Predicting environmental learning from spatial abilities: An indirect route

INTELLIGENCE22, 327-355(1996)

Predicting Environmental Learning From Spatial Abilities: An Indirect Route GARY L. ALLEN KATHLEEN C. KIRASIC SHANNON H. DOBSON University of South Carolina RICHARD G. LONG SHARON BECK Atlanta VA Rehabilitation

Research and Development

Center

Relationships among spatial abilities, as assessed by a battery of psychometric tests and experimental tasks, and environmental learning, as assessed by a series of macrospatial tasks, were examined in two studies using confirmatory factor analysis with directional paths. The initial study indicated the utility of a five-factor model, one (general spatial ability) derived from psychometric tests, two (spatial-sequential memory and spatial perspective-taking latency) from experimental tasks, and two (topological knowledge and Euclidean direction knowledge) from measures of environmental learning. The best fitting path model further indicated that the spatial-sequential memory factor mediated the relationship between general spatial ability and topological knowledge, and that perspectivetaking latency mediated the relationship between general spatial ability and Euclidean direction knowledge. The second study confirmed the five-factor path model using a different participant sample and environmental setting. The only failure to replicate involved the path between perspective-taking latency in the lab and Euclidean direction knowledge in the environment. Results indicate that the relationship between basic spatial abilities and environmental learning is significantly mediated by cognitive processes that can be assessed using laboratory tasks.

The past 15 years have seen a dramatic increase in our understanding of human spatial cognition. Much of this new understanding has resulted from psychometric and information-processing research focused on spatial ability, defined as the ability to generate, retain, and transform abstract visual images (Lohman, 1979). This research has led to an improved understanding of spatial factors traditionally identified in psychometric research (Egan, 1979; Lohman, 1979; Lorenz & Neisser, 1986; McGee, 1979), new insight into the relationships The authors acknowledge with gratitude the financial support from a VA-DOD Collaboration Grant (D525-R) to Richard Long, the assistance of Phoebe McLeod with data collection, the advice of Doug Wedell concerning data analysis, and the comments of John Rieser regarding the findings. Correspondence and requests for reprints should be sent to Gary L. Allen, Department of Psychology, University of South Carolina, Columbia, SC 29208. E-mail: . 327

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among traditionally identified factors (Pellegrino, Alderton, & Shute, 1984; Pellegrino & Kail, 1982), examination of the information-processing characteristics that differentiate individuals with high and low spatial ability (Just & Carpenter, 1985; Kyllonen, Lohman, & Snow, 1984; Mumaw & Pellegrino, 1984), and the discovery of a dynamic variety of spatial ability involving movement in the visual field as opposed to static images (Hunt, Pellegrino, Frick, Farr, & Alderton, 1988). Quite separately, significant advances have been made in the study of environmental learning, referring to the acquisition of information about the spatial attributes of physical environments. Evidence supports a distinction between different types of environmental knowledge, including landmark knowledge, route knowledge, and survey (or configurational) knowledge (Byrne, 1979; Lorenz & Neisser, 1986; Siegel, Kirasic, & Kail, 1978). However, disagreement continues between perceptual learning theorists and constructivist-representational theorists concerning the acquisition process itself (Heft, 1983; Rieser, 1989; Spencer, Blades, & Morsley, 1989). Much of the recent work on environmental learning has focused on the means by which spatial knowledge is acquired in the absence of vision (see Loomis et al., 1993). Another issue of interest has been the acquisition of environmental knowledge through symbolic means, such as prose comprehension (Taylor & Tversky, 1992) and map interpretation (Presson, DeLange, & Hazelrigg, 1989). Despite noteworthy progress in each of the two separate research areas, efforts to establish an empirical link between spatial abilities, as assessed by psychometric tests, and environmental learning, as assessed by experimental tasks, have been few in number and generally inconclusive. For example, performance on wayfinding and orientation tasks has been found to be related to measures of visual memory ability (Berry, 1966; Kirasic, 1991; Thomdyke & Hayes-Roth, 1982) and field dependence and field independence (Berry, 1966; Thomdyke & Hayes-Roth, 1982). Although the number of participants in these studies was small, the remarkable diversity of the populations-Canadian Inuits and African Temne tribe members in Berry’s (1966) cross-cultural study, young and elderly adults in Kirasic’s (1991) study, and young adults in Thomdyke and HayesRoth’s (1982) study-draws attention to the findings. Nevertheless, there is a notable absence of studies reporting significant relationships between environmental wayfinding and orientation tasks and the abilities most frequently cited as spatial (i.e., visualization and spatial relations). This lack of direct links between spatial ability measures and measures of environmental learning is illustrated clearly by the results of Lorenz and Neisser (1986), who administered an extensive battery of environmental wayfinding and orientation tasks along with a series of spatial ability tests, which according to previous research should assess visualization and spatial relations abilities, to a sample of 76 individuals. Exploratory factor analysis revealed three distinct facets of environmental knowledge (specifically, landmark knowledge, route knowledge, and awareness of geographic directions) and a single spatial ability factor.

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Pointedly, all three facets of environmental knowledge were essentially independent of psychometrically assessed spatial ability (Lorenz & Neisser, 1986). The absence of direct links, however, does not preclude the possibility of a mediated relationship. Certain cognitive skills examined predominantly in the context of experimental studies are attractive as potential mediators. Spatialsequential memory as exemplified in small-scale visually based maze learning is an excellent example. On the one hand, memory for a sequence of moves through a visually experienced two-dimensional maze should have a logical relationship to basic abilities such as spatial relations and, more certainly, visual memory. On the other hand, such memory has been posited as the basic mechanism in route learning (Siegel & White, 1975). Accordingly, it is reasonable to examine the possibility that spatial-sequential memory mediates the relationship between basic spatial ability and certain aspects of environmental learning. Another potential mediator is spatial perspective-taking skill. The ability to determine how an array of objects would appear from a perspective other than the one immediately perceived bears at least an informal similarity to visualization or spatial relations ability. More importantly, research by Olson and Bialystok (1983) indicates that the crucial cognitive operations required in performing perspective-taking, mental rotation, and oblique discrimination tasks are formally the same. From an environmental learning perspective, there is some evidence indicating that perspective-taking skill as assessed in an experimental setting using a model town is related to knowledge and use of goods and services in an actual urban environment (Walsh, Krauss, & Regnier, 1981). Again, it is reasonable to examine the possibility that this skill mediates the relationship between basic spatial ability and certain aspects of spatial learning. To test these reasonable possibilities as experimental hypotheses, an unusual research strategy was employed in which identical batteries of spatial ability tests, experimental tasks, and environmental learning tasks were administered to two separate samples in different environmental settings. After data collection and initial scoring of the data, one setting was randomly selected to serve as Experiment 1. Exploratory factor analysis was used to provide a preliminary view of the appropriate number of factors necessary to represent the data set, and confirmatory factor analysis with path models was used to test the hypothesis that spatial-sequential memory and spatial perspective-taking skill mediate the relationship between basic spatial ability and environmental learning outcomes. Regardless of whether this hypothesis was confirmed, the research strategy called for using the best fitting model from Experiment 1 as the hypothesis for Experiment 2, which involved data from the other environmental setting. EXPERIMENT

1

In testing the hypothesis that spatial-sequential memory and spatial perspectivetaking skill mediate the relationship between basic spatial ability and environmental learning, a research plan was implemented that involved obtaining single

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measures from a variety of spatial ability tests, single measures from a variety of environmental tasks, and multiple measures from a maze learning task and a spatial perspective-taking task. This plan allowed the number of factors representing spatial ability and environmental learning to vary, while constraining the factors that would emerge from the experimental tasks. The rationale for this plan was as follows: Existing evidence indicates that spatial ability batteries resembling the one used in this experiment tend to yield either a single spatial factor (Lorenz & Neisser, 1986) or two spatial factors differentiated by complexity (Allen, 1984), whereas measures of environmental knowledge tend to yield multiple factors (Lorenz & Neisser, 1986). Thus, an adequate test of the hypothesis should allow for the emergence of multiple factors from both of these groups of measures. In contrast, it was advantageous on conceptual and pragmatic grounds to treat performance on the maze learning and perspective-taking tasks as single mediating factors. It was expected that subjecting all of the measures from Experiment 1 to an exploratory factor analysis would yield either one or two spatial ability factors, two factors corresponding to the experimental tasks, and two or three environmental learning factors. As suggested previously, the spatial ability tests could result either in a single general factor or two factors: a simple ability factor emerging from tasks requiring memory for or detection of figural stimuli and a complex ability factor based on tasks requiring the manipulation of figural stimuli. The environmental tasks could result in either two or three factors. A twofactor outcome might differentiate between tasks requiring landmark knowledge and route knowledge, as found by Lorenz and Neisser (1986), although a distinction between route knowledge and configurational knowledge would also be plausible. A three-factor outcome would be expected to reflect even greater sensitivity to task complexity: landmark knowledge, route knowledge, and configurational knowledge. Alternatively, a two-factor solution might reveal a distinction along Piagetian lines of analysis (Piaget & Inhelder, 1967; Piaget, Inhelder, & Szeminska, 1960) between topological knowledge, concerned predominantly with the dimensions of proximity and openness, and Euclidean knowledge, involving equal-interval metrics of distance and direction. Specific hypotheses regarding relationships follow from these expectations regarding factor solutions. A single spatial factor would be expected to be related directly to both spatial-sequential memory and perspective-taking ability, but not to any of the environmental learning factors. Spatial-sequential memory would, in turn, be related directly to each environmental factor, based on the assumption that most of the environmental tasks could be solved on the basis of landmark recognition, memory for sequences of environmental features, and topological knowledge. However, perspective-taking skill would be related only to the environmental factor involving configurational knowledge or Euclidean knowledge, if such factors emerged in the factor solution. This prediction is based on (a) the

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presence of conceptual similarities between the cognitive demands of the perspective-taking task and those environmental tasks requiring participants to indicate direction or distance relationships among a set of environmental locations; and (b) the absence of commonalties between the cognitive demands of the perspective-taking task and those of the landmark recognition or route learning tasks. If two spatial ability factors emerged, then direct relations between the simple spatial factor and spatial-sequential memory and between the complex spatial factor and perspective-taking ability would be expected. This expectation is again based on conceptual similarities; visual memory or the detection of spatial patterns should be related to success in maze learning, and the manipulation of figural stimuli should be related to success in imaging alternative spatial perspectives. However, there is no reason to anticipate a relationship between a complex spatial factor and maze learning or between a simple spatial factor and perspective-taking skill, especially when a more complex spatial factor is included in the same analysis. The relations between the mediating factors and the environmental learning outcomes would be same as though described in the single spatial factor scenario.

Method Purticipunts. Data were collected from 100 participants, 57 men and 43 women, between the ages of 17 and 36 years (M = 21.2 years). Participants were volunteers residing in the Atlanta, Georgia metropolitan area, 97% of whom were university students. In this sample, 94% of the participants reported being right-handed; 20% reported being from racial or ethnic minority groups. As a condition of participation, individuals had to rate their familiarity with the geographic setting involved in the environmental learning tasks at 3 (not sure), 4 (relatively unfamiliar), or 5 (very unfamiliar) on a 5-point scale. Mean familiarity rating for this group was 4.9. Each participant was paid $45 for his or her participation in the experiment. All federal and professional guidelines regarding the treatment of human research participants were followed. Psychometric Test Battery. Each participant was administered a battery consisting of six psychometric tests selected from the Kit of Factor-Referenced Cognitive Tusks (Ekstrom, French, & Harman, 1976) to represent a range of abilities involving figural stimuli. 1. Surface Development Test. This test assesses visualization, or the ability to imagine or anticipate the appearance of objects as they undergo spatial transformations. Each item requires participants to study a flat, unfolded two-dimensional drawing of an object and then compare it to a corresponding drawing of an object folded and presented in three-dimensional form. Participants had to match

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edges numbered 1 through 5 in the unfolded object with edges lettered A through H in the folded object. The test consists of 12 such objects, presented as two sets of six. Six minutes are allowed for each set of six items. Performance was scored in terms of the number of correct responses minus the number of incorrect responses divided by number of response options. 2. Cube Comparison Test. According to Ekstrom et al. (1976), this test assesses spatial orientation, or the ability of an observer to remain oriented with regard to different perspectives of the same figural stimuli; however, it may be more accurate to construe it as a measure of spatial relations (Lohman, 1979), or the ability to accommodate angular disparity in determining whether figural stimuli are identical. Each item on the test consists of a pair of cubes drawn in three dimensions with a letter on each of three visible faces of the cube. Either one or two of the letters on the cubes are the same. Participants had to determine whether the pair could be different perspectives of the same cube. The response was either “same” or “different.” The test consists of 42 such pairs, presented as two sets of 21. Three minutes were allowed for each set. Performance was scored as the number of correct responses minus the number incorrect divided by the number of response options. 3. Hidden Figures Test. This test assesses flexibility of closure, or the ability to detect figural stimuli within a visually similar context. On each page of this four-page test, there is a set of five irregular polygons at the top (labeled A through E), followed by a series of framed, complex linear stimuli, each of which has the letters A through E listed below it. These stimuli contain many possible polygons, including a subset of those at the top of the page. Participants had to determine which polygons at the top of the page were contained within each of the complex stimuli on that same page. The response consisted of circling the letters below each complex stimulus to indicate the included polygon(s). The test includes 32 such complex stimuli, 16 in each of two parts. Twelve minutes were allowed for each part. Performance was scored as the number of correct responses minus the number incorrect divided by the number of response options. 4. Gestalt Completion Test. This test assesses speed of closure, or the ability to integrate related parts of figural stimuli into an identifiable whole. The items on this test are framed drawings of familiar objects with substantial portions of the drawings absent. Participants had to write the names of the objects shown in the drawings. The test consists of 20 drawings, 10 in each of two sets. Two minutes were allowed for each set. Performance was scored as the number of drawings named correctly. 5. Map Memory Test. This test assesses visual memory, or the ability to remember the configuration, location, and orientation of figural stimuli. The items

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on this test are framed, complex figural stimuli that strongly resemble cartographic maps showing such features as roads, coastlines, and rivers. After studying a page containing 12 such maps, participants then had to decide which of 12 maps on a subsequent page were identical to ones seen on the page studied previously. Responses consisted of circling either y for yes or II for no below each of the maps. The test consists of two parts, each of which has a study page and subsequent test page. Three minutes were allowed for study pages, and 3 minutes were allowed for responses on the test pages. Performance was scored as the number of correct responses minus the number of incorrect responses. 6. Map Planning Test. This test assesses spatial scanning, or the ability to perform speeded visual exploration of a wide or complicated visual array. The stimuli on this test are simplified versions of a square grid map of a city. The beginning and end of each line on the edge of the map are labeled with a letter, so that beginning in the upper left-hand corner and continuing in a clockwise direction, the line endpoints are labeled with the letters A through Z. Scattered within the matrix adjacent to the intersection of various pairs of lines are small squares numbered 1 through 10; also scattered within the matrix directly on various lines are 30 small circles. In the instructions, the letters at the beginning and ending points of the lines are explained to be starting points and endpoints, the lines are referred to as roads, the numbered squares are referred to as buildings, and the small circles are explained to be roadblocks. To the right of each grid are listed 10 test items that specify routes in terms of beginning point and endpoint, as, for example, “F to I.” Participants had to determine which numbered square in the matrix (explained as which building within the city map) would be passed on the shortest possible version of the specified route, taking into consideration indicated roadblocks. The test is presented in two parts, each of which consists of two grid maps and 10 routes referring to each. Three minutes are allowed for each part of the test. Performance was scored in terms of the number of correct responses.

Experimental Tasks and Apparatus. Participants tal tasks, two involving

maze learning

completed four experimenand two involving a model town.

I. Maze Learning Task. This task was designed to assess spatial-sequential memory. The objective of the task is to learn a designated pathway through a six by six matrix of squares printed on an 8.5 X 1 l-inch sheet of paper. The task is presented in alternating study and test phases. In a study phase, which lasted 15 seconds, participants attempted to commit to memory a pathway indicated by a broken line through the maze. The pathway, which did not cross or double back on itself, consisted of 21 moves. In a test phase, participants were provided a copy of the matrix of squares with only the beginning point of a pathway indicated and they were instructed to mark with a pencil the correct pathway through the maze. Study and test phases were continued until the participants completed

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two successive reproductions of the correct pathway. Performance was scored in terms of the number of trials to criterion and total time required to reach criterion. 2. Maze Reversal Task. This task was designed to yield alternative measures of spatial-sequential memory. After criterion was achieved on the maze learning task, participants were provided with a copy of the matrix of squares with only the endpoint indicated and were instructed to mark with a pencil the correct pathway from the endpoint to the beginning. Participants were required to begin at the endpoint of the pathway and were not allowed to draw the path in the original direction at any point in the solution. Study phases were provided after each attempt at reversing the pathway, but during these study opportunities, the maze was presented from the perspective viewed during learning. Study and test phases were continued until the participants completed two successive trials without an error. Performance was scored in terms of the number of trials to criterion and total time to criterion. 3. Perspective Verification Task. This task was designed to assess perspectivetaking skill. The principal apparatus used for this task consisted of a model town (nicknamed “Tinytown”) constructed of HO scale (1:87 scale) model railroad structures, including 35 separate buildings and a mountain. The model town was mounted on a painted plywood base that measured 4.5 feet wide and 9 feet long and stood 2.5 feet off the floor. The base was ringed at 45” intervals by seven small indicator lights mounted on 1.5-foot tall wooden posts. Thus, there was one light at each comer and one halfway along each side of the base-with the exception of one of the 4.5-foot sides, which served as the point of observation throughout the task. An additional indicator light was suspended 30 inches directly above the center of the model. A slide projector was mounted on a stand behind the point of observation, and a large viewing screen was placed approximately 3 feet beyond the opposite side of the model so that an observer could easily view slides projected onto it. At the point of observation was a small handheld response box featuring two buttons labeled yes and no. From the point of observation, the most obvious features in the model town were a mountain in the near left quadrant, a commercial area in the far left quadrant, two factories in the far right quadrant, and a residential area consisting of small houses in the near right quadrant. A system of roadways was logically situated within the model in the sense that there were fewer roads in the quadrants with the mountain and the factories than in the residential area, and fewer in that area than in the commercial district, which was laid out in a typical squareblock grid. All of the streets were lined with functioning street lights. The model included much detail, including people, vehicles, and animals. The perspective verification task involved a brief study phase and a lengthy test phase. During the study phase, a participant walked around the model once,

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observing how it appeared from different perspectives. The test phase consisted of a series of trials in which the participant indicated whether a slide projected onto the screen beyond the model corresponded to a perspective of the town indicated by one of the indicator lights surrounding or above the town. A tone signaled the beginning of a trial. After the tone, one of the indicator lights was illuminated. The participant pressed the yes button to acknowledge that he or she had seen the indicator light. This response resulted in a slide being projected onto the screen. The participant then had to respond yes if the slide showed the perspective corresponding to the view from the indicator light or no if it did not. Instructions were to respond as quickly as possible without making a mistake. An IBM PC controlled the illumination of indicator lights, the activation of the slide projector, and the recording of participants’ responses and response times. There was a total of 46 trials. Each of the seven indicator lights surrounding the model was paired with the correct perspective three times and with an incorrect perspective three times. The 21 foils were always selected from actual perspectives of the town (i.e., from views that were 45”, 90”, 135”, or 180” from the perspective dictated by the indicator light); the arrangement of features within the model was not altered to create foils. In addition to these 42 trials, an additional four trials were included that involved the indicator light suspended above the model. Twice this light was paired with overhead views of the model, and twice it was paired with the perspective that was 180” from the point of observation. The 46 trials were presented in random order with regard to combinations of the eight indicator lights and perspective matches versus foils. A participant’s performance on the perspective verification task was summarized by two variables: the total number of correct responses and the mean response time for correct responses. 4. Map Verification Task. This task involved the same basic apparatus as described in the perspective verification task. However, the trials required participants to determine whether or not a particular route through the “Tinytown” model was the same as that depicted in a map projected onto the screen. On each of 28 trials, participants first studied for 15 seconds a route through the model indicated by the illumination of a pattern of street lights, and then viewed a slide depicting a map of the town with a route indicated by a broken line. All maps were simple black-and-white cartographic representations, with buildings and roads indicated. The 28 trials involved only four routes. Each of the routes was matched with correct maps four times, once with the map projected on the screen with the point of observation at the bottom, once with the point of observation rotated 90” once with the point of observation rotated 180” and once with the point of observation rotated 270”. This yielded a total of 16 trials in which the route shown on the model matched the one depicted in the maps. The remaining 12 trials were foils, three for each route. Trials were presented in a random order with respect to

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combinations of map orientation and matches versus foils. Participants were instructed to respond as quickly as possible without making a mistake. A participant’s performance on this task was scored in terms of the total number of correct responses and mean response time for correct responses. The description of the map verification task was obligatory in this case because it was administered to each participant. However, the task was not designed to assess a skill pertinent to the hypothesis being tested in this study. Instead, it is concerned quite obviously with map interpretation skills. Thus, the results from this task will be presented in a separate paper that will acknowledge the context in which the task was administered.

Environmental Learning Tasks. The environmental learning tasks were used to assess participants’ knowledge after a walk through a small city. The walk was 1,424 meters in length and included nine turns. The initial portion, which was 393 meters long and included three turns, passed through a residential setting. The middle portion, which was 404 meters in length and included two turns, was a transitional area that included historic buildings and a church. The final portion, which covered 627 meters and included four turns, passed restaurants, government buildings, public transportation, and small businesses. After being escorted on the walk, participants were administered a series of six tasks designed to assess various aspects of their knowledge about the area. 1. Route Reversal. This task required participants to retrace the walk they had originally taken, starting at the endpoint and finishing at the point of origin. During the task, the experimenter walked just behind and to one side of the participant and recorded his or her movement. Performance was scored in terms of the number of correct turns at choice points divided by the total number of choice points along the walk. 2. Euclidean Distance and Direction Judgment. This task required participants to provide Euclidean or “crow-fly” distance and direction estimates from one viewpoint to a series of six unseen target locations along the walk. Direction estimates were made using a simple directional indicator manipulated by the participant. Distance estimates were made in terms of standard units (1 unit = 5 feet, 6 inches). The length of a unit could be demonstrated on the sidewalk in front of a participant, and a IO-unit distance from the testing position to an environmental feature visible to the participant was provided as an example. The testing position was located near the midpoint of the original walk but just off the actual pathway. Target locations were specified in photographic prints from the walk. They were presented in random order with respect to distance from the testing position. Performance was scored in terms of mean units of error over the six distance estimates and mean angular error over the six direction estimates.

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3. Scene Recognition. This task reflected participants’ ability to recognize scenes from the original walk. Participants were shown a series of 50 photographic prints, half of which were from the walk and half of which were from visually similar walks. They were instructed to respond yes or no to the question of whether the picture showed a viewpoint from the original walk. The photographs were presented in a random order with regard to distance from the beginning point of the walk and originals versus foils. Performance was scored in terms of the number of correct responses divided by the total number of responses . 4. Scene Sequencing. This task was designed to assess participants’ nonmetric temporal-spatial knowledge of the original route. Participants were provided with 25 randomly ordered photographic prints showing scenes from the walk, and were instructed to arrange them in proper temporal sequence starting with the beginning point of the walk. Performance was scored in terms of a rank-order correlation coefficient for each individual. 5. Intraroute Distance Judgment. This task was designed to assess participants’ knowledge of metric distances along the original route. The same 25 photographs used in the scene sequencing task were employed, with the order produced by the participant in the scene sequencing task preserved. Participants produced distance estimates (in standard units as explained earlier) between adjacent scenes. Specific environmental features in the foreground of each photograph were specified as reference points for generating estimates. Performance was scored in terms of the mean distance error. 6. Map Placement Task. This task was designed to assess participants’ configurational knowledge of the area through which the original walk passed. Task materials consisted of the same 25 photographs used in the previous two tasksrandomized for this task-and a street map of the area (scale: 1 cm = 60 m) in which the route was situated. Participants were shown the photographs one at a time and instructed to mark on the street map with a pencil the exact location depicted in the scene. Specific environmental features in the foreground of each photograph were specified as reference points for making placements. Performance was scored as the mean placement error expressed in millimeters. Procedure. Participants were tested individually in two separate data collection sessions. At the beginning of the initial session, which took place in a laboratory setting, participants were briefed regarding the nature of the study and extent of time involved, and informed consent was obtained. They were then administered the battery of six psychometric tests in the order in which they were described in the previous section. Completion of the battery required approx-

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imately 90 min, after which time a brief break was available. The break was followed by the maze learning, maze reversal, perspective verification, and map verification tasks, respectively. Completion of these tasks required between 60 and 90 min. For the second data collection session, participants returned to the site of initial testing and were then transported by automobile to the area involved in the environmental learning tasks. Prior to being led on the walk, participants were instructed to pay very close attention to the environmental features along the route, the order in which things appeared, the direction of travel, and the overall layout of the area, so that they could travel the same route again without error from the beginning point. After the walk, participants were escorted back to a testing position at the beginning of the route, where the six environmental leaming tasks were administered in the order in which they were described in a previous section. Completion of these activities required approximately 2.5 hrs. On completion of the second session, participants were debriefed, paid, and thanked for their participation. Results Means and standard deviations for each dependent measure are shown in Table 1. The correlation matrix for these measures is shown in Table 2.

Exploratory Factor Analysis. To suggest how many psychometric ability factors and environmental learning factors should be included in the subsequent model of mediated relationships, the covariance matrix for this data set was subjected to exploratory factor analyses using a maximum likelihood method with varimax rotation to arrive at the factor structure. Two approaches were used. In the first approach, all of the measures were included in the analyses. In the second approach, measures derived from a common task or a highly related task were combined as mean z scores before they were included in the analyses. These included (a) trials to criterion and time to criterion in the maze learning task, (b) trials to criterion and time to criterion in the maze reversal task, (c) accuracy and response time in the perspective-taking task, and (d) accuracy in the scene recognition and scene sequencing tasks. The second approach was employed as a check on the emergence of artifactual factors resulting in the inclusion of measures with highly correlated errors in the exploratory analyses. If the two approaches resulted in a different number of factors in the factor solution, then the one with the fewer factors was to be taken as the more valid. With the first approach, the hypothesis that more than five factors were necessary to describe the factor structure for these data was confirmed, x*(86) = 130.74, p < .Ol,but the hypothesis that more than six factors were necessary was not confirmed, x2(72) = 91.05, p > .05. The scree plot also suggested the validity of a six-factor solution, with each of the factors having an eigenvalue of

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TABLE 1 Means and Standard Deviations for Psychometric Tests, Laboratory Experimental Tasks, and Environmental Learning Tasks (n = 100) M

SD

Psychometric Tests Surface development Cube comparison Hidden figures Gestalt completion Map memory Map planning

40.52 21.62 16.50 13.33 19.20 27.00

14.25 9.90 7.66 3.35 3.98 7.04

Laboratory Experimental Tasks Maze learning (trials) Maze learning (time) Maze reversal (trials) Maze reversal (time) Perspective-taking (accuracy) Perspective-taking (rtlcorrect)

1.44 5.86 3.88 3.14 38.90 5.08

5.14 5.52 5.13 6.13 5.10 4.05

0.06 188.16 22.13 38.13 0.40 48.64 21.23

0.09 397.57 8.61 3.84 0.41 53.38 18.96

Environmental

Learning

Tasks

Route reversal (errors) Euclidean distance (error) Euclidean direction (error) Scene recognition (accuracy) Scene sequencing (correlation) Intraroute distance (error) Map placement (accuracy)

0.96 or higher. With the second approach, the hypothesis that more than three factors were necessary was confirmed, x*(63) = 94.80, p < .Ol, but the hypothesis that more than four factors were necessary was not confirmed, x*(51) = 63.80, p > .05. The scree plot also suggested the validity of a four-factor solution, with each of the factors having an eigenvalue above 0.89. Thus, the fourfactor solution was taken to be a more valid representation of the factor structure for this group of tasks and was examined in more detail. Nevertheless, it should be acknowledged that the implications of the factor solutions obtained under each approach were identical as far as the subsequent model-fitting exercise was concerned. A conservative approach was taken in designating factor loadings, with only those loadings of .40 or higher being considered significant. The first factor to emerge from the analysis was a unitary spatial ability factor, on which five of the six psychometric tests loaded significantly. Specifically, the significant loadings were as follows: surface development test (. 80), cube comparison test (.79), map

I. Surface development 2. Cube comparison 3. Hidden figures 4. Gestalt completion 5. Map memory 6. Map planning 7. Maze laming (trials) 8. Maze learning (time) 9. Maze reversal (trials) IO. Maze reversal (time) 11, Perspective-taking 12. Perspective-taking (a) 13. Route reversal 14. Euclidean distance 15. Euclidean distance 16. Scene recognition 17. Scene sequencing 18. Intraroute distance 19. Map placement

0.73 0.52 0.47 0.35 0.61 -0.53 -0.55 -0.38 -0.38 0.45 -0.45 -0.22 -0.03 -0.31 0.20 0.16 -0.17 -0.29

1

~ 0.55 0.40 0.28 0.58 -0.46 -0.48 -0.32 -0.33 0.40 -0.40 -0.20 -0.03 -0.37 0.03 0.18 -0.15 -0.25

2

0.32 0.43 0.52 -0.37 -0.39 -0.16 -0.19 0.35 -0.28 -0.07 0.02 -0.19 0.04 0.15 -0.14 -0.16

3

0.25 0.30 -0.39 -0.37 -0.34 -0.34 0.34 -0.40 -0.17 -0.10 -0.20 0.02 0.12 -0.26 -0.31

4

0.25 -0.36 -0.31 -0.15 -0.18 0.37 -0.04 -0.22 -0.16 -0.04 0.09 0.15 -0.11 -0.17

5

-0.47 -0.47 -0.32 -0.33 0.31 -0.31 -0.13 0.01 -0.33 0.13 0.15 -0.27 -0.29

6

0.96 0.64 0.65 -0.43 0.52 0.26 0.03 0.35 -0.14 -0.26 0.17 0.46

7

0.69 0.72 -0.41 0.56 0.20 0.02 0.38 -0.10 -0.25 0.12 0.42

8

0.98 -0.35 0.19 0.12 -0.09 0.19 -0.04 -0.22 0.09 0.44

9

-0.35 0.21 0.07 -0.06 0.20 0.00 -0.21 0.08 0.41

10

~ -0.19 -0.34 -0.15 -0.32 0.05 0.33 -0.31 -0.33

11

0.32 -0.06 0.45 -0.04 -0.13 0.12 0.32

12

~ 0.07 0.26 -0.18 -0.32 0.39 0.58

13

14

~ 0.05 0.04 -0.08 0.22 -0.02

TABLE 2 Correlation Matrix Including Psychometric Teat Scores, Experimental Task Measures, and Environmental Learning Task Measures (With r > 0.20 significant at p < .05)

-0.07 -0.38 0.26 0.31

15

0.42 -0.36 -0.31

16

-0.56 -0.63

17

0.55

18

~

19

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planning test (.69), hidden figures test (.67), and gestalt completion test (.40). This factor accounted for approximately 40% of the solution variance. The second factor may be referred to as topological environmental knowledge because it included measures of environmental knowledge that required relational judgments rather than Euclidean direction and distance judgments. The measures .loading on the factor included error from the map placement task (.81), error from the intraroute distance judgment task (.70), the z score representing a combination of the scene recognition and scene sequencing tasks (- .62), and errors from the route reversal task (.59). This factor accounted for approximately 27% of the solution variance. The third factor may be considered perspective-taking skill. It included only the z score representing response time and accuracy measures from the perspective-taking task (.88). This factor accounted for about 19% of the solution variance. The fourth factor in the solution was bidirectional spatial-sequential memory, so called because significant loadings included the z scores representing the combination of total time to criterion and trials to criterion from the maze reversal task (.88) and the z score representing the combination of total time to criterion and trials to criterion from the maze learning task (.5 1). This factor accounted for approximately 14% of the solution variance. These exploratory findings indicated the appropriateness of designating a unitary spatial ability factor in the structural equation modeling analysis. With regard to the environmental learning tasks, the findings suggested the utility of including a major factor, topological knowledge, and two additional manifest variables: Euclidean distance error and Euclidean direction error. Clearly, the topological knowledge factor was warranted; all measures from the environmental tasks loaded on this factor, with the notable exception of those from the distance and direction judgment task. Designating Euclidean distance error and Euclidean direction error as separate manifest variables was desirable on pragmatic and theoretical grounds. Euclidean spatial knowledge is an important aspect of several theories of spatial cognition (e.g., Piaget & Inhelder, 1967); yet measures reflecting direction and distance knowledge did not correlate highly with each other or load significantly on any of the factors in the solution. The results of the exploratory factor analysis had additional influences on how the variables from the experimental tasks were represented in the subsequent modeling effort. All four measures from the maze learning and maze reversal tasks were designated as defining a bidirectional spatial-sequential memory factor, and the two measures from the perspective-taking task were designated as defining a spatial perspective-taking skill factor. Structurul Equation Modeling. Stated in terms of the factors resulting from the exploratory factor analysis, the principal hypotheses under investigation were that (a) the relationship between general spatial ability and the acquisition of

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topological knowledge of the environment would be mediated by bidirectional spatial-sequential memory, and (b) the relationship between general spatial ability and the acquisition of Euclidean distance and direction knowledge of the environment would be mediated by spatial perspective-taking skill. In both cases, the direct or unmediated relationships between general spatial ability and environmental knowledge were expected to be insignificant. The analyses that follow were performed using the CALIS procedure from SAS; the chi-square and goodness-of-fit statistics were the result of covariance structure analyses using maximum likelihood estimation. A preliminary effort to model these variables revealed three problems. The first problem concerned insignificant loadings of scores on factors. The t tests for the parameter estimates relating map memory test scores to the latent factor of general spatial ability and perspective-taking accuracy scores to the latent factor of spatial perspective-taking skill were insignificant, p > .05. These variables were eliminated from the analysis, thus leaving response time for correct responses (perspective-taking latency) as a manifest variable within the model. Second, time to criterion and time to completion measures from the maze learning task and from the maze reversal task, respectively, were necessarily very highly correlated with each other, causing problems in terms of parameter estimates. In simple terms, measures that are virtually perfectly correlated scores cannot yield satisfactory parameter estimates for a latent variable. To resolve this problem, a single measure from each task, namely, trials to criterion, was selected to define the latent variable of bidirectional spatial-sequential memory. Third, variance from the intraroute distance judgment task, which was a variable loading on the latent factor of topological environmental knowledge, was far out of scale with variances from the other tasks. To resolve this problem, log values of this variable were included in the analysis. Note that the same solution was applied to the manifest variables Euclidean distance judgment (a distance error measure) and perspective verification skill (a response time measure). With these steps taken, the measurement model yielded an overall fit to the data that was adequate in light of the strictly experimental nature of the majority of measures, x2(54) = 133.76, p = .OOOl, Goodness of Fit Index = .828, Bentler and Bonnet’s Non-normed Index = .790. Neither reassignment of variables to factors nor examination of residuals indicated an obvious way to improve the model. The procedure used to determine significant paths between variables within the model involved starting with a full model, including latent and manifest variables, with paths indicated (a) from all three designated predictors (the latent variable general spatial ability, the latent variable bidirectional spatial-sequential memory, and the manifest variable spatial perspective-taking latency) to all three designated outcomes (the latent variable topological knowledge, the manifest variable Euclidean distant knowledge, and the manifest variable Euclidean direction error), and (b) from general spatial ability to the two hypothesized mediating variables (bidirectional spatial sequential memory and perspective-taking laten-

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cy). Then, one at a time, the significance of each path was determined by comparing the full model to a constrained version of the model with one path omitted. If the difference between the chi-square values yielded by the two models was significant (treated as a chi-square test with a single degree of freedom), then the path was retained. If the difference was insignificant, then the path was omitted. Using this procedure, seven paths were omitted and four were retained. Omitted were the direct paths from general spatial ability to topological knowledge, x2( 1) = 1.23, p > .05; to Euclidean distance error, x2( 1) = 0.36, p > .05; and to Euclidean direction error, x2( 1) = 1.18, p > .05. Also dropped were the paths from perspective-taking latency to topological knowledge, x2(1) = 0.03, p > .05; and to Euclidean distance error, x2 = 0.05, p > .05; and those from spatialsequential memory to Euclidean distance error, x2( 1) = 1.16, p > .05; and to Euclidean direction error, x2(1) = 3.26, p > .05. The remaining paths with standardized coefficients are shown in Figure 1. The overall fit of this model again reflected the fact that most of the variables were experimental measures, x2(75) = 138.56, p = .OOOl, Goodness-of-Fit Index = .843, Bentler and Bonett’s Non-normed Index = .862. Discussion Given the paucity of previous evidence of significant relationships between psychometric measures of spatial ability and measures of environmental learning, the results of Experiment 1 were truly noteworthy. The hypothesis that spatialsequential memory and spatial perspective-taking skill would mediate the relationship between general spatial ability on the one hand and environmental knowledge on the other received strong support. As shown in Figure 1, the mediated relationships were quite specific. Spatial-sequential memory mediated the relationship between spatial ability and topological knowledge, but not the ones between spatial ability and the two Euclidean aspects of environmental knowledge. In contrast, perspective-taking skill mediated the relationship between spatial ability and Euclidean direction knowledge, but not the ones between spatial ability and topological knowledge and between spatial ability and Euclidean distance knowledge. The factors included in this model generally conformed with expectations based on prior research. The unitary spatial ability factor in this study mirrored the results of Lorenz and Neisser (1986) and is sensible in terms of the wide variety of tasks included in the factor analysis. The alternative hypothesis of two spatial factors, one simple and one complex, had been derived from a study in which there were a variety of psychometric tests but only one macrospatial task (Allen, 1984). The factor structure for environmental knowledge was difficult to predict on the basis of other studies, primarily because of task differences. Lorenz and Neisser (1986) identified factors for general directional knowledge, landmark knowledge, and route knowledge, but the inclusion in the study report-

Maze Reversal

Error

Figure 1. Results from structural equation modeling analysis showing significant path coefficients among general spatial ability (left portion of figure), two spatial-cognitive skills assessed in the lab (center portion), and three facets of environmental knowledge assessed in the field (right portion). Maze learning and maze reversal measures (trials to criterion) were reverse scored to facilitate interpretation of signed path coefficients.

!I

Maze Learning

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ed here of only one task specifically requiring directional knowledge and one task specifically requiring the recognition of potential landmarks made the replication of this factor pattern unlikely. Instead, one factor emerged that represented knowledge of the general “lay of the land.” This factor represented the ability to recognize scenes from the walk, traverse the walk in the direction opposite of that in which it was learned, make ordinal and interval distance estimates to features along the walk, and place features from the environment on a map of the area. This combination of landmark, route, and relational information was labeled topological knowledge, in part because it is metaphorically apt and in part because it provides a conceptual contrast to the other two variables-straight-line distance and direction knowledge -that did not load onto this factor. Consistent with metaphor and the Piagetian tradition, these two variables were labeled Euclidean, but because they were not highly related to each other, they were assigned the status of independent outcomes of environmental learning. This differentiation is consistent with the findings of Lorenz and Neisser (1986) and has precedent in the experimental literature (e.g., Anooshian & Kromer, 1986). In general terms, the results of Experiment 1 indicated that general spatial ability, construed as basic facility with figural stimuli, does not directly influence environmental learning. Instead, such facility plays an important role in somewhat more complex cognitive operations, which in turn are related to successful environmental learning. However, more detailed explication of the pattern of results found in Experiment 1 awaited the replication of this pattern in Experiment 2.

EXPERIMENT 2 The purpose of Experiment 2 was to test the path analytic model obtained in Experiment 1 with a new sample of participants and a new environmental setting. Specifically, predictions were that (a) spatial-sequential memory would be a significant mediator of the relationship between general spatial ability and topological environmental knowledge, but not of those between spatial ability and Euclidean distance knowledge and between spatial ability and Euclidean direction knowledge; (b) spatial perspective-taking skill would be a significant mediator of the relationship between spatial ability and Euclidean direction knowledge, but not of those between spatial ability and topological knowledge and between spatial ability and Euclidean distance knowledge; and (c) the unmediated relationships between spatial ability and all three environmental learning variables would be insignificant.

Method Participants. Data were collected from 103 participants, 34 men and 69 women, between the ages of 17 and 36 years (M = 19.8 years). All were volun-

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teem residing in the Columbia, South Carolina metropolitan area, all of whom were university students. In this sample, 90% of the participants reported being right-handed; 21% reported being from racial or ethnic minority groups. As a condition of participation, they had to rate their familiarity with the geographic setting involved in the environmental learning tasks at 3 (unsure), 4 (relatively unfumiliar), or 5 (very unfamiliar) on a 5-point scale. The mean familiarity rating was 3.7. Each participant was paid $45 for his or her participation in the experiment. All federal and professional guidelines regarding the treatment of human research participants were followed. Psychometric Test Battery. The battery of six psychometric study was the same as that administered in Experiment 1.

tests used in this

Experimental Tasks and Apparatus. The experimental tasks administered in this study were the same as those described in Experiment 1. An exact duplicate of the “Tinytown” apparatus was used for the perspective verification task. Environmental Learning Tasks. The six tasks used to assess participants’ environmental knowledge in Experiment 1 were administered to participants in this study. As in the previous experiment, these tasks were administered after the participant had been escorted on a walk through an urban area. In this case, the walk was 2,720 meters in length and included eight turns. The initial portion, which was 458 meters long and included three turns, passed through a residential setting. The middle portion was 1,360 meters in length and included four turns; it went through a small business district with numerous restaurants and shops. The final portion, which covered 892 meters and included one turn, was through another residential area. Procedure. The procedure that involved multiple data collection sessions was the same as that followed in Experiment 1. Results Means and standard deviations for each dependent measure are shown in Table 3. The correlation matrix for these measures is shown in Table 4. The covariance matrix from these data was fit to the model derived from Experiment 1 using the CALIS procedure with maximum likelihood estimation. The results were highly congruent with those from the previous study, x2(75) = 135.95, p = .OOOl, Goodness-of-Fit Index = .849, Bentler and Bonett’s Nonnormed Index = .859. The paths with standardized coefficients are shown in Figure 2. In contrast to the results of Experiment 1, the test of the path between perspective-taking latency and Euclidean direction judgment revealed it to be nonsignificant. Apart from this exception, the findings from Experiment 1 were replicated. Relationships between general spatial ability and both experimentally

PREDICTING

ENVIRONMENTAL

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LEARNING

TABLE 3 Means and Standard Deviations for Psychometric Tests, Laboratory Experimental Tasks, and Environmental Learning Tasks (n = 103) M

SD

Psychometric Tests Surface development Cube comparison Hidden figures Gestalt completion Map memory Map planning

28.98 14.27 16.50 10.98 18.33 22.20

14.74 9.87 7.66 3.37 4.79 7.91

Laboratory Experimental Tasks Maze learning (trials) Maze learning (time) Maze reversal (trials) Maze reversal (time) Perspective-taking (accuracy) Perspective-taking (rticorrect)

10.61 10.91 4.32 4.72 34.60 6.03

6.18 8.13 5.97 7.19 5.40 2.65

Environmental Learning Tasks Route reversal (errors) Euclidean distance (error) Euclidean direction (error) Scene recognition (accuracy) Scene sequencing (correlation) Intraroute distance (error) Mao olacement (accuracv)

0.04 192.22 14.39 45.37 0.90 62.80 9.99

0.08 166.07 15.25 3.28 0.14 53.61 8 41

assessed skills (i.e., spatial-sequential memory and perspective-taking latency) were significant, as was the link between spatial-sequential memory and topological environmental knowledge. The insignificant path between perspective-taking latency and Euclidean direction error prompted between-experiment comparisons of performance levels. A proper context for these comparisons could be provided only by an exhaustive set of comparisons. Participants in Experiment 1 scored higher than did participants in Experiment 2 on all of the psychometric measures included in the general spatial ability factor, all ~(201) > 4.56, and learned the maze more quickly as an assessment of the spatial sequential memory factor, t(201) = -3.97. There was no difference in how quickly the maze was learned in reverse. The difference between mean response times in the perspective-verification task was literally on the statistical criterion, t(201) = 1.95, suggesting faster perspective-taking performance on the part of participants in Experiment 1. In contrast, participants in Experiment 2 outperformed those in Experiment 1 on all measures included in

1. Surface development 2. Cube comparison 3. Hidden figures 4. Gestalt completion 5. Map memoty 6. Map planning 7. Maze learning (trials) 8. Maze learning (time) 9. Maze reversal (trials) 10. Maze reversal (time) 11. Perspective-taking 12. Perspective-taking(It) 13. Route reversal 14. Euclidean distance 15. Euclidean direction 16. Scene recognition 17. Scene sequencing 18. Intraroutedistance 19. Map placement

0.68 0.53 0.44 0.29 0.56 -0.52 -0.50 -0.26 -0.30 0.58 -0.26 -0.07 0.00 -0.23 0.21 0.33 -0.28 -0.41

1

0.43 0.31 0.26 0.41 -0.47 -0.40 -0.28 -0.29 0.51 -0.19 -0.14 0.03 -0.19 0.14 0.13 -0.24 -0.35

2

0.24 0.17 0.39 -0.40 -0.35 -0.18 -0.21 0.29 -0.36 -0.09 -0.08 -0.18 0.05 0.19 -0.19 -0.27

3

0.23 0.16 -0.25 -0.14 0.00 -0.03 0.14 -0.27 -0.04 0.18 -0.09 0.14 0.13 -0.14 -0.19

4

0.14 -0.26 -0.22 -0.14 -0.18 0.33 -0.21 -0.10 0.10 0.02 0.33 0.24 -0.32 -0.34

5

-0.45 -0.41 -0.33 -0.32 0.27 -0.33 -0.14 0.08 -0.38 0.25 0.27 -0.28 -0.37

6

~ 0.85 0.55 0.60 -0.55 0.39 0.27 -0.05 0.36 -0.20 -0.27 0.32 0.39

7

0.39 0.47 -0.54 0.31 0.22 -0.07 0.52 -0.21 -0.41 0.35 0.49

8

0.96 -0.33 0.31 0.00 0.00 0.30 -0.01 -0.16 0.17 0.27

9

-0.37 0.36 0.00 -0.03 0.35 -0.03 -0.20 0.20 0.30

10

-0.07 -0.15 0.08 -0.25 0.15 0.31 -0.34 -0.47

11

0.02 -0.04 0.07 -0.14 -0.18 0.05 0.09

12

-0.13 0.10 -0.18 -0.11 0.26 0.33

13

14

-0.08 -0.02 -0.04 0.03 -0.06

TABLE 4 Correlation Matrix Including Psychometric Test Scores, Experimental Task Measures, and Environmental Learning Task Measures (With r > 0.20 significant at p < .05)

-0.15 -0.35 0.45 0.50

15

~ 0.23 -0.30 -0.46

16

-0.62 -0.59

17

0.78

18

-

19

/

-.463

\

\

1

‘1

II

I

Route

Error

Reversal

Figure 2. Results from structural equation modeling analysis showing all path coeffkients involved in the model specified on the basis of Experiment 1. Maze learning and maze reversal measures (trials to criterion) were reverse scored to facilitate interpretation of signed path coefficients.

\

General Spatial Ability

/ Topological

I

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ANDBECK

the topological knowledge factor except one, ts > 2.75, the exception being intraroute distance judgment. In addition, Euclidean direction error was more accurate for participants in Experiment 2, ~(201) = 4.43. Within this context of differences, the focus was specifically on possible explanations for the insignificant path between perspective-taking latency and Euclidean direction error. Participants in Experiment 1 were superior on the perspective-taking task (mean response time: 5.1 s vs. 6.0 s), and participants in Experiment 2 were superior on the Euclidean direction judgment task (mean error: 14.4” vs. 22.1”). With these mean levels of performance, ceiling and floor effects could be ruled out as the cause for the differences in the path coefficients between experiments. Participant-related differences were a more probable cause. The mean familiarity rating for the geographic environment involved in the Euclidean direction judgment task in Experiment 2 was higher than the corresponding rating in Experiment 1. However, partialing out familiarity left the first-order correlation between perspective verification time and Euclidean direction judgment in Experiment 2 even smaller. Furthermore, it must also be noted that the relationships among the others factors in the model were apparently unaffected by this difference in familiarity. The experiments also differed significantly in the number of men and women included as participants, with Experiment 1 including more men than women and Experiment 2 including more women than men. Again, however, partialing out the impact of participant gender did not alter the first-order correlation between the variables of interest, and the lack of impact of participant gender on the other relationships in the model stands out. Discussion The results of Experiment 2 confirmed the hypothesis that spatial-sequential memory mediates the relationship between general spatial ability as assessed by psychometric tasks and topological environmental knowledge as assessed by measures in the field. The pattern of relations among these three latent variables were virtually identical and lend considerable confidence to the conclusions of this study. However, the hypothesis that perspective-taking skill mediates the relationship between general spatial ability and Euclidean direction knowledge was not sustained. On the one hand, in view of the major success of the model-fitting effort, it is inappropriate to focus too much attention on a .152 decrease in one path coefficient. On the other hand, it was important to exhaust ready accounts of this difference. Some issues involving methodological problems and participant variables were examined without a conclusive pattern emerging. Two additional considerations can be offered. First, it may be the case that measures of perspective-taking ability involve inherent unreliability related to strategy selection and implementation. Michael, Guilford, Fruchter, and Zimmerman (1957) and espe-

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cially Barratt (1953) found that examinees reported a wider variety of strategies to tests requiring perspective-taking ability than to those involving either visualization of transformed surfaces or mental rotation of objects. Consistent with this finding, experimental studies of perspective-taking skill have revealed significant effects of strategies or type of instructions (see Huttenlocher & Presson, 1973, 1979). Thus, strategy-shifting, in the context of the experimental perspectivetaking task could conceivably have affected the relations between the general spatial ability factor and perspective-taking skill and between perspective-taking skill and Euclidean direction knowledge in the environment. A second consideration involves differences between the two environments. The setting for the environmental learning tasks in Experiment 2 included a distal landmark, a 12-story dormitory building with a circular room on top, which was not adjacent to any part of the route but could be seen from almost all parts of the walk. This is precisely the type of landmark that can be used to facilitate accuracy in direction judgment tasks in geographic-scale environments (see Sadalla, Burroughs, & Staplin, 1980). It can also be argued that such a landmark would not necessarily be of benefit in the performance on the environmental learning tasks included in the topological knowledge factor (e.g., scene recognition and intraroute distance estimation). Thus, in the absence of empirical evidence pointing to another account. it seems reasonable to suggest that the weaker relationship between the laboratory measure of perspective-taking skill and the environmental measure of direction judgment be attributed to the relative ease of the direction judgment task in the second experiment.

GENERAL

DISCUSSION

The findings of Experiments 1 and 2 constitute the most convincing and informative evidence to date of the nature of the relationship between general spatial ability as assessed by psychometric tests and environmental learning as assessed by tasks administered in the field. This evidence indicates clearly that spatialsequential memory skill, defined as efficiency in learning a visually experienced, temporally organized spatial pattern, mediates the relationship between general spatial ability and the acquisition of environmental knowledge that may be described as topological. Furthermore, the evidence suggests that perspective-taking skill, defined as efficiency in determining the appearance of an array of objects from a perspective other than the one perceived, mediates the relationship between general spatial ability and the acquisition of Euclidean direction knowledge of the environment. It is worth noting that these relationships have been established empirically despite obvious method-related variance and “noisy” experimental data. These results lend themselves to speculation regarding fundamental mechanisms and processes responsible for the discovered relationships. General spatial ability as a latent factor in these experiments reflects the ability to detect, impose

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AND BECK

a frame of reference on, and, if necessary, perform a transformation on figural stimuli outside of a meaningful context. Ultimately, it may be most convenient to consider these abilities as involving basic propositions specifying spatial relationships with a set of rule-based transformations (see Just & Carpenter, 1985; Olson & Bialystok, 1983; Pellegrino & Kail, 1982). Because of the nature of the stimuli, long-term memory for prior spatial experiences in the real world affords little in the way of directly applicable strategies to employ on test items. Longterm storage of information even as a general content-free resource plays a very small role. Indeed, the visual memory test did not load on this factor and was subsequently eliminated from the model in Experiment 1. Instead, the demand is on temporary, active memory for the propositions and transformation necessary for each item. Naturally, such demands would be expected to diminish over testing as strategies emerge and processing steps are restructured (Just & Carpenter, 1985). The two mediating constructs appearing in the model are both directly related to general spatial ability as just described, but they are differentiated by processes that result in their being unrelated to each other. In the case of spatial-sequential memory skill, the additional mechanism is obviously information storage and retrieval. Participants must impose a frame of reference on the maze and commit to memory a series of simple locational transformations. The shuttling of information between active memory and long-term memory involved in the task evokes the concept of working memory in the form of a hybrid of Baddeley’s (1986) and Anderson’s (1983) conceptualizations. Consistent with Baddeley’s model, one can think of an individual employing a strategy and frame of reference-derived from previous experience with serial memory tasks-in the executive function as he or she maintains actively processed information in either the phonological loop (in the form of rehearsed moves) or the visual-spatial sketch pad (in the form of an image of the maze solution). Anderson’s (1983) notion of working memory as an activated long-term representation also seems applicable, as individuals could be construed to construct during acquisition and “read off” during testing a linear-order representation of the maze solution. Performance could also be construed to reflect a shift from declarative to procedural knowledge. The basic processes involved in general spatial ability map onto perspectivetaking skill rather directly. As mentioned earlier, the processes of fixing a frame of reference and performing prescribed spatial transformations within that frame have been described by some theorists as formally the same in mental rotation and perspective-taking tasks (Olson & Bialystok, 1983). Thus, a close relationship could be anticipated. In the present studies, the response time measure from the perspective-taking task was assumed to represent a high skill level, literally, rapid responding with accurate responses. Accordingly, it served as the candidate mediating variable in the model. It can be speculated that such a skill level results from employing a qualitatively more effective strategy, a prospect that can be examined rigorously in future studies. The absence of a significant path coeffi-

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353

cient between perspective-taking latency and spatial-sequential memory skill may be interpreted as reflecting the relatively low demands on long-term memory imposed by the perspective-taking task. The unifying processing demand for the various environmental learning tasks that loaded on the topological environmental knowledge factor was memorymemory for environmental features and their spatial interrelationships. As has often been pointed out, spatial cognition in large-scale environments can reliably be differentiated from spatial cognition on psychometric tests and in small-scale arrays by the fact that spatial relationships among locations cannot be perceived from a single perspective within the environment (Allen, 1985; Moore & Golledge, 1976). Unseen locations and relations must be remembered. The critical link between spatial-sequential memory skill and topological environmental knowledge, then, can be characterized in terms of demands for information storage and retrieval; stated in constructivist terms, a frame of reference must be imposed (e.g., one based on landmarks or on the abstract concept of cardinal directions), and an organized representation of spatial relationships constructed. Memory for unseen locations is also a task demand that differentiates the Euclidean direction judgment task in the environment from the perspective-taking task in the lab. Also, the lab task requires a perspective transformation that is not necessary in the environmental task. Nevertheless, the tasks share the requirements of establishing a frame of reference and then determining a specific angular relationship between features within that frame. The requirement for specific angular information is logically at the heart of the empirically based distinction between the Euclidean direction judgment measure and the topological factor, which may be characterized in general as being based on principles of proximity and boundedness. With respect to Euclidean knowledge, it should be pointed out that none of the variables included in the study were significantly related to performance on the Euclidean distance knowledge task. Whether this was due to methodological factors (e.g., the magnitude estimation procedure employed) or the genuine lack of predictive validity cannot be determined without additional research. Overall, the findings are compelling, but they must be interpreted with their limitations recognized. Given an expanded test battery, multiple spatial ability subfactors (e.g., visualization, spatial relations, spatial orientation, visual memory) with perhaps differential relationships to the mediating variables might be in evidence. Of course, the construct validity of these mediating factors should be examined further as well. In addition, it should be emphasized that the environmental learning outcomes included in these analyses were the result of very limited experience in an unfamiliar setting. Different relationships and perhaps even a different factor structure for environmental knowledge could emerge in instances in which the tasks were administered in a well-known area (see Kirasic, 1990). Nonetheless, the current findings offer a model that affords a heuristic framework for future work aimed at specifying and explaining predictive relationships within the domain of spatial cognition.

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KIRASIC,

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