ABSTRACT

Geoscience learning requires mastery of variousspatially demanding tasks, and the learning-scienceliterature offers research findings that illuminate themental processes underlying such geospatial tasks.Research on spatial abilities shows that there are largeindividual differences in performance on spatial tasks,that spatial skills can improve with appropriate trainingbut that the improvement may not transfer to relatedtasks, and that the form of effective training may varywith the student's spatial ability. Research on use ofmaps in real-world settings shows that the map-readingtask involves three constituent understandings:representational correspondence, configurationalcorrespondence and directional correspondencebetween a map and the real world. Research ontopographic-map use has uncovered consistent,teachable strategies used by successful map users. Theseinclude grouping features into configurations ratherthan focusing on individual features separately, andevaluating multiple hypotheses about one's viewpoint.Research on how people comprehend 2-Drepresentations of 3-D structures aids in diagnosing thenature of students' errors on such tasks. Students makingnon-penetrative errors, in which they only useinformation visible on the exterior of the 3-D volume,may need different interventions than students whomake penetrative errors, in which they try to envision theunseen portions of the 3-D volume.

INTRODUCTION

A typical geoscience course at the high-school orundergraduate level is replete with tasks that requirehigh-level spatial thinking. Students are expected tomake, use, and interpret spatial representations, such asmaps, cross-sections, and three-dimensional models.They must mentally visualize geologic structures andprocesses in three dimensions, by interpreting one- ortwo-dimensional data. They may be asked to exercisespatial-thinking skills in a large-scale field area, and tothink about phenomena on scales ranging from micronsto thousands of kilometers. Geoscience instructorscommonly find that a significant portion of studentsstruggle with these kinds of spatial tasks and may notimprove substantially even with practice.

For geoscience instructors to effectively helpstudents with spatial tasks, it is useful to know whatcognitive abilities and processes those tasks tap into andwhy those tasks can be difficult to master. The cognitivescience literature reports a body of research findingsconcerning mental processes by which humans thinkabout objects or processes in two- or three-dimensionalspace. Unfortunately, this literature has not been easilyaccessible to geoscientists or geoscience educators. Ourgoals in this paper are to summarize major research

findings about humans' use of spatial representations,and to cast these findings into terms that are relevant togeoscience learning and accessible to geoscienceeducators.

Spatial representations can include both physicaland mental representations, in which the position, shape,or orientation of objects represents meaning about theworld or one's view of the world. In this paper, we aremostly concerned with external spatial representations,which are tangible, material representations, as opposedto internal (i.e., mental or "in the mind") representations.We are concerned with static two-dimensionalrepresentations, conveyable on a piece of paper, asopposed to dynamic representations such as animations,or three-dimensional physical models. Finally, we areconcerned with representations in which the dimensionsof the representation correspond to spatial dimensions inthe real world, as opposed to representations that usespace metaphorically to convey nonspatial information(e.g., time, pressure, temperature, or stress).

The most common external, two-dimensional spatialrepresentations in the geosciences are maps, profiles,cross-sections, and block diagrams. More specializedspatial representations, such as the structural geologist'slower-hemisphere equal-area projections of beddingplains or foliation and the crystallographer's system ofMiller indices for describing crystal faces, are beyond thescope of this work. We focus on spatial representationsbecause (a) they are central to geoscience learning and (b)they have been sufficiently well studied that the findingsare robust enough to provide useable guidance forin-the-trenches geoscience educators.

An online version of some of this material has beenprovided in a self-study tutorial for college-levelgeoscience faculty (Kastens and Ishikawa, 2004). For abroader discussion of spatial thinking in the geosciences,see Kastens and Ishikawa (in press); for a yet broaderdiscussion of the relationship between the geosciencesand cognitive sciences, see Manduca et al. (2003).

ABOUT SPATIAL THINKING

Spatial ability has been studied extensively for over 100years. Researchers have shown that spatial ability formsits own category, separate, for instance, from verbalability, and that it consists of, or can be classified into,different types or subcategories. Eliot and Smith (1983)defined spatial ability as "the perception and retention ofvisual forms and the mental manipulation andreconstruction of visual shapes" (p. 9).

In the con text of geosciences, Kastens and Ishikawa(in press) de scribe spa tial think ing as (a) rec og niz ing, ob-serv ing, re cord ing, de scrib ing, clas si fy ing, re mem ber-ing, and com mu ni cat ing the two- or three-dimensionalshapes, struc tures, ori en ta tions, and po si tions of ob jects,prop er ties, or pro cesses; (b) men tally ma nip u lat ing thoseshapes, struc tures, ori en ta tions, and po si tions by ro ta-tion, trans la tion, de for ma tion, or par tial re moval; (c)

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Why Some Students Have Trouble with Maps and Other SpatialRepresentations

Toru Ishikawa Lamont-Doherty Earth Observatory, Columbia University, Palisades, NY 10964,ishikawa@ldeo.columbia.edu

Kim A. Kastens Lamont-Doherty Earth Observatory and Department of Earth and EnvironmentalSciences, Columbia University, Palisades, NY 10964,kastens@ldeo.columbia.edu

Ishikawa and Kastens - Why Students have Trouble with Maps 185

Figure 1. Examples of how cognitive scientists assess spatial abilities. (A) (Left) The psychologist's embeddedfigures test requires the participant to find a simple figure embedded within a complicated figure. (From Eliotand Smith, 1983, p. 409. Reproduced by permission of NFER-Nelson, The Chiswick Centre, 414 ChiswickHigh Rd., London W45TF.) (Right) The geoscientist exercises a similar skill when looking for significantshapes or patterns in a complex geologic map or in image data. (From Owen, Pirie, and Draper, 2001, EarthLab: Exploring the Earth Sciences, p. 323. Reproduced by permission of Brooks/Cole, a division of ThompsonLearning, Pacific Grove, CA.) (B) (Left) Psychologists use the water-level and plumb-line tasks to assesspeople's understanding of the horizontal and vertical. (After Vasta et al., 1996, p. 556. Reproduced bypermission of Blackwell Publishing, Oxford, UK.) (Right) Geologists record the orientation of a sloping planarsurface by measuring the strike and dip of the surface, relative to an imaginary horizontal plane and withinan imaginary vertical plane. (Photo by Kim Kastens. Figure from McGeary and Plummer, 1998, PhysicalGeology: Earth Revealed, 3rd ed., p. 130. Reproduced by permission of McGraw-Hill Companies, Inc.) (C) (Left)To examine learning of spatial layout in large-scale spaces, Ishikawa (2002) drove participants individually ontwo separate routes and a connecting route in an unfamiliar environment. He tracked how their knowledgeabout the routes developed over 10 weeks, by asking them to estimate distances and directions to unseenlandmarks. To do well on this task, participants need to understand the shapes of the routes accurately.(Right) Field-based learning of spatial layout is an aspect of fieldwork. (Photos by Kim Kastens.) (D) (Left)Piaget and Inhelder (1967) developed the three-mountain problem to examine children's ability to envision aspace from different viewpoints. (From Piaget and Inhelder, 1967, p. 211. Reproduced by permission ofNorton, New York.) (Right) Geologists do a similar task when envisioning how a 3-D data volume would look inprofile based on a map-view representation of the data. (From Tarbuck and Lutgens, 1994, Earth Science, 7thed., pp. 232 and 233. Pearson Education, Inc.)

mak ing in ter pre ta tions about why the ob jects, prop er-ties, or pro cesses have those par tic u lar shapes, struc-tures, ori en ta tions, and po si tions; (d) mak ing pre dic tionsabout the con se quences or im pli ca tions of the ob servedshapes, struc tures, ori en ta tions, and po si tions; and (e)us ing spa tial think ing as a short cut or met a phor to thinkabout the dis tri bu tion of pro cesses or prop er ties acrosssome di men sion other than length-space.

Basic Spatial Abilities and their Relationships toGeoscience Tasks

Recognizing patterns and shapes - The ability torecognize patterns and shapes in the background ofcomplex patterns or "noise" has been assessed by theembedded figures test. In this test, the participant isshown a simple figure and asked to find and trace thesimple figure hidden within a complex figure (Figure 1A,left). To successfully do this, the participant needs toretain an image of the simple figure in mind, and look forit by suppressing lines irrelevant to the task at hand.

This ability seems to be tapped when geologistsidentify patterns of significance in a geologic map, suchas anticlines and synclines (Figure 1A, right). Thegeologist's task differs from the embedded figures test inthat the geologist's pattern may be of various sizes andorientations, whereas the simple figures sought withinthe embedded figures test are always the same size andorientation as the example figure.

Recalling previously observed objects - The ability torecall an array of objects that was previously seen iscalled object location memory. To assess this ability, theparticipant studies an array of objects, and then is shownan altered array; the task is to identify which objects havebeen moved or replaced (Silverman and Eals, 1992).Interestingly, females do better on this task, on average,than males (in contrast to some other spatial tests thatfavor males, such as the mental rotations test). Someresearchers have interpreted this finding from anevolutionary perspective, noting that women in ancienthunter-gatherer societies needed to remember locationsof food and medicinal plants to harvest them when theyripened (McBurney et al., 1997). For the interestedreader, Tooby and Cosmides (1992) offer a discussion ofthe rationale for evolutionary psychology.

One telling anecdote is the exceptionally goodlocation memory attributed to William Smith, the makerof the world's first geologic map. His biographer wrotethat he remembered exact locations of fossils and wentdirect to recover them after many years had passed(Winchester, 2001, p. 270). Geoscientists who madelandmark syntheses of regional geology of large orcomplex areas (e.g., Dewey et al., 1973; Robertson andDixon, 1984) must draw upon a vast mental catalog ofgeological observations, referenced in space and time.

Understanding the vertical and horizontal frames ofreference - Piaget and Inhelder (1967) developed thewater-level task and plumb-line task to assess children'sunderstanding of the vertical and horizontal. Forchildren to achieve this understanding, they need toconceptualize the orthogonal axes fixed onto thesurrounding space. Piaget and Inhelder described thisunderstanding as one of the major Euclidean spatialconcepts, which emerge at a late stage in children'scognitive development. In the water-level task, theparticipant is shown a drawing of a bottle that contains

some water, and asked to draw a line to indicate thesurface of water when the bottle is tilted to variousdegrees (Figure 1B, upper left). In one version of theplumb-line task, the participant is shown a drawing of avan with a weight hanging from a rope inside; the task isto draw the rope and weight when the van is parked on ahill (Figure 1B, lower left). Researchers have found that asignificant portion of children, and even college students(particularly females), fail to draw the surface of water ashorizontal and the plumb-line as vertical when the wallsof the bottle or van are tilted (e.g., Liben, 1978; Thomas etal., 1973).

A central task of geologic mapping is to determinethe dip and strike of inclined rock surfaces (Figure 1B,right). To find the strike, the student must be able to findthe horizontal plane in spite of the distraction of inclinedsurfaces, a skill similar to that tested by the water-leveltask. To find the dip of the rock surface, the student mustbe able to find the vertical plane, a skill similar to thattested by the plumb-line task.

Field-based learning: Synthesizing separately madeobservations into an integrated whole - An importantspatial ability that seems to be different from thoseassessed by paper-and-pencil spatial tests is the ability tolearn spatial layout in large-scale spaces (Figure 1C, left).By "large-scale space," spatial cognition researchersmean a space that is larger than and surrounds thehuman body, and cannot be viewed in its entirety from asingle viewpoint (e.g., Ittelson, 1973); thus, tocomprehend the spatial layout, a person needs to movearound and integrate objects or scenes observedseparately into a common frame of reference. This"integration" has been found to be a sophisticated step inthe acquisition of spatial knowledge in a newenvironment: the resulting "maps in the head" tend to bedistorted, schematized, and fragmented (e.g., Golledge,1978; Ishikawa, 2002; Lynch, 1960).

Learning in the field (Figure 1C, right) plays anindispensable role in geoscience education (e.g.,Karabinos et al., 1992; Kern and Carpenter, 1986;Kirchner, 1997; McKenzie et al., 1986). The field geologistmust move through the field area, gathering informationfrom separately observed objects and views, andintegrate this information into a coherent mental imageof the field area's terrain, structures, and stratigraphy.

Mentally rotating an object and envisioning scenesfrom different viewpoints - The ability to mentallyrotate an object or image has been assessed by the mentalrotations test. In this test, the participant compares pairsof object drawings, and answers whether or not they arethe same object, merely rotated into differentorientations. Drawings may be of three-dimensionalobjects (e.g., Vandenberg and Kuse, 1978) ortwo-dimensional patterns (e.g., Cooper and Shepard,1973). A major finding about people's performance onthe mental rotations test is that people take longer as theangular difference in orientation between the twodrawings increases from 0° to 180°, suggesting thatpeople in fact mentally rotate the objects as if they wererotating physical objects in space (Shepard and Metzler,1971).

The ability to imagine and coordinate views fromdifferent perspectives has been identified by Piaget andInhelder (1967) as one of the major instances of projectivespatial concepts. To assess children's understanding ofthis concept, Piaget and Inhelder developed the

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Ishikawa and Kastens - Why Students have Trouble with Maps 187

Figure 2: Highlights of research findings on spatial abilities. (A) (Top) College students' scores on the mentalrotations test have large individual differences, ranging from near zero to near perfect. (Data from Hegarty etal., 2004.) (Bottom) On field-based learning, people's performance varies greatly. After traveling the twoseparate routes and the connecting route (see Figure 1C), participants in Ishikawa's (2002) study estimateddirections between landmarks on each route (U- and S-routes) and between landmarks on different routes(integrated routes). Participant #1 acquired a very accurate "cognitive map" of the two routes early on(absolute errors of 20° or below). Participant #8, in contrast, failed to acquire an accurate "configurational"knowledge of the routes even after repeated experience. (B) College students' scores on the mental rotationstest and a vocabulary test correlates only .01. You may encounter high-verbal but low-spatial students, andvice versa, in your class. (Data from Hegarty et al., 2004.) (C) On the mental rotations test, males do betterthan females on average. But the distributions of the two groups' scores overlap considerably, and thevariability within each sex is larger than the difference in the means for the two sexes. (Data from Hegarty etal., 2004.) (D) On the mental rotations test, people became faster by merely taking the same test twice.However, intensive training with feedback improved response times much more, as indicated by the decreasein the slope and the drop of the intercept. (After Kail and Park, 1990, p. 233. Reproduced by permission ofElsevier.)

three-mountain problem (Figure 1D, left). In one versionof this task, the participant views a physical model ofthree mountains that vary in size, color, and the shape ofan object located at the peak. The participant is thenshown a map of the three mountains, and asked toindicate from which side of the map he or she would seethe view just seen on the physical model. Youngchildren's responses to these perspective-takingproblems are tied to their own current perspectives.Gradually, over the course of cognitive development,they develop the ability to distinguish and coordinatemultiple viewpoints.

Either mental-rotation ability or perspective-takingability could be relevant to those geoscience tasks thatinvolve envisioning what a geologic structure or datavolume would look like if seen from another position(Figure 1D, right). For example, a field geologistobserving an outcrop of a structure might project his orher viewpoint to envision the view down the axis of aprominent fold. Alternatively, the person mightmentally rotate the outcrop and underlying structure toafford the desired view. Similarly, a seismologistworking with a plan-view map of earthquake locationsand depths could envision a profile view of the samedata either by projecting his or her viewpoint to the sideof the dataset or by mentally rotating the data volume90°.

In the cognitive science literature, the ability tomentally manipulate an object and the ability to imaginetaking different perspectives have been found to beseparate; in other words, they do not necessarily co-occurin the same individuals (e.g., Huttenlocher and Presson,1973, 1979; Kozhevnikov and Hegarty, 2001). Geologyinstructors may take advantage of this finding: a studentwho finds it difficult to envision scenes from differentperspectives may have more success if instructed tomentally rotate the outcrop or data volume.

Mentally manipulating a surface or volume - Theability to mentally manipulate a surface or volume hasbeen assessed by the paper folding test and the surfacedevelopment test. In the paper folding test, theparticipant is shown a piece of paper that is folded in acertain way and punched through the thickness of thepaper. The participant is then asked to choose, among aset of alternatives, the one that shows where the holeswould appear when the paper has been unfolded. In thesurface development test, the participant is shown a flatpiece of paper and a drawing of an object that can beformed by folding the flat paper along indicated lines.The participant is then asked to figure out which edges ofthe flat paper correspond to which edges of thefolded-paper object.

Structural geologists face a similar task when theyenvision the formative processes that could have causedthe observed geometry of folded and faulted strata. Inboth the psychometric tests and the structural geologist'stask, one must create some kind of "mental animation" inwhich an initially static surface is transformed intoanother configuration according to implicit rules ofdeformation (e.g., the paper may be folded but not cut;the rock body must conserve cross-sectional area).

Research Findings on Spatial Thinking and TheirImplications for Geoscience Learning and Education

Individual differences in spatial ability - Individualdifferences in performance on spatial tests can be quitelarge. For example, in Hegarty et al.'s (2004) study, 233people (most of college age) took the mental rotations

test. As shown in the top panel of Figure 2A, individualscores vary greatly from person to person, ranging fromnear zero (score of 5 out of 40 possible) to near perfect(score of 39), even though the group of participants wasfairly homogeneous in age and educational level.

People also differ greatly in their ability to learnspatial layout in large-scale spaces. Ishikawa (2002)drove 24 college students individually along twoseparate routes and a route that connected the two routes(Figure 1C, left). He examined how the participants'knowledge about the routes developed over 10 sessions,based on their distance and direction estimates andhand-drawn sketch maps. The levels of theirunderstanding of the shapes of the two individual routesand the integrated routes varied greatly from person toperson. The bottom panels of Figure 2A show two peopleat the extremes, with respect to absolute errors ofdirection estimates. Participant #1 acquired a veryaccurate "cognitive map" of the routes early on in a newenvironment; in contrast, Participant #8 failed to acquirean accurate configurational knowledge of the routeseven after 10 weeks of trying.

Educational implication - Instructors should expectlarge individual differences in students' performance onspatially demanding tasks, whether in the lab or in thefield.

Spatial versus verbal ability - Spatial ability correlatesweakly with verbal ability. In the Hegarty et al. (2004)study, the participants took the mental rotations test anda vocabulary test. As shown in Figure 2B, the scores onthe two tests correlated only .01. That is, high-verbalstudents do not necessarily do well on spatial tasks, andvice versa, at least within the college-level population.

Educational implication - You may encounter studentswho are accustomed to doing well on school tasks, whichtend to be verbal in nature, but struggle on spatiallydemanding assignments. Conversely, you may findstudents who usually do poorly on traditionalassignments, but excel on map and spatial assignments.

Sex-related differences in spatial ability - Sex-relateddifferences are among the most frequently discussedissues concerning spatial ability. On some spatial tests, ithas been documented that males do better than females(see Linn and Petersen, 1985; Voyer et al., 1995). Themental rotations test is one of the tests that show robustmale-female differences in performance; for example,Vandenberg and Kuse (1978) reported male superiorityacross a wide range of ages.

Having said that, however, we point out that there isa large overlap between the distributions of male andfemale scores even on the most male-favored spatialtests. In the Hegarty et al. (2004) study, there was asignificant difference in the mean performance for malesand females on the mental rotations test: on average,males (n = 90, mean score = 22.5) did better than females(n = 143, mean score = 17.6), t(231) = 5.72, p < .001. But, ascan be seen in Figure 2C, the variability within each sex islarge, compared to the difference in the means for thetwo sexes. Stated differently, the fact that males do betterthan females on average does not mean that every malescores higher than every female on the test.

Educational implication - Be sensitive to the possibilitythat female students in your class may need morepractice or instruction on spatially demanding tasks. Atthe same time, however, you should not pre-judge the

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Ishikawa and Kastens - Why Students have Trouble with Maps 189

Figure 3: Research findings about map use in a real-world setting. (A) Liben et al. (2002) led college studentsto various locations on their own campus, and asked them to indicate their positions by placing stickers on acampus map. As shown by the scattered sticker locations, many students found the task difficult, and somestudents made dramatic errors. (From Liben et al., 2002, p. 277. Reproduced by permission of Elsevier.) (B)When asked to show the location of a flag on a building by placing a sticker on a map, many fourth gradersplaced stickers on a grass area, not on a building. In contrast, the few errors made by college studentsinvolved stickers placed on a wrong building. This indicates that many children lacked the understanding ofrepresentational correspondence between a building in the real space and a map symbol for a building, butcollege students generally achieved that level of understanding. (From Kastens and Liben, unpublished data.)(C) In this data set, some students understood the correspondence between a building in the real space and amap symbol for a building (representational correspondence), but failed to distinguish different buildingsshown on the map (configurational correspondence). (From Kastens and Liben, unpublished data.) (D)Directional correspondence requires matching azimuths on a map and azimuths in the real space. When amap is not aligned with the real space, many people have trouble identifying positions and directions on themap. (From Liben and Downs, 1993, p. 746. Reproducd by permission of the American PsychologicalAssociation.)

performance of individual students based on whetherthey are male or female. Some men will struggle; somewomen will excel.

Effectiveness of training on performance on spatialtasks - Given that some people have difficulty withspatial tasks, educators wish to know whether suchspatial skills can be improved by training or instruction.The answer seems to be generally positive. For example,Kail and Park (1990) had 16 adults take a mental rotationstest using alphabetical letters as the rotated symbols.Half the participants received training on the task andthe other half did not. The training consisted of hundredsof trials with feedback on correctness. During thetraining, participants received a monetary reward if theiraverage response time improved without a drop inaccuracy. As shown in Figure 2D, the group withouttraining improved on their second try at the task, but thegroup who received training improved much more.They improved on (a) the speed of mentally rotating theletters, as indicated by the decrease in the slope; and (b)the speed of encoding the stimuli, as indicated by thedrop of the intercept.

As to whether participants can transferimprovement gained through training on a specific taskto another related but different task, mixed results havebeen reported. Vasta et al. (1996) found that studentswho received training on the water-level task showedimprovement on that task, but their performance on therelated plumb-line task did not improve after thewater-level training. On the other hand, Kyllonen et al.(1984) found that students who received training on thepaper folding test showed improvement both on that testand on the related surface development test.

Educational implication - Please do not give up.Low-spatial students in your class can learn spatiallydemanding skills, with sufficient appropriate trainingand practice.

Re la tion ship be tween spa tial abil ity and in struc-tional meth ods - Kyllonen et al. (1984) trained 14high-spatial/high-verbal and 14 low-spatial/high-ver-bal sec ond ary school stu dents on the pa per fold ing test,by one of three meth ods. One method is vi sual train ing,in which par tic i pants viewed a si lent film dem on strat ingthe pro cesses of fold ing, punch ing, and un fold ing pa per.An other method is vi sual plus ver bal train ing, in whichpar tic i pants viewed the same film ac com pa nied by ver -bal ized strat e gies. A third method is self-guided prac ticewith feed back on cor rect ness. The re sults, among oth ers,showed that high-spatial stu dents im proved mostthrough self-guided prac tice and feed back. Low-spatialstu dents im proved more with spe cific strat egy train ing,ei ther vi sual or vi sual plus ver bal, than with self-guidedprac tice and feed back.

Educational implication - Different students may learnbest from different training methods, depending on theirspatial ability. It may be necessary for you to tailor theinstructional methods to different abilities of yourstudents.

USING MAPS IN THE REAL WORLD

Liben (1997) has emphasized the distinction between (a)map tasks that require making correspondences betweenobjects in the represented space and symbols on the mapwhile the participant is situated within the represented

space, and (b) map tasks that can be performed entirelywithin the context of the map without referring to therepresented space in the real world. The findings ofstudies in which participants use maps in the real worldare pertinent to the teaching of all field sciences,including field geology, ecology, and environmentalscience. We focus here on a common road-map-typerepresentation that people often use in their daily lives;topographic maps are considered separately below.

Understanding Where You Are Relative to a Map

Research findings have shown that many adults havedifficulty with the common task of locating themselveson a map. Liben et al. (2002) led college students to aseries of positions on their own campus. At eachposition, students were asked to place a sticker on a mapof the campus to indicate where they thought they werestanding (Figure 3A). As shown by the scattered stickerlocations, many students found this seeminglystraightforward task difficult, and some students madedramatic errors.

Rep re sen ta tional cor re spon dence - Liben and Downs(1993) have pointed out that to lo cate one self on a map,one needs to un der stand the re la tion ship among the self,the map, and the rep re sented space. The un der stand ingof the re la tion ship be tween the map and the rep re sentedspace re quires the idea that a sym bol on a map stands forsome thing in the real world, and the abil ity to matchsym bols on the map with ob jects in the real world. Libenand Downs called this “rep re sen ta tional cor re spon-dence.” Young chil dren of ten make er rors at the level ofrep re sen ta tional cor re spon dence, whereas such mis takesare rare for col lege stu dents. For ex am ple, Liben andDowns (1989) re ported that when they showed chil drenan or di nary road map and asked them to de scribe it, onechild picked out a river as a road but re jected road sym -bols as roads, say ing that only the for mer was wideenough for cars to go on (p. 184).

Kastens and Liben (un pub lished data) asked fourthgrad ers and col lege stu dents to find flags of dif fer ent col-ors lo cated on cam pus, and then to show the lo ca tions ofthe flags by plac ing col ored stick ers on a cam pus map.Fig ure 3B shows their re sponses for a flag lo cated on abuild ing. Many chil dren's er rors show the lack of un der-stand ing of rep re sen ta tional cor re spon dence: stick ers areplaced on a grass area or a path way rather than a build -ing. In con trast, col lege stu dents' er rors (not many in thisex am ple) are seen as a sticker placed on a wrong build -ing, in di cat ing that they at least have an ac cu rate un der-stand ing of rep re sen ta tional cor re spon dence ("build ing"cor re sponds to "black-filled poly gon").

Educational implication - Children need instruction thatwill foster understanding of representationalcorrespondence, whereas college students usually do nothave a problem with that level of understanding.

Configurational correspondence - Complete masteryof the relationship between the map and the representedspace requires understanding that the internalrelationships among features on the map are consistentwith the internal relationships among correspondingfeatures in the real world, and the ability to use theseinternal relationships to distinguish among multipleoccurrences of the same map symbol. We call this“configurational correspondence.” In the Kastens andLiben data, errors made by college students are seen as

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stickers placed on wrong buildings or on the wrong partof the correct building (Figure 3C). These students havean understanding of representational correspondence,but failed to distinguish between different buildings orparts of buildings on the map (i.e., they lackunderstanding of configurational correspondence).

Educational implication - Students may appear to havemastered map use when a problem can be solvedthrough representational correspondence, but until youassess their competence in tasks requiringconfigurational correspondence, you cannot be sure thatthey have fully mastered map use.

Directional correspondence - In addition tounderstanding the internal relationships among featureson the map and in the real world, map use in the realworld requires people to align, physically or mentally,azimuths on the map with azimuths in the real world.We call this “directional correspondence.” Liben andDowns (1993) asked children to place arrow stickers on amap of their classroom to indicate where anexperimenter was standing and which direction he wasfacing. When the map and the classroom were aligned,the children placed arrow stickers correctly overall; butwhen the map was rotated 180° relative to the classroom,many children placed arrow stickers diagonally oppositeto the correct position and direction (Figure 3D).

This "map alignment effect" has also beendocumented with respect to "you-are-here" maps inpublic spaces. When the posted map is not in alignmentwith the surrounding space, people often go in thewrong direction, by erroneously thinking that theupward direction on the map corresponds to the forwarddirection in the space (e.g., Levine et al., 1984).

Educational implication - Some of your students mayfind it difficult to mentally rotate a map into alignmentwith the surroundings. It may help such students if youencourage them to physically rotate the map.

Perspective taking - The ability to envision views fromdifferent positions has been identified as one of theimportant components of spatial abilities (see Piaget'sthree-mountain problem above). This ability seems to berelated to map use in the real world, since one effectivemap-reading strategy for locating oneself on a mapinvolves (a) looking at the map and making asupposition about where you might be, (b) envisioningwhat you would see from that perspective, and (c)comparing the imagined view with what you see in thereal world. In fact, Liben and Downs (1993) found thatstudents who were poor at perspective taking tended tomake errors in identifying on a map the position andfacing direction of a person standing in the classroom.

Educational implication - Some of your students maynot good at perspective taking. It may help such students if you explicitly model the process of imagining viewsfrom different positions on a map.

TOPOGRAPHIC MAPS

On a topographic map, features of the landscape aredepicted by contour lines that connect points of equalelevation. From such a symbolic two-dimensionalrepresentation, people need to envision in threedimensions what the real terrain looks like. Conversely,from the real terrain, people need to envisionappropriate topographic contours.

How Do Cog ni tive Sci en tists Study Peo ple's Un der-stand ing of Top o graphic Maps?

Top o graphic-map read ing is one of the few top ics in atyp i cal geoscience cur ric u lum that has been ex plic itly re-searched from a cog ni tive per spec tive. The tech niquesthat cog ni tive sci en tists have used to ex am ine peo ple'sun der stand ing of top o graphic maps may re sem ble testques tions from a geoscience course, but the ma jor ob jec-tive of cog ni tive sci en tists us ing those tech niques is to re-veal men tal pro cesses un der ly ing top o graphic-mapread ing, rather than to as sess whether stu dents can givea cor rect an swer.

Answering questions about a terrain by referring to amap - Potash et al. (1978) developed a set of tasks inwhich participants answer questions about a terrain byreferring to a topographic map. For example, given atopographic map, participants are asked to indicatewhether lines shown on the map run along a ridge or avalley. Other examples of such tasks are (a) to estimatethe height of a terrain marked on a map, (b) to judgewhich direction a river would flow, (c) to indicate theshortest route between two points on a map withoutgoing below a certain height, (d) to judge whether aperson standing at a specific point would be visible fromanother point on a map, and (e) to mark the highest andlowest points on a map.

Comparing a map with another representation - Asecond set of Potash et al.'s (1978) tasks has participantscompare a map with another kind of spatialrepresentation, such as a sketch or a photograph. Forexample, participants are asked to choose amongsketches of landscapes the one that they would see if theywere standing at an arrow shown on a topographic map.Other examples of such tasks are (a) to identifytopographic profiles that coincide with line segmentsshown on a map, and (b) to identify the position andviewing direction on a map from which a given viewshown as a photograph would be seen.

Comparing a map with the represented space - Pick etal. (1995) examined how experienced topographic-mapusers located themselves in the field (Figure 4A).Experienced map readers were taken to an unfamiliarfield area of rolling hills in central Minnesota, and givena topographic map of the area from which allnontopographic information had been deleted; theywere then asked to determine the position on the mapthat they thought corresponded to the location wherethey were standing. They were asked to "think aloud"and videotaped while solving this"drop-off-localization" problem. By analyzing theparticipants' verbal protocols, Pick et al. identified thetypes of information on the map or in the field that theseexperienced map readers attended to: (a) features such ashills, valleys, ridges, slopes, and flat areas; (b) attributesof individual features such as large/small,narrow/wide, and steep/shallow; and (c) relations orconfigurations among features expressed as "in front of,""behind," "next to," and so on.

Findings and Implications of CognitiveStudies of Topographic-Map Use

Misconceptions and difficulties - Clark et al. (2004) hadnonscience-major students do topographic-map taskssimilar to those developed by Potash et al. (1978). They

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Figure 4: Research findings about understanding and use of topographic maps. (A) When taken to an unknown fieldarea and asked to locate themselves on a topographic map, experienced map readers focused on features in theterrain and tried to describe the attributes of individual features and their relationships. (From Pick et al., 1995, pp.261 and 263. Reproduced by permission of the Lawrence Erlbaum Associates, Inc.) (B) Even experienced mapreaders found the "drop-off-localization" task very difficult. Those who succeeded in identifying their positions onthe topographic map used specific strategies, such as generating multiple hypotheses about the viewpoint andevaluating them by disconfirmation. (After Pick et al., 1995, p. 265. Reproduced by permission of the LawrenceErlbaum Associates, Inc.) (C) Experienced map users identified and focused on only the information on a map that isnecessary for a task at hand. Adding redundant information to the map did not affect study time or judgment timeany further in a terrain visualization task. (Data and figures from Eley, 1991, pp. 408-411. Reproduced bypermission of John Wiley & Sons, Lmtd.) (D) Students who were skilled at topographic-map reading had bettermemory for topographic maps than students who were not, but the two groups of students did not differ in memoryfor ordinary town maps. High-skill students tended to organize information on the topographic map using"specialist schemata," whereas low-skill students used only "lay schemata." (Topographic map U.S. GeologicalSurvey. Town map from Thorndyke and Stasz, 1980, "Individual Differences in Procedures for KnowledgeAcquisition from Maps," Cognitive Psychology, 12, p. 141. Reproduced by permission of Elsevier.)

found (a) that one of the major misconceptions abouttopographic maps was that "tightly spaced contour linesrepresent higher elevation," and (b) that some studentshad difficulty visualizing a terrain from a directiondifferent than the one in which they viewed the map.They also found that through instruction, some of themisconceptions disappeared and the students had moreconfidence in reading topographic maps.

Strat egies used by suc cess ful, ex pe ri enced mapread ers - The par tic i pants in the Pick et al. (1995) studyof the drop-off-localization task had con sid er able trou-ble: only 7 out of 29 par tic i pants cor rectly iden ti fied thepo si tion on the top o graphic map. Pick et al. iden ti fiedstrat e gies that the suc cess ful map read ers used: (a) togen er ate and eval u ate mul ti ple hy poth e ses about theview point; (b) to try to disconfirm, rather than con firm,hy poth e ses gen er ated about the view point; (c) to changeone's view point by mov ing around in the field; (d) to payat ten tion to lo cal ter rain fea tures near the view point; (e)to or ga nize fea tures into con fig u ra tions, rather than fo-cus on in di vid ual fea tures sep a rately; and (f) to con cen-trate on and rec og nize fea tures in the field rather than onthe map first (Fig ure 4B).

Ed u ca tional im pli ca tion - Stu dents in yourfield-geology course may find it dif fi cult to po si tionthem selves us ing a top o graphic map. The strat e gies de -scribed above may help such trou bled stu dents lo catethem selves and iden tify fea tures in the field area.

Selective encoding - Eley (1991) gave orienteeringenthusiasts either a complicated or a simple topographicmap of a terrain, and asked them to study the map untilthey felt that they knew the map (Figure 4C). Complexityof the map was varied by the density of contour lines(dense vs. sparse) and whether or not watercourses wereshown on the map. The participants were then shown aland-surface drawing and asked to judge whether it wasthe same terrain as the map depicted. The time theseexperienced map readers took to respond was longest forthe least detailed map (the map with sparse contours andno watercourses), and became shorter as moreinformation was shown on the map (either densecontours and no watercourses, or sparse contours andwatercourses). However, adding redundant information (dense contours plus watercourses) did not improve thespeed of judgment any further.

Educational implication - Expert topographic-mapreaders attend only to details needed for a task at hand,ignoring redundant or extraneous information.Encourage your students to identify which subset of theinformation shown on the map is necessary for the taskand then focus on that subset.

Effects of schemata - Gilhooly et al. (1988) gaveundergraduate students a screening test for anunderstanding of topographic maps, and classified theminto two groups (high skill vs. low skill). These twogroups of students viewed ordinary town maps andtopographic maps, and then took a memory test aboutthe maps, by answering multiple-choice questions andsketching the maps from memory (Figure 4D).

High-skill students remembered the topographicmaps better than low-skill students, whereas high- andlow-skill students remembered the town maps equallywell. In their analysis of the students' think-aloud

processes while learning the maps, Gilhooly et al.stressed that high-skill students used "specialistschemata" such as interlocking spurs, as well as "layschemata" such as hills, rivers, and valleys. In contrast,low-skill students used only lay schamata. Cognitivescientists use the term "schema" (plural "schemata") toindicate a general knowledge structure that is composedof various relations, events, agents, actions, and so on.People apply a schema to a specific situation to guidetheir behavior and understanding. High-skill studentspossessed a rich and detailed knowledge base aboutgeomorphology and applied it to the topography-relatedlearning.

Educational implication - Efficient topographic-mapreading requires the ability to recognize significant ormeaningful chunks of information among the profusionof detail on the map. You can help your students developsuch "specialist schemata," by teaching a workingvocabulary of geomorphological terms and concepts, asthey work with topographic data.

3-D PHENOMENA

Geoscientists commonly envision a structure or object inthree dimensions, and then hypothesize about itsformative processes. The amount of observableinformation may be small compared to the hidden,unobserved part. For example, structural geologistsmake observations at scattered rock outcrops andcombine them to envision a mostly buried rock structure,or marine geophysicists make observations along a gridof seismic profiles and combine them to envision thesubseafloor stratigraphy.

Visualizing Internal Structures in 3D from 2D

Difficulty of the task for novices - Kali and Orion(1996) developed an assessment of students' ability tocomprehend geologic structures, called GeoSAT. Tenthgraders were shown drawings of block diagrams of ageologic structure, and asked to imagine the hidden,internal structure. For example, by examining the blockdiagram shown in Figure 5A, students were asked toconstruct a vertical cross-section along A-B. Kali andOrion reported that only 7 out of 101 students gavecorrect answers to four out of four problems of this type.

Educational implication - Keep in mind that the skill ofenvisioning hidden, internal structures from partialobservations is very difficult for novice learners.

Types of errors: non-penetrative vs. Penetrative - Bylooking at students' responses to the cross-sectionproblems discussed above, Kali and Orion (1996)identified two major types of errors: non-penetrative andpenetrative errors. In the non-penetrative type of error,students' responses are entirely based on externalinformation exposed on the visible surfaces of the cube.For example, in the first panel of Figure 5A, the studentscopied the external pattern on one of the faces orunfolded the pattern on two faces. In the penetrative typeof error, students' responses are not correct but somehowindicate an attempt to infer internal structures of theblock diagram. For example, in the second panel ofFigure 5A, one student vertically continued the patternon the top face down into the block and then horizontallycontinued the pattern on the side face laterally into the

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Figure 5: Research findings about 2-D representations of 3-D structures. (A) Kali and Orion (1996) askednovice geoscience learners to visualize hidden, internal structures in a geologic block diagram and show theirunderstanding by drawing a vertical cross-section along A-B. They found two types of errors. Non-penetrativeerrors are based on external information visible on the faces of the cube. Penetrative errors show an attemptto infer internal structures from observable information. Students who made errors tended to show one typeof error consistently. Non-penetrative errors were predictive of poor performance on other geospatial tasks.(After Kali and Orion, 1996, pp. 376-378. Reproduced by permission of Wiley-Liss, Inc., a subsidiary of JohnWiley & Sons, Inc.) (B) Mayer et al. (2002) examined the effectiveness of two training methods for the task ofenvisioning geologic features from profiles. Showing labeled sketches of possible geologic structuresfacilitated students' performance on the task, whereas delineation of step-by-step strategies similar to thoseused by professional marine geologists did not. (From Mayer et al., 2002, pp. 172 and 174. Reproduced bypermission of theAmerican Psychological Association. Screen shot from Prothero, 2001.)

block. Kali and Orion found that most of the studentswho erred on the cross-section problems consistentlymade either non-penetrative or penetrative errors.Non-penetrative errors on the cross-section problemspredicted poor performance on a range of other spatiallydemanding geoscience tasks.

Educational implication - You should be alert fornon-penetrative type of errors in your students' work.Such students may well have trouble with other spatialtasks in geoscience.

Training on a 3-D Task

Different approaches: pictorial vs. strategic - Mayeret al. (2002) studied the effectiveness of training on thetask of identifying geologic structures from profiles,using the multimedia simulation Geology Profile Game(Prothero, 2001). Students in an introductory psychologyclass were told, "You are a geologist looking down ontoan area of land or ocean, which is hidden from view. Youneed to find out which one of these geologicalfeatures-island, ridge, trench, basin, or seamount-ishidden below you." Then the definitions of the fivegeologic features were given. For this Profile Game task,Mayer et al. examined two different training approaches,called pictorial scaffolding and strategic scaffolding(Figure 5B).

In pictorial training, students were shown labeledsketches of all the possible geologic features before theybegan the task. The pictorial-training group solvedsignificantly more problems correctly (mean = 3.3 out of5) than did a control group who received no training(mean = 2.4). Mayer et al. attributed the effectiveness ofpictorial training to the largely visual nature of the task.

In strategic training, students were given an explicitstep-by-step strategy for positioning their profiles tomethodically narrow down the range of possiblegeologic features: draw a few profile lines, look for achange in elevation in any profile, see if the profile is flator has a drop in elevation, and so on. This strategyresembles the traditional way in which marine geologistsmap an unknown feature on the seafloor by using anecho-sounder. The number of problems correctlyanswered by the strategic-training group (mean = 2.9)was not significantly different from that of the controlgroup (mean = 2.4).

Educational implication - Merely articulating anddemonstrating a strategy used by professionalgeoscientists to solve a three-dimensional problem maynot be an effective training method for novice geosciencelearners.

Interactive computer materials - Reynolds et al. (2002)designed two interactive computer modules, called thetopographic module and the block diagram module, toincrease spatial-visualization skills of students in anundergraduate geology class. The modules cover realgeologists' tasks of using topographic maps anddetermining geologic structures. In the topographicmodule, students had access to animations in which theycould control shading, rotate landscape from top to sideview, raise and lower water levels, and slice into terrains.In the block diagram module, which dealt with faults,intrusions, and unconformities, students had access toanimations in which they could rotate block diagrams,change transparency of the blocks, offset faults, erodesurfaces, and so on.

In Piburn et al.'s (2002) study, two groups of studentstook an introductory geology course with differentmethods of instruction: one group of students used thetwo computer modules described above duringlaboratory sections; the other group was in a traditionallaboratory section. Piburn et al. compared the twogroup's performance on a 30-item multiple-choice testbefore and after the course; the test was about contentfrom the laboratory sections that was judged to be spatialin nature. They found that the computer-module groupimproved significantly more between a pretest and aposttest than did the control group. Also, they comparedthese participants' scores on the surface developmenttest before and after the experiment. Thecomputer-module group's scores improved on theposttest, but the control group's did not.

Educational implication - Interactive computermaterials seem to be a promising tool for developingeffective educational approaches to difficult spatial tasksin geology. Also, mastery of spatially demandinggeologic tasks may help improve students' spatial skillsoutside of geology.

CONCLUDING REMARKS

The data discussed in this paper were taken fromscientific studies of human cognition and learning, butare only a subset of the results presented in those studies.We focused on the results that we think are mostimportant and relevant to geoscience education, but theinterested reader can learn much more from the originalstudies listed in the reference section.

In surveying the state of knowledge of cognitive andlearning sciences as it pertains to spatial thinking in thegeosciences, we have found much that resonates with theintuition of experienced geoscience educators: Peoplevary widely in their ability at spatial tasks. People whoare usually good at verbal schoolwork may struggle withspatial tasks, and vice versa. Different people mayrespond better to different strategies for mastering thesame task. Locating themselves on a map and visualizingthe hidden, internal portions of three-dimensionalstructures are difficult for novice learners.

In addition to confirming these intuitions, thissurvey has found two kinds of new insights thatcognitive and learning sciences can bring to bear ongeoscience education. A first kind of insight is to breakdown complex spatial tasks into "constituentunderstandings" or "constituent strategies." Experiencedgeoscientists, especially those who have high spatialability, tend to leap across such tasks in a single bound,and may be at a loss to articulate how they did what theydid. An example of constituent understandings is therealization that sophisticated map use in the real worldrequires mastery of representational correspondence,configurational correspondence, and directionalcorrespondence between the map and the representedspace. An example of constituent strategies is Pick et al.'s(1995) finding that successful topographic-map usersemploy a consistent set of strategies in locatingthemselves on the map, such as generating andevaluating multiple hypotheses about the viewpoint,and attempting to disconfirm rather than confirm thehypotheses. This knowledge of constituentunderstandings and strategies enables geoscienceeducators to design instructional interventions to fosterspecific understandings, or to practice specific strategiesfor mastering a complex spatial task.

Ishikawa and Kastens - Why Students have Trouble with Maps 195

A second kind of insight that cognitive and learningsciences can bring to bear on geoscience education is aidin diagnosing specific problems. Kali and Orion's (1996)classification of students' errors on block diagrams intonon-penetrative and penetrative errors strikes us as auseful starting point for designing differentinterventions for the populations of students who areprone to the two different types of errors.

To the ques tion prob a bly up per most in the minds ofmany geoscience ed u ca tors-"What can I do to help thoseof my stu dents who strug gle with spa tial skills?"-an-swers re main sparse. We know that per for mance on spe -cific spa tial tasks can be im proved by ex ten sive prac ticewith feed back and mo ti va tion, as in Kail and Park's(1990) hun dreds of tri als on the men tal ro ta tions test, butim prove ments through this sort of train ing will not nec -es sar ily trans fer well, even to closely re lated tasks. Weknow that merely ar tic u lat ing and mod el ing the strat e-gies used by pro fes sion als will not nec es sar ily work fornov ices (e.g., Mayer et al., 2002). We know thathigh-spatial and low-spatial stu dents may re spond bestto dif fer ent strat egy-training meth ods (e.g., Kyllonen etal., 1984), but we do not know enough to be able to op ti-mize in struc tional ap proaches to tar get low-spatial stu-dents.

We hope that this paper serves as an entrée point forgeoscience educators into the field of cognitive research,and for cognitive and learning scientists into the field ofgeosciences. We believe that unearthing deeper answersto the question "What can I do to help those of mystudents who struggle with spatial skills?" can best beachieved by collaboration between these fields.

ACKNOWLEDGMENTS

This material is based on work supported by theNational Science Foundation under Grant No. GEO01-22001. Any opinions, findings and conclusions orrecommendations expressed in this material are those ofthe authors and do not necessarily reflect the views of theNational Science Foundation. We thank MaureenAnders for the illustrations, and for the design of theonline version of this material. We are grateful toDanielle Kaplan and Lynn Liben for their valuablecomments on an earlier draft of the online tutorial, and toMichael Piburn and Dexter Perkins for their reviews ofthis manuscript. This is Lamont-Doherty EarthObservatory contribution number 6730.

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