visual and verbal processes in problem-solving

COGNITIVE PSYCHOLOGY 1, 201-214 (1970)

Visual and Verbal Processes in Problem-Solving

SHEILA JONES

University College London

The present paper investigates the relationship between the spatial assignments used by Ss in solving linear syllogisms and the lexical marking of the comparative adjectives used in the premises. This relationship is used to test predictions from two different theories about the relative difficulty of various types of linear syllogism. One theory is based on “spatial paralogic,” and the other concerns the deep structure analysis of language processing. The comparisons favored the latter theory. However, it is suggested that certain experimental conditions may have favored the use of verbal rather than visual processes in problem solution.

Recent research (Clark, 1969a,b; Desoto, London, & Handel, 1965; Handel, DeSoto, & London, 1968; Huttenlocher, 1968) in deductive reasoning has produced conflicting theories about the strategies used in solving linear syllogisms (sometimes called “three-term series” problems). This type of inference involves the serial ordering of three terms (A, B, C) from two premises stating their relationship on some common dimension; e.g., A is better than B; C is worse than B; who is best? The difficulty of a problem can be varied by using different (rather than the same) comparative adjectives in the two premises and also by chang- ing the order of presentation of the premises.

According to DeSoto et al. (1965) subjects solve linear syllogisms by constructing a mental picture of the terms A, B, C and assign spatial directions to the nonspatial relationships contained in the premises. This strategy involves ordering the terms on a directionally marked axis (vertical or horizontal) in cognitive space. The DeSoto et al. theory of “spatial paralogic” states that there is a preference for ordering terms in one direction rather than another: from top to bottom for vertical axes and left to right for horizontal orderings. The theory predicts that syllogisms containing relational terms assigned to the top of the vertical axis (or left of the horizontal axis) will be easier to solve because of these directional preferences.

Clark (1969a), however, considers that spatial paralogic theory cannot fully account for the relative difficulty of various linear syllogisms. In his view, reasoning is accomplished through the same mental operations used

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202 SHEILA JONES

in understanding language, and this entails interpretation at deep structure level. Clark argues that any theory in which Ss are assumed to work from linear encoding at surface structure level must therefore be inadequate. In place, of spatial assignments, Clark proposes, the principle of lexical marking. Certain “unmarked” or positive adjectives, such as tall, big, good, are assumed to be stored in a less complex form in memory and are more available than their opposites or “marked” forms. Because these unmarked adjectives are more readily registered and retrieved, syllogisms containing them will be more easily solved.

Clark claims that the crucial test between spatial paralogic and his theory can be made from predictions of the relative difficulty of “negative equative” forms of linear syllogisms; i.e., from premises in which “A is not as bad as B” replaces “A is better than B.” However, Clark assumes that Ss would use the same spatial assignment for the negatively expressed premises as for their positive forms. DeSoto et al. present no evidence for spatial assignments of negatively related terms. One aim of the first experiment is to obtain such evidence.

The chief aim of the first experiment, however, is to investigate a method for eliciting spontaneous directional preferences for ordering the terms in linear syllogisms and to examine the relationship between the spatial assignment of comparative adjectives used in the premises and their lexical marking.

EXPERIMENT 1

Method

Subjects

The Ss were 72 students of London University. They were tested in- dividually.

Materials

Table 1 shows the types of linear syllogisms used. Four, common to both sets, used the relation words better-worse, not as bud as, not as good US. The remainder consisted of alternative forms (a) and (b) to enable comparisons to be made between adjectives with two different opposites (i.e., light-dark cp. light-heavy), together with their negative equivalent forms. In Table 1, the list of adjectives used in the first premise of the various problems is given. Variety was introduced into the problems to avoid stereotyped solutions; no two contained the same relation words, and four different relative orderings of the premise terms A, B, C were

PROCESSES IN PROBLEM-SOLVING 203

used so that the problems varied in difficulty. Men’s names replaced the letters A, B, C in the problems presented to the Ss. Sheets of blank paper (8 in. square) were provided.

TABLE 1 Linear Syllogisms Used in Experiment 1

1. A is better than B; C is better than A. 2. A is not as bad as B; C is not as bad as A. 3. A is worse than B; C is better than B. 4. A is not as good as B; C is not as bad as B.

5(a). A is happier than B; C is sadder than B. 6(a). A is not as sad as B; C is not as happy as B. 5(b). A is happier than B; C is unhappier than B. 6(b). A is not as unhappy as B; C is not as happy as A. 7(a). A has a fatter face than B; B has a fatter face than C. 8(a). A’s face is not as thin as B’s; B’s face is not as thin as C’s 7(b). A has thicker hair than B: B has thicker hair than C. 8(b). A’s hair is not as thin as B’s; B’s hair is not as thin as C’s, 9(a). A weighs lighter than B; C weighs lighter than A.

IO(a). A is not as heavy as B; C is not as heavy as A. 9(b). A has lighter hair than B; C has lighter hair than A.

IO(b). A is not as dark as B; C is not as dark as A.

Procedure

The syllogisms with alternative forms (a) and (b) were assigned to alter- nate Ss, the first four problems being solved by all Ss. The problems were presented in a different random order to each S, and the questions to be answered (i.e., Who is best? or Who is worst?) were also randomized between Ss. The problems were not timed in the first experiment because the aim was to elicit directional preferences from the Ss during the process of problem-solving.

The method used to elicit spontaneous spatial representations is best described by the instructions given to them:

1 am going to give you a set of problems like the following: “Mary is older than Tom: Peter is younger than Tom; who is the eldest?” This may sound a little difficult as I say it to you like this, but you will be allowed to write down the three names mentioned in each problem on the piece of paper provided. This will help you to remember the names and stop you from confusing them between problems.

You can write the names anywhere you like on the paper but use a fresh sheet for each problem otherwise the names may get mixed up. Remember only the names are to be written down, nothing else. I shall read the first part of the problem to you and then you can jot down the two names, then when you are ready, I will read the second part of the problem and you can then jot down the third name. After that I shall ask you the question. Is that clear? There is no time limit, and if you want any part of the problem repeated I will do so.

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Results and Discussion

Spatial Representation

The device of providing pencil and paper as a memory aid proved suc- cessful in eliciting spontaneous representations of the ordering of the terms in the syllogisms. Seventy-two percent of the Ss wrote down the three names in systematic orderings on vertical or horizontal axes. The remainder simply wrote down the names verbatim in the order given in the premises. Two-thirds of the Ss using axes to order the names preferred vertical axes, the remainder horizontal. The majority of Ss assigned specific directions to the different relational terms in the syllogisms, the strategy being to write down the first two names in the first premise in a preferred order on the axis and then to add the third name to conform with the order.

A further point elicited by this method was that given a free situation, Ss selected a preferred axis for ordering the terms and retained the same axis for all the different relation words used in the syllogisms. Only three Ss changed from vertical to horizontal axes in solving the set of problems. This finding represents an important difference from the results obtained by DeSoto et al. (1965), using a different method for obtaining spatial assignments. Their Ss were presented with both vertical and horizontal axes and asked to place the terms of a premise statement in appropriate posi- tions at the ends of the axes. A preference was shown for placing terms on the vertical axis, as in the present experiment, but DeSoto et al. found that some relation words were consistently assigned to vertical axes, whereas others were inconsistently placed at either end of both axes. It seems possible that the provision of two axes made the Ss feel obliged to use both, and this may have led to less consistency than was found using the present method.

The Ss who chose to use axes in this experiment used them to solve linear syllogisms, rather than to represent the relation between terms of a single premise. This involved placing three terms, sometimes connected by two opposite relation words, i.e., happy-sad, on the same axis. The consistent use of one axis, vertical or horizontal, to solve these problems suggests that this was a convenient strategy for ordering three terms, rather than a representation of their spatial assignment in cognitive space, as DeSoto et al. suggest. The preference shown for writing the names in top to bottom, or left to right, orderings accords with common practice for reading and writing.


Directional Preferences

Table 2 shows the percentage of Ss displaying vertical directional preferences for the various relation words used in the syllogisms. The directions are those assigned to the terms A and B used in the first premise of each of the syllogisms shown in Table 1. (It should be noted, however, that the same direction was maintained by Ss in ordering the terms in the second premise.)

In the case of the Ss choosing horizontal axes, one-third adopted the strategy throughout of placing the first two terms, A and B, in the order left to right and then ordering the third term appropriately. When these were omitted, only 12 Ss showed differential horizontal directional preferences for the various relation words. Data for these Ss will be given only for problems common to both sets of syllogisms.

TABLE 2 Percentage of Directional Preferences for Relation Words

Used in First Premises

Positive comparative

form

A at top of vertical

axis

Negative equative

form”

A at top of vertical

axis

A better*than B A worse than B A happier’+ than B

A fatter than B

A thicker* than B

A lighter than B (weight)

A lighter than B (shade)

100 23

100

loo

100

18

A not as bad as B A not as good* as B A not as sad as B A not as unhappy as B A not as thin as B

(face) A not as thin as B

(hair) A not as heavy* as B

67 17 65 70 43

60

24

71 A not as dark as B 20

(1 Equivalent in meaning to corresponding positive comparative form in column 1, * Unmarked adjectives.

Positive Comparative Forms of Premise

Vertical axes. Table 2 shows that when better was used in the first premise, the better of the two terms (A) was assigned to the top of the vertical axis with 100% consistency. However, when worse was used in the first premise, A was assigned to the top in 23% of cases, i.e., a significant number of Ss changed direction for the better-worse relation pair

206 SHEILA JONES

(McNemar test for significance of changes: p = .008, two tailed). This result suggests that directional preference is modified by a tendency to assign the first term mentioned in the premise to the top of the axis, what- ever actual relation word is used.

In the positive comparative form of relation words, happier, thicker, and fatter were also assigned top to bottom directionality by all Ss. However, a remarkable difference in directional assignment is shown for lighter depending on the sense in which it is used. The first term in the premise (A) is assigned to the top of the vertical axis in 7 1% of cases when light is used in contrast to dark, but only in 18% of cases when light is contrasted with heavy. This indicates a complete reversal of directional preference for light depending on its semantic use (chi-square, df= 1, p < .Ol).

Introspective reports on directional preferences, given by 33 Ss, showed an overall tendency to assign top to bottom directionality to “positive” adjectives or “those containing most of a quality.” The following adjectives were most frequently mentioned as positive (in descending order of frequency): good, happy, heavy, and thick.

Horizontal axes. Fifty-eight percent of the Ss using horizontal axes (n = 12) showed a preference for left to right orderings for premises of the formA is better than B and also for A is worse than B. Thus there was no evidence for directional preference for the better-worse relation on the horizontal axis.

Negative Equative Form of Premise

These are listed in the third column of Table 2 and are equivalent in meaning to the corresponding positive forms in the first column of the Table.

Vertical axes. Table 2 also gives the directional preferences for the negative equative forms of premise. These were less strongly manifested than for the equivalent positive forms, and in the case of not as sad and the two forms of not as thin, the percentages did not differ significantly from chance.

For the negative equative form A is not as bud as B 67% of Ss using vertical axes assigned the better of the two terms (A) to the top. This com- pares with 100% assignment for the equivalent positive form A is better than B. A significant number of Ss changed directional preference for the negative equative (McNemar test, p = .OOl, two tailed). Similarly, a significant number of Ss changed their preferred direction for the negative equative forms of happier and thicker (McNemar test, p = .032, two tailed, in both cases).

A complete reversal of preferred direction was obtained for not as dark


compared with lighter (McNemar test, p = .02, two tailed) and also for not as thin compared with fatter (p = .004, two tailed).

The results in Table 2 indicate that changes in directional preference for negative equative forms are influenced by a tendency to assign top to bottom directionality to the actual adjective used in the first premise. In general, it can be seen that the finding that an adjective is consistently assigned top to bottom directionality in its positive comparative form is no guarantee that the same preferred direction will be assigned to its negative equative form.

Horizontal axes. Seventy-five percent of Ss showed a preference for left to right orderings for not us bad and 42% a similar preference for not as good. These percentages did not differ from chance probability.

Introspective evidence on strategies used for handling negatives showed that 13 out of 20 Ss stated that they converted negative equative comparatives to their equivalent positive forms, i.e., changed A is not as bud as B into A is better than B. Clearly the extent to which these transformations are made will influence the directionality assigned to the comparative statement. This is therefore an important factor to be considered in spatial assignments of negative equative forms of comparison.

Lexical marking

The results shown in Table 2 suggest a relationship between lexical marking and directional preference on the vertical axis. The adjectives marked with an asterisk in the first column of Table 2 are those designated as “unmarked” as opposed to “marked” on the criteria of lexical marking proposed by Clark (1969a). (In general, unmarked adjectives can be used in both a neutral as well as a contrastive sense.) Thus the adjective pairs better-worse, heavy-light, thick-thin, happy-sad, and tall-short are asym- metrical, the first member of the pair being unmarked and the second marked. The pairs dark-light, and fat-thin, however, are symmetrical- both members of the pair are marked.

For positive comparative forms of premise, the results in Table 2 show that unmarked adjectives are assigned top to bottom directionality in 100% of cases. When the marked members of these pairs are used in the first premise, the tendency to assign the unmarked adjective top to bottom directionality is present but to a lesser degree.

For the negative equative forms of the unmarked-marked pairs, there is a similar tendency to assign top to bottom directionality to the unmarked member of the pair but less consistently than for the positive comparative forms. Only two-thirds of the Ss show this directional preference in the case of not as bad and not as sad.

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For pairs in which both adjectives are marked, however, there is no consistent assignment of directionality to either adjective; for the premise A fighter than B the lighter of the pair(A) is assigned to the top by 7 1% of Ss, but for the negative equative form A not as dark as B, A is assigned to the top by only 20% of Ss. Similarly for A fatter than B, A is assigned to the top by 100% of Ss compared with only 43% of Ss for A not as thin as B.

Comparison between the unmarked-marked pairs of adjectives heuvy- light and the marked pair dark-light showed a significant difference in consistency of directional assignment (chi-square, df= 1, p < .Ol). A similar comparison for the unmarked-marked pair thick-thin and the marked pair fat-thin failed to show a difference in consistency of assignment.

Thus unmarked-marked pairs of adjectives tend to be hierarchically organized, whereas pairs with both adjectives marked are not. Table 2 suggests that knowledge of the lexical marking of an adjective should enable consistent spatial assignments to be made, with the unmarked adjective on top, as Clark (1969a) has proposed. However, in all cases, the present data indicate that this relationship between lexical marking and directional assignment is modified by a tendency to assign the first term mentioned in the premise to the top.

The main interest of the directional preferences shown in Table 2 is their implications for predictions of the relative difficulty of certain syllogisms based on spatial paralogic and deep structure theory. Clark (1969a) based the crucial test between these theories on comparison of syllogisms using the relation words not us good, not us bud in the premises. He assumed that directional assignments for these would be the same as for their positive equivalents worse than, better than, respec- tively. No evidence was presented by DeSoto et al. for spatial assignments of negative equative forms of premise. The data in Table 2 show that although a significant number of Ss changed their directional preference for not us bud compared with better than (and similarly for not us good compared with worse than), nevertheless a majority of Ss retained the same direction. Similarly, top to bottom directionality was maintained for the other unmarked-marked pairs of adjectives heuvy- fight, thick-thin, happy-sad for both positive and negative forms. Thus Clark’s assumption appears to be justified, and his contention that spatial paralogic theory would incorrectly predict the relative difficulty of certain syllogisms containing negative equative forms of premise is confirmed by this data.

However, the introspective reports in the present experiment, suggest- ing that some Ss adopted the strategy of translating the negative equative formA is not us bud us B into A is better than B, would affect predictions


based on deep structure analysis. If the negative equative form of premise was invariably transformed into its positive comparative form before being processed for memory storage, then the underlying base strings for both forms of premise would be the same. Analysis and predictions based on retrieval from base structure would then have to be revised.

The extent to which these transformations occur is obviously related to the experimental procedure. In the present experiment, no time limit was imposed, and Ss had ample opportunity to rephrase the premises if desired. Each S solved 10 problems, and, in order to discourage stereotyped solutions, four different orderings of the premise terms were used and different relation words used in each problem. In Clark’s experiment, on the other hand, Ss solved 96 problems under time pressure, with eight different orderings of premise terms, using the relation words better- worse throughout. The strategies adopted under such conditions would obviously differ considerably from those reported in the present experiment.

EXPERIMENT 2

The data from Experiment 1 enable further predictions to be tested based on spatial paralogic and deep structure theory. Previous experiments have mainly used unmarked-marked pairs of adjectives as relation words, e.g., taller-shorter, faster-slower, more-less and, of course, better-worse which has been extensively employed to test predictions from spatial paralogic and deep structure theories. Few studies have used marked pairs of adjectives. Problems based on negative equative forms of premise have also been confined to the unmarked-marked pair better- worse. The data in Experiment 1 allow further tests between the two theories to be made.

Problems using the comparative lighter would be expected to vary in difficulty depending on whether lighter is contrasted with heavier (unmarked adjective) or with darker (marked adjective). In Table 3, the types of problem to be considered are listed. Both theories would predict that problems of type I: A is heavier than B; B is heavier than C should be easier than type II: A is lighter than B; B is lighter than A. In the case of spatial paralogic theory, the prediction is based on the preference for top to bottom directionality of type I compared with bottom to top for type II. In terms of deep structure analysis, the prediction is based on the lexical marking characteristics of the unmarked adjective heavy compared with its marked opposite light; heavier has a simpler memory coding than light and is therefore more readily understood.

In the case of the marked adjective pair dark-light, however, there should be no difference in coding complexity, and deep structure analysis

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TABLE 3 Mean Time (set) to Solve Linear Syllogisms Using

Different Pairs of Relation Words

Problem type Lexical variations

Mean solution time (set)

I II

I II

I II

I II

III IV

V VI

V VI

A heavier than B; B heavier than C A lighter than B; B lighter than C

A darker than B; B darker than C A lighter than B; B lighter than C

A thicker than B; B thicker than C A thinner than B; B thinner than C

A fatter than B; B fatter than C A thinner than B; B thinner than C

A not as bad as B; C not as good as B A not as good as B; C not as bad as B

A not as happy as B; C not as happy as A AnotassadasB;CnotassadasA

A not as happy as B; C not as happy as A A not as unhappy as B; C not as unhappy as A

8.0 9.4

11.1 11.5

9.4 13.9

8.4 10.3

10.5 10.4

8.4 11.8

12.7 15.0

would predict no difference in difficulty if this pair of adjectives was substituted in problem types I and II. Spatial paralogic considerations would also predict no difference in difficulty since the data from Table 2 indicate no change in preferred directionality for dark vs. fight. The above analysis and predictions hold equally for comparisons of the unmarked pair thick-thin and the marked pair fat-thin when substituted in problem types I and II (see Table 3).

The two theories diverge, however, in prediction of relative difficulty of problems using negative equative forms of statement. Directional preferences shown in Table 2 indicate that problem type III A is not as bud as B; C is not us good us B has top to bottom directionality for the first premise and the reverse for the second premise. Between premises the better pair is given first and the worse pair second. Thus the premise combination for problem type III proceeds from top to bottom. A similar analysis of problem type IV, which contains the same two premises as type III but in reverse order, shows that between premises the directionality is bottom to top, i.e., the reverse of type III. Because of this difference in directionality between premises, spatial paralogic would predict type III should be easier than type IV. Predictions for deep structure theory, however, are that both problem types will be of equal


difficulty because their underlying base strings are the same. Clark’s data (1969a and b) confirm this analysis in terms of solution times and errors for these problem types.

The two theories also diverge in their prediction of relative difficulty of problem type V A is not as happy as B; C is not as happy as A and type VI A is not as sad as B; C is not as sad as A. Clark would predict that type V, with underlying base structure happy (unmarked), should be easier than type VI with underlying base sad (marked). Clark (1969a) demonstrates this difference between problem types V and VI for the relationship better-worse.

However, according to spatial paralogic theory both these problems should be of comparable intermediate difficulty. Type V has bottom to top directionality within each premise but top to bottom directionality between premises. For type VI, however, there is top to bottom directionality within each premise and bottom to top between each premise. This reversal of directionality in the premise combinations of both types of problem leads to the prediction that types V and VI should be of equal difficulty on spatial paralogic considerations.

Method and Procedure

Two sets of problems were constructed, using the linear syllogisms shown in Table 3. Each set contained two problems of type I, two problems of type II, and one each of problem types III, IV, V, and VI. In the first set, the comparatives heavy-light, fat-thin (problem types I and II), better-worse (problem types III and IV), and happy-sad (problems types V and VI) were used. In the second set, the comparatives dark- light, thick-thin (problem types I and II), better-worse (problem types III and IV), and happy-unhappy (problem types V and VI) were used. Men’s names replaced the letters A, B, C. Each problem was typed on a separate card together with the question to be answered. The question was always congruent with the relation word used in the syllogism-for the problem types II and IV in which both the relation words better-worse were used, the question asked was “Who is worst?” in both cases.

All Ss obtained practice in solving linear syllogisms in Experiment 1 which immediately preceded this experiment. The two sets of problems were allocated in such a way that each S used the same pairs of relation words in both experiments. Ss were instructed to turn each card face upwards when told and to read it silently and give the answer as quickly as possible consistent with accuracy. They were timed from when they turned up the card to the production of an answer. Two practice trials were given before the experimental set was presented. Each S received the cards in a different randomized order.

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The Ss were the final 32 Ss from the sample used in Experiment 1. Data from their directional assignments indicated that 18 used vertical axes to order the names in the syllogisms, 5 used horizontal axes, 1 used the same direction for each pair of relation words, and the remainder wrote down the names verbatim in the order read to them.

Results and Discussion

Mean solution times for the lexical variations used in problem types I to VI are shown in Table 3. The effect of the lexical variations heavy-light vs. dark-light in problem types I and II was tested, using a 2 x 2 analysis of variance of the time scores (converted to reciprocals). For the main effects, only the problem type was significant [F(1,30) = 4.41, p < .05]. The interaction between problem type and lexical variation was significant [F(1,30) = 6.43, p < .025], i.e., the difference in solution times for problem types I vs. II is greater for the unmarked-marked pair heavy-light than for the marked pair dark-light. This result supports predictions from lexical marking.

A similar comparison of solution times for the lexical variations thick- thin vs. fat-thin showed a significant main effect for lexical variation [F(1,30) = 4.30, p < .05], but there was no significant interaction effect. However, there was a significant difference in solution times of problem type I and II for the unmarked-marked pair thick-thin (p < .05) but not for the marked pair fat-thin. This result accords with lexical marking predictions.

When time scores for Ss showing directional preferences in Experiment 1 (n = 18) were considered separately, the predicted difference for heavy- light was obtained but not in the case of thick-thin. There was no significant difference for either of the marked pairs dark-light or fat-thin, and this accords with predictions based on directionality.

In the case of negative equative forms of syllogism, comparison of problem types III and IV showed no significant difference between time scores (z = .22, Wilcoxon signed ranks test). This is in agreement with predictions based on deep structure analysis. However, on the basis of directionality it was predicted that type III should be easier than type IV. No significant difference was found when the scores of Ss, using directional preferences in Experiment 1, were considered separately. However, only 12 of these Ss conformed to the directionality of not as bad, not as good shown in Table 2, and this may have been too small a sample to detect a difference, if present.

For the negative equative problem types V and VI, the effect of the lexical variations happy-sad vs. happy-unhappy on solution times was compared by means of a 2 X 2 analysis of variance. Both the main effects of problem type and lexical variation were significant [F(l,30) = 5.3,


p < .05; and F(1,30) = 5.2, p < .05]. There was no significant interaction effect. Thus problem type V using the unmarked adjective happy was significantly faster in solution time than problem type VI using either of the marked adjectives sad or unhappy. This result is in accordance with predictions from lexical marking. Predictions based on directional preferences, however, were that both these problem types would be of equal difficulty. When scores for Ss for whom directional preferences were known were considered separately, a significant difference was found for happy-sad, (p < .05) but not for happy-unhappy.

GENERAL DISCUSSION

The relationship between lexical marking and directional preferences shown in Experiment 1 indicates that the asymmetry of unmarked-marked pairs of adjectives is reflected in their hierarchic 1 arrangement on the vertical axis. The “positive” member of the pair is placed at the top. In the case of symmetrical pairs of adjectives, in which both members are marked, this distinction disappears, and the adjectives are given equal status on the vertical axis.

The relationship between spatial assignments and lexical marking was more strongly established for the positive comparative forms of premise than for the negative equative forms. In the latter case, the tendency was shown to assign directionality in a more arbitrary fashion; the first term used in the premise was often placed at the top of the axis regardless of the lexical marking of the actual relation word used.

In Experiment 2, both spatial paralogic and deep structure theory were able to account satisfactorily for the relative difficulty of the syllogisms using positive comparative forms of premise. However, for syllogisms using negative premises, directional preferences based on spatial paralogic principles were less strongly evident, and deep structure theory gave a more reliable prediction of the relative order of difficulty.

However, a further possibility exists that the directional preferences shown in Experiment 1 are not made use of in the solution of problems in Experiment 2. In the first experiment, Ss listened to the problems before making directional assignments, whereas in the second experiment Ss read the problems silently to themselves. Brooks (1967) has shown that reading can suppress visualization and force the Ss to deal with informa- tion in a more exclusively verbal form than does listening. The results from Experiments 1 and 2 suggest that although the majority of Ss make use of axes to order the terms of linear syllogisms when conditions permit, such spatial assignments are not necessary for problem solution. Differences in problem difficulty can be adequately accounted for in terms of language comprehension, as formulated by deep structure theory, without recourse to speculations based on spatial imagery.

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REFERENCES

BROOKS, L. R. The suppression of visualization by reading. Quarterly Journal of Ex- perimental Psychology, 1967, 19, 289-299.

CLARK, H. H. Linguistic processes in deductive reasoning. Psychological Review, 1969,76, 387-404. (a)

CLARK, H. H. The influence of language on solving three-term series problems. Journal of Experimental Psychology, 1969, 82, 205-2 15. (b)

DESOTO, C. B., LONDON, M., & HANDEL, S. Social reasoning and spatial paralogic. Journal of Personality and Social Psychology, 1965, 2, 5 13-52 1.

HANDEL, S., DESOTO, C., & LONDON, M. Reasoning and spatial representation. Journal of Verbal Learning and Verbal Behavior, 1968, 7, 351-357.

HUTTENLOCHER, J. Constructing spatial images: A strategy in reasoning. Psychological Review, 1968, 75, 550-560.

(Accepted March 18, 1970)

visual and verbal processes in problem-solving

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