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Scaling Giant State Maps: Learning at the Intersection of Mathematics and Geography

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Scaling Giant State Maps: Learning at the Intersection of Mathematics and Geography
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Thoeobald, R., P. Anthamatten, L. Bryant, B. Ferrucci, S. Jennings and C. McAnney (2017). "Scaling Giant State Maps: Learning at the Intersection of Mathematics and Geography." Research in Geographic Education 19(2): 11-35.
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Anthamatten, Peter
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San Marcos, TX
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The Gilbert M. Grosvenor Center for Geographic Education, Texas State University
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Transformative research in geography education requires approaching classrooms with innovative methods to invigorate lessons involving basic skills. Our pilot project has demonstrated how educators can employ a standardized pre- and post-assessment of student knowledge of spatial thinking, math skills, and geographic content in classrooms in different locations in the United States. While this resaearch project assessed gains in student skills through exploration of giant maps, the project will require additional support to improve the rigor and validity of the study design. The transformative potential of this project is evident in the capacity-building afforded by developing and testing research instruments and procedures capable of replication across other classrooms, schools, and districts. Support from the Research Coordination Netowrk has enabled this group to undertake research activities that are potentially transformative. Otherwise, this group of geographers would have concentrated simply on sharing the map with teachers and schools, rather than investigating how students are learning by using the map.
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Collected for Auraria Institutional Repository by the Self-Submittal tool. Submitted by Peter Anthamatten.
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Volume 19 Number 2 2017 -Special Issue -Papers from the ational Center for Research in Geograph y Education s Research Coordination Network. SPEC I A L EDITOR Michael N Solem MANAGJ G EDITOR Joann Zadro z n y 1lu: Cilbc:rt M. Cros vc:nor Ce ntl'r forCeogrnph k E ,\ucation The Gilbert M. Gros v enor Center for Geographic Education

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Scaling Giant State Maps: Learning at the Intersection of Mathematics and Geography Rebecca Theobald U niv e rsi ty of Co lorado Colorado Sprin g s Peter Anthamatten U niv e r s i ty o f Co lorad o D e nver Lara Bryant K ee n e Stat e Co ll ege Beverly J. Ferrucci K ee n e Stat e Colle ge Steve Jennings U niv e r s i ty of Col o rad o Co l orado Sprin gs Cathleen McAnneny U ni ve rsi ty of M aine Farmin g to n Acce pt e d Sept e mb e r 19, 201 7 Abstract 11 Transformative research in g eo g raphy education requires approaching cla s srooms with innovative methods to invigorate lessons involving basic skills Our pilot project has demonstrated how educators can employ a standardized pre and post-assessment of student knowled g e of spatial thinking math skills and geo g raphic content in classrooms in different locations in the United States. While this research project assessed gain s in student skills through exploration of giant maps the project will require additional support to improve the rigor and validity of the study design. The trans formative potential of this project is evident in the capacity-building afforded b y developing and testing research instruments and procedures capable of replication across other classrooms schools and districts Suppoti from the Res e arch Coordination Network has enabled this group to undetiake research activities that are potentiall y transformative Otherwise this group of geographers would have concentrated simply on sharing the map with teachers and schools rather than investigating how students are learning by using the map Keywords: spatial thinkin g kinesthetic learning, math geo g raphy

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12 Theobald, Anthamatt en Bryant Fer r ucci Jennin g s McAnne ny Introdu c tion The formation of our res earch group took s h a p e at the American Associa tion of Geogra phers annual meeting i n April 2 016 w h e n several geography educa tor s learned details abou t a g r a n t program admini stered by the National Cente r for Research in Geog raph y Edu c a tio n (NCRGE) d esigned to cata l yze geography e ducation research. Aro und t h e same time the National Geographic Society provided t h e Network of Alliances f o r Ge o g raphic Education with a g i ant vinyl floor map of each state and the District of Columbia, approximately 14 by 20 feet for use in classroom s C h allenged to develop new theories of geograp h y learnin g and approaches to c urriculu m dev e l opme n t teacher education and assess m e n t practices we discover e d a nee d to i n vest i gate l ea rning p r ogressions in mathematic s whil e focu sing on t h e c ore c onc epts in geography. We a s sem bled a team of geogr a p h er s mathem a tici a ns, and c urriculu m s p e cialist s to identify w ays to u s e t h e s tat e giant maps t o t each math and spatial thinking skills and concepts with a pilot project directed at fourth grade. Research on s patial think i n g has y ielded intriguing con nectio n s to leat11ing proc esses in mathe m atic s and science. However research o n geo g raph y e duc ation "is a fragile field with few practitioners little funding, and wea k ins tituti onal suppor t (Bednarz, Heffro n & Huynh, 2013, p. 33). In o rder to addres s this challe nge, it is important to int e r act with res earche r s in m ultipl e dis ciplines In US schools much o f the day is consumed by instruction focu sed o n r eading and mathema tics, wit h l ittle time devo ted to geog r ap h y ( Theobald Dixon, Moha n & More 20 13). Geog raphy educators c annot rely on s chools to carve out instructional time devo ted t o geography or eart h scie nce a n d must c onstruct opp01t u nities for sys tematic cross-disciplinary connectio n s Buildin g on spatial thinking lit eratur e and informed by esta blished m athematical learnin g pro gressions we d eveloped a framework for analyzi n g how students l earn f undamental mathematics a n d s p at i al-a n alytica l skills using stat e gia n t viny l floor m aps (gia n t maps). Objective research is essenti a l for dev e lopin g a foundation for ge ograph y instruction ; teaching geog raphy skills and concep t s should not depend on t h e patticipation of educa tors alread y int e rested and trained in geog raphy. Rather r esearc h s hould identity w hat teacher s know what t h ey n eed to know how they deploy their knowle dge, and how t h eir knowledge of geography and geography education can be promoted and supported ( Bednarz et al., 2013 p 47). Our pilot project has demonstrated how educators can employ a stand a rdized preand post assess ment of student knowledge of geographic content and mat hematical skills r elated to spat i a l t hinking in cla ssroo m s in d i fferen t loca tion s in the U nited States. The limited time devoted to geog raph y in classrooms presents a n additional challenge to g row the project so that it can be replicated in multiple

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Scaling G iant Sta te Maps 1 3 loc at ions. T h ere are few sc hool s distr ict s a nd states w h e r e geogra ph y i s regularly taught, making com p a r at i ve projects difficult. E l e m e ntar y teachers se ldom have m o r e than thirty minutes in a school da y for both sc i ence and social studies (L. Fuller personal comm unic at i on, June 29 2017). The production and distribution of g i a n t maps creates a n e n t r y p o int for introducin g geogra ph y, particularl y in the ear l y grades a nd provides a way to e n gage educa tor s in research activities. The inclusion of add ition a l geography cu rricul a w ill open o pp01tunities for mo re substa nti al a nd l o n g -t erm studies of pedagogy. This project developed procedures for inter ac tin g with teachers and r esearchers to pave the way for f utur e resea r c h invest i gati n g ho w ex p e rience with g iant m a p s imp acts st ud e nt s understanding of space a nd mathematical thinking. Ele m enta r y school teachers as well as faculty a nd gra duat e students from geogr aphy ed u catio n a nd mathematics participated in the development of the math act i vit i es and assessment. This research addresses four of the six goals of the ationa l Center for R esearc h in Geography Ed ucation (Solem & Boehm 2017 p.2). Cata l y ze resea rch planning w ith stron g potential to re su l t in transformative research projects in geography ed ucation. Facilitate collaborative research a mon g geographer s and STEM e duc atio n researchers. Incr ease research productivity a nd the know led ge b ase in geog r aphy e du c atio n Promote the u se of research to impro ve practice in geography educat i on. The transformative pot e nti a l of this project i s evident in the capacity building afforded by d eve l opi n g and testing researc h instr um e nt s a nd proc e dure s capable of r eplica tion across other classroo m s schoo l s an d distr icts. Literature Review Spatia l thinking i s an essent ial component in a var i ety of disciplin es including mathematics scie n ce technology e n g i neering, histo r y art literatur e and the soc ial scie nc es (Golle d ge, Mars h & B atters b y 2008; Solem, Foote, & Monk 20 1 3). There is a st r ong positive connection bet wee n spatial and m at h ematical abilities and success in STEM-re lated fields driven b y buildin g these basic skills (e .g., Can et al., 2017; C h e n g & Mix 2014; LeFevre et al. 2013; Mi x et al. 2016; Stieff & Utta l 2015 ; Verdine Golinkoff, Hir s h Pasek & Newcombe 20 1 7 ; Zhang & Lin 20 1 7) Outreach to the e duc at ion community ha s d emonstrated the benefits of learning spatia l skills related to mathematic s and STEM (Gagnier & Fis her, 2016; ewcombe 2010 ; Newco mbe 2013). Downs

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14 T heobald Anthamatten Bryant Fer r ucci, Jenn i n g s McAnnen y (20 17) states t hat "Spatia l t h inking ... uses ve rbal, mathematical and statistical app r oac hes. I n turn mathemat ical thinkin g draws on notions of space a n d statistics, and can be represented verbally a n d graphical l y" (p. 8). Verdin e et al. (20 17) point out that spa tial s kills h ave not bee n a common part of formal education, but that t h ere i s i n creasing att e ntion t o these analytic a l skills T h e Natio nal R esearc h Counc i l [NRC] (2005) defines s p atial t hinkin g a s t h o u ght about space, r e p rese n tation and reasoni n g Inc luded in these components ar e the ways o f knowing the a rr ange m ent of objects in space underst anding how those objects are g i ven m eaning, a n d h ow gen era l ization s can be m ade from s pati a l inform atio n T h e fund ament a l skills include the a bility to det e r mine and des cr i b e l ocatio n distance direction, and prox i mity which can form the basis for the d e v elop m ent of mor e comp lex s p atia l concepts. Addit i o n ally, egoc e ntric ( u sing o ne's ow n bod y as a f r ame of reference) a n d allocentric (t h ought about s p atia l r efere n ces wit h r es p ect to a fixed environment) f r a m ework s are import a n t co n cepts for s p a tial thinking. Usin g the giant map as learni n g mediu m students a r e able t o position t h e msel ves physica lly in a n allocen tric representation but from a n egoce n tric per s p ective w hich may serve to h lp students make the t r ans i t i o n Anothe r impott ant fac et of s patia l l earning is the a bility to use symbols t o repr ese n t spat i a l objects ( D eLoac h e 2004 ; Goria & Papadopo ulou 2 0 17). Gerbe r Boulto n Lewis & Bru ce ( 1995 ) posi t that an u nder s tandi n g of a st udent s r ea l w orld interact i o n with a g r ap hic r epresentation of quanti t ative dat a i s impo rtan t in determ i ning how the g raphics are interp r ete d Skemp ( 1 976) discu sses the diffe r ence b etween "rel at i o n a l a n d inst rum e n tal" understand ing. R e l at i o n a l unde r s t a ndin g i s know l e dge b ased on exp erie n tial and reas oned solving of m athe m a tical probl e m s G r oves (2012) discusses several exampl es of classr oom s tr a t eg ies that h ave the p ote n t ial to b uild relati o n a l understanding. Playful learnin g i s see n as a n impo ti a n t app roac h t o l e arnin g; Fishe r HirshPasek & G olinkoff (2012 p 83) a r g u e for concept u a l unde r s tanding throu g h child cente r e d a n d inquiry-based exp erie n ces." While the r e i s disagre emen t a b out the effe c tive n ess of s p atia l train ing (e. g ., N R C 20 05), U tt a l e t al. ( 2 013) s u ggest t h at t h ese effotts a r e effective a n d that the skills l earne d in these tr ainings wer e p ers i s t e n t ove r t i m e a n d t r a n sferable t o othe r s p atia l tasks. Spatia l pers p ect ives are imp ortant for a varie t y of d i s c i plin es. Logan (20 1 2 ) wro t e a bout the role of s p atia l skills in t h e soc ial sciences s pecifically s ociol ogy New c ombe (2013) explic i t l y discu sses the r o l e of s pati a l s kill s i n S T E M a n d t h e soc i a l s tudies. A n unde r s t a ndin g o f s p at i a l r e l atio n ships i s imp o tian t a l so i n t he geosc i e n ces. This under s t a ndin g includes c r ystalline s tructur e as well as m a p s and cross s ecti o n a l d e piction s o f s ubs urf ace s tru ctures (Kas t e n s & I s hikawa, 2006; N RC, 2 005). Dorn e t al. (2005) found tha t t e ach e r s o b serve d a n incre ase in the p01tio n o f students mas t ering geo g raph y p e rform ance objectives w h e n they used l essons t h a t linked ge o g r aphy and m ath. Libe n &

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Scaling Giant State Maps 15 Downs (1994) discuss the advantages of the interdisciplinary research in geography and developmental psychology to address the lack of geographic knowledge in school children. Researchers from a variety of fields of study have been involved in research about spatial skills related to the use of maps and remotely sensed images (Anderson & Leinhardt 2002; Blades & Spencer, 1994 ; Blaut 1997a ; Blaut 1997b ; Blaut & Stea 1971; Blaut Stea, Spencer & Blades 2003; Diana & Webb, 1997 ; Downs Liben & Daggs, 1988; Golledge, Marsh & Battersby 2008 Liben & Downs, 1989 ; Liben & Downs 1992 ; Liben & Downs 1994 ; Liben & Downs 1997 ; Liben Kastens & Stevenson 2002; Lobben & Lawrence 2015 ; Metoyer Bednarz & Bednarz 2015 ; Newcombe & Huttenlocher 2000; Uttal 2000). Some researchers argue that map skills are learned (e .g., Downs Liben & Daggs 1988) while others state that they are intrinsic (e.g. Blaut & Stea 1971) ; see Mohan & Mohan (2013) for a summary. Writing about the ability of children to acquire spatial skills Uttal (2000) states that [m]aps provide a cognitive tool that helps children extend their reasoning about space in a new way Over time children can internalize the tool and think about space in map-like ways even if the y are not looking at a map at the time (p. 249). Using maps may improve a child s understanding of abstract concepts of space like measures of distance (e.g. miles) and coordinate systems (e.g. latitude and longitude) On the other side of the debate Blaut et al. (2003) argue that [w]e hypothesize that mapping behavior the thinking and action involved in reading making and using map-like models -is a cultural universal an ability to cognize and act that is acquired early in life in all cultures (p. 165). More recently work has shed light on specific parts of the brain that play a role in spatial understanding (Gersmehl & Gersmehl 2007; 2011 ; Lobben & Lawrence 2015). This improved understanding on brain functions may shed light on how and when to teach spatial skills Geography educators have long struggled with determining an appropriate learning progression for spatial skills (Bennets 2005). At what age should young students be prompted to think spatially and which spatial concepts should teachers start with? Gersmehl and Gersmehl (2007) argue that, similar to verbal and mathematical reasoning the human brain is well designed to perform spatial thought and that children acquire spatial thinking skills through an accumulation of experiences starting at a very young age. Consequently they argue teachers should prompt students to practice engaging with age-appropriate spatial tasks from a very young age Gollege Marsh and Batter s b y (2008) offer a task-based framework to serve as a learning progression of spatial thinking skills Their proposed model drawn from experience working with elementary-aged students consists of a hierarch y of specific concepts ranging from primitive to complex Through an experimental stud y of third and sixth graders they found that there was not a clear or consistent progression in students abilities to a1ticulate even simple spatial

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16 Theobald Anthamatten Bryant Ferrucci Jenn ings, McAnneny concepts Consequently, the y argue students s hould begin with low-tech accessible task s designed to teach s tuden ts the vocabulary and basic constructs which they m ay use later in their educations to grapple with more advanc ed spatial concepts They ident ify a ne ed for researcher s to exp lore and catalogue at what age students are able to engage with fundamental s patia l vocabularies an d tasks to deve l op a systematic progression. The mathematical concepts and skills related to ratio, scale, measurement, area, perim eter, and Cartesian coordinates are particularl y fundamental to the infrastructure of g eo g raphy. The i de a that mat h ematical thinking provides a foun dation for geographical models of the world is a rtic ulated well in the Colorado state standards: Mathematic s is indispensable for understand ing our world. In addition to pro viding the tools of arithmetic, a l ge br a, geome try a nd statistics, it offers a way of t hink ing about patterns and relationships of qu antity an d space and the connections among them Mathematical reasoning allows us to devi se and evaluate methods for solving problems make and test conjectures about prop ert i es and relationships and model the world around us ( Pittman 2010 p. 3). Although l imited formal analysis h as been undertaken about learn ing with large format maps education researcher s ha ve observed that "children in early elementary learn through sensory experiences and do best wi th tactile hands-on mapping activities .... Maps should also be big in s ize to a llow children to explore them with their whole bodies (Mohan & Mohan 2013, 4) Luc y Sprague Mitchell (2010 p 61), an early 201h century American educator who emphasized children s development through experience, encouraged students to create floor maps Dan Beaupre creator of the giant map pro g ram at the National Geographic Society observed "We want students to discover knowledge on the map ... T h e map is more of an experience than an object. It is unlike anything kids normally experience in school. It is an opportunity for them to be inspired have their worldview shaped and come away wanting to learn more (G lade 2009). A common challenge in teaching i s to engage the s tudents There is ample testimon y regardin g the effectiveness of the g iant map s as teaching tools; what remains to be undertaken is formal assessment of assumptions that students learn by doing

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Scaling Gian t State Maps 17 "Transformative research" in the context of the Research Coordination Network I RCN I The Nat i onal Science Foundation (Nationa l Science Board 2007) defines tr a n sformat ive r esearc h as: ideas dis coveries or tools that r a dic ally change our unde rstanding of a n i mp01tant existing scien tific or e n gineering concept or educat i o n a l practice or lead s to the creation of a new paradigm o r field of sci ence, e n g ineerin g or educati o n Such r esearc h c h alle n ges c urr ent under sta ndin g or provides path ways to new frontiers ( p 1 ) This work aims to c hall e n ge c urrent paradi g m s in geog r a phic education throu g h r e thinkin g tr aditional methods for teaching geog raph y concepts and skills throu g h kine sthetic learnin g by getting student s t o move physicall y a round in the map s pac e This project drew from research on s p a tial cognition map l ea rnin g and GIS educatio n to frame assessments of student geog r aphic knowledge b y extendin g geog r a phic concepts through m a thematic s and e ducati o n fields. The construction of sample s and assessment ite m s for quantitative a n a lysi s provid e d an oppo1tunity to complement o b serva tion s of students inte r acting with g iant maps Assess ment s of s tud ents skills and concepts l ea rned throu g h exp erience on g i ant m a p s have the potenti a l to provide a foundation for discoveri n g best practic e s in geog raph y e ducation in a broad range of school setti ngs. The intenti o n of this project i s t o combine background knowledge in geog raphic skills with h ands -on t eaching resources. Usin g s p atia l context provides student s with an a ddition a l p e r spe ctiv e for a n a l yzing issues and concepts in eac h of t h ese disciplines. Previous work identifi e d and c l assified spatial skills in a hie r a r cha l fashion in a five-level scope and sequenc e (Golledge Marsh & Battersby 2008). Schools a r e behind in incorporating spatia l l ea rnin g in their curricula with their focus ins t ead b eing on the development o f m athe m a tical and verbal reasoning skills. However many s p atial skills are r e l a ted to mathe matical con cep t s ; consequently geog raph y and the assoc i ated s patial context could b e used to teach m at h e matical skills. For example m easure m ent skills are r e quir e d to d eter mine dist ance and work with sca l e in s pit e of the fact that m easu r e m ent is not traditionall y considered to b e a s patial skill. Maps especially very l a rge maps could benefit students b y applying m at h e m at ical concepts to spat i a l skills Some schoo l s h ave s uccessfully used playground maps to teac h scale and direction and posit that the kinesthetic aspect of u sing the playground map i s b e n efic i a l ( P etzold and Heppen 2005). The r e is a nee d for sys tematic res earch not only to determine the t ea chin g effective n ess of u sing g i ant maps but a lso to introduc e s tudent s to scaffold their s pati a l reasoning skills incorporating the best proces ses. Due t o time constraints and limited

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18 Theobald Anthamatten Bryant, Ferru cci Jennings McAnneny accessibility to the giant maps it is important to ident ify the skills that truly benefit from their use in the classroom, and to develop a sound pedagogical model for teaching those skills This explorato ry study took advant age of previous foundational resear ch in spatial th inkin g and mat hemat ics "to investigate approaches to education problems to establish the basis for desi gn and development of new intervention s or strategie s, and /or to pro v ide evidence for w h ether an established intervention or strategy is ready to be tested in an effica cy study (Joint Com mitt ee, 2013 p l2). The work undertaken thus far by the r esea rch group provides evidence that by creating a strong framework for futur e investigation, subsequent work could contribute to understanding ho w s patial t hink ing and geography affect student knowledge gro wt h Other math emat ical concept s cr itical for spatial skills include measuring angles ident ifying geometric figures and their attributes, and visualizing geo metric transformations. Tea chin g these funda mental concepts takes up a substantial portion of early gra de mathematic s ed ucation with numerica l skills and descriptive geometry as import ant preli minaries. Ou r s tud y worked with middle grade elementary (Grade 4) students, who alread y had expos ure to and experience with the mathem atical skills c rucial to developi ng spatial thinking. Much of the current research occurs in disciplinary isolation. Due to the intersection of the c ommon skills in both mat hema tics and geog raph y, there is a need to engage researchers in both field s to study the acqui s itions of tho se skills. Working collaboratively across these fields incorporates the knowledge and perspectives of both disciplines and enhances the va lid ity a nd under sta ndin g of the learning progressions associated with the se Additi o nall y, c ollabora tion enables the investigation of alignment of these skills in the current c urricular models in the schools. Geography educators have too ofte n relied on dedicated geograph y teachers to explore ho w students learn By preparing validated assessments of students skills and concept s for re plication in multiple se ttings future work may serve to deve l op a pedagogical model u sing quantitativ e data to analyze stude nt knowledge acquis i tion. A major objective of this proje ct is to move toward efficacious research to determ ine whether an intervent ion or strategy can improve outcomes under what are sometimes called ideal conditions or toward "effe ctiveness research to estimate the impact s of an intervention or strategy w h en implemented under conditions of routine practi ce (Joint Committee 2009 p.14) The use of experimental research designs can give geog raphy ed ucation research greater credence and applicability.

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Scaling Giant State Maps 19 Framework of Study There has been little systematic assessment of much of the previous work by the National Geographic's Network of Alliances for Geographic Education. Professional development providers often rely on their own reputations and occasionally state standardized test results to measure success in sharing knowledge about geography teaching to elementary and secondary teachers The alliance coordinators associated with this project seized on the opportunity to implement a pre-and post-test process focusing on spatial thinking with the intention of providing evidence to teachers administrators and other educators about the importance of learning geography. The National Geographic State Traveling Giant Maps were created using the expertise ofNational Geographic s Ca1tographic Division and research on elementary spatial thinking (Perrotti 2016, p 2). Restricting the pi lot project to the fourth grade the grade level initiall y intended for use with the g iant maps provided a framework for assessing students across multiple states. Geographic alliance coordinators and educators from Colorado New Hampshire and Maine participated in this project. Pa1ticularl y since the 2002 No Child Left B ehind Act, which tied funding to standards-based academic performance teaching standards have become an imp01tant driver in elementary school curriculum. Geography educators have long argued that geography and particularly spatial thinking skills should be an important part of these standards. While geography has certainly had a presence in state standards for some time -by 2004 for instance 46 states had specific geography standards (Anthamatten 2004) there has been little formal or organized effo1t to include spatial thinking skills in educational standards per se. However at least since 2007 (Anthamatten 2010) basic spatial thinking skills including basic concepts such as identifying and describing locations local conditions and the ways in which places are connected to others have been present in nearl y all state standards in some form. All states participating in the pilot project have adopted Common Core mathematics s tandards and so the fourth graders in the study were working with the same instructional goals. The Common Core Standards for Mathematics for Grade 4 in Measurement and Geometry are the most pertinent to the project. These standards generally indicate that fourth graders should solve problems using measurement (including dista nce) and conversion of measurements manipulate fractions and decimals understand concepts of angles and angle measures as well as draw and identify lines and angles and classify shapes by properties of their lines and angles. Each of the specific national measurement and geometry standards are relevant to the giant map activities. As a result students understanding of ratio scale measurement estimation and quantitative reasoning skills are prerequisite to success in working with giant maps. Among the

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20 Theobal d Anthamatten Bryant F errucci Jenn ings McAnneny curricular goals for fourth graders included fractions, decimals, multi-digi t multiplication and division manipula tion of fractions, and basic concepts in ge om etry. Soc ial studies sta nd ards are l ess uniform a nd specific t han math sta nd ards. In Colorado fourt h graders are expected to master conte n t and skills using "several types of geographic tools to answer questions about the geography of Colorado a nd "con nec t ions withi n and across human and ph y sical systems are de ve lop ed" (Ha rtm an, 2009, p 8) In addition to describin g the interaction between the ph ysica l environment and hum ans, s tudents m u st use maps to : a Answer questions about Colorado regions using maps and other geogra phic too l s b. Use geograph ic grids to locate places o n map s and images to a n swer que st ion s c. Create and invest i gate geographic questions about Colorado in relati on to othe r places d Illu st r a te usi ng geogr aphic too l s how places in Colorado h ave changed a nd d eve l oped over time due to human activity e De scribe s imilarities and differences betwee n the physical geogra ph y of Colorado and its n eighboring states These co nc epts dovetail wit h the spatial t hin king skills required in mat h ematics. ln Main e, the social st udi es standa rd s closel y reflect those for Colorado. It i s fortuitous that the outcomes o utl ined for Geograp hy in the Maine L ea rning Results align well with t h e Common Core math o utcom es for the sa me grade levels Students a r e expected t o be ab l e to make sense of probl ems and solve them with quantitative abstract rea soni n g, construct viab l e arg um ents, cri tique the reasonin g of others and model wit h mat hem a tics. In New Hampshire, the s t a t e department of ed u cation acce pted the K -12 Social Studies New Hampshire Curric ulum Fra m ework in 2006 (New Hampshire Department of E duc atio n [NHDOE], 2006). This fra m ework include s geogra ph y standards for each gra d e that are aligned wit h the initi a l Natio n a l Geo gra ph y for Life Standards (Geography Education Standards Proj ect 1994). However the New Hampshire state social studies curriculum framework does not includ e any phys ical geography standards, as those are a ddre ssed in sc ienc e sta ndards. This se paration of the ph ysica l and human elements of geograp h y illu stra tes ho w in the s t a te o f New Hampshire geograph y i s not considered a se parat e subject or disc ipline but instead is integrated and supplements other courses. This distinct separation also fail s to address how inte g rat e d both the human and phys ical elements of the world a re interrelated Social studies is not t es ted in New Hamp s hir e, and therefore i s often not a focus in elementary schools which, as in Colorado are loc ally governed School districts de ve lop their own scope and sequences curriculum and often assessment

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Scaling Giant State Maps 21 and accountability plans However most schools in New Hampshire do include a New Hampshire history unit in the 4th grade. The giant state map at that grade level supports the state histor y unit as well as the spatial skills included in the 4th grade expectations aligned with the national geography standard associated with the world in spatial terms Generally state academic standards in each state supp01t the project. The researchers also collected qualitative data from each of the participating teachers throu g h initial and summative questionnaires regarding their use of the map in the classroom. Prior to conducting the activities all of the teachers saw a relationship between geography and mathematical skills pmticularly related to usin g grid systems measuring distances and scale. Other skills mentioned by the teachers included direction ratios statistics, angles perimeter and area as well as spatial reasoning After conducting the lessons the respondents noted that map curriculum supp01ted content they had already been covering in their classroom such as area and perimeter angles, and grid systems. Several teachers noted that usi"n g these skills on the map not only improved student under sta ndin g of the concepts but enabled them to m ake the connection that mathematics was a skill that applied to other disciplines as well. One of the teach ers observed that "the practical use of math with the map and to use the map to answer real question s makes the learning valid, authentic and lasting." Based on te ac her feedback the two mo st effective lessons were Getting your Bearings and Measurement ". While overall teacher responses were positive regarding their experiences respondents mentioned that with large classes student engagement was an issue and recommended modifications be made to include more st udents on the map at once. Other teachers using multiple groups on the map at one time commented that usin g the map encouraged social skills associated with cooperation One of the goa l s of this project was to include students in the research process. The research g roup collaborated with a g roup of undergraduate students enrolled in a se nior seminar geogra ph y course at Keene State College in New Hampshire that requires a semester lon g research project. As part of the exploratory research regar din g using the giant map to teach mathematical skills, these education majors developed a survey to gauge teacher interest in using the giant map in their classrooms and the pos sible applications that teachers felt were most appropriate. Surveys were distributed at the New Hampshire and Maine Council for the Social Studies and the Association of Teachers of Mathematics in New England conferences held in the fall of 20 16. A total of 123 surveys were collected from 66 elementary and 57 high sc hool teachers ; this included 56 surveys from teachers who attended the mathematics conference and 67 who attended the socia l studies conferences. Only nine of the teachers surveyed had ever used a giant map in their classroom seven of whom would consider using the giant map again. Among 114

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22 Theobald Antham atten Bry an t Ferrucci Jennings McAnnen y teac her s who had n ot used the giant map previously 7 3 ( 6 4%) w ould c o n sider u sing the m a p This result implies that once t e acher s h a v e u sed the map the y are more l i kely to continue using it in t h e futur e Th e m ost impo rta n t limi ting factor for teachers was the size of the map but cla ssroom management and st uden t e ngagem e nt were frequently mentioned as a ben efit. Part of the survey asked teacher s t o rank subject s in t e rms of t h e i r relevance to the g iant map on a five point sca le. Social s tudie s w a s r anke d a s t h e m ost relevant followed b y s cience m ath English a n d phy sical educati o n. Interestin g ly, when comparing the diffe rence s i n r ank teac h ers who att ende d t h e social studies confere nces r anked E n g lish slightl y hig h er t h a n math e m a tics. Furthermore teachers who attend ed the math ematic s c onfer e n ce ra nk e d m ath as more rele vant. Thi s finding s u ggests that socia l studi es te a c h ers ge nerall y would not teach math a ppli cation s as they relate to m a p s and that t h e r e is a n eed to provide training, curriculum and materials th a t can be u s ed to s upp o r t interdisciplinary instruction. E l ementa r y teachers indi cated m o r e interest in usin g the map s to reinfor ce m at hematical conc epts in their classroom t han did high school teachers. T h e pr oje ct so u g ht to build connections bet ween maps and mathematics through a n interventio n st r ategy overview based o n the p remise that we depend o n m ath to represent the Earth The p r imary questio n revolved around the e ffect of the g iant map on teac h i n g the geographic skills that ar e part of the fourth g rade mathematics curriculum. T hese tasks includ ed th e applicatio n of mathematical conce pt s such as s cale ( distance) Cattesian coordinates perim e ter a n d area calc ulati ons. Through t h e collaboration with the mathemat ics research fellow it was discove red that there was a connection between the math ex pec t ation s tha t s tudents a r e learning such as angles and the instruction of t eaching dir ection Inst ea d of focusing so l ely on cardinal dir ections instruction could include bearings thereb y reinforcing mat hema tical c o ncept s that are alread y inc luded in the 4th g rade mat h ematics c urriculum. Tabl e I link s activitie s and skills based on the Mathematics Common Core and the second e dition of Geo g raphy f o r Life (201 2) In order t o con duc t a pre I imina r y analysis of the e ffec tiveness of using the giant 1nap to support the learnin g of these co ncept s we designed a t wenty question preand post-ass ess m ent. We develop ed four questions for eac h of the five skills, each o f which incl uded tw o geography-foc u sed and two math-focuse d question s The sample assess ment item s for each of the skills a r e described in Table 2.

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Scal i ng Giant State Maps 23 T bl I AI' a e t g nment b etween M h at emattcs an dG h Sk'll eograpl 1 c I s. Day Activity Geography Mat h S kill Exa mple Skill Crea t e Cartes i a n One Grid Activity I Location Cartesian Grid grid with twine Grid Acti vity 2 GSI 5 G.I and 5.G.2 and loca t e coordinates. Stand on map Direction Activity I and practice Two Direction Activity 2 Bearings A n g les rotating angl e GSI 4.MD.5.a and b amounts and Angle R otation Act. determinin g new directions. Distance Activity I Distance Measurement Use a jump rope Three Estimation to measure D i sta nce Activity 2 GSI 4.MD.A2 distance. Area & Perimeter I Area Perim e t er and Create rope Four Area & Perimeter 2 GSI a rea (grid a rea) perimeters and 4.MD.3 determine a reas. Using graph Scale R epresentative p a per draw/copy Five Scal e Act i v ity I Graphic Fractions map. Scal e Act ivity 2 Scale 2 Convers ions Estimate GSI 4.MD.I distance using sca l e b I Tab l e 2. Samp l e Assessment It e m s ) y Skil Skill Sample Assessment Item Location / Grids Using an image with a s u pe rimp osed g rid w h at is at (x,y)? Direction I f yo u are faci n g North and rotate 90 degrees w h at (Bea rin gs) / direction are yo u facing? Ang l es Distance / What is the dist a nce between point A and B using a Measu r e m ent defined unit of mea s u rement. (i.e one segment of rop e = 100 miles )? Area and I f a room m easures 10 f ee t b y 20 feet w hat is the total area P erimeter of the room ? Sca l e I f I em= 300 mile s h ow far is it from point A to p oi nt B ?

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24 Theobald, A n thama t ten Brya n t F errucci Je n n i ngs McAn neny Throu g h th e cour se of thi s p ro j ec t we learn e d th at geographers and mathematici a n s d o not ne c essa ril y exam i n e s i m ilar concep ts i n th e same way. Fo r instance when t each ing s c ale geogr aphers us e g r aphic scales, v e rbal scales, a n d representative fraction (RF). Teach e r s a nd stud e n ts duri n g the course o f t h e project were adept at using the sca l e. They u se d th e gra p hic s c a l e i n t he corner of the map or the writte n equat ion to d e t ermine dista n ce. In t his r egard, the s cale is a tool. However sc a l e i s a l s o a co ncept i t is a p r opo rti onate size Geographers ca tegori z e maps as larg e s c a l e or s mall scal e ma ps. T each ers a n d s tud ents should also be able to deter min e the s cale o f the map itse l f w h ich is a n RF or ratio. There needs to b e more c l a rit y in e ducat i onal mat er i a l s b etween u s i ng a scale as a tool for determinin g dist a nce and fo r d e t e rminin g the s c a l e of the map Comm on RF in geograph y i s 1 : 2 4 000 (t h e sca l e of a USGS 7 5-minu te qu ad r ang l e map) ; m eaning o n e unit of dis tance on th e map e qu als 24, 000 units on the map Any unit can b e used b ecause t h e RF i s a r atio. A mat he m atician would use a verba l scale to describe the same d i st ance on a map such as, I i nc h = 2 0 00 feet or 1 em = 240 m eters Mat hem aticia ns a lso teach scale usin g mu ltip le co n ve r s ion s of different units inst ead o f rep r es e n t at i ve fr ac tions Fu t ur e resear c h wou l d benefit from s u ch collaborat i on as the re s h ould be mo r e math em b ed d e d i n ge o graphy in t h e ear l y g r a de s so that stude n t s a re abl e to d eve lop s p atia l t hinki ng a n d m a t hemat i cal s k ills from multipl e per s p e c tives. We develop e d pilo t l essons th a t integ r ated mathe mati c al and spat i al skills foc usin g on conc e pts of sca l e The u nd erlying m ath sk ills for s cal e inc lud e l ocation measurement ( distanc e) perime te r are a an d bea rings (ori e nta t ion ). The l e s sons were pil oted a t an ele m entary schoo l in New H a m psh ire a nd m i nor adjus tm ents were made based p rimaril y on classroom ma n age m ent a n d the log i sti cs of imple m enting t h e lesson efficiently. It wa s also fo und that bas ed o n the s ize of the map and the m easurement e x e rc i se usin g the jump rope t h at th e estima ted amount too cl o sel y m atched the act ual scal e and t h e refor e was adju sted to help r einforce t h e con cept. T h e pa r ticipa ting teac h e r a l s o had so me s uggesti ons rega rdin g creativ e ad diti on s s uc h as role p l a y i ng a pilot and u sing a c it y with an airport as the center o f the cir cle during th e bearing l esson increas i n g t h e i nterest and relevance to the st u dents. A critical com ponent of this project was the recruitm e nt o f teachers and s ch oo l s to pa rtici p ate in the proj ect. The plan was for each classroom teache r to have the g iant map for two weeks. Reason s gi v en for n o t pa rticipatin g incl ud ed bein g intimidated by the l ength y co n se nt forms r e quired b y stude nt s and parents not b eing able to interrup t state -m a nda ted te s t i ng, and not having s uffici e nt time. We successfully recruit e d ten teachers from s even sc hool s to pmticip ate. Sc hool s in Main e we re unab l e to co mpl ete the cons e nt or assent for m s, so results only reflect s tud ents in Colorado a nd New Hamp s hire. T h e t otal n umb er of s tud e nt p a rticip a nts in the study was 163.

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Scaling Giant State Maps 25 Description of Activity National Geographic Society's State Giant Traveling Map program grabbed the attention of administrators teachers parents and especially students opening the door for geography instruction in schools and districts across the country by providing resources and professional development to teachers. Geography educators reviewed the existing instruments for testing spatial thinking concepts and geographic knowledge The Mathematics Research Fellow participating in the project examined the giant map and identified approaches to including mathematics in instruction and assessment which focused on scale and the underlying skills needed to understand the concept such as location measurement and distance The materials and procedures incorporated the national geography and mathematics standards as well as state standards into the project. Partners piloted the assessments in two states in nine different schools analyzed results of assessments communicated preliminary results with the intention of inviting new partners from the Alliance Network. Due to the dissolution of the Alliance Network by the National Geographic Society another method for disseminating math lessons using the giant map will need to be identified. Project partners consulted with education experts and conceived a pedagogical approach to using giant map lessons and the assessment in classrooms. All teachers were given the maps for at least two weeks except for teachers at the pilot school and were encouraged to use the map for any classroom activity during the first week. They were instructed to give the assessment work through the five exercises and then administer the same test in the second week. A protocol was prepared for teachers to implement the lessons. Data were collected via written student assessments. A unique identifier was given to each student that contained no personally identifiable data information and recorded in an electronic collection database. In some instances the geographic alliances also sent teachers a video explaining the project to the students. The map and accompanying kit contained all the material needed for the activities. Participating teachers received a $200 honorarium in appreciation for their work. The project also included a teacher study. Data from students who did not complete both the preand post-tests were removed from the analysis. In total ten tests were discarded from a total of I 75 assessments.

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26 Theobald, Anthamatten B ryant Ferrucci Jennings McAnneny Figure 1. Stud ents m eas u ring with the Gia nt Map of Maine Results Ninety -on e (55%) ofthe pmticipants were boys and 73 (45 % ) were gir l s Between the preand po s t assessments, students demonstrated statist i c ally significant improvem ent in all skill sets (for p < 0 05) with the greatest increases in sca l e, and area and perimeter test items (Figure 2). T h ere were s ta tist i cally significant differences betw ee n students from ew Hamp sh ir e a nd Colora do with New H a mpshire students ge nerally performin g better and e x hibiting greater i mpro veme nt. These p re lim inary data s u ggest so m e i nterestin g results that merit further investigation using a control group and larg e r sample size. There were challenges to compl eti n g this wo rk Some teachers were unabl e to facilitate the completion of consent forms b y st udent s and familie s, which reduc e d the sample size. Tt was di ffic ult to control the environment in w hich instruction was provided. For examp l e, some sc hools used multi grade classrooms or team teac hin g and some student s had prior knowledg e o f the relevant skil l s in ge o g raphy or mathematics. Four of the nin e teachers had previously been trained in how to use the giant maps in their c l assrooms, whereas for others it was the first time they had encountered t he gia nt maps. While the training and content were consistent training was provided b y differe nt p e opl e at different t imes

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d i s t ance ( p=.Ol O ) d irection ( p <.OOl ) scal e ( p = .OOl ) coor d i n a t e syst ems ( p<.OOl ) area and per imeter (p=.002 ) 0 2 Scalin g G iant S t a te Map s 27 pre-test average pos t -test average 9 5 % confidence interval 3 4 Figure 2. This graphic s h ows the ave r ages and assoc i a t e d c o nfid e nce inte r vals f o r the test s prio r to a n d f ollowin g t h e m a p act i vity T h e p-values ar e the result of a o n e-tailed t-test for diffe r e n ce b etwee n the two ave r ages E nablin g Potentiall y Tran s formative Research T h e par t icip ants in this resea r c h n etwo r k wer e abl e t o creat e a n inte r d i scipli n a r y researc h g r oup focu se d o n the deve l opment of s p atia l skills in e l e m e ntar y school c hildr e n p a r t icul arly r e l a t e d t o using the g i ant map. T h e R esea r c h Coor dinati o n etwo r k project coinc ided with t h e introdu c tion of this r esource c r eating a l eve l ins tructi o n a l field. We wer e a l so able t o f r a m e interdis c i plin a r y activities ce nter e d o n t h e g i a n t m a p s and the impr ove m e n t of stude n t geog r aphi c k nowl e d ge and mat h e m at i ca l skills. T h e int erdisciplin a r y nature of the resea r c h has b ee n ver y positive and geography e ducat o r s from across the count ry h ave exp r esse d interest in the m ath l esso ns. We observed that n ot only are t eac h e r s and admini stra t o r s excite d a b out the oppo r tunity t o use the g i ant m a p they a r e equally excite d t hat they can use it dur i n g math time whic h i s a cr i tica l and significa n t p01tio n of t h e day Prelimi n a r y teac h e r surveys indica t e d that sec onda r y social stud ies t eac h e r s we r e mor e like l y to arti cula t e connection s t o m athe m atics, while e l e m e ntar y t eac h e r s wer e l ess lik ely to see and under s tand c onnectio n s t o geog r a phy. The use of t his tool to teac h m ath skills c ould have s i g n ifican t implicatio n s for c urriculum, m ate rial s and teac h e r tr aining. G i a n t m a p s pro v i de a n opp01tunity for s tud ents t o gain a sense o f the w orld that t hey might not e ncounter f r o m a m a p o n their phon e o n p a p e r o n a place m a t o r onli n e Using differe n t t y p es of m a p s e n ables the ins tru c tor to introdu ce s p a tial con cep t s that can b e r einforce d l ate r in t h e c l ass r oom, such as

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2 8 The ob ald Antha matt en B ryant Ferrucci J enn ings, McAnneny s c ale, proj e c t ion a nd p urp o se. We w ill share materials with the NCRGE clearing hous e i nclud i n g t h e existing mathematic s curriculum to use with giant maps to support g eograph i c c onc epts and a l ign wi th existing learning progressions in mathematic s, the piloted a ssess m ent instrume n t, IRB guidelines and obser vations for n avig atin g between higher e du cat i on and sc h ool districts. Futur e Resear c h Opportuniti es Interdi s c i plinar y s tu dies are c h alle n ging, but ca n be extremel y rewarding f o r both d e si g n ers and p r a c t ition e rs. Fo r example, a teacher may ask students to u se a s cale to 'meas ure' t h e dist a n ce be b etween two places when in reality stude nt s need to be abl e to m eas ure a rep r esen t at i o n of the distance on a map and u se t h e s cale to determine th e act ual dist an ce. Are they math or geography skills? While teachers from ea c h di scipline f und a m entally understood one another, their approache s w e re differen t and they o ften u sed different terms to refer to common c oncepts Often the a ppr oach t o sco p e an d se qu ence or learning progressions w as differ ent in each fie l d It m ay be a diffe r e n ce between teaching the fundament a l s kill s and ho w t h ey are applied in different settings, which became ev ident while working on the l es son s a nd t h e assess m ent instrument. Perhaps aligning geo g raphic s kill s to math pro g re s sion s would provide a good starting point f o r e s tablishin g a lea rning p rogre ssi on for geographic skills. A cle ar l e arning pro gre s s ion h as be e n d eveloped for mathematics for teaching spa tia l s kills. Thi s project shows t he opportuni ty for using the establ i shed mathemat ics p rogression to infor m teac hin g tho s e sk ill s i n a geographic context. This will as s ist in identi fying c om p o nen t s a n d skills nee d ed to perform spatial ta s ks, s uch as tho se re l ate d to dista nce Th e Co lor ado Ac ademic Standards state that G e ometric s en se a llo ws stude nt s to co mp rehend space and s h ape Students anal y ze th e char ac t e ristics and relat ionship s of s h a p es an d s truct ures e n gage in logic a l rea s oning a n d u s e tools and t ec hniques t o d ete rm i ne measurement. Stude n t s learn that geom e tr y and mea s uremen t a r e u se fu l in r e p rese n ting and solv i n g p r obl e ms in the re a l w orld as w ell as i n ma th e m atics" ( Pittm a n 2 010 p 8). More detailed individual i te m a nal y sis for the area a n d per imeter a nd s c a l e activities will assis t in this area. Future work will e x amine the impa c t of k ine stheti c learn i n g and how students approach l e arnin g wit h a g iant map ver s u s w i t h a p a p e r m a p Th e twe nt y question assessment needs t o b e va lidated wit h an inter-i t e m a n a l ysis and s hould include control groups who did not learn wi th the giant maps. Test i ng with different grades and s kill level s ma y also yield insights about learning progression Future work will also se ek to add r es s confoundin g variables associated with student mathematical sk ills to include workin g with decimals versus fractions to ensure that onl y applicable math s kills are measured. The pilot project can be scaled up using the g iant map as a resource in the classroom as an

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Scaling Giant State Maps 29 incentive. Classrooms in the control groups would be able to host the giant map following their participation in the study. Connections with geospatial technology tools might develop to explore mathematics and spatial kills using GIS activities. The preliminary results suggest that students learn the skills we had hoped they would learn by using the giant maps. Additionally, investigating geography and mathematics instruction using kinesthetic learning may further our understanding of learning progressions in spatial thinking. By explicitly linking this project to national standards and to a resource bank of interest to educators we hope to build a body of work that can both excite students and provide the foundation for research in spatial thinking and mathematical skills that supp01ts geography learning. We also find that the complexity of assessing learning outcomes relative to the national geography and mathematics standards, particularly results which offer perspectives on differences in gender knowledge and learning will be of significant interest to the educational community more broadly. Acknowledgements This material is based upon work supp01ted by the National Science Foundation under Grant No. 1560862. Any opinions findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. Additional supp01t was provided through National Geographic Society's Network of Alliances for Geographic Education specifically for the donation of State Giant Traveling Maps. The project could not have been undertaken without the cooperation of teachers and students in Colorado Maine and New Hampshire. Additional perspective on assessment was provided by Grant Clayton, Assistant Professor Curriculum and Instruction College of Education University of Colorado Colorado Springs. References Anderson, K C. & G. Leinhardt. (2002). Maps as representations : Expett novice comparison of projection understanding. Cognition and fnslruclion 20(3) 283-321. Anthamatten P (2004). State geography standards in 2004. Journal of Geography 103(4) 182-184. Anthamatten P (20 1 0). Spatial Thinking Concepts in Early Grade-Level Geography Standards Journal of G e ography I 09(5) 169-180

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30 Theobald Anthamatt en Bryant Ferruc ci, Jennings McA nneny Bedn arz, S W., S Heffron & N.T. Huynh (Eds.) (2013). A r oad map for 2 1 st century geography educati on: Geograph y educa tion research (A report from the Geograph y Educa tion Research Committee of the Road Map for 21st Ce ntury Geograph y Educ atio n Projec t) Was h i ngt on, DC: Association of American Geograp hers. Benn ets, T. (2005) Progression in Geographical Understanding. International R esea r c h in Geogr aph i ca l and Environm e ntal Education, 14 (2), 112 -132 Blades M & C. Spencer. ( 1994) The devel opment of children's ability to use s pati a l representations. Advances in c hild devel o pm e nt and behavior, 25 157 -199. Bla ut, J. M. (1997a) The Map p ing Abilities of You n g Children: Chi ldren Can. Annals of the Assoc iation of American Geographers, 87( 1 ), 152-158 Blaut J M. (1997b). Piagetian p essim ism and the mappin g abi l ities of youn g children: A rejoinder to Libe n and Downs. A n nals of the Associ at ion of America n Geographers 8 7(1 ), 168177. Blaut J. M. & D Stea. (1971). Stud ies of ge o gra phi c l ea rning. Anna l s ofthe Associat ion of American Geogra ph ers, 6 1 (2) 3 873 93. Bla u t J. M., D. Stea C. Sp encer & M Blades. (2003). Mapping as a cul tur a l and co g nitive universal. An nal s of the Assoc iati on of American Geog raph e r s, 93(1), 165-185 Carr M., N. Alexeev L. Wang N. Barned E. Horan & A Reed. (2017). The Development of Spatial Skills in Elementar y School St udents. C hil d D e velopment. the e vid ence. doi: 10.1111/ cdev .l2753 Cheng, Y. L. & Mi x K S. (2014) Spatial training improve s c h ildren's mat h ematics ability. Journal ofCogni t ion and D evelopment 1 5(1), 2-11. Common Core State St andar ds Initia tive. (20 17). Mathematics Stand ards. http: // w w w .corestandards org/Math/ DeLoache J. S. (2004). Becomin g symbol minded. Tre nds in cog nitive sc i e nces, 8(2) 66-70. Diana E. M. & J. M. Webb ( 1997 ) Using geographic maps in cla ssroo ms: The conjoint influence of individual d if ferences and dual coding on l earn i ng facts. L earning and Ind ividua l D ifferen ces, 9( 3) 195-2 1 4 Dorn R. 1., J. Dougla ss G. 0. E kiss, B. Trapido-Lurie M Co meaux, R Mings, & B. Ramakri shna ( 2005). Learning ge o graphy pro motes lea rnin g math : Results and implications of A rizon a's GeoMath grade K 8 pro g r am. J ournal of Geography, I 04 ( 4), 151-159

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Scaling Giant State Maps 31 Downs R M., Liben L. S & D aggs D. G ( 1 988). On education and geograp h e rs: The role of cog nitive developmental theory in geogra phic educat ion. Annals of the Assoc iati on of Ame rican Geographers, 78(4) 680-700. Downs R. M (20 1 7). Spat i a l Thinking Cog nition and Learning. The International Encyclopedia ofGeography. doi : I 0 1 002 / 9781118786352.wbieg0700 Fisher K., Hirsh-Pasek K & Go l inkoff R M (20 1 2). Fostering mathematical thin king through playful l ea rnin g In S. S u ggate & E. R eese (Eds.) Conte mp o r ary D ebates o n Child D eve l opme n t and Education (pp. 8192) New York NY: Routl edge Gagnier K., & Fisher K (20 1 6). Spatial Thinking : A Missing Buildin g Blo ck in STEM Education. John s Hopkins Schoo l of Educatio n, Ins titute for E duc at i o n Policy Commenta r y Geograph y E duc ation Standards Pro ject. ( 1994) Geograp h y for Life: Na tional Geography Standards Washington DC: National Geographic R esearc h and Exploration. Gerber R., BoultonL ew i s G., & Bruc e C. ( 1 995). C hildren' s understandin g of grap hic r ep r esen tations of qua ntit ative d a ta. Learnin g and In structio n 5( 1 ) 77-100 Gersmehl P J., & Gersmehl C. A (2007) Spatial thinkin g by young children : Neurologic evidence for early development and "educability". J ourna l of Geography, I 06(5) 181-191. Gersmehl P. J., & Gersmehl C. A (20 11 ) Spat i a l thinking ; whe r e p e d agogoy m ee t s n eurosc i ence. Pr ob l ems of Education in the 2 1 st Centwy 27,48-66. Glade D 2009 Geography Education is Lar ge r than Life w ith Nat ional Geographic's Giant Traveling Maps: I nterview w ith Dan B e aupre. Accessed 23 J anua r y 20 1 7 Wandering Educators. http s : / / www. wanderi n geducators.com/best/stories/ geog r aphy edu cation-la r ger-! i fe. htm I Goria, S., & Papadopoulou M. (20 17). Icons vers us symbols: investigating preschoolers' cmtog raphic design meta e m-to-s e mi otics 5(1 ) 1-18. Golledge R M. Marsh and S. Battersby. (2008). A conceptual framework for facilitating geospatial thinking A nnal s of the Assoc iation of A m e ri ca n Geographers 98 (2), 285 308. Groves, S. (2012). D eveloping math e matical proficiency. Journal of Sc i e n ce and Mathematics Education in Southeast Asia, 35(2), 119-145.

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32 Theobald Anthamatten Bryant Ferrucc i Jennings McAnneny Hartman S (2009) Co l orado Aca d e mi c Standards: F ou r t h Grade Social Studies. Office of Standards and I nst ru ctio nal Sup port. D enver CO: Colorado Department of Education. Heffron S. & R. Down s, E d s. (20 12) Ge og raphy for Life: The N ati on al Geography Stand a rds Second Edition. Geo graphy E ducation National Implement at ion Proj ect. Washington DC. Joint Committee. (2013) Commo n Guidelines for Education Research and D evelopment. In stitute of Education Sciences U.S. Departm e nt of Education and the National Scienc e Fo und at ion Washin gton D C Kastens, K.A. & Ishika wa, T. (2006). Spatial thinking in the geosciences and cognitive sciences: A cross-discip l inary look at the intersection of t h e two fields. In C .A. Manduca & D. Mogk, (Eds ) Earth and Mind : H ow Geol og ists Think and Learn abo u t the Earth: Geolo gic al Society of America Special Paper 413 (pp. 5174). Boulder CO: Geological Society of America. LeFevre, J. A., Lira C. J., Sowinski C. Cankaya 0., Kamaw a r D., & Skwarchuk, S. L. (2 013) Chartin g the role of the number l ine in mathematical development. Frontiers in P sychology. https : / / doi.org/1 0.3389 / fpsyg.20 13.00641 Liben L. S., & Downs R. M. (1989). Understanding maps as sym bols: T h e development of map concepts in children. Advances in C hild Development and B ehav i or, 22 145-201. Liben L. S., & Downs R M. (1992). Developing an understandin g of gra phic representations in children and adults : The case ofGEO-gra phics. Cog niti ve D eve l opment, 7(3), 33 1 -349 Liben L. S., & Downs R M. (1994). Fostering geographic literac y from early childhood: The contributions of interdi s ciplinar y research J ournal of Applied D eve lopm ental Ps ychology 15( 4), 549-569. Liben L. S., & Downs R. M. (1997). Can ism and Can'tianism: A Straw Child. An nal s of the Associat ion of American Geograp h ers, 87 ( 1 ) 159167. Liben L. S., Kasten s, K. A., & Stevenson L. M (2002). Real-world knowledge through real-world maps: A developm e ntal guide for navigating the educational terrain. Developmental Review 22(2) 267-322. Lobben A. & Lawrence M. (2015). Synthesized model of geospatial thinking. The Profess ional Geographer 67(3) 307-318. Logan, J. R (2012). Making a place for space: Spatial thinking in social science. Annual R eview ofSociology, 38 507-524.

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Scaling Giant State Maps 33 Metoyer S. K., B e dnarz S B & Bednarz R. S. (20 15). Spatial Thinking in Education: Concepts Development and Assessment. In 0. Muniz Solari A. Demirici & J. van der Schee (Eds.) Geospatial Technologies and G eog raphy Education in a C han ging World Geospatial Pra ctices and L esso ns L ear n ed (pp. 2133). Tok y o Japan : Springer. Mitchell L.S. (2010). Young Geographers ( 1934). Schools: Studies in Education 7 (1): 56-63 Mix, K S., Levine S.C. Cheng Y. L., Young C., Hambrick D. Z., Ping R., & Konstantopoulos S. (20 16). Separate but correlated: The latent structure of space and mathematics across development. Journal of Experimental Psycholog y : General 145(9), 1 206. Mohan A. & L. Mohan (2013). Spatial Thinking about Maps : D eve l o pm e nt of Co n cep t s and Sk ill s Across the Early Y e ars. Washington DC: National Geographic Education Programs. National Governor s Association for Best Practices & Council of Chief State School Officers (20 1 0) Com m o n Co r e State Standards for Mathe mati cs. Washington DC: Author. National Research Council & Geo g raphic a l Sciences Committee. (2005). Learnin g to think spatially: GIS as a support system in the K-12 curriculum Washington DC: National Academies Pr ess National Science Board (2007). Enha n cing Support ofTransformativ e R esearc h at th e Nat i o nal Scien ce F oundation. Retrieved from: https:/ / www. n sf.g ov / about/transformati ve research / defi n ition j sp New Hampshire Department of Education. (2006). K-12 C urri c ulum Frameworks for So c ial Studies. Retri eve d from: https : / / www .education nh. gov / i nstruction / curricu I um/ social_ studies / Newcombe N. S. (2010). Picture this: Increasin g m ath and science learning by improvin g spatial thinking. America n Educa t or 34(2) 29. Newcombe N. S. (2013). Seein g R e lationship s : Using Spatial Thinking to Teach Science Mathematics and Social Studies. American Educator 37( 1 ), 26. Newcombe N. S., & Huttenloch e r J. (2000). Makin g s pace The development of spatial representation and reaso ning. Cambridge, MA: MIT Press Perrotti A. (2016). S t ate G iant Trav e lin g Maps National Initiativ e H a ndbook Washington DC: ational G e o g raphic Society. Petzold D., & J Heppen (2005). A service-learning project for geography: Designin g a painted playg round map of the U nited States for elementary schools. J o urnal of Ge og raphy 104 (5) 203-210.

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34 Theobal d Anthamatten Bryant Fer rucci Jennings McAnnen y Pittman M. (20 1 0). Colorado Academi c Standards : F o urt h G ra d e Math Offic e of Standards and Instructional Support. D enver CO: Colorado Department o f E du cation. Skemp R. R ( 1976). Rel at i o nal u nderstandin g and instrumental und erstandin g Mathema tics Teaching 77 20 26 Solem, M. N., & R. G. Boehm (2017). RCN : Tran s formativ e Resea rch in Geography Ed ucation Annu a l Pro j ect Report Washington DC: National Science Foundation https://reporting.research.gov / rppr web / rppr?execu tio n = e 1 s4 Solem M K., F oote & J. Monk. (2013) Practicing Geograph y: Ca r ee r s for Enhancing Society and the Environm e nt. Boston: Pear s on Education Inc Stieff, M. & Utta l D. (2015) How much can spatial training improve STEM a chievement? Educational P sychology R evi e w 27( 4) 607-615. Theobald R S Dixon A. Mohan, & Z. Moore (2013) Whe r e i s Geograph y on the Social Stud i es Map?" In J. Passe a nd P. G. Fitchett (Eds.) The Status ofSocial Studies: View s from the Fie l d Information Age Publishing pp 181196 Uttal D H. (20 00) Seeing the big picture : Map use and the deve l opment of spat i a l co gnition. D eve l o pm e nt al Scien ce, 3(3), 247-264. Uttal, D. H., Meadow, N. G., Ti pton E., Hand L. L., Alden, A. R., Warren C. & Newcombe N S. (2013). The malleabilit y of sp atia l sk ills: A meta analysis o f training stu dies. Ps ycho lo gical Bulletin 139(2) 352 402 Verdine B N. Go l inkoff, R. M Hirsh-Pasek K., & New c ombe, N S. (2017). Spatial skills, t h e ir development and t heir lin ks to m a th ematics Monographs of t he S ociety for R esearch in Child Development 82(1 ) 7-30. Wilbanks T. J. (2 004) Geography and Technology. InS. D Brunn S. L. Cutter and J. W. Harrington (Eds.) pp 3 -16, Geography and T ec hnology Dordrech t, The Net h erla nds: Kluwer Academic Pub I ishers. Z hang X., & Lin D (2017) Does growth ra te in spatial abi lit y matter in predicting early arithmetic comp etence? L e arning and Ins t ruction 49 232-241 R e b ecca Theo bald hold s an a ppointmen t as Assistant Res earc h Professor in the Department of Geograph y a nd Environmental Studies at the Uni vers ity of Colorado Colorado Sprin gs where she coordinate s the Colorado Geo g raphic

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Scaling Giant State Maps 35 Alliance and edits The Geography T e acher. She explores the challenges of providing public services across diverse geographic locations. Peter Anthamatten is Associate Professor of Geography and Environmental Sciences at the University of Colorado Denver. His research focus is on health geography, particularly around children's environments Lara Bryant is an Associate Professor of Geography and Coordinator of the New Hampshire Geographic Alliance at Keene State College. She has a doctorate in Geographic Education and masters in applied geography. Her research focuses on the applications and implementation of geospatial technologies in the K-12 classroom spatial thinking and literacy and learning in the affective domain. Beverly J. Ferrucci is a Professor of Mathematics and Director of the Elementary School Mathematics Program at Keene State College. She holds doctorates from Boston University in Mathematics Education and from Boston College in Psychometrics. She is the editor of the New England Mathematics Journal past president of the New England Educational Research Organization, the Association of Teachers of Mathematics in New England and the New Hampshire Teachers of Mathematics and a former member ofthe Research Advisory and Educational Materials Committees of the National Council of Teachers of Mathematics. Steve Jennings is an Associate Professor of Geography and Environmental Studies at the University of Colorado Colorado Springs. He does research in biogeography and geography education. Cathleen McAnneny is a professor of Geography in the Depattment of Geography and Environmental Planning. Her research foci is on environmental health and geography education. She is the Coordinator of the Maine Geographic Alliance