This article was downloaded by: [66.31.30.1] On: 02 January 2015, At: 19:41 Publisher: Routledge Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Journal of Geography Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/rjog20 Components of Spatial Thinking: Evidence from a Spatial Thinking Ability Test Jongwon Lee a & Robert Bednarz b a Ewha Womans University , Seoul , South Korea b Texas A & M University , College Station , Texas , USA Published online: 27 Dec 2011. To cite this article: Jongwon Lee & Robert Bednarz (2012) Components of Spatial Thinking: Evidence from a Spatial Thinking Ability Test, Journal of Geography, 111:1, 15-26, DOI: 10.1080/00221341.2011.583262 To link to this article: http://dx.doi.org/10.1080/00221341.2011.583262 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/terms-and-conditions
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This article was downloaded by: [66.31.30.1]On: 02 January 2015, At: 19:41Publisher: RoutledgeInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,37-41 Mortimer Street, London W1T 3JH, UK
Journal of GeographyPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/rjog20
Components of Spatial Thinking: Evidence from aSpatial Thinking Ability TestJongwon Lee a & Robert Bednarz ba Ewha Womans University , Seoul , South Koreab Texas A & M University , College Station , Texas , USAPublished online: 27 Dec 2011.
To cite this article: Jongwon Lee & Robert Bednarz (2012) Components of Spatial Thinking: Evidence from a Spatial ThinkingAbility Test, Journal of Geography, 111:1, 15-26, DOI: 10.1080/00221341.2011.583262
To link to this article: http://dx.doi.org/10.1080/00221341.2011.583262
PLEASE SCROLL DOWN FOR ARTICLE
Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) containedin the publications on our platform. However, Taylor & Francis, our agents, and our licensors make norepresentations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of theContent. Any opinions and views expressed in this publication are the opinions and views of the authors, andare not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon andshould be independently verified with primary sources of information. Taylor and Francis shall not be liable forany losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoeveror howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use ofthe Content.
This article may be used for research, teaching, and private study purposes. Any substantial or systematicreproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in anyform to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions
Components of Spatial Thinking: Evidence from a SpatialThinking Ability Test
Jongwon Lee and Robert Bednarz
ABSTRACTThis article introduces the development andvalidation of the spatial thinking abilitytest (STAT). The STAT consists of sixteenmultiple-choice questions of eight types.The STAT was validated by administering itto a sample of 532 junior high, high school,and university students. Factor analysisusing principal components extraction wasapplied to identify underlying spatialthinking components and to evaluatethe construct validity of the STAT.Spatial components identified throughfactor analysis only partly coincided withspatial concepts used to develop thequestions that compose the STAT andwith the components of spatial thinkinghypothesized by other researchers.
Key Words: spatial thinking, spatialthinking ability test (STAT), factor analysis
Dr. Jongwon Lee is an assistant professor ofsocial studies education (geography educationmajor) at Ewha Womans University, Seoul,South Korea. His research interests are in theareas of geography education: spatial cognitionand skills, especially the role of geospatialtechnology in spatial thinking.
Robert Bednarz is professor of geography, TexasA & M University, College Station, Texas, USA,and North American Commissioning Editor ofthe Journal of Geography in Higher Education.His recent research has focused on spatial think-ing, the impact of using geospatial technologieson spatial thinking skills, assessment of spa-tial thinking skills, and the implementation ofgeospatial technologies in science and geosciencecurricula.
INTRODUCTIONSpatial thinking has been actively investigated during the last decade, especially
with respect to its relationship to geospatial technologies and its relevanceto problem solving in everyday life, the workplace, and science (Albert andGolledge 1999; Battersby, Golledge, and Marsh 2006; Bednarz 2004; Golledge 2002;Marsh, Golledge, and Battersby 2007). However, long before researchers beganto focus on spatial thinking, psychologists and others sought to identify andmeasure spatial ability. Spatial ability—typically defined as spatial perception,visualization, and orientation—is seen as a narrower concept than spatial thinking(Committee on Support for Thinking Spatially 2006). It is beyond the scope ofthis article to provide a comprehensive review of the literature concerning thedifferences and distinctions between spatial ability, spatial reasoning, spatialcognition, spatial concepts, spatial intelligence, and environmental cognition.Learning to Think Spatially, published by the National Research Council, whilerecognizing that no clear consensus as yet exists concerning spatial thinking,provided a significant step toward understanding its nature and its importancein the school curriculum. The Committee (26) saw spatial ability as “a trait that aperson has and as a way of characterizing a person’s ability to perform mentallysuch operations as rotation, perspective change, and so forth. The conceptderives in part from the psychometric tradition of intelligence measurementand testing . . . ” The Committee viewed spatial thinking, on the other hand, as aconstructive amalgam of three mutually reinforcing components: the concept ofspace, tools of representation, and processes of reasoning. In order for individualsto conceptualize space, understand representations, and reason spatially, theymust possess the appropriate spatial skills (Committee on Support for ThinkingSpatially 2006).
The Committee (2006) also recognized the educational value of spatial thinking,arguing that it can be taught and learned; thus spatial thinking should be animportant part of the educational curriculum at all levels. The Committee furthersuggested that GIS and other geospatial technologies can play a powerful role inpromoting spatial thinking. In fact, many studies have pointed to the advantageof integrating GIS into the classroom (e.g., Allen 2007; DeMers and Vincent 2007;Doering and Veletsianos 2007; Milson and Earle 2007; Patterson, Reeve, and Page2003) and have shown explicit links between GIS learning and students’ spatialthinking skills (Kerski 2008; Lee and Bednarz 2009; Schultz, Kerski, and Patterson2008).
However, researchers have also argued that “to be most effective, GIS teachingand curriculum development strategies should begin with an assessment ofstudent understanding of spatial relationships. . . ” (Wigglesworth 2003, 282),emphasizing the importance of establishing viable spatial thinking assessmentbased on a scientifically rigorous definition (Eliot and Czarnolewski 2007).Unfortunately, such a standardized measure of essential knowledge and skillsdoes not exist. In fact, the Committee stated explicitly that “[t]here are neithercontent standards nor valid and reliable assessments for spatial thinking”(Committee on the Support for Thinking Spatially 2006, 232).
This article begins with a brief discussion of concepts of spatial thinkingskills and the instruments available to measure them. Next, the article presentsthe development and validation procedures of the spatial thinking ability test
(STAT) that is modeled after the spatial skills test (Leeand Bednarz 2009). Data are presented that support thevalidity and reliability of STAT based upon a field testof 532 junior high, high school, and university students.The differences in the performance of these three levelsof students are explored and tested for significance usingANOVA. In addition, factor analysis is applied to identifyunderlying spatial thinking components, to determine ifthe identified components support the structure of spatialthinking proposed by other researchers, and to evaluate theconstruct validity of the STAT.
CONCEPTS OF SPATIAL THINKINGBecause the term “spatial thinking” has been used in both
nonacademic and academic areas extensively, a variety ofdefinitions exist (Committee on the Support for ThinkingSpatially 2006; Eliot and Czarnolewski 2007; Gersmehl 2005;Gersmehl and Gersmehl 2006; 2007; Golledge and Stimson1997; Harris 1981; Marsh, Golledge, and Battersby 2007;Montello et al. 1999). In addition, substantial disagreementcontinues to occur about the scale (from tabletop scaleto geographic scale) and dimensions (thinking in, about,and with space) of spatial thinking, about the nature ofcognitive processes involved, about the number of majorcomponents, and, as noted in the introduction, about therelationship, if any, between spatial ability and spatialthinking.
A few studies provide valuable input for the develop-ment of spatial thinking assessments. These studies suggesta series of spatial thinking concepts and describe differencesbetween expert and novice performance in spatial thinking.Some of the most useful studies include Learning to ThinkSpatially (Committee on the Support for Thinking Spatially2006), Gersmehl’s (2005) spatial thinking taxonomy, andGolledge and others’ categorization of geospatial concepts(Battersby, Golledge, and Marsh 2006; Golledge 2002;Golledge and Stimson 1997; Golledge, Marsh, and Battersby2008; Marsh, Golledge, and Battersby 2007).
Learning to Think Spatially (Committee on the Support forThinking Spatially 2006) introduces three spatial contexts:life space (cognition in space), physical space (cognitionabout space), and intellectual space (cognition with space).The first of these involves thinking about the world in whichwe live. It often includes way-finding and navigation inthe real, geographic world. It also includes other everydayactivities including assembling it furniture by followinginstructions, packing the trunk of a car to maximize carryingcapacity, etc. The second context, cognition about space,focuses on “a scientific understanding of nature, structure,and function of phenomena that range from the microscopicto the astronomical scales” (30). It is useful in explainingthe structure of the atom or DNA, the movement andarrangement of the elements of the solar system, etc.Other examples include “shapes and structures of urbanareas, the diffusion of cultures and agriculture, or the
organization of the world economy” (Bednarz n.d.). Theconcept or object investigated through the third context isnot necessarily spatial but can be spatialized by time-spacecoordination. For example, written linguistic symbols arespatially defined and spatially arranged, and readers mustestablish word order so that sentence and passage meaningcan be determined. Patterns in complex numerical data canoften be revealed and best understood by portraying theinformation graphically.
Although Learning to Think Spatially (Committee on theSupport for Thinking Spatially 2006) provides multicontex-tual and interdisciplinary definitions of spatial thinking, ithas been criticized for its lack of a conceptual framework,an essential prerequisite for development of assessmenttools (e.g., Gersmehl and Gersmehl 2006). Previous researchis not devoid of conceptual frameworks, however, asGersmehl and Gersmehl (2006, 2007) and Golledge andothers (Battersby, Golledge, and Marsh 2006; Golledge1995, 2002; Golledge and Stimson 1997; Golledge, Marsh,and Battersby 2008; Marsh, Golledge, and Battersby 2007)have proposed hierarchies of spatial thinking skills andconcepts. In a study to specify a taxonomy of spatialthinking, Gersmehl and Gersmehl (2006, 2007) definedspatial thinking as skills that geographers use to analyze thespatial relationships in the world. They identified thirteenmodes of spatial thinking: defining a location, describingconditions (the geographic concept of site), tracing spatialconnections (situation), making a spatial comparison, infer-ring a spatial aura (influence), delimiting a region, fitting aplace into a spatial hierarchy, graphing a spatial transition,identifying a spatial analog, discerning spatial patterns,assessing a spatial association, designing and using a spatialmodel, and mapping spatial exceptions. They argued thatbrain research suggests that these modes of spatial thinkinghave distinct or independent neurological foundations.They offered no empirical evidence or other rigorousassessment to support their hypothesis that the modes theyidentified are independent, however.
A hierarchical set of spatial thinking concepts was pro-posed by Golledge and his colleagues (2008). This sequenceprogresses from four basic spatial concepts (or primitives)to more complex and abstract concepts through five differ-ent levels as follows (Golledge, Marsh, and Battersby 2008,91–92): (1) primitive level (identity, location, magnitude,space-time); (2) simple level (arrangements, distribution,line, shape, boundary, distance, reference frame, sequence);(3) difficult level (adjacency, angle, classification, coordi-nate, grid pattern, polygon); (4) complicated level (buffer,connectivity, gradient, profile, representation, scale); and(5) complex level (area association, interpolations, mapprojection, subjective space, virtual reality). The spatialthinking skills suggested by the Gersmehls (2006, 2007)and geospatial concepts proposed by Golledge, Marsh,and Battersby (2008) share the common context of thegeographic scale. However, whereas Gersmehls’ conceptsare related to geographic analysis, the geospatial concepts
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Table 1. Core concepts of spatial thinking suggested by Gersmehl and Gersmehl (2007),Golledge, Marsh, and Battersby (2008), and Janelle and Goodchild (2009).
Gersmehl and Golledge et al. Janelle and GoodchildGersmehl (2007) (2008) (2009)
Condition Identity Objects and FieldsLocation Location LocationConnection Connectivity Network
Distance DistanceScale Scale
Comparison Pattern MatchingAura BufferRegion Adjacency, Classification Neighborhood and
identified by Golledge and his colleagues are intendedprimarily to address the functions of GIS.
The present investigation, using experiments that beganin 2006, could not benefit from the most recent workconcerning hierarchical geospatial ontology. However itdid incorporate key spatial thinking concepts from severalstudies conducted by Golledge (1992, 1995, 2002). Alongwith Gersmehls’ spatial thinking taxonomy, Golledge’s listof geographic thinking elements presented in 2002 guidedthe development of the spatial thinking ability test on whichthis study is based. The following list from Golledge’s 2002study specifies the spatial thinking elements he thoughtwere important and illustrates the ideas and concepts hiswork shares with Gersmehls’ (2005):
Comprehending spatial association (pos-itive and negative); comprehending spa-tial classification (regionalization); com-prehending spatial change and spatialspread (spatial diffusion); comprehendingnon-spatial and spatial hierarchy; com-prehending spatial shapes and patterns;comprehending locations and places; com-prehending integration of geographic fea-tures represented as points, networks, andregions; comprehending spatial closure (in-terpolation); and recognizing spatial form.(Golledge 2002, 4–6)
The core concepts of spatial thinking from three recent im-portant sources including Gersmehl and Gersmehl (2007),
Golledge, Marsh, and Battersby(2008), and Janelle and Goodchild(2009) are summarized in Table 1.Although the terms and number ofcore concepts that they used aredifferent, it is not difficult to findsimilarity among them.
MEASUREMENT OF SPATIALTHINKING ABILITIES
A variety of psychometric tests(Clements et al. 1997; Dean andMorris 2003; Hall-Wallace andMcAuliffe 2002) have been widelyused to measure individuals’ spa-tial abilities, especially in psycho-logical research. However, psycho-metric measures are limited to theassessment of psychologically andnarrowly defined spatial abilitiesrather than spatial thinking asdefined by the Committee (2006)(Hegarty et al. 2002; Lee and Bed-narz 2009). Consistent with thisview, Eliot and Czarnolewski (2007,362) argued that “researchers need
to go beyond the limits of existing spatial tests andconsider the possibility that spatial intelligence is a moreencompassing construct of human activities . . . .”
Self-assessment questionnaires are believed to assessbroader aspects of spatial thinking (Hegarty et al. 2002),and there are a few examples of these available on the Web(e.g., Golledge 2000, 2001). A typical question from theseinstruments might ask people to rate on a five- or seven-point scale a statement such as, “When traveling, I takeshortcuts as frequently as possible.” Although researchershave found that self-report measures are capable of assess-ing spatial skills on both the small (or pictorial) and large (orenvironmental) scales (Hegarty et al. 2002) and are usefulin assessing individuals’ spatial behaviors in everyday life,they are more appropriate for classifying types of spatialbehavior than determining levels of spatial ability. Anothershortcoming of subjective self-report measures is that oftenthe results from different instruments are incomparable.
There have been some important attempts to measurespecific aspects of spatial thinking skills (e.g., Albertand Golledge 1999; Battersby, Golledge, and Marsh 2006;Gilmartin and Patton 1984; Golledge 1992; Kerski 2000;Lloyd and Bunch 2003). For example, Golledge (1992) inves-tigated how completely people understand spatial conceptssuch as “nearest neighbor” using a map-based laboratoryexperiment. Battersby, Golledge, and Marsh (2006) deviseda task assessing individuals’ understanding and abilityto apply one of the most essential GIS functions—mapoverlay. In that study, participants were provided two mapsof the same area and asked to derive conclusions about
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the spatial relationships. In order to answer the questionsproperly, participants had to combine two thematic layersof information and perform logical functions (i.e., Booleanlogic). In a similar study, Albert and Golledge (1999) useda simplified set of thematic layers to evaluate how well GISusers could select appropriate map layers and operationsand visually verify map overlay processes to achieve aspecific result.
Another type of spatial task used to assess individuals’spatial ability includes map-reading skills such as followingdirections, judging distances, comprehending geographiccharacteristics, and recognizing patterns (Carswell 1971;Gilmartin and Patton 1984). Map-reading skills devised byGilmartin and Patton (1984) provided students with repre-sentations of a country’s population distribution, topogra-phy, and climate that they then used to answer multiple-choice questions such as “Which of the country’s threemajor cities has the largest population?” Also includedin the same study was a road map-reading task to assessabilities such as distance estimation, route comparison (e.g.,visually compare two straight-line distances and judgewhich is shorter), and pattern recognition (e.g., choosewhich of four generalized diagrams best represents theoverall road pattern in the study area). Finally, Kerski(2000) created a task that assessed both the spatial concept,“best location,” and map reading simultaneously. He askedstudents to analyze geographic information and select thebest location for a fast food restaurant in a hypothetical areabased on a given set of variables including traffic volume,existing fast food locations, locations of high schools, andannual median income.
DEVELOPMENT OF THE SPATIAL THINKING ABILITYTEST (STAT)
One goal of the present study was to develop a standard-ized test of spatial thinking abilities (the spatial thinkingability test (STAT)) that integrates geography contentknowledge and spatial skills. Currently no standardizedinstrument for assessing the set of spatial thinking skillsdiscussed previously exists. In addition, the reviewedstudies using questionnaires or other measures to assessspatial skills often ignored issues of reliability and validity.
The current study extends the authors’ research (Lee andBednarz 2009) that developed and deployed spatial skillstests (SST) to measure changes in students’ spatial skillsafter they completed GIS coursework. That research founda significant relationship between the completion of one ormore geospatial technology courses and students’ scores onthe spatial skills test. The components of spatial relationsas defined by Golledge and Stimson (1997) provided guide-lines for developing test items. The spatial skills tests consistof a set of multiple-choice questions and performance tasksthat were designed to evaluate students’ skills includingoverlaying and dissolving a map, reading a topographicmap, evaluating several factors to find the best location,recognizing spatially correlated phenomena, constructing
isolines based on point data, and differentiating amongspatial data types.
The initial motivation to revise and augment the originalspatial skills test was to measure students’ mastery of thecontent and skills contained in the Association of AmericanGeographers’ Teachers’ Guide to Modern Geography (TGMG)project materials. The primary aim of the TGMG, fundedby the U.S. Department of Education, is to improve thepreparation and ability of geography teachers to incorpo-rate spatial thinking skills into their classes. The TGMGproject produced a variety of print and digital materialsfor preservice and in-service teacher preparation programs,for example, a multimedia CD with animated instructionalunits that deal with the analytical skills specified in theNational Geography Standards, such as measuring direction,distance, slope, and density; analyzing map patterns andmaking rigorous map comparisons; formulating and testinghypotheses; identifying exceptions to patterns predictedby hypotheses; and buffering, overlaying, windowing, andother methods of spatial analysis. The spatial thinkingability test (STAT) was designed to assess individuals’growth in spatial thinking skills and to help determinethe effectiveness of the TGMG materials in promotingthe spatial thinking skills of teachers. The revised andexpanded spatial skills test also provided a data set thatcan be used to provide a preliminary assessment of thereliability and validity of the previously noted spatialthinking conceptualizations proposed by other researchers.
The initial step in the construction of the STAT was thedelineation of the assessment objective and the descriptionof the test contents to be measured. Two sets of spatialthinking concepts were analyzed and combined and servedto inform the development of STAT. The first set of conceptswas identified by Gersmehl (2005) whose ideas served asthe theoretical foundation of the TGMG project. The secondset was comprised of Golledge’s (2002) list of spatial think-ing skills, which played a key role in the development ofthe original spatial thinking ability test. Golledge’s conceptswere especially useful because they were detailed enoughto develop test items, potentially leading to improvementof test content validity. Additionally, both lists share somecommon concepts and features as noted previously.
Each test item was designed to measure one or twocomponents of spatial thinking identified by one or both ofthese two studies. The aspects of spatial thinking abilitiescovered by STAT include: (1) comprehending orientationand direction; (2) comparing map information to graphicinformation; (3) choosing the best location based on severalspatial factors; (4) imagining a slope profile based ona topographic map; (5) correlating spatially distributedphenomena; (6) mentally visualizing 3-D images basedon 2-D information; (7) overlaying and dissolving maps;and (8) comprehending geographic features represented aspoint, line, or polygon (see Table 2).
During the development of STAT, we focused on acentral problem related to test construction: how toensure practicability while at the same time providing
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Table 2. Description of question types and spatial thinking components to measure.
Type Item Spatial Thinking(Item Number) Description Components to Measure
I (#1, #2) In order to solve item #1 and #2,participants should visuallynavigate road maps usingverbal information includingparticipant’s current location,directions to destination, streetinformation, etc. (See Fig. 1)
Item #1 and #2 evaluate the traitof “comprehending orientationand direction (e.g.,forward-backward; left-right;up-down; back-front;horizontal-vertical;north/south/east/west)”(Golledge 2002).
II (#3) In order to solve item #3,participants should recognizemap patterns and representthem in graphic form.
Item #3 assesses the trait of“discerning spatial patterns”(Gersmehl 2005) and “graphinga spatial transition” (Gersmehl2005).
III (#4) In order to solve item #4,participants should select anideal location for a fictitiousfacility based on multiple piecesof spatial information such asland use, elevation, populationdensity, etc.
The basic rationale behind item #4is to assess the trait“comprehending overlay anddissolve” (Golledge 2002) and“inferring a spatial aura(influence)” (Gersmehl 2005).
IV (#5) In order to solve item #5,participants should create aprofile of topography along aproposed line on a contour map.In addition, the participantsneed to properly orientthemselves in situ.
In solving item #5, participantsdeal with several cognitive traitsincluding “recognizing spatialform (such as cross-sections tothree-dimensional blockdiagrams or image)” (Golledge2002), “being able to transformperceptions, representationsand images from one dimensionto another and the reverse”(Golledge 2002) and “graphinga spatial transition” (Gersmehl2005).
V (#6, #7) In order to solve item #6,participants should identifyspatial correlations betweensets of maps. Additionally, item#7 asks participants to displaythe identified spatial relationshipin a graphic form. (See Fig. 1)
Item #6 and #7 evaluate the trait“comprehending spatialassociation (positive andnegative)” (Golledge 2002),“making a spatial comparison”(Gersmehl 2005), and“assessing a spatialassociation” (Gersmehl 2005).Item #7 additionally assessesthe trait of “graphing a spatialtransition” (Gersmehl 2005).
VI (#8) In order to solve item #8,participants need to mentallyvisualize a 3-D image based on2-D information. (See Fig. 1)
Item #8 assesses the trait of“being able to transformperceptions, representationsand images from one dimensionto another and the reverse”(Golledge 2002).
VII (#9, #10,#11, #12)
In order to solve item #9, #10, #11,and #12, participants shouldvisually verify a map overlayprocess and then select theappropriate map layers involvedin the overlay. (See Fig. 1)
Item #9, #10, #11, and #12correspond to the trait“overlaying and dissolvingmaps” (Golledge 2002).
(Continued on next page)
maximum comprehensibility ofspatial thinking concepts. A num-ber of other factors were alsoconsidered in the design of theSTAT. These factors included (1)cognitive process (i.e., maximizingspatial processes and minimizingverbal processes); (2) psychometricrationale; (3) mode of represen-tation (text, picture, graph, map,color versus black and white, etc.);and (4) practical constraints (e.g.,amount of time required to com-plete the test).
The current version of the testis fourteen pages long and hastwo equivalent forms (one thatcan be used for a pretest andone for a post-test) allowing forthe evaluation of changes in spa-tial thinking skills over a periodof time. The pre- and post-testswere composed of slightly differentquestions covering the same spatialthinking skills. Each form, contain-ing sixteen multiple-choice ques-tions, consists of eight differenttypes of questions (Table 2). Figure1a and 1b contain a sample of itemsfrom the STAT. We also constructeda three-item questionnaire to col-lect information about the subject’sgender, academic major (geogra-phy major or not), and amount ofgeospatial coursework completed(e.g., GIS and cartography).
Formal and informal reviewof STAT took place in a vari-ety of venues, mostly conductedas part of the evaluation planof the TGMG project. After adraft of STAT was completed, allitems were carefully reviewed bya team of experts consisting pri-marily of the TGMG project teamand steering committee members.The team included two individ-uals who teach geographic edu-cation courses for undergraduateand graduate students; these mem-bers conducted an informal reviewand then pilot-tested the instru-ment with their students. Twenty-seven undergraduate students par-ticipated in a pilot test that helpedestimate the difficulty level ofSTAT and reduce the incidenceof errors in test administration.
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Table 2. Description of question types and spatial thinking components to measure.(Continued)
Type Item Spatial Thinking(Item Number) Description Components to Measure
VIII (#13, #14,#15, #16)
In order to solve item #13, #14,#15, and #16, participantsshould visually extract types ofspatial data from verballyexpressed spatial information.(See Fig. 1)
Item #13, #14, #15, and #16measure the trait“comprehending integration ofgeographic featuresrepresented as points,networks, and regions”(Golledge 2002) and“comprehending spatial shapesand patterns” (Golledge 2002).
Figure 1a. Selected items from the STAT. Each item corresponds to Type I, V, andVI, respectively.
Revisions were made as a conse-quence of the pilot tests: questionsthat were perceived to have morethan one correct answer or weredifficult to score objectively wereeliminated or revised; a pair ofquestions (for pre- and post-test)that proved to have different levelsof difficulty were adjusted; anditems whose graphics or directionswere unclear were improved.
When workshops to reviewthe TGMG project materials werescheduled during a variety of ge-ography meetings and conferences,STAT review sessions were alsoconducted. For example, a STATreview session occurred in con-junction with the annual meetingof the National Council for Geo-graphic Education. During that ses-sion twenty-two TGMG workshopparticipants including a preserviceteacher, education students, sec-ondary school geography teachers,and professional geographers, tookand commented on the STAT.
TEST RESULTS
Reliability and Construct Validityof STAT
Test results from 352 universitystudents from four different U.S.states who took STAT were used toexamine the reliability and validityof STAT. The number of studentswho completed the tests at the fouruniversities varied from 11 to 146.The variation of the sample sizesresulted from the access to studentsby faculty volunteers who agreedto administer STAT at each of theschools. As a measure of inter-nal consistency, Cronbach’s alphawas calculated. Cronbach’s alphais a measure of the intercorrelationof items, measuring the extent towhich item responses obtained atthe same time correlate with eachother. A value of 0.7 for Cronbach’salpha is generally considered toindicate a reliable set of items (deVaus 2002). The Cronbach’s alphafor the latest version was 0.721and 0.701 for Forms A and B,
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Components of Spatial Thinking: Evidence from a Spatial Thinking Ability Test
Figure 1b. Selected items from the STAT. Each item corresponds to TypeVII and VIII, respectively. Note: all items of STAT may be viewed athttp://home.ewha.ac.kr/∼ziriboy/STAT.pdf.
respectively. When STAT was administered for the firsttime, we were somewhat disappointed by the relativelylow validity and reliability statistics. As we reconsidered theresults, however, we realized that recent conceptualizationsof spatial thinking skills support the notion that spatialthinking skills are composed of several elements thatmay be at least somewhat independent of one another.Therefore, it is not surprising that some individuals mightperform significantly differently on questions that assesseddifferent skills thereby lessening the internal consistency orintercorrelation. Although originally Golledge and Stimson(1997) proposed “spatial relations” as an additional spatialability to visualization or orientation, it seems likely that“spatial relations” included a variety of skills that are likelyuncorrelated.
In order to explore to what ex-tent spatial thinking skills are com-posed of distinct components, theconstruct validity of STAT was ex-amined using factor analysis. Fac-tor analysis is a statistical tech-nique used to identify the minimalunderlying factors needed to ex-plain the intercorrelations amongthe test items. Principal compo-nents analysis revealed six factorswith eigen-values of 1.0 or more,accounting for 54.66 percent ofcumulative variance. In general, afactor analysis accounting for 60–70 percent or more of the totalvariance is considered a good fitto the data. Varimax rotation wasthen applied to the six factors.This procedure rotates the set ofindividual scores within the spacedefined by principal componentaxes, thereby creating a new setof factor loadings (increasing thedifference between high and lowloadings) for the factors that havealready been found. The rotatedfactor matrix is presented in Table3. The nature of each of the factorsin Table 3 is determined by thecharacteristics of the variables thathave high loadings on these factors.Six factors accounted for 11.1, 10.7,10.5, 7.9, 7.6, and 6.9 percent of thevariance, respectively.
If the skills tested by the eightquestion types displayed in Table 2are independent components ofspatial thinking, we would expectthe factor analysis to yield factors
that reflect those components. That is, questions thatassess a specific component should be grouped. Althoughsome factors directly or indirectly show high levels ofcorrespondence, others do not. For example, four of thequestions that load on factor 2, items #13, #14, #15, and#16, are based on the spatial skill “visually extract types ofspatial data from verbally expressed spatial information”(Type VIII) although #10, which is not a Type VIII item,also loads as highly on factor 2 (0.484). Factor 3 generatesheavy loadings for the items related to question type VII(#9, #10, #11, and #12) requiring “participants to visuallyverify a map overlay process and then select the appropriatemap layers involved in the overlay.” It is interesting that,in addition to the type VII questions, item #7 had the highloading (0.529) on this factor. This result might be explained
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Table 3. Results of the factor analysis of the pretest of the STAT.
by the existence of similar cognitive processes in solvingtype VII (“visually verify map overlay processes”) and item#7 (“comprehending spatial association”).
However, unlike factors 2 and 3, other factors werenot clearly connected to specific question types. Factor1, with heavy loadings for items #4, #5, #12, and #14,spans several question types. Furthermore, some items
Table 4. A percentage of correct answers per item and mean score by groups.
Univ. A Univ. B Univ. C Univ. D Junior High HighItem (N = 29) (N = 11) (N = 59) (N = 146) (N = 52) (N = 149)
load equally on more than onefactor such as item #8, which loadson four factors—1 (0.292), 2 (0.207),4 (0.195) and 5 (0.288)—althoughat relatively low levels. This mayoccur partly because the questionitems are inadequately specified(i.e., they represent or require morethan one spatial thinking skill) orbecause of the failure of STAT tocapture the full range of spatialthinking.
Analysis of STAT Test ResultsThe STAT was administered to
students at a wide range of aca-demic levels—at four universitieslocated in Texas, Ohio, Illinois, andOregon, and at a junior high andhigh school in Ohio (Table 4).
In general, as students advancedfrom junior high to university theirperformance improved. For everyquestion, the average score for highschool students exceeded that for
junior high school students. Similarly, the average scoresfor university students were greater than the scores for highschool students for every question, although the averagehigh school scores were greater for some questions than theaverage scores of university B and C students.
Analysis of the test data showed that a sizeable majorityof university students could identify patterns on a map
and choose a correct graphicaldisplay of a spatial pattern (item#3). In addition, a large percentof university students (63.6 to 93.1percent) could find locations, un-derstand orientations and direc-tions, and navigate on road mapsfollowing directions (item #1 and#2). Whereas nearly 90 percent ofthe participants could comprehendspatial association between twomaps (item #6), less than half werecapable of transforming a spatialrelationship into a graphic form(item #7). Although items #9, #10,#11, and #12 were designed toassess the same skill (Type VII),students performed most poorly onitem #12 (see Fig. 1b), the questionthat required the most complexBoolean logic.
A few question items werefound to have better discriminat-ing power than other items. Forinstance, question items such as #1,
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Figure 2. Score comparison per item by groups.
#2, #3, #10, and #11 most clearly separate the junior highschools students from others (Fig. 2). Nevertheless, as thegraph illustrates, students at all levels displayed similarperformance patterns, in the sense that scores for allstudents were uniformly higher for some questions thanothers. The lines representing the scores for the six studentsamples are relatively parallel, indicating that students,from junior high to university, scored higher and loweron the same questions. This result would seem to indicatethat some skills are more challenging than others and offersupport for the argument that spatial thinking is composedof more than one skill or ability (in addition to the widelyaccepted spatial visualization and orientation abilities).
Table 5. ANOVA for Form A scores by groups (University students only).
SS df MSE F p
Between groups 359.524 3 119.841 14.936 .000Within groups 1933.643 241 8.023Total 2293.167 244
Table 6. Post-hoc comparison of Form A scores by groups.
Univ. A Univ. B Univ. C
Univ. B 4.295** (.000)Univ. C 2.863** (.000) 1.431 (.416)Univ. D 0.616 (.708) −3.679** (.000) −2.247** (.000)
**p < .01.
Analysis of variance (ANOVA)was used to determine whethersignificant differences in scoresamong four university groups ex-isted. When analysis of variance(ANOVA) was performed on FormA scores of the four schools, signif-icant differences were found (p =.000) (Table 5). Post-hoc compar-isons (using Tukey method) re-vealed that students of universityA and D scored significantly higherthan those of university B and C(Table 6). No significant differencewas found between scores of uni-versity A and D and between thoseof university B and C, respectively.
The number of geography ma-jors in each group may account forthe differences in scores (Table 7).School groups with the highestpercentages of geography majors,
university A (41.38% majors) and D (26.03%), scored higheron Form A than university B (9.09%) and C (16.95%).The format of STAT, including maps and spatial terms,may be more challenging or less familiar to nongeographymajors.
Because two versions of STAT were developed (FormA and Form B), it was important to verify that thetwo forms were equally difficult. This was achieved bycomparing participants’ mean scores on the two formsof the STAT using a t-test for independent samples. Thestudent participants of university A, B, and C (students ofuniversity D took only Form A) were randomly dividedinto two groups each taking either Form A or Form
B of the test. In order to verify theequivalency of two forms of theSTAT, three separate t-tests wereconducted for the three groups(Table 8). All of the t-tests indicatedthat the two forms of STAT aregenerally equivalent in difficultyexcept for university B where twostudents who completed Form Ascored very low on the test (an-swering only two of sixteen ques-tions correctly).
DISCUSSION ANDCONCLUSIONS
In this study, we developedand evaluated standard measuresof spatial thinking skills. Inter-nal consistency reliability estimatesfor the STAT were in the moder-ate range. Although these resultsmay raise concerns regarding the
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Table 7. A comparison of Form A scores by major (geography major versus nongeographymajor).
N Mean S.D. t p
Geography major 61 11.77 2.58 −3.264 0.067Nongeography major 184 10.32 3.14
Table 8. Independent sample t-test.
Form N Mean S.D. t p
University A A 29 11.93 2.64 .908 .368B 26 11.23 3.08
University B A 11 7.64 3.67 −1.945 .065B 13 10.38 3.25
University C A 59 9.07 2.78 −0.771 .442B 47 9.49 2.81
completeness of the measure, there are several issues thatmay account for the moderate reliability. With regard tointernal consistency reliability, Cronbach’s alpha increasesas the number of items increases. Ceteris paribus, increasingthe number of items can increase the level of alpha.
In terms of the construct validity, the factor analysisusing principal components extraction with varimax meth-ods provide mixed results with regard to the researchhypothesis. We hypothesized that factor analysis wouldidentify the independent components of spatial thinkingby generating factors that reflected the eight components ofprevious researchers’ spatial thinking conceptualizationsthat were represented by questions in STAT. Whereas somefactors were directly or indirectly connected to the questiontypes, some were not. This result might be attributed tothe participants’ styles of spatial problem solving. It iswidely accepted that different people employ differentstrategies when solving spatial tasks (Kyllonen, Lohman,and Woltz 1984; Lohman and Kyllonen 1983). Furthermore,spatial tasks are often solved using nonspatial processingstrategies. For instance, Just and Carpenter (1985) foundthat many spatial test items may also involve verbal analyticprocessing. They argued that verbal strategies are routinelyemployed for spatial tasks including 3D rotation, spatialorientation, and others. Thus, for at least some individuals,relative success on spatial items could be due to a verbalor another type of ability rather than this spatial ability.As mentioned previously, care was taken when devel-oping STAT to maximize spatial processes and minimizeverbal processes required to answer correctly. Because noinformation about how students solved questions wascollected however, studies with additional items are neededto explore the spatial thinking processes employed by
individuals engaged in spatialproblem solving before this issuecan be addressed reliably.
Perhaps another reason that thefactor analysis did not identifyeight independent components isthat independence of the eightcomponents is not as great or ascomplete as hypothesized. Spatialthinking skills may be comprisedof fewer than eight components orsome skills may be correlated toothers, which may or may not bethe same thing. If spatial think-ing consists of fewer independentcomponents, what do the resultsof the factor analysis suggest thosecomponents might be? Three of thefour items loading highly on factor1 require the skill to overlay or vi-sualize spatial data. Four of the fiveitems that load on factor 2 requirethe ability to distinguish amongthe map elements point, line, and
area. Three of the items that load on factor 3 test respon-dents’ skill in performing Boolean operations on geometricpattern; the fourth item requires identification of the natureof spatial correlation between two mapped distributions.The two items loading on factor 4 do not appear to havemuch in common: one concerns a way-finding task and theother requires the creation of a cross-section diagram from amapped distribution. Factors 5 and 6 are, for the most part,comprised of one item, a way-finding question for factor 5and identification of a positive spatial correlation for factor6.
Thus, the analysis of STAT offers relatively little supportfor the existence of the independent spatial thinkingcomponents hypothesized in the literature. The analysisalso suggests that Golledge and Stimson’s spatial rela-tions ability is almost certainly not a single ability butinstead is comprised of a collection of different skills.Based on the clusters identified by the factor analysis,the following spatial thinking components emerge: mapvisualization and overlay, identification and classificationof map symbols (point, line, area), generalized or abstractBoolean operations, map navigation or way-finding, andrecognition of positive spatial correlation. We do not assertthat these five components are the five spatial thinking skillsets. Nevertheless, intuitively these skills do seem differentenough that individuals might be able to use one or moresuccessfully while they are having difficulty with others.For example, it is not hard to believe that a person who isskilled at solving Boolean problems might not necessarilybe a skilled navigator.
We do think that the analysis strongly supports thehypothesis that spatial thinking is a collection of differentskills and that more work must be done to identify those
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component skill sets. The results also help explain why indi-viduals perform well on some spatial thinking tasks whileperforming poorly at others. For geography educators theseresults suggest that because students perform well on sometasks does not mean that they will perform well on others. Ifdifferent tasks require different skill sets, performance maybe uneven. The results also suggest that giving studentsa variety of ways to demonstrate what they have learnedmight reveal a student’s knowledge or ability that would goundetected if only one method of assessment is employed.
The two forms of STAT were equivalent in difficulty atbaseline, and therefore, the two forms of STAT can be usedfor pre- and post-test designs to evaluate changes in spatialthinking abilities over a brief period. In addition, the fieldtests in several different environments showed STAT wasuseful for testing both university and high school students.
Our standardized measure needs to substantiate contentvalidity more rigorously. This measure, however, providesrigorous bedrock for testing that can be expanded withnew tests in the near future. The current version of STATrepresents considerable developmental work based ona solid theoretical foundation. Additional research andrefinement of the measures could strengthen their testingabilities and contribute to research on spatial literacy in thelong run.
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