Quarterly Journal of Experimental Psychology

ISSN: 0033-555X (Print) (Online) Journal homepage: http://www.tandfonline.com/loi/pqje19

Knowledge of spatial relations: A preliminary investigation R. N. Wilton & Portia E. File To cite this article: R. N. Wilton & Portia E. File (1975) Knowledge of spatial relations: A preliminary investigation, Quarterly Journal of Experimental Psychology, 27:2, 251-257, DOI: 10.1080/14640747508400484 To link to this article: http://dx.doi.org/10.1080/14640747508400484

Published online: 29 May 2007.

Submit your article to this journal

Article views: 9

View related articles

Citing articles: 5 View citing articles

Full Terms & Conditions of access and use can be found at http://www.tandfonline.com/action/journalInformation?journalCode=pqje19 Download by: [University of Birmingham]

Date: 05 November 2015, At: 14:04

Quarterly Journal of Experimental Psychology (1975)27, 25 1-257

KNOWLEDGE OF SPATIAL RELATIONS: A PRELIMINARY INVESTIGATION R. N. W I L T O N

Downloaded by [University of Birmingham] at 14:04 05 November 2015

University of Dundee AND PORTIA E. FILE University of Texas T h e mechanism underlying our knowledge of spatial relationships was investigated. I n the first experiment subjects were asked to examine an array of circles, located in different positions on a background ; after removal of the array, they answered questions about the spatial relations between the circles. The array was constructed so that the number of circles and the number of relations between circles could be independently varied. The results showed that the number of correct answers decreased as the number of circles increased, but was unaffected by the number of relations between circles. This suggests that subjects learn the positions of the circles, from which relations between circles can be computed, rather than learning the relations directly. Evidence from the second experiment, using a similar experimental paradigm, suggests that the positions of the circles are learned by organizing them into higher-order units or groups.

Introduction Animals and men typically have a knowledge of the spatial arrangement of objects and paths in their environment; for example, the city resident knows where the nearest cinema is, how to get from one district to another, whether there is a shopping centre in this direction, and so on. I n the present paper two experiments are reported that investigate man’s knowledge of spatial relations. Experiment I Two general hypotheses about our knowledge of spatial relations were tested. One hypothesis states that the spatial relations between differently located objects are generated, as required, by mental operations on stored information that specifies only the positions of the objects. Thus, as with Tolman’s (1948)cognitive map, the relations themselves need not be remembered. T h e second hypothesis, requiring much greater storage, but little mental computation, states that the relations themselves are stored, and recalled when appropriate. According to this hypothesis our knowledge of spatial relations corresponds directly to the contents of memory. 2-51

252

R. N. WILTON AND P. E. FILE

Method

Downloaded by [University of Birmingham] at 14:04 05 November 2015

Subjects Eighty-eight students, enrolled in an introductory psychology course at the University of Texas, were randomly assigned to four groups of equal size. Apparatus and design T h e subjects were to examine an array of 1 3 circles, drawn on a sheet of paper, so that, following removal of the array, they could answer questions about the spatial relations between circles. The details of the apparatus and design were as follows. First, a prototype array of 13 circles, each of z cm diameter, was drawn on a 28 x 22 cm sheet of white paper. The positions of the circles were determined randomly with the restriction that no circles overlapped or were horizontally or vertically aligned. Each circle was divided into quadrants and labelled with a different consonant ; this allowed a subject to be questioned about the spatial relationship between any pair of circles. The questions were of the following type: “If a straight line was drawn from the centre of circle X to the centre of a circle Y which quadrant of X would it leave (pass through)?” The question was answered by specifying the appropriate quadrant of X: upper left, lower left, upper right or lower right. A subject’s answer, correct or incorrect, showed whether he knew how X and Y were spatially related. 64 Relations

44 Relations

FIG.I . The four arrays used in Experiment I.

KNOWLEDGE OF SPATIAL RELATIONS

253

Downloaded by [University of Birmingham] at 14:04 05 November 2015

In the experiment four variations of the prototype were used. Each variation was produced by blackening some of the quadrants in the circles of the prototype (Fig. I). When a quadrant was blackened, no question was asked about the relation of that circle to another if the straight line connecting the two circles passed through the blackened quadrant; thus the possibility of a subject being questioned about some of the relationships was eliminated. Quadrants were blackened selectively so that each variation of the prototype corresponded to the cell of a z x z factorial design. One variable in this design was the number of questions (44 or 64) that could be asked about an array. The other variable was the number of circles to which questions could refer: quadrants were blackened so that questions could be asked about all 1 3 circles or only nine of the circles (Fig. I ) . For illustration of an array produced for this design consider the top left-hand array of Fig. I . The 64 possible questions, involving nine circles, consist of the following: 2-7 (i.e. seven questions about a straight line drawn from 2 to another circle), F-8, Q-7, S-8, M-8, X-7, P-6, L-7 and W-6. Procedure Aided by a sample array, written instructions informed each subject that he was to memorize an array so that he could answer questions of the type described. The following paragraph, explaining the blackened quadrants, was included in the instructions. “One further point can now be made. In the sample map (array) you can see that some parts (quadrants) are blacked out. This will occur also in the experimental map. If a part is blacked out it means that questions involving straight lines going through that part will not be asked. Hence that part can be ignored. Also, of course, if two parts of a circle are blacked out both can be ignored. And if all four parts are blacked out no question will be asked about any part of that circle at all. Ask the experimenter if you don’t fully understand this”. The instructions also explained the sequence of events in the experiment. This consisted of 12 trials, with each trial allowing a 30-s exposure to the array, followed by 10 written questions of the described type. For each trial the questions were randomly selected from the set of questions possible for that array (thus a different sample of questions was asked on each trial). The subject was allowed 90 s to complete his answers and was told to guess when necessary. At no time was a subject allowed to draw an array.

Results

T h e total number of correct answers was computed for each subject over the 12 trials. Analysis of variance showed a significant effect of number of circles, F= 8.42, df= I, 84,P < 0.01,but no effect of number of possible questions, F < 1.0. T h e interaction did not approach significance, F < I ‘0.

Discussion As the subjects knew, when examining the array, the questions that could follow, they could have tried to memorize the answers to these questions. This approach-a type of paired associate learning in which the question is the stimulus and the answer is the response-would be suited to an organism with a large memory and no computational ability. However, since the subjects who should have been learning 4paired associates performed no better than subjects who were supposedly learning 64 paired associates it seems that such paired associates were not being learned. I n defence of the paired associate hypothesis one might argue that the subjects misunderstood the instructions and tried to learn the relationships of each circle to every other circle without regard to the blackened quadrants. T h e

Downloaded by [University of Birmingham] at 14:04 05 November 2015

254

R. N. WILTON AND P. E. FILE

number of paired associates would then be the same for each group. However, the number of “effective” circles (i.e. nine or 13) influenced performance, implying that the subjects understood the meaning of the blackened quadrants and acted appropriately when an entire circle was blackened. Therefore, the paired associate hypothesis can be maintained only by arguing that the subjects selectively ignored the instructions when memorizing relationships between circles that were only partially black; this seems implausible. T h e effect of number of effective circles on performance suggests that a subject learns the positions of the circles, and that answers to questions, rather than being learned, are generated by computation from the specification of a circle’s position. Thus our knowledge of spatial relationships is not knowledge drawn directly from memory; rather it is the consequence of our ability to manipulate stored information to produce appropriate and novel responses.

Experiment I1 Further progress in understanding our ability to specify spatial relationships requires investigation into the structure of the stored information and the computational procedures that are brought to bear on such information. Of these two requirements it seems necessary first to explore the structure of stored information : operations can then be postulated which link the stored information with the behavioural output. T h e information could be structured in a number of ways. I n the present paradigm, one possibility is that each circle is assigned an individual position in relation to a common reference point-as, for example, in a co-ordinate system in which the entire array is represented on a grid with a single origin. One advantage of such a common reference system is that the computation required for the derivation of relationships between circles is relatively straight-forward. An alternative structure for the information follows from the coding of circles in the same locality into higher order units. Rather than being assigned individual positions, as required by the co-ordinate hypothesis, the circles are stored as approximations to familiar patterns such as “triangle” or “diamond” shaped, or to a symmetrical or rule-governed arrangement (Attneave, 1954, 1955, 1957; Bartlett, 1932; Miller, 1956; Oldfield, 1954; Posner, 1972; Woodworth, 1938). I n utilizing previously stored patterns or rules from which the positions of individual circles can be determined, this system of organizing the circles may have the advantage of economy in storage load. Its primary disadvantage seems to be that the computation of relationships between circles in different patterns or codes cannot be simple. T h e position of a circle may be directly specified in relation to other circles in the same pattern as itself, but will be related to circles in other patterns only by a specification of the relationship between the patterns. Thus, when circles in different patterns are involved in computation, specifications on two levels must be manipulated. I n the following experiment the co-ordinate and pattern hypotheses were tested in a recognition task. Since, according to the pattern hypothesis, circles are stored as patterns, their recognition may depend on whether they fall into the same

KNOWLEDGE OF SPATIAL RELATIONS

255

patterns as in the original array. The co-ordinate hypothesis predicts no such dependency. Accordingly, the recognition task, in which the test items were incomplete reproductions of a memorized array, was designed to determine the existence of this dependency.

Method

Downloaded by [University of Birmingham] at 14:04 05 November 2015

Subjects Twenty students, volunteers from the University of Dundee, were used. Apparatus and design Eight memory arrays (arrays that were to be memorized) were constructed, each in the following manner. From a IOO x 60 matrix, provided on a 33.0 x zo.3-cm (foolscap size) sheet of graph paper, 12 points were randomly selected, subject to the constraint that no point was within 0.7 cm of another point. T h e selected points were then traced on to a sheet of white paper (the same size as the graph paper), and a circle of 0.7 cm radius (the size of a halfpenny) was drawn around each point. Two test arrays, for use in the different conditions of a recognition test, were constructed for each memory array. Both test arrays were incomplete reproductions of the memory array; one was designated random and the other designated adjacent. The random test array was constructed by randomly selecting six of the IZ circles of the memory array for reproduction. The adjacent test array was constructed by randomly selecting one of the 12 circles of the memory array and then selecting the five circles of the memory array nearest to that circle. For both kinds of test array the six circles selected from the memory array were drawn on a sheet of paper identical to that used for drawing the memory arrays. The design of the experiment was as follows: for every other subject, that is for any odd numbered subject in the experimental running order, five arrays were randomly selected from the eight memory arrays. These five arrays were to be memorized by that subject. In addition, the 16 test arrays were arranged in a random order for presentation in a later recognition test. Ten of these arrays were (necessarily) incomplete matches of the five memory arrays-one random and one adjacent test array for each memory array; the other six test arrays matched none of the memory arrays (being one random and one test array for each of the three memory arrays not given to the subject). Each even numbered subject was assigned the same five memory arrays as the preceding odd numbered subject. However, the 16 test arrays were reordered so thar the adjacent test array and the random test array, for a particular memory array, were interchanged. This eliminated possible bias in the ordering of adjacent and random test arrays. Procedure Each subject, run individually, was informed that the experiment was to consist of two phases, and that the second phase would be described on completion of the first phase. For the first phase a subject was told that he was to memorize and reproduce, from memory, each of five arrays. (The requirement to reproduce the arrays was inserted to prevent the subject adopting a strategy of partial memorization adequate only for a test of recognition.) Thus, after being allowed I ’5 min to examine the first array, the subject drew the array from memory. On completion of the drawing the procedure was repeated for subsequent arrays. I n the second phase the subjects examined the 16 test arrays, one at a time, indicating in each case, by saying “Yes”, “No”, or “Don’t know”, whether the six circles were located in positions previously assumed by six circles of a memory array.

Results The Wilcoxon test for matched pairs was used to compare performance in the adjacent and random conditions. The results showed that when the circles of a

256

R. N. WILTON AND P. E. FILE

Downloaded by [University of Birmingham] at 14:04 05 November 2015

test array had previously appeared in a memory array, the probability of a “Yes” response (which was 0.64 in the adjacent condition and 0.46 in the random condition) was significantly higher in the adjacent condition ( P < 0.02, two-tail). Thus, subjects were more likely to recognize correctly adjacent test arrays. Further analysis showed that when the circles of a test array had not previously appeared in a memory array the probability of a “Yes” response (0.25 in the adjacent condition and 0.18in the random condition) failed to differ significantly in the two conditions (P>o.o5, two-tail), This latter finding suggests that the greater tendency to recognize adjacent test arrays correctly was not part of an indiscriminate tendency to respond yes to all adjacent arrays without reference to the memorized arrays.

Discussion I n the second experiment, recognition performance was measured when subjects were presented with an incomplete reproduction of an array they had previously tried to memorize. T h e results showed that performance depended on the structure of the incomplete array: when the six circles of the incomplete array occupied adjacent positions in the original array, recognition was more likely than when the six circles were randomly selected from the original array. Such a result is neither predicted nor easily explained by the co-ordinate hypothesis : since recognition then depends upon the matching of individual circles in the incomplete array to circles in the original array, the distribution of circles in the incomplete array should be without effect. Turning to the pattern hypothesis, it should first be noted that two retrieval processes may contribute to recognition : either the circles may be recalled without reference to the test input, and then matched with the input, or they may be located in memory through the test items being classified in the same way as the original items and thereby arriving at the same storage locations (Kintsch, 1970). Provided that this latter (content address) process operates to some degree (as suggested, for instance, by recognition being usually better than recall), the pattern hypothesis predicts the present results. According to the pattern hypothesis, subjects group the circles into higher-order units and store these units rather than the individual circles. Thus, with recognition depending on the test items being classified in the same way as the original items, the probability of recognition will be increased when an incomplete array contains a group previously contained in the memory array. Moreover, with the added assumption that such groups generally consist of adjacent circles (Wertheimer, 1923; Kohler, 1940)it follows that an incomplete array of adjacent circles is more likely to be recognized than an incomplete array of circles randomly selected: the adjacent circles are more likely to “make contact” with the stored information. No formal questionnaire followed this experiment but the subjects usually volunteered information about the method they attempted to use in memorizing the arrays. Although a few were unclear as to the method used, most indicated that they had grouped the circles into patterns. Moreover, in a number of reproductions of the memorized arrays, it was obvious that groups of circles were simplified so that, in comparison with the original array, they more nearly approxi-

2-57

Downloaded by [University of Birmingham] at 14:04 05 November 2015

KNOWLEDGE OF SPATIAL RELATIONS

mated the shape of a triangle or straight line (Bartlett, 1932). One subject had actually drawn a framework of triangles, squares, and straight lines on which he had superimposed the circles. Thus, although these data should carry little weight, since they were gathered without reliable and precise measurement, they further support the pattern hypothesis. To store spatial locations in patterns may be advantageous in terms of memory load; but, as noted previously, it seems to make the computation of relations between arbitrarily selected locations more complicated : the computation of relationships between circles in different patterns must proceed at two levels of reference-between patterns and within patterns. Furthermore, a similar implication seems to hold for any theory which explains our results. Apparently, in all such theories, the position of a circle must be described in relation to other circles in its vicinity; therefore computation is always indirect when relations between circles in different locations are required. Thus, assuming our results to hold generally for the storage of spatial information, hypotheses about the operations carried out on such information may have to relinquish the characteristic of simplicity in order to be compatible with the organization of the information in memory.

References ATTNEAVE, F. (1954). Some informational aspects of visual perception. Psychological Review, 61, 183-93. ATTNEAVE, F. (1955). Symmetry, information, and memory for patterns. American Journal of Psychology, 68, 209-22. ATTNEAVE,F. (1957). Transfer of experience with a class-scheme to identificationlearning of patterns and shapes. Journal of Experimental Psychology, 54, 81-8. KOHLER,W. (1940). Dynamics in Psychology, New York: Liveright. KINTSCH,W. (1970). Models for free recall and recognition. I n NORMAN, D. A. (Ed.), Models of Human Memory. New York: Academic Press. MILLER,G. A. (1956). The magical number seven plus or minus two: some limits on our capacity for processing information. Psychological Review, 63, 8 1-97. OLDFIELD,R. C. (1954). Memory mechanisms and the theory of schemata. British Journal of Psychology, 45, 14-23. POSNER, M. I. (1969). Abstraction and the Process of Recognition. In BOWER, G. H. (Ed.), The Psychology of Learning and Motivation. Vol. 3. New York: Academic Press. TOLMAN, E. C. (1948). Cognitive maps in rats and men. Psychological Review, 55, 189208. WERTHEIMER, M. ( I 923). Untersuchungen ZUT Lehre von der Gestalt 11 Psychologische Forschung, 4, 301-35. WOODWORTH, R. S. (1938). Experimental Psychology. New York: Holt. Revised manuscript received

I

May 1974

Knowledge of spatial relations: a preliminary investigation.

Quarterly Journal of Experimental Psychology ISSN: 0033-555X (Print) (Online) Journal homepage: http://www.tandfonline.com/loi/pqje19 Knowledge of s...
566KB Sizes 0 Downloads 0 Views