain structural strength. If you wish to carry many items of known weights in it, is it possible to load the Knapsack to its capacity? 2. If you are loading cargo ships for trans-oceanic trips, and these ships have a definite carrying capacity, assume your cargo can be palletized to certain weights, can you load the ship to capacity? Note that each of these examples were only concerned with feasibility, not optimality. Otherwise, we would have assigned a monetary value for each piece of equipment or cargo, and then tried to maximize the profit. In solving the Knapsack Problem, Dynamic Programming and Branch and Bound algorithms have historically been used. We will use a boolean version of these types of algorithms later in this paper as a check, both for feasibility and efficiency. These algorithms can be time consuming, however, when the problem 2


needs to be solved many times (with slight variations with the data) and/or they are LARGE, i.e., many coefficients or large right hand sides. We will be interested in developing an algorithm to test feasibility of KS(b) for many b's. 3


Chapter 2 Historical Solutions In the past, solving the Knapsack Problem has often been accomplished using Dynamic Programming techniques. These algorithms are useful when a sequence of inter-related decisions (usually time-dependent) is needed. Consider the fol-lowing example: Example 1. [3] Suppose you had a ship with a carrying capacity of 9 tons, and you had 3 pallet configurations which you could load on this ship. Each pallet has a weight and a cost (profit) benefit as shown below: wt(a,) benefit( ci) PALLET 1: 3 8 PALLET 2: 4 11 PALLET 3: 5 7 The problem formulation would then be: "' E 4


Now define f(r) as the maximum benefit derived from an r-capacity ship as follows: f(r) = maxi{c1 + J(ra1)}, always assuming that a1:::; r. Also define x(r) as any pallet which attains the maximum for r, x(r) = 0 means that none will work. If we put pallet j in the ship, the maximum benefit derived is Cj (the profit) +f(aa1 ) (the maximum benefit for the rest of the cargo). In solving this version of the equality Knapsack Problem, we will then vary r from 0 to b. In doing so, we now solve for: (KS(r)) a.,! = 1' 2, ... 'nb, r E z+' X, E z+. Note here we used an inequality so the maximum benefit function would have a solution for J( r ), 0 :::; r :::; a1 The problem would then be solved as follows: CARRYING CAPACITY SOLUTIONS f( r) I I max1{c, + f(ra1)} I f( r) x(r) f(O)l =-! max{O, 0, 0} 0 0 f(1) i = i max{O,O,O} I 0 0 f(2) I = I max{O, 0, 0} 0 0 f(3fT = ] max{ c, + /(0), 0, 0} = 8,0.0 = 8 1 f(4) I= I max{c1 + /(1),c2 + /(0),0} = 8,11,0 = 11 2 f(5) I=! max{c1 + f(2),c2 + f(1),c3 + /(0)} = 8,11,7 = 11 2 f(6)1 = l max{c, + f(3),c, + /(2),c:. + /(1)} = 8+8,11 '7 = 16 1 f(i) I= I max{c, +f(4),c,+f(3),c3+f(2)} -8+11,11+8,7 = 19 1 f(8)1 =I max{c, + f(5),c, + /(4),c, + /(3)} = 8+11,11+11,7+8 = 22 2 f(9) I= I max{c1 + /(6),c2 + /(5),c3 + /(4)} = 8+16,11+11,7+11 = 24 1 So for this example, to load the ship to its capacity of 9 tons and derive maximum profit, x(9) = 1, x(93) = x(6) = 1, and x(3) = 1, so you would load 5


3 pallets of type 1 on the ship for a benefit of 24. To study feasibility, we have modified the maximum benefit function f( r) as a boolean function as follows: Consider for 0 :S r :S b. Define f such that f(r) = 1 if KS(r) is feasible and f(r) = 0 otherwise. We use this boolean function as a means of tracking feasibility and the feasible solutions by the following method: 1. Recognize that f(O) = 1 always, and f(r) = 0 for all negative r. 2. Also note that there will be no feasible solutions to any Knapsack Problem for 0 < r < assuming a1 is the smallest coefficient. Therefore, f( r) = 0 for every 0 < r < a1 3. Starting at r = a1 check f(r-a;), for every coefficient a;. If f(r-a;)= 1 for some i, then f(r) = 1. Iterate this step from a1 to b. 4. The total complexity for this method is 0( nb ), since you check all coeffi cients b times. Since we are only checking feasibility, the algorithm used exits the loop upon finding the first feasible solution for a particular rhs. This speeds the algorithm up considerably for problems with small Frobe nius numbers, which will be discussed in the next chapter. 6


5. Keeping track of each iteration which produces a feasible solution allows us to reconstruct the feasible solution via back-substitution. As an example, consider 3x 1 + 8x2 = 10. We want to know if there exists a feasible solution (x1,x2). Performing the above sequence of steps, f(O) = 1. Starting at r = 3, we obtain the following results: a1 = 3 a2 = 8 x(r) f(3) f(3-3)=f(0)=1 f(3-8)=f(-5)=0 1 FEASIBLE f( 4) f(4-3)=f(1)=0 f(4-8)=f(-4)=0 0 f(5) f(5-3)=f(2)=0 f(5-8)=f(-3)=0 0 f(6) f(6-3)=f(3)=1 f(6-8)=f(-2)=0 1 FEASIBLE f(7) f(7-3)=f( 4)=0 f(7-8)=f(-1)=0 0 f(8) f(8-3)=f(5)=0 f(8-8)=f(O)=l 2 FEASIBLE f(9) f(9-3)=f(6)=1 f(9-8)=f(l )=0 1 FEASIBLE f(10) f(10-3)=f(7)=0 f(10-8)=f(2)=0 0 We can see there does not exist a feasible integer solution ("' h x2 ) for the problem 3x1 + 8x2 = 10. As mentioned, any solution can be reconstructed by back-substitution. For example, K 5(9) is feasible, using one x1 for f(9), one from f(6), and one from f(3), giving a feasible solution of x1 = 3, x2 = 0. This technique works well if you are are only trying to determine feasibility of a single b. However, if b is very large, this algorithm becomes inefficient, especially if there are many coefficients. If you have many b's to check feasiblity for, this method will soon become intractible, especially if they are growing in size. Rather than repeat this entire process for each different right hand side, it would be handy indeed if we could perhaps compute an intermediate result of 7


some sort once, and then avoid all this computation every time, merely checking each new right hand side against this intermediate result. We shall see in the next section that this is indeed possible. 8


Chapter 3 Alternative Approaches Consider the following approach for solving equation K S(b ). If the coefficients are not relatively prime, divide by the greatest common factor to make them relatively prime. If b is not divisible by this factor, then the problem is infeasible and a feasibility testing algorithm can stop. If b is divisible, then procede with the algorithm. In the case that the coefficients are relatively prime, K S(b) can be further characterized by the existence of a number F called the Frobenius number, whose existence has been known for a long time. Theorem 1: The Frobenius number F exists for KS(b), and is the largest possi ble bE Z+ for which KS(b) is infeasible. Any integer n > F will have a feasible solution to K S( n ). Proof:[l] Let a1 ::; a2 ::; a 3 ::; .. ak be relatively prime integers, and let Now, using induction, show that for n > S there exists a feasible solution (x,,xz,x3, ... ,xk) E Z! to KS(n). g


Let k = 2. Since GC D( a11 a2 ) = 1, then there exists p, q E Z such that pa1 + qa, = 1. (1) We can assume that p ?:: 0 and q ::; 0. Let n = a1a2 + r,r E Z+. Multiplying both sides of (1) by r gives rpa1 + rqa2 = r. Let rp = :r1 Then a1:r1 = rrqa2 Thus we have (2) When r > 0, :r1 can always be found such that 1 :S :r1 :S a2 and (2) are true. Solving K S(r) for :r2 gives :r2 = (r ;;xi), which will also be a positive integer. For k = 2, n > S has a feasible solution. Let k?:: 3 and n > S. Assuming the hypothesis is true up to k-1, let Then GC D( a2 d) = 1, and there exist integers p and q with pa2 + qd = 1. Multiplying both sides by n we get npa2 + qdn = n. Let :r2 = np and solve for a2:r2 gives us a similar congruence relationship of a2:r2 = n (mod d) (3) where 1 :S :r2 :S d. According to (3) and the induction hypothesis, (4) (5) 10


Since 1 :S a:2 :S d, (5) is satisfied whenever: (6) So we can solve KS(n) and (4) if (6) is satisfied. To see that it is whenever n > s, let the right hand side of (6) be denoted as sd. If sd::; s, we are done. Combining like terms and simplifying gives So for K S(b ), the Frobenius number F exists. In the above proof, S is used as a bound for determining solubility, and F will be the least upper bound. and x = (a:2,a:3 ... ,a:n) E Note that the fact that F exists assures us that each t;, fori= 0, 1, ... a1 -1, must also exist. Also note that it is not necessary to include a1a:1 in the definition, as we are concerned with i (mod at), and this would only add unnecessarily to our calculations, i.e., t0 = 0, not a1 Interestingly enough, we find that the set of feasible rhs's is a monoid, i.e., a set of vectors containing 0 and closed under addition and scalar multiplication by a positive integer. This monoid has holes near the origin, but the existence of Frobenius number allows the monoid to cover the integers a sufficient distance away from the origin. 11


Theorem 2: If b = i (mod a1), then (7) is feasible if and only if b 2: t;. Proof: Let b = i (mod a1 ) and K S( b) be feasible. Then since t; is the minimum integer t congruent to i for which KS(t) is feasible, we must have t;::; b. Conversely, lett; ::; b. Then since both band t, are congruent to i (mod a!), b = t; + ka1 k E Z+. Then, by definition oft;, there exists :v2 :va, ... "'" E Z+ so that b = azXz + a3x3 + + a,x, + ka1 Since the restrictions on x1 and k are identical, let x1 = k, and KS(b) is therefore feasible.D Theorem 3:[2] Let a1 a2 a3 a, be relatively prime. Then (8) where t; is defined above. Proof: Let Then b = k (mod ai), and b < tk, and by Theorem 2 is infeasible. Now let Let b = j (mod ai). Then b > tk-a1 2: ti-ah and tib < a1 Since b = j (mod al), b 2: tj. By Theorem 2, b has a feasible solution. D 12


Any number larger than F will have a feasible solution. We will be calculat ing the t's checking for feasibility and since the a;s are known, calculating the Frobenius number is a trivial operation. From Theorem 2, once we find these t;s, all we need to do is to check b against the correct t, and we will know whether or not there is a feasible solution to the problem K S(b ). We handle this algorithmically by keeping a table that contains O's in place of the t;s, and begin checking right hand sides for feasibility via our boolean algorithm from the previous chapter. As feasible rhs's occur, we check them for congruence with i (mod a1 ), and if that is the first occurence of a solution for that particular congruence, we update the table. Assuming the a;s are relatively prime, we will fill up the table. Once the table has no zeros, we are done. Now, for every new b, we only need to find what b (mod a1 ) is, and see if t; :S b. If so, then b is a feasible solution. Let T be the theoretical bound for the largest t. Assume a1 is the smallest coefficient, and an is the largest. Brauer [1] (with Schur) established the bound B =(a!-1)(an-1)-1 = (a1 -l)an-a1 as an upper bound for the Frobenius number. It follows from Theorem 3 that is an upper bound on the maximum t;. The number of rhs's and the number of coefficients do not affect this bound, so this technique is well suited for handling 13


many b's and/or many coefficients. As shown in the results, this bound does not appear to be very tight, and it remains an open problem to find a tighter bound. One approach to this problem could be as follows: By Brauer and Schur, for F( a1 a 2), B = ( a1 -1 )( a2 -1) -1, which could improve on the bound for large n. This assumes that a1 and a2 are relatively prime. If they are not relatively prime, then algorithmically, one could check GCD(a1,a2 ) with a3 and continue until a subset is found that is relatively prime. This approach will certainly improve the bound, but is still not a closed form, which would be preferable for large problems. Filling in the table can be done various ways. We have coded two ways: 1. Starting at a1 for a solution, we increase the rhs by one for each iteration, and check feasibility with our boolean function. If feasible, we check congruency and place in our table if possible. When the table is full, we are done. 2. Using a shortest path algorithm such as Dijkstra's Algorithm, visualize the problem as a network with a1 nodes, and arcs with the weights being the coefficients. The arcs travel between the nodes according to modular 14


arithmetic with (of course) the modulus being a 1 The shortest path from node 0 to node i will be the t;s, for i = 1, 2, 3, ... a1 -1. This approach is elaborated upon in the following chapter. Note that the complexity of the historical solution is 0( nb). Using the first method, the complexity is reduced to 0( ntmax) to compute the t' s, and an ad-ditional 0(1) to check each rhs. As we shall see in the next chapter, Dijkstra's Algorithm improves upon this to O(n +at)+ 0(1). To illustrate this approach, consider the example 3:v1 +8:r2 = b. The bound for the maximum tis (a1 -1)an = 2(8) = 16. If we fill in the Dynamic Programming table up to 16 as the largest rhs using the boolean algorithm, we obtain the following: a1-3 a2 = 8 (3) f(3-3)=f(0)=1 f(3-8)=f( -5 )=0 FEASIBLE f( 4) f( 4-3 )=f( 1 )=0 (4-8)=(-4)=0 (5) (5-3)=(2)=0 (5-8)=(-3)=0 (6) (6-3)=(3)=1 f(6-8)=f(-2)=0 FEASIBLE f(7) f(7-3)=f(4)=0 f(7-8)=f(-1)=0 f(8) f(8-3)=f(5)=0 f(8-8)=f(O)=l FEASIBLE f(9) f(9-3)=f(6)=1 f(9-8)=f(1)=0 FEASIBLE f(10) f(10-3)=f(7)=0 f(l0-8)=f(2)=0 f(ll) f(ll-3)=f(8)=1 f(ll-8)=f(3)=1 FEASIBLE f(12) f(12-3)=f(9)=1 f(12-8)=f( 4)=0 FEASIBLE f(13) f( 13-3)=f( 10 )=0 f(13-8)=f(5)=0 f(14) f(14-3)=f(11)=1 f(14-8)=f(6)=1 FEASIBLE f(15) f( 15-3)=f( 12)=1 f(15-8)=f(7)=0 FEASIBLE f(16) f( 16-3)=f( 13 )=0 f(16-8)=f(8)=1 FEASIBLE Note that tu = 0. As we progress from a1 we test each feasible rhs to see what it is congruent to moda1 The smallest rhs congruent to 1 (mod 3) is 16, and 15


the smallest congruent to 2 (mod 3) is 8. The table of t;s will then be: tu 0 tl 16 tz 8 The Frobenius number is then (16 3) = 13, so any rhs larger than 13 will have a feasible solution. Additionally, any rhs greater than or equal to than 8 and also congruent to 2 (mod 3) will be feasible. The original rhs of 10, which is congruent to 1 (mod 3) is less than t1 = 16, so it does not have a feasible solution. As the number of rhs 's gets large, it is to see that it will be much quicker to check each rhs against a particular t; rather than repeat the entire boolean algorithm multiple times. 16


L Chapter 4 Dijkstra's Algorithm To improve efficiency in calculating the t:s, Dijkstra's Algorithm works very well, and has been used by others for similar applications, (see e.g. [4]). Consider the following approach: 1. Set up an edge vector with edge costs of each coefficient. Let a1 be the smallest coefficient. Complexity for this step: 0( n ). 2. Create a graph with vertex set V = {0,1,2, ... ,a1 -1}, and edge set where the costs of the edges are the coefficients of KS(b). Compare all the coefficients that are equivalent to each other (mod a!), and select the smallest coefficient to be the edge. This will eliminate redundant edges travelling to the same vertex with higher costs. So the edge set E will be E = {(v,w) I v + aj = w (mod a!), where aj is the smallest coefficient congruent to i (mod a!)}. Complexity for this step: O(ai). 17


3. Apply Dijkstra's Algorithm to find the shortest path from node 0 to all other nodes. The cost of each shortest path from node 0 to node i will be t;. Complexity for this step: O(af). 4. The total complexity for Dijkstra's Algorithm is then O(n + af). The formulation of this graph ensures that any path in this graph will be a non-negative integer combination of the a;s, i = 2, 3, 4, ... n, and this combination will be congruent to i (mod a!). Conversely, any non-negative integer combina tion = i(moda!) is also a path. Dijkstra's Algorithm will give us a non-negative integer combination that is congruent to i (mod a!). Dijkstra's Algorithm will give us the shortest path from node 0 to node i, which, by definition, is the minimum non-negative integer combination required for t;. Recall from Chapter 3 that this is exactly the definition we chose for the t;s. Corollary: Let (re2,re 3 ,re4 ,re .. ) E Z+ such that t; = min{a2re2 + a3re3 + + anaJn I a,re,+aareJ+ +a .. re,. = i (mod a1)}. Then re2+re3+re4+ +ren S a1-l for every t; as defined above. Proof: The sum re2 + re3 + re4 + + re,. = the number of edges in the shortest path :::; a1 1. Example 2. Borrowing again from the example in Chapter 3, now let 3re1 + 8re2 + llre3 = b. Note that 8 and 11 are both congruent to 2 (mod 3). Setting 18


L up the nodes a.nd edges as discussed giYes us the following network: 0 8 II Setting node 0 as part of the tree, and assign it a value of 0. All other nodes have value infinity. The outbound edges from the tree are the two from node 0 to node 2, with weights of 8 and 11. Since 8 < oo, we update node 2 having a value of 8, selecting the edge with weight 8, and now include node 2 in our tree. The outbound nodes from the tree are now from node 2 to node 1, again with weights of 8 and 11. Since the value of node 1 is infinity, the cheapest path to node 1 is 8 + (value of node 2) = 8 + 8 = 16. We update node 1 as having value 16, add it to our tree, and Dijkstra's algorithm is finished. The t' s are the values of the nodes: 19


tu 0 tl 16 tz 8 This is exactly the same result as we obtained before. Note that if there are many arcs, an edge vector containing the minimum of each of these arcs as they travel to each node saves much calculating. In this example, the 11 arc will never be used, since the 8 arc is cheaper, and they both travel to the same node, since they both are congruent to 2 (mod 3). 20


Chapter 5 Results The results of this study are quite encouraging. The results were obtained on a VAX 8800, using FORTRAN77 as the programming language. The code is located in the appendix of this thesis. To set up large problems, a random number generator was used which gives a Uniform(0,1) distribution, then scaled appropriately. This generated the coefficients and right hand sides for the runs. The coefficients were limited to a maximum of 900 and a minimum of 10 (to eliminate trivial runs), and the rhs's were limited to a maximum value of 100,000. Both the number of coefficients and the number of rhs's were increased, while the other was held constant. The CPU times given are in milliseconds, and the results are averages from 3 runs. It is interesting to note that since the coefficients were constrained between 10 and 900, the Frobenius number for very large runs was invariably 9. The theoretical bound from Chapter 3 is (a1 1)a,, where a1 and a, are defined as the smallest and largest coefficients, respectively. Just as the smallest coefficient 21


tended toward 10 for large runs, the largest coefficient tended toward 900 for large runs. This gives us a theoretical bound of (9)900 = 8100, which is not very good. As of this writing, it remains an open problem for finding a tighter bound. In the following tables, the Historical method was the Dynamic Programming algorithm which checked feasibility from a1 to b solving KS(r) for each new rhs. The Dynamic Programming method used the same boolean version of the maxi-mum benefit function to find the t;s, and the rhs's were merely checked against their corresponding t;. The Dijkstra method used Dijkstra's Algorithm, setting up a network as previously discussed, and finding the shortest path through the network to find the t;s. Each rhs was compared to the corresponding t; to determine feasibility, just like the previous Dynamic Programming method. Recall the complexity of the Dynamic Programming method was O(nb), for the Dynamic Programming algorithm computing the t's O(ntmax), and for Dijk-stra's Algorithm, 0( n + ai). For the latter 2 methods, 0(1) is added for each rhs to be checked. Increasing the number of coefficients, 3 rhs's: no. of ais 1000 5,000 10,000 50,000 75,000 100,000 Historical Method 7117 9600 9600 12,133 13,267 15,783 Dynamic Prog. 10,450 7400 6950 12,200 12,500 14,300 Dijkstra 150 350 800 3750 5400 7900 no. of ais 150,000 175,000 200,000 250,000 Historical Method 14,250 13,050 15,900 20,800 Dynamic Prog. 16,000 14,700 15,400 16,950 Dijkstra 10,450 14,000 16,950 19,950 22


Increasing the number of rhs's, 100 coefficients: no. of rhs's 10 20 50 75 100 Historical Method 7600 15,850 44,300 72,350 100,700 Dynamic Frog. 12,300 8300 6100 3750 6000 Dijkstra 100 150 200 350 400 Increasing the number of rhs's and coefficients: no. of rhs's/coeff. 10/100 20/500 30/1000 40/5000 50/10,000 Historical Method 14,250 37,100 50,300 68,300 93,000 Dynamic Frog. 11,750 7500 6000 6800 7400 Dijkstra 50 100 200 450 900 Increasing the number of rhs's, 10,000 coefficients: no. of rhs's 10 100 500 1000 5000 Historical Method 12,650 114,250 526,900 1,072,550 5,220,900 Dynamic Frog. 12,100 7850 7400 9650 7900** Dijkstra 900 900 2400 3600 800** ** Indicates the memory capacity of the computer account was reached, and the remainder of the algorithm was unable to finish. The Historical algorithm has a much better complexity than 0( nb) when the problems get very large. The reason for this is that the algorithm, as it searches for feasible solutions, checks for feasible solutions of f(r-aj), as discussed in Chapter 3. Once r 2: F + a1 the algorithm returns after one iteration with a feasible solution. As discussed in the paragraphs above, with very large problems, the Frobenius number tended to 9. The Historical method was then displaying a "best case" complexity of O(b). Had the Frobenius numbers been larger, such as not allowing the smallest coefficient to be less than 100 or 1000, this method would not have been nearly as efficient. 23


The alternative Dynamic Programming algorithm is generally faster than the traditional algorithm, and shows its savings especially when comparing many rhs's. Note that it actually speeds up as the problems grow up to about 10,000 coefficients, since the complexity of this algorithm tends to O(tmax ). Clearly, Dijkstra's Algorithm is superior to both of these other techniques. As the problems get very large, the n term in the complexity factor for Dijkstra's Algorithm appears to be the dominant term, giving it less of an advantage when comparing few rhs's. It is still, however, more efficient than either of the other two methods, and when many rhs's are checked, it is several orders of magnitude faster than the traditional algorithm. This approach would result in great savings in processing time for testing feasibility of equality Knapsack problems. 24


Chapter 6 References 1. A. Brauer, On a problem of partitions, American Journal of Mathematics 64 (1942), 299-312. 2. A. Brauer and J.E. Shockley, On a Problem of Frobenius, Journal fiir reine und angewnadte Mathematik, 211 (1962), 399-408. 3. F. Budnick, D. McLeavey, and R. Mojena, Principles of Operations Research for Management, Irwin, Homewood, Illinois, 1988. 4. E. Denardo and B. Fox, Shortest-Route Methods: 2. Group Knapsacks, Expanded Networks, and Branch-and-Bound, Operations Research 27 (1979), 548-566. 5. R. Kannan, Solutions of the Frobenius Problem and Its Generalization, NSF Grant COR 8805199 (1990), 1-36. 6. J. Ryan, The Structure of an Integral Monoid and Integer Programming Feasibility, Discrete Applied Mathematics 28 (1990), 251-263. 25


Appendix A Batch Process Controlling Source Code C BATCHO.FOR C This file produce a batch job on the VAX to subnit C CJ r__;mber of ru'"S to con-pare the checking algorithm to C Jenny's using the T's in files called Dijkstra and T. (*************************************************** !MPLJCJT NONE INTEGER !, J, K, 8(10000), N, MAXRHS, M, MAXCOEFF, H INTEGER 1(1,500000), BSI1E, P 1NTEGER*4 SEED, ORJG SEED, CPUT!M lNTEGER*4 TOTAL CHECK CHARACTER*1 MARK REAL RANDOM [*************************************************** 900 FORMAT (A1) 910 (2X, /) 920 fORMAT (2X, 8(!8, 2X)) 930 FORMAT C2X, !8, /) C Create an file for the subroutines to C 0

C Now we have all the information we need to process the C data. \ole will use a Random Number Generator (Rand.exe) to C set up the equations, then .. e will call Check.exe, run it C for all equations, then run Knap.exe and T.exe and con-pare C the two solutions. C DO J = 1 10 C CALL RAND(RANDOM, SEED) C (*,*) C ENDDO C No" we fill up the matrix and go to work. DO l = 1, M DO J 1, N CALL RAND(RANDOM, SEED) A{I,J) = ((MAXCOEFF 1) *RANDOM)+ 1 IF (A(l,JI .LT. 101 THEN A(I,J) 50+ A(l,J) ENOl F ENDDO ENDDO C Now fill up the RHS DO I 1, BSIZE CALL RANO(RANDOM, SEED) 8(1) = MAXRHS *RANDOM ENDDO C the output for now. (1, *) The seed is (1, 920) ORIG_SEED WRITE (1, 910) IF((M .LE.6) .AND. (N .LE. 6) .AND. IBSIZE .LE. 10)) THEN (1, *) The A matrix is WRITE (1, 910) DO l = 1, M WRITE (1, 920) ((A(I,J)), J 1, N) WRITE (1, 910) ENDDO WRITE (1,*) The RHSs are: WRITE (1, 910) DO I 1, BS I ZE WRITE (1, 930) B(!) ENDDO ELSE 'WRITE (1,*) 'M = I M WRITE (1,*) 'N :: < N WRITE (1,*) 'BSIZE = I BS!ZE END IF C Write the total cputimes to a file called totat.dat OPEN(7, FILE= 'TOTALD.OAT', STATUS= 'OLD') C Now we do our comparing. We will use H instead of I as the C soubroutines use I and things tend to get confused as control C goes back and forth. 27


DO H :: 1, H TOTAL CHECK 0 00 K; 1, BS!ZE OPEN (3, FILE :: 'CHECKJN.DAT1 STATUS 10LD1 ) (3) W'RITE (3, *) N (3,) ((A(H,J)), 1, N) (3,*) S(KJ CLOSE (3) CAll CHECK(CPUTIMJ TOTAL CHECK :: TOTAL_CHECK + CPUTIM -W'R1TE(7,*)' CPU Time for Check::', TOTAL_CHECK OPEN (4, FILE REIJlND (4) WRITE (4,*) N 'KNAPIN.DAT', STATUS:: 'OLD') (4,*) ((A(H,J)J, J = 1, NJ CLOSE (4) CAll OlJKSTRA(CPUTlM) IJRITE(7,*)' CPU Time for Oijkstra :: CPUTIM OPEN (5, FILE :: 'T!N.OAT1 STATUS = 'OLD') (5) (5,*) BSIZE (5,*) ((S(J)), J = 1, BSIZEJ CLOSE (5) CALL TCHECK(CPUTIMJ IJRITE(7,*)' CPU Time forT::', CPUTIM ENOOO END DO C=============================================== CLOSE (1) STOP END C===================================================== function Rand(RANOOM, SEED) INTEGER*4 Seed REAL Random Seed mod(((25173*Seed)+13849),65536) C write(*,*) seed C Seed is in terms of mod 65536 if (Seed .LT. 0) then C write(*,*) 'Seed::', Seed end if Random:: real(Seed) I 65536 C write(*,*) random, *** return end 28


C BATCH.FOR C This file will produce a batch job on the VAX to submit C a number of runs to compare the checking algorithm to C Jenny's approach using the T's in files called Knap and T. C*************************************************** IMPLICIT NONE INTEGER I, J, K, 8(10000), N, MAXRHS, M, MAXCOEFF, H INTEGER A(2,500000), BSIZE, P JNTEGER*4 SEED, ORIG SEED, CPUTIM INTEGER*4 TOTAL CHECK CHARACTER*1 MARK REAL RANDOM [*************************************************** 900 FOR"AT (A1) 910 FORMAT (2X, /) 920 FORMAT (2X, 8(!8, 2X)) 930 FOR"AT (2X, 18, /) C Create an output file for the subroutines to C write to. OPEN (1, FILE= 'BATCHOUT.DAT', STATUS= 'OLD') I>D ( 1) C will set up the system of equations using (of course) C matrices, such as Ax ::: b. Note that b doesn't have C tobeMx1. C Input the values from a datafile DO P 1, 5 OPEN (2, FILE = 'BATCHJN.DAT', STATUS READ (2,*) SEED READ (2,*) BSIZE READ (2,*) MAXRHS READ (2,*) M READ (2,*) N READ (2,*) MAXCOEFF C Save the seed for future reference. ORIG_SEED ::: SEED C Now we have all the information we need to process the C data. We will use a Random Number Generator (Rand.exe) to C set up the equations, then we will call Check.exe, run it C for all equations, then run Knap.exe and T.exe and compare C the two solutions. C D0fo1,1Q C CALL RAND(RANDOM, SEED) C (*,*} RANDOM C ENDDO C Now we fill up the matrix and go to work. C No zero's for coefficients, it is trivial. DO I 1, M OOJ=1,N 29


CAll SEED) A(f,J) = ((MAXCOEFF 1) *RANDOM) + 1 IF (A(I,J) .LT. 10) THEN A(I,J) =50+ A(I,J) END IF ENDDD END DO C Now fill up the RHS DO I = 1, BSIZE CAll SEED) 8( I) :: MAXRHS RANDOM ENDOD C the output for now. (1, *) The seed is (1, 920) ORIG SEED (1, 91D) -IF((M .LE.6) .AND. (N .LE. 6) .AND. (BSIZE .LE. 10)) THEN (1, *) The A matrix is (1, 910) DO I = 1, H (1, 920) ((A(l,J)), J = 1, N) (1, 910) ENDDO WRITE (1,*) The RHSs are: (1, 910) 00 I = 1, BSIZE (T, 930) B(I) END DO ELSE WRITE {1,*) 1M=', M \./RITE (1,*) 'N = I N WRITE (1,*) 'BSIZE'= BSIZE END IF C Write the total cputimes to a file called total.dat OPEN(?, FILE = 'TOTALK.DAT', STATUS = 'OLD') C Now we do our comparing. We will use H instead of I as the C soubroutines use I and things tend to get confused as control C goes back and forth. DOH= 1, M TOTAl CHECK = 0 DO K ; 1, BS I ZE OPEN (3, FILE ::: 'CHECKJN.DAT', STATUS 'OLD') (3) (3,*) H (3,*) ((A(H,J)l, J = 1, N) (3,*) B(K) CLOSE (3) CAll CHECK(CPUTIM) TOTAL CHECK = TOTAL CHECK + CPUTJM ENODO WRITE(?,*)' CPU Time for Check=', TOTAL_CHECK OPEN (4, FILE= 'KNAPJN.DAT', STATUS= 'OLD') (4) 30


IJRITE (4,*) H WRITE (4,*) ((A(H,J)), J = 1, NJ CLOSE (4) CALL KNAP(CPUTIM) IJRJTE(7,*)1 CPU Time for Knap = ', CPUTIM OPEN (5, FILE= 'TJN.OAT', STATUS= '0L01 ) REWIND (5) WRITE (5,*) BSIZE WRITE (5,*) ((B(J)), J 1, BSIZE) CLOSE (5) CALL TCHECK(CPUTIM) IJRITE(7,*)1 CPU Time for T = CPUTIM WRITE(7,910) ENDDD ENDDO C========================================================= CLOSE (1) STOP END C========================================================= function Rand(RANDOM, SEED) JNTEGER*4 Seed REAL Random Seed= mod({(25173*Seed)+13849),65536) C write(*,*) seed C Seed is in terms of mod 65536 c if (Seed .LT. 0) then write(*,*) seed = endif Seed Random rea!(Seed) 1 65536 C write(*,*) random, 1 *** return end 31








Appendix B Dynamic Programming Check Algorithm Sut.J.-outirw (hec>ing A.lgo't""' A'l algcithrto check c a">d t'-,: solut .o" to thr Knapsad: peot !""" ====== ==== """"""'""' = =' = = === == = = = =" === == ===' = c c r c c 6 = c vector of size W SlH' of pobOI"" ... ector in:eger calculated ha'ld side, suppliE'd a: un tHilC C=========""""""'""'"""""'""'"""""'""""'""""""'""""""""'""''"''"""""""" ............................... ,. ...................... ,. ................... ll'l>'i.lC!T norw i"HGtR J, J, l, 1'1, lri, R, q0:1000000),C001iHP HolGER 6, CkE(I:_TOTA.l,8ACK(100G000J CPUT!l'l ..................... ............................... ,. .............. 900 foP".tT (2X, IS, ?x, is 910 C2X, !8, is nc: feas1bte7'J 9(Q 'C,.!C!:. Your CFJ usage IS: !8) (=::=========""'"""""""""""""""'""""""""""""""'""""""""""'" C llere we inpvt t'le prob!e;:1 vec:or from a datal \!e. c (3, FilE= 'Chedin.dac', status= 'old') REAO {3,"') Ji c3,"') {{AC )), I = 1, h) REA.;J C3,") 6 ClOSE {3) (:::""""""""""'"""""":::""'""'"""'"""'""""""""""'""'"'"'"""""'""""""" C ow .. e call CPl..i to start the CPU counter CAll CPIJT ( CPUTl"') CPU TEMP "' CPUT I II

C set the notation as follows: c C f(r) if r has a feasible solution for the C original problem, C = 0 otherwise. c Call FBOOL (A, B, BACK, F, Nl C Again call CPUT to mark the end of the calculations CAll CPUT(CPUTIM) CPUTIM = (CPUTIM CPUTEMP)*100 IF (F(S).E0.1) THEN (1,900) B ElSE (1,910) B END! F (1,920) CPUTIM RETURN END [========================================================= SUBROUTINE FBOOl (A, B, BACK, F, N) c C This subroutine will calculate the boolean C function, F, and give us the following values: C f(r) = if r has a feasible solution for the C original problem, C = 0 otherwise. DECLARATIONS INTEGER A(*), f(O:*), B, BACK(*), BIG, H, G INTEGER N, I, J, COUNTER Cc 100 FORMAT(!8) 1(0) : 1 COUNTER = 0 DO 200 I = A(1), B COUNTER = COUNTER + 1 BIG : 0 BACK(! )=0 DO 210 J : 1, N IF ((!A(J).GE.0).AND.(F(!A(J)).E0.1)) THEN BIG : 1 BACK(!) = J GOTD 205 END IF 210 CONTINUE 205 F(!) = BIG 200 CONTI HUE COUNTER COUNTER RETURN END C========================================================= SUBROUTINE RPR!ME (A, FACTOR, lARGESTF, N, SMAll) C DECLARATIONS INTEGER A(*), FACTOR(*), N, SMALl 36


INTEGER l, J, LARGESTF REAL P, O, R(500000) LOGICAL OK C C Initialize all the factors to Zero. 00 l = 1, SMALL FACTOR (!) = 0 END DO c Initialize all the R's to A1s 00 I = 1, N R(l) =A(!) END DO C First we find all factors of A(1), which is smattest, and C check them with the other A's. C Here we find the factors of A(1) Q = SMALL DO l = 1, SMALl p = 0/l IF (!NT(P) .EO. P) THEN FACTOR (!) : l END IF END DO C Now check all factors of A( 1) with the other A's DOl= 1, SMAll J = 1 OK= .TRUE. ((J .LE. N) .AND. (OK)) P = R(J)/l l F (!NT(P) .NE. P) THEN OK ::: .FALSE. END! F J = J + 1 ENDDO IF (OK) THEN FACTOR (!) = l ELSE FACTOR ( l) : 0 END IF END DO C Save the largest factor LARGESTF : 1 DO I = 1, SMALL IF (FACTOR(!) .GE. LARGESTF) THEN LARGESTF = FACTOR(!) END IF ENDDD RETURN END 37


Appendix C Dynamic Programming Algorithm Computing the t's c c c SUBROUTINE KNAP(CPUTIM) The Knapsack Problem Revisited -an introspective approach C================================================================ c C A = C N C X C B c probtem vector of size N size of problem vector integer variables calculated right hand side, supplied at to determine feasibility run time C================================================================ c *********************************************************** IMPLICIT none INTEGER I, J, L, M, N, R, F(0:1000000), 8 INTEGER A(500000),TEMP,T(0:1000),SMALL,LARGE,FACTOR(500000) INTEGER LARGESTF, KNAP TOTAL, BACKC1000000), FROB JNTEGER*4 CPUTIM, CPUTEMP CHARACTER*1 MARK c *********************************************************** 900 FORMAT (2X, 'KNAP Your CPU usage is:', 2X, 18) 910 FORMAT (2X, 18, /) 920 FORMAT (2X, !8) C==================================================== C Here we input the problem vector from a datafile. OPEN (4, FILE= 'KNAPIN.DAT', STATUS= 'OLD') READ (4,*) N READ (4,*) ((A(!)), I = 1, N) CLOSE (4) C Now we call CPUT to start tracking CPU usage CALL CPUT(CPUT!M) CPUTEMP = CPUTIM C Now we will put the smallest term first (A(1)). C will also keep track of the largest term (TEMP). TEMP A(N) DO I N, 2, IF (A(!) .LE. A(!)) THEN J A(!) A(!) A(!) A( I ) J END! F IF (A(!) .GE. TEMP) THEN TEMP= A(!) END! F 38


END DO C A%ign the nJmes sm.1t, and large to A( 1) and TEMP SMALL::::A(1) LARGE :::: TEMP C Now we check to see 1t any of the A's are relatively pr1me. C Call RPRJME (A, FACTOR, LARGESTF, N, SMALL) (::::::::=========================== C lf the largest comnon fa::tor is larger than 1, then C we divide by it to force the rest of the numbers to C be relatively prime, and carry on. C Make the A vector relatively prime C IF (LARGESTF .GT. 1) THEN C DO J = 1, N C A{J) :::: A(J) I LARGESTF C ENDDO C Correct sma'll and large to the new problem c c SMALL LARGE C END IF A( 1) LARGE/LARGESTF LARGESTF = 1 C The right hand side is bounded by the following bound: 8 :. (SMALL 1 )*LARGE C Initialize F, T to all zeros c DO l 1 1 000000 f ( l ) 0 ENDDO c DO I 1, 1 0000 c c ENDOO c DO ENDDO C Now we will use a Boolean function to test for C feasibility for the possible non negative C values of the test variable r, as r ranges C from 0 to b. this Boolean function, we C set the notation as follows: c c c c c f ( r) if r has a feasible solution for the original problem, 0 otherwise. Call FTBOOL (A, B, BACK, F, N, T, SMALL) C Now we wit l determine the Frobenius nurrber, and also C calculate the smallest b necessary to ensure C feasibility. C The Frobenius number is the largest number smaller C than the largest T(i) by A(1}. T(O) 0 TEMP T(D) 39


00 I 1, SMALL IF (TEMP .LE. T(l)) THEN TEMP T( I) END IF ENDDO FROB = TEMP SMALL C Now we mark again the CPU time CALL CPUT(CPUTIM) CPUTIM = (CPUTIM CPUTEMPJ*100 C===== WRITE (1,900) CPUTJM WRITE (1,*)' The Frobenius number is: WRITE (1,920) FROB WRITE (1 ,*)1 SMAll = 1 WRITE (1,920) SMALL WRITE (7,*) The Frobenius number is: 1 "RITE (7,920) FROB C========:===== C Create fi te cal led KNAPT .OAT C This file will be used by the Program called TCHECK to C check various RHS's against OPEN (6, FILE= 'Knapt.dat', status= 'new') "RITE (6, 910) LARGESTF "RITE (6, 910) SMALL DO I 0, SMALL-1 "RITE (6, 910) T(IJ END DO CLOSE (6) C===.,====== 100 CONTINUE RETURN E"'D C====================================== SUBROUTINE FTBOOL (A, B, BACK, F, N, T, SMAll) c C This subroutine wilt calculate the boolean C function, F, and give us the following values: C f(r) = if r has a feasible solution for the C original problem, C = 0 otherwise. C - --------DECLARATIONS --------------------INTEGER A(*), FCO:*), 8, BACK(*), BJG, H, G N, J, J, T(O:*), SMALL, TEMP, COUNTER c---.--.-----.. ----.----------------.---------------.-.--. c f ( 0) 1 COUNTER 0 I = SMALL DO "HILE ((I.LE.BJ.AND.(COUNTER.LT.SMALL)J BIG 0 BACK( I ) D0210J=1,N IF ((!-A(J).GE.OJ.AND.(F(J-A(J)J.EQ.1)) THEN BIG 1 BACK(!) J GOTO 205 END IF 210 CONTINUE 205 F(!J BIG IF (f(IJ .NE. OJ THEN TEMP =MOD(!, SMALL) 40




Appendix D Dijkstra's Algorithm c--O!JKSTRA(CPUTJM) -DE ClARA i l ON S------- ---------- -IMPLiCIT INTEGER llf'EGER HH::GER INTEGER NONE P(2,0:1G0000), 1(0:100000), l, J, K, N, E, V A(500000), SMALL, M00A(500000), NEXT, TEMP, T PRICE CPUT!M, CPUTEMP, FACTOR(500000), LARGESTF, FROB EDGECO:SOOODD), TEMPJ c-------------------------------------------------------------c c c IWTES: P( 1, N) P(2,<) WE ALWAYS SELECT ZERO AS THE ROOT. IS THE DISTANCE FROM THE ROOT JS THE PREVIOUS VERTEX c C P !S THE PREDECESSOR MATRIX C IS THE TREE 900 FORMAT (2X, 'DlJKSTRA --Your CPU usage is:', 2X, !8) 9i0 FORMAT {2X, 18, /) 920 FORHAT (2X, 18) C Here we input the problem vector from a datafile. OPEN (4, FILE = 'K"'AP!N.DAT', STATUS= 'OLD') READ (4, *) N READ (4,*) ((A(!)), I = 1, N) CLOSE ( 4) C START THE CLOCK CALL CPUT(CPUTJM) CPUTE"''P = CPUTJM C FIND THE SMALLEST COEFFICIENT TEMP! ::: AC1) TEMP ::: 1 00 I o 1, N IF CA(l) .LT. TEMPJ) THEN TEMPI A(l) TEMP = l END l F ENDDO 42


C PUT THE SMALLEST COEFFICIENT INTO A(1) IF (TEMP .NE. 1) THEN A (TEMP) A( 1) A(l) =TEMPI END l F SMALL = All) c Call RPRIME (A, FACTOR, LARGESTF, N, SMALL) C============================= C If the largest coi11Tlon factor is larger than 1, then C we divide by it to force the rest of the numbers to C be relatively prime, and carry on. C Make the A vector relatively prime C and correct small to the new problem c IF (LARGESTF .GT. 1) THEN c DO J = 1, N c A(J) = A(J) I LARGESTF c ENDOO c SMALL= A(l) c END IF largestf = 1 C CALCULATE WHAT EACH A(!) IS SMALL. THIS WILL C BE USED FOR THE NEXT MODA(l) = 0 DO l = 2, N MODA(!) = MOD(A(I),SMALL) END DO C SET EACH DISTANCE VERY LARGE C MAKE THE TREE THE NULL SET C ZERO OUT THE PREDECESSORS INITIALLY DO I = 0, P(1, I) P( 2, I ) T(l) EDGE( I) END DO SMALL 1 100000 0 0 0 C NOW SELECT THE ROOT (0 MOD SMAlL), AND START GROWING THE C TREE. AS THE TREE GROWS, SELECT GES LEAVING THE TREE C AND UPDATE THE PREDECESSOR /lATRIX. FOLLOW THE LEAST EDGE C TO FIND THE NEXT TREE ROOT. v 0 P(l,O) 0 P(2,0) 0 1(0) 1 Initialize an edge vector which the smallest value C edge congruent to mod(sma(\). This edge vector will be used if C A(l) <= N, rather than Jll the edges. !F (SMALL .LE. N) THEN EDGE(Q) = A(l) DO l = 2, N TEMP = MOOA( I) IF ((EDGE(TEMP) .EO. 0) .OR. (EDGE(TEMP) .GT. A(!))) THEN EDGE(TEMP) =All) END IF END DO END IF 43




FROB write (1,*)1 Small ::.1, SMALL (1,920) SMALL 'WRITE(7,*)' The Frobenius nLITber is: FROB C C 'WRITE(*,*) Your CPU usage was: C WRITE (*,*) CPUTIM C WRITE {*,*) 1 THE T''s ARE:' C (P(l,l), I 0, SMALL 1) C Create file catted SUB KNAPT.OAT C This file witt be used-by the Program called TCHECK to C check various RHS's against OPEN (6, FILE= 'Knapt.dat', status = 1new') ORITE (6, 910) LARGESTF WRITE (6, 910) SMALL DO I 0, SMALL-I OR!TE (6, 910) P(l,l) END DO CLOSE (6) RETURN END 45


Appendix E Algorithm Checking the t's SUBROUTINE TCHECK(CPUTIM) C This program will compare a given RHS for certain C previously calculated values of the Knapsack problem. C========================================================= IMPLICIT none INTEGER I, J, K, T(0:1000), N, SMALL INTEGER 8, LARGESTF, RHS(1000), T TOTAL REAL RHSR(1000), P INTEGER*4 CPUTIM, CPUTEMP C========================================================== 900 FORMAT (2X, I8, is feasible.') 910 FORMAT (2X, I8, 1 is not feasible.') 920 FORMAT ( 2X, 1 TCHECK Your CPU usage is: I 8) OPEN (6, FILE= 'Knapt.dat', status= old') READ (6,*) LARGESTF READ (6, *) N SMALL = N J = N READ (6,*) ((T(l)), I 0, J) CLOSE (6) C=========================================== C Here we input the problem vector from a datafile. OPEN READ READ CLOSE (5, FILE= 'Tin.dat', status= 'old') (5, *) N (5,*) ((RHS(i)), l : 1, H) (5) C Now record CPU time CALL CPUT(CPUTIM) CPUTEMP = CPUTIM 00 I = 1 I N RHSR(l) RHS (!) ENDDO C First creek the largest common factor to see if it C is larger chan 1 C If the largest factor is greater than 1, to C check feasibility, check first to see C if the supplied RHS's also share the largest C corrrnon factor. If they don't, that RHS is C infeasible. If they do, divide by it and C continue checking against the T's. IF (LARGESTF .GT. 1) THEN DO l 1, N P RHSR(l)/LARGESTF IF ( L

C If the RHS shares the greatest common factor. then C divide by the factor and compare to the T's as normal K INT(P) J = MOO (K, SMAll) IF (K .GE. T(J)) THEN ORITE (1,900) RHS (I) ELSE WRITE (1,910) RHS (!) END IF ELSE ORITE (1,910) RHS (!) END! F ENDDO ElSE C If the the greatest common factor is 1, we C compare the RHS to the appropriate T DO I 1, N J MOD (RHS(Il, SMAll) IF (RHS(I) .GE. T(J)) THEN WRITE (1,900) RHS (IJ ELSE WRITE (1,910) RHS (IJ END! F END DO END IF C Call CPUT to end marking CPU usage CAll CPUT(CPUTIM) CPUT(M (CPUTIM CPUTEMP)*100 ORITE (1,920) CPUTIM C========================================================= RETURN END 47