Reasoning strategies

Published in: European Journal of Cognitive Psychology (2008), vol. 20, pp. 1065-1086 Status: Postprint (Author’s version)

Reasoning strategies: The role of working memory and verbal-spatial ability Alison M. Bacon, Simon J. Handley, Ian Dennis & Stephen E. Newstead University of Plymouth, Plymouth, UK

Abstract Evidence increasingly suggests individual differences in strategies adopted on reasoning tasks and that these are either verbal-propositional or visuospatial in nature. However, the cognitive foundations of these strategies remain uncertain. Experiment 1 examined the relationship between the use of working memory resources and strategy selection for syllogistic reasoning. Verbal and spatial strategy users did not differ on working memory capacity, but confirmatory factor analysis indicated that while verbal reasoners draw primarily on verbal working memory, spatial reasoners use both this and spatial resources. Experiment 2 investigated the relationship between strategies and verbal and spatial abilities. Although strategy groups were similar in overall ability, regression analysis showed that performance on a spatial ability measure (Vandenberg mental rotation task) predicted syllogistic reasoning performance, but only for spatial strategy users. The findings provide converging evidence that verbal and spatial strategies are underpinned by related differences in fundamental cognitive factors, drawing differentially on the subcomponents of working memory and on spatial ability. DOI: 10.1080/09541440701807559

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Introduction Reasoning involves the manipulation and transformation of knowledge and information in order to make inferences about the world. Theories have often assumed the existence of a universal mechanism to explain the processes involved in reasoning, be it the construction of mental models (e.g., Johnson-Laird & Byrne, 1991) or the application of logical mental rules (e.g., Rips, 1994). However, there is growing evidence to suggest that individuals differ in the strategies spontaneously adopted during reasoning tasks. For instance, Bacon, Handley, and Newstead (2003) and Ford (1995) have shown that for syllogistic reasoning, most individuals spontaneously adopt one of two strategies: either visuospatial or verbal-propositional. Syllogisms are logical arguments comprising two premises and a conclusion, for example, ‘‘All teachers are psychologists; Some writers are teachers; Therefore, Some writers are psychologists’’. Each syllogism contains three terms (teachers, psychologists, and writers in this example), one of which is common to both premises (in this case, teachers). Each premise contains one of four possible quantifiers (either All, Some, None, or Some ... not), which describe the relationship between terms. The classic syllogistic inference is to determine, from the information given in the two premises, the one relationship which is not explicitly stated, that between the two other terms (e.g., psychologists and writers) which forms the conclusion (i.e., ‘‘Some writers are psychologists’’). Such problems encapsulate many aspects of everyday reasoning such as deciding what conclusion, if any, can be drawn from assumptions about category membership, using stored knowledge and evaluating arguments. Bacon et al. (2003) and Ford (1995) both present verbal and written protocol data in support of the verbal-spatial strategy distinction. According to Bacon et al., Spatial reasoners produced an explicit representation of relationships between 2


terms and premises. Their written protocols showed terms placed in differing spatial arrays to represent the relationship between them and verbal reports described premise content in terms of groups or subsets. Spatial reasoners first construct a representation of the relationship between the first two terms (Premise 1) and then augment this by adding information about the third term from Premise 2. Verbal reasoners, on the other hand, manipulate information in its abstract form, frequently simply swapping around the terms in the premises. This substitution strategy involves obtaining a value for the common term from the first universal (All) premise encountered and simply substituting that value for the common term in the other premise to reach a conclusion. Their verbal protocols describe this substitution behaviour, sometime combined with the use of simple rules which define conclusions as associated with particular combinations of quantifiers, for instance, All+None = a None conclusion. In addition, in the Bacon et al. (2003) study, participants completed a questionnaire that identified a further range of strategy traits which again fully supported the verbalspatial strategy classification based on the written protocols. Questionnaire responses also suggested that protocols did not result from vestigial memories of earlier experiences, such as skills learned in school. Importantly, such strategy distinctions are not limited to syllogistic reasoning. Many everyday decisions are based on inferences about the relationship between objects, for instance, evaluating the relative merits of several products before deciding which to purchase. In this type of relational reasoning, objects can be ordered in a single dimension, for instance a scale where A is above B and B is above C. Hence, A must necessarily be above C and the recognition of this relationship is described as a transitive inference. Bacon, Handley, and Newstead (2004) directly compared strategies used for transitive inference and syllogisms. Individuals who used a spatial strategy for syllogisms presented protocols for transitive inference that showed an 3


explicit visual image of the relational adjectives involved. Conversely, those reasoners who employed a verbal strategy for syllogisms presented written protocols for transitive inference that indicated no explicit representation of the meaning of relational terms, rather they just ordered terms in a sequence that reflected their position on a relational scale. These findings reflect those of early work by Egan and Grimes-Farrow (1982), who also identified two groups of reasoners on transitive inference tasks, one using an imagistic process and the other preferring a more functional, systematic approach. Furthermore, the verbal-spatial distinction has been found in studies of strategies for sentence-picture verification (e.g., MacLeod, Hunt, & Mathews, 1978) and compass point direction tasks (Roberts, Gilmore, & Wood, 1997). The distinction is further supported by brain imaging studies that have indicated that reasoners instructed to use either a verbal or spatial strategy show differing patterns of activation when subjected to fMRI (Reichle, Carpenter, & Just, 2000). The degree of activation observed was further related to levels of verbal and spatial ability. Overall, this evidence converges to suggest that interstrategic differences are not epiphenomenal; rather they represent a fundamental difference in the way individuals use and represent information during reasoning. However, despite this growing body of evidence, the question remains as to whether strategies are underpinned by a universal mechanism or by distinct mechanisms supported by separate cognitive structures. One way of addressing this question is to evaluate the extent to which spatial and verbal reasoners draw upon distinct cognitive resources. In this paper we focus on two approaches for indexing variations in resource, differences in working memory and individual differences in ability. Findings suggest that individual differences in these domains and reasoning are inextricably linked. Cooper and Mumaw (1985) presented a series of studies which suggested that individual differences in strategies for spatial problem solving 4


were related to differences in spatial ability. They assessed ability by means of a mental rotation test developed by Shepard and Metzler (1971) and also a visual comparison task, which involved matching a three-dimensional figure to a corresponding (or not) orthographic representation. Two strategies were identified from verbal protocols: a constructive strategy (thought to involve the construction of a three-dimensional internal representation) and an analytic strategy (involving the sequential comparison of individual features). High ability individuals who adopted the constructive strategy (thought to be most compatible with their ability) were both faster and more accurate reasoners. Low spatial ability individuals using an analytic strategy, however, performed similarly, suggesting that this approach was more suited to their level of aptitude. Kyllonen, Lohman, and Snow (1984) also showed that even when aptitude is not reflected in initial strategy choice, it could influence accuracy and efficiency in appropriate tasks (e.g., high spatial ability individuals performing a spatial task). MacLeod et al. (1978) identified both a pictorial and a linguistic strategy for a sentence-picture verification task (where participants have to decide whether a picture accurately represents a verbal description). Although the strategy groups differed in spatial ability (the pictorial group presenting higher levels), measures of verbal ability (which incorporated comprehension, vocabulary, and verbal analogy) could not discriminate between them. Another candidate set of resources for indexing the role of different systems in reasoning are spatial and verbal working memory. The working memory system is typically characterised as a tripartite system comprising three distinct, but related, components, a regulatory central executive and two slave systems responsible for verbal and spatial memory storage and processing (see Baddeley & Logie, 1999, for review). Working memory capacity has been shown to relate to individual differences in verbal abilities such as reading comprehension 5


(e.g., Daneman & Carpenter, 1980; Oakhill, Yuill, & Parkin, 1986) and performance on Scholastic Aptitude Tests (e.g., Just & Carpenter, 1992; see Daneman & Merikle, 1996, for a metaanalysis). Low spatial ability individuals are reported to have difficulty maintaining spatial memory traces whilst concurrently processing object transformations (Just & Carpenter, 1985). Moreover, working memory capacity has been closely associated with reasoning performance (Kyllonen & Christal, 1990) and studies employing dual-task methodology consistently report a role for the central executive and verbal working memory in both syllogistic and conditional reasoning (Gilhooly, Logie, Wetherick, & Wynn, 1993; Gilhooly, Logie, & Wynn, 2002; Klauer, Stegmaier, & Meiser, 1997; Toms, Morris, & Ward, 1993). Surprisingly, these studies consistently indicate little, if any, involvement of the spatial working memory system in reasoning. The spatial reasoners observed by Bacon et al. (2003) and Ford (1995) clearly use a visuospatial* approach presumably spatial working memory is an important resource for those people. An fMRI study of imagery during conditional reasoning has indicated a role for spatial processes (Knauff, Mulack, Kassubek, Salih, & Greenlee, 2002) and tasks that are thought to have a spatial component, such as linear syllogisms containing spatial adjectives, are affected by secondary tasks that load spatial working memory, though again the central executive also seems to play a major role (e.g., Vandierendonck & de Vooght, 1997). Shah and Miyake (1996) have suggested the central executive may contain distinct resources for spatial and linguistic information and Handley, Capon, Copp, and Harper (2002) presented evidence that two systems for dealing with spatial and verbal representations were involved to a different degree in different types of problem solving task. Capon, Handley, and Dennis (2003) extended this research to syllogistic reasoning. They argued that if Shah and Miyake’s 6


(1996) thesis was correct, and verbal and spatial central executive resources are dissociable, then established theories of reasoning would offer differing predictions regarding the role of the different working memory systems in reasoning. Rule-based theories, which emphasise the role of propositional or language-based representations (hence presumably a verbal strategy), suggest that syllogistic tasks would draw preferentially on verbal resources. In contrast, model theories, (which encompass the spatial strategy), predict a more important role for spatial working memory. Subjects completed two syllogistic reasoning tasks (with visual and verbal presentation of the premises) plus a series of working memory span measures. Correlational analysis indicated that syllogistic reasoning performance was predicted by both spatial and verbal working memory resources. Furthermore, a confirmatory factor analysis showed that an orthogonal three-factor model, comprising a verbal, a spatial, and a general factor, fitted the data well. Interestingly, Capon et al. (2003) have tested this three-factor model on Shah and Miyake’s data and found it to be an excellent fit. Overall, syllogistic reasoning performance (irrespective of presentation modality) loaded significantly, and to a similar degree, on both verbal and spatial working memory resources, and also on a third, general factor. Capon et al. offer two possible explanations; either that syllogistic reasoning involves both verbal and spatial forms of representation, or that individual differences exist: loadings on the two factors may in fact reflect different groups of individuals. They relate this hypothesis to the strategies identified by Ford (1995) and suggest that some individuals may be using a verbal strategy that draws on verbal memory resources, whilst other individuals use a spatial approach, influenced by spatial working memory. Experiment 1 investigated this hypothesis, that loadings on the verbal and spatial factors represent two distinct groups of individuals, reasoning with a verbal and a spatial strategy respectively. 7


EXPERIMENT 1 Methods Participants One hundred and fifty five undergraduates from University of Plymouth took part in return for their choice of course credit or £5. The sample comprised 27 males and 128 females, mean age 22.08 years. All were native English speakers and none had received formal training in logic. Materials and procedures Participants were tested in small groups of up to four people in sessions lasting about 1 hour. The sessions were administered by an experimenter whose role was to set up each task for the participants and answer questions following the practice trials. Participants worked through the following six tasks, one at a time, in the order given here. They were not permitted to read aloud on any task, or to write during the computer-based tasks. Syllogistic reasoning. All participants completed two syllogistic reasoning tasks. In the first they were asked to generate conclusions to five categorical syllogisms with terms consisting of well-known occupations or hobbies, whilst also providing concurrent written protocols detailing their working out. The problems were presented in a booklet, one to a page, with space below for the protocol. Two practice problems were presented first. This was in effect a shortened version of the task described by Bacon et al. (2003) and has been shown to allow for successful identification of strategy preference (Bacon et al., 2004). Second, they completed the visually presented syllogistic reasoning performance task as used by Capon et al. (2003) and shown by them to possess a high level of internal reliability (Cronbach’s alpha=.82). This involved generating conclusions to 8


16 syllogistic problems presented individually on a computer screen. Conclusions were typed into a box provided and the computer recorded these responses. No written working out was allowed. The 16 problems, together with their logical conclusions, are shown in the Appendix. All possible syllogistic figures and mental model counts are represented within this list, affording a range of problem difficulty. We wished to avoid responses based on believability hence purposely presented problems which we (Bacon et al., 2003; 2004) and Capon et al. (2003) have found to be relatively belief- neutral. No syllogisms were repeated across the two reasoning tasks. Working memory measures. Participants completed four working memory measures. These tasks originated in the work of Shah and Miyake (1996) and were developed in the present form by Capon et al. (2003). Simple verbal word span. This is designed to measure passive storage capacity for verbal information, with no explicit processing requirement. To- be-remembered words were presented in sets of increasing size from two to seven words, with five sets of each size. Each word appeared on the computer screen individually for 800 ms, with an interstimulus interval of 50 ms. At the end of each word set, a lightbulb symbol appeared on the screen and the program paused to allow the participant time to write down the words presented on a simple paper response sheet. They were instructed to write down as many words as they could recall in the order presented on computer and hence difficulty increased with set size. The simple verbal word span score was calculated by awarding one point for each correctly recalled word, in each correctly recalled set, regardless of level. For instance, if a participant completed four two-word sets correctly and two three-word sets correctly, the score = (4x2) + (2x3) = 14.The maximum possible score was 135.

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Simple spatial arrow span. Again this task originated in the work of Shah and Miyake (1996) and developed in the present form by Capon et al. (2003). The task was designed to measure passive storage capacity for spatial information, with no explicit processing component. Again the stimuli were presented in sets of ascending size, with 3 sets at each level of two to six items, 15 sets in total. In this task, each test item comprised an arrow pointing in one of eight possible orientations. Each arrow remained on the screen for 1000 ms, with an interstimulus interval of 250 ms. Following each set of arrows, a grid was presented, showing all eight possible orientations. The task was to indicate, via a mouse click, the directions of each of the arrows in the set, in the order presented. The simple spatial arrow span score was calculated by a similar procedure to that for the simple word span described previously. One point was awarded for each correct arrow, in each fully correct set; i.e., if a participant got three two arrow sets correct and one three arrow set, (3x2) + (1x3) = 9. The maximum total score for this task was 60. Complex verbal sentence span. This task was based on the reading span test devised by Daneman and Carpenter (1980). It is intended to be a span measure of functional working memory capacity for verbal material and also requires the simultaneous maintenance and processing of information. The task required participants to verify sets of sentences as either true or false, whilst also remembering the final word of each sentence. Sentence order was randomised prior to the experiment and remained in that same order for all participants. Sentences were presented on computer in sets of increasing size from two to six sentences. Five sets were presented at each level. Each sentence remained on screen for 800 ms after which two buttons labelled ‘‘true’’ and ‘‘false’’ appeared. Participants were asked to click on the appropriate button to make their response. After, an interval of 250 ms, the next sentence in the set appeared. After all the sentences in a set had been presented, the computer 10


program would pause and allow time for the to-be- remembered words to be recalled and noted on a written response sheet. Again, participants were instructed to write down as many words as they could recall in the order presented. Scoring was by the same principle as for the previous two tasks. Hence, the maximum score was 100. The number of errors made in the verification component of the task (true/false judgement) was also recorded. Complex spatial letter span. This task was a span measure of functional working memory capacity for spatial information which also required the simultaneous maintenance and processing of spatial material. Again, the test items were presented on computer in sets of ascending size, from two to five items, with five sets at each level. Each item comprised one of five letters (F, J, L, P, or R) presented in one of eight possible orientations, and either as a normal or mirror image. Presentation was constrained so that opposing orientations were not presented successively within a set and that each orientation appeared only once per set. The letters remained on the screen for a maximum of 5000 ms and participants were required to respond whether the letter was a normal or mirror image by clicking on an appropriate button. After an interstimulus interval of 250 ms, the next letter would appear. After each set, participants were presented with a grid identical to that used in the simple arrow span. They used a mouse click to indicate the direction in which the top of each letter was oriented, in the order the letters were presented. Scoring was calculated exactly as for the complex verbal sentence span. If a set was correct, regardless of level, one point was recorded per letter. The total possible score was therefore 80. The number of errors on the verification component (normal/mirrored judgment) was also recorded.

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Results and discussion Strategies were first identified from written protocols produced when generating conclusions to the five syllogisms in the strategy identification task. Categorisation was based on the characteristics identified by Bacon et al. (2003) and Ford (1995), described previously. Ninety-three (60%) of participants presented evidence of a verbal strategy and a further forty-eight (31%) of a spatial strategy throughout. The remaining 9% either produced no protocols (despite instructions) or a mixed strategy with evidence of both verbal and spatial strategies being used. Figure 1 presents examples of written protocols produced by verbal and spatial reasoners respectively. The protocols show the typical characteristics attributable to verbal and spatial reasoners.

Typical protocols produced by verbal and spatial reasoners for the syllogism: Some of the carpenters are dancers All of the dancers are birdwatchers

Verbal reasoners Participant 7

Some of the carpenters are dancers All of the dancers are birdwatchers

Spatial reasoners Participant 20

C

D

B

Figure 1. Experiment 1: Typical written protocols produced by verbal and spatial reasoners.

These characteristics are fully in line with those observed in previous studies and no significant within-strategy variation in protocol style was observed. In the verbal reasoner’s protocol, the left-hand a r r o w indicates how she has swapped over the premises in order to begin reasoning with the universal premise (indeed she annotates the arrow to this affect, explaining her 12


tactic). The right-hand arrow shows her recognition that birdwatchers means dancers and hence the terms can be substituted to give the correct conclusion, ‘‘Some of the carpenters are birdwatchers’’. In the spatial reasoner’s protocol, the terms in the first premise (carpenters and dancers) have been represented as having an overlap relationship with the two circles presented as is typical for spatial reasoners with premises involving the quantifier Some. The third term (birdwatchers) has t h e n been added to the initial representation as a further oval. This totally encompasses that of dancers (because All dancers are birdwatchers), and hence also contains the part of the carpenters’ oval which overlaps with dancers. By this means this participant also gave the correct conclusion, ‘‘Some of the carpenters are birdwatchers’’. Verbal and spatial reasoners performed similarly on the syllogistic reasoning task (verbal 47% correct, SD=17; spatial 49% correct, SD=22, p>.05). Table 1 compares their performance on the working memory measures. The only measure where a significant difference in performance was observed between strategy groups was the complex spatial error (number of incorrect normal/mirror image judgments). Here spatial reasoners made significantly fewer errors, t (139) =2.00, p=.05. This suggests the two strategy groups do not differ significantly in working memory capacity. TABLE 1. Experiment 1: Comparison of verbal and spatial reasoners on all measures (percentage scores). Simple verbal

Verbal Spatial

Complex verbal

Complex verbal error

Simple spatial

Complex spatial

Complex spatial error

Mean

SD

Mean

SD

Mean

SD

Mean

SD

Mean

SD

Mean

SD

78.8 79.5

21.2 31.9

27.8 26.3

15.7 17.8

8.2 9.1

5.6 5.9

36.5 39.5

14.6 16.5

22.6 22.8

16.1 19.9

15.8 11.9

10.9 10.8

Table 2 shows correlations between measures, and with syllogistic reasoning performance, again by strategy group. 13


The relationship between syllogistic reasoning and the simple verbal span is considerably stronger and differs in polarity for verbal reasoners compared to spatial strategy users. The difference is close to significance (z=1.74, p=.08), which offers some evidence that performance of the two groups may not be predicted by wholly the same factors. The two spatial measures correlate similarly with syllogisms for both strategy groups. In terms of the working memory measures, the two verbal span measures are strongly, and similarly, correlated for both groups. However, the relationship between the two spatial measures is almost twice as strong in spatial reasoners as it is in the verbal (z=1.92, p=.05) suggesting more common variance between these tasks for the spatial reasoners. TABLE 2. Experiment 1: Correlations with syllogistic reasoning and between working memory span measures, compared across strategy group

Syllogisms Syllogisms Verbal 1 Spatial 1 Simple verbal .36** Verbal Spatial -.06 Complex verbal Verbal .37** Spatial .38** Complex verbal error Verbal -.27** Spatial -.16 Simple spatial Verbal .30** Spatial .35** Complex spatial Verbal .20 Spatial .19 Complex spatial error Verbal -.18 Spatial -.15

Simple verbal

Complex verbal

Complex verbal error

Simple spatial

Complex spatial

1 1 .57** .53**

1 1

-.27* -.15

-.23* -.22

.26* -.02

.22* .26

-.24* -.20

.38** .30*

-.33** -.33*

.36** .14 -.05 -.09

-.04 -.06

1 1

.03 -.10

1 1 .33** .60** -.28** -.21

1 1 -.24* -.13

*Significant at .05, **significant at .01. Correlations in bold type highlight those specifically discussed in the text.

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In order to test whether the two strategy groups draw differentially on working memory resources, a multipopulation confirmatory factor analysis was conducted. The relatively few measures of each construct (and relatively low N in the spatial group), precluded testing a three-factor model (as Capon et al., 2003). Instead we tested a correlated two-factor model, loading the spatial measures on one factor and the verbal measures on the other. This approach was motivated by the work of Handley et al. (2002) mentioned earlier. The correlation represents common variance which would be accommodated in the third factor of Capon et al.’s model, making the two models conceptually similar. Syllogistic performance was allowed to load on both factors and the models were run separately on each strategy group. The model fitted well, χ2 (24) = 29.8, p=.19, CFI=0.96. Table 3 shows the standardised loadings for each strategy group. TABLE 3. Experiment 1: Standardised loadings for the two-factor model for both strategy groups Measure Syllogisms Verbal Spatial Simple verbal Verbal Spatial Complex verbal Verbal Spatial Complex verbal error Verbal Spatial Simple spatial Verbal Spatial Complex spatial Verbal Spatial Complex spatial error Verbal Spatial

Factor 1 (Verbal resource)

Factor 2 (Spatial resource)

R2

.43* .28*

.10 .31*

.26 .22

.75*** .53***

.56 .28

.73*** 1.00***

.53 1.00

-.39 -.22

.15 .05 .55*** .92***

.3 .85

.68*** .65***

.46 .42

-.37 -.22

*Significant at .05, ***significant at .001.

15

.11 .05


The findings provide evidence consistent with the notion that, during syllogistic reasoning, verbal and spatial reasoners draw on different working memory resources. As Table 3 shows, for the verbal strategy group, syllogistic performance loaded significantly on Factor 1 (verbal resource), whereas that of the spatial reasoners loaded significantly on both this and to a similar extent on Factor 2 (spatial resource). For spatial reasoners, the correlation between factors was moderate, though significant, r = .30, p < .05, but for verbal reasoners the relationship was noticeably stronger, r = .68, p< .01, suggesting that there is a greater dissociation between spatial and verbal factors in the spatial strategy group, compared to the verbal group. Overall, Experiment 1 showed that variations in reasoning performance can be predicted by different factors depending on the strategy adopted. Spatial and verbal working memory predict spatial reasoners’ performance, while only verbal working memory predicts that of verbal strategy users.

EXPERIMENT 2 In Experiment 2, we investigated the relationship between differences in verbal and spatial ability and strategy choice. More specifically, we expected spatial ability to predict reasoning performance for spatial reasoners, and verbal ability to predict performance for verbal reasoners. In the introduction to this paper, we highlighted research on abilities and strategies in simple reasoning tasks and evidence showing that strategy selection is influenced by abilities within the spatial domain. Working memory and abilities are known to be related, and both may be influenced by general cognitive factors, such as executive functioning (e.g., Miyake, Friedman, Rettinger, Shah, & Hegerty, 2001). However, correlations are typically modest and in a meta-analysis of 86 samples, Ackerman, Beier, and Boyle (2005) claim less than 25% shared variance between 16


working memory and ability. A recent paper by Colom, Rebollo, Abad, and Shih (2006) stated that any correlation can only be tentatively interpreted as a shared capacity for temporary storage of information. Overall, although related, abilities and working memory are not isomorphic and may differentially influence the strategies people adopt for reasoning. Methods Participants One hundred and ten undergraduates from University of Plymouth took part in return for their choice of course credit or £5 cash. The sample comprised 24 males and 86 females, mean age 21.7 years. All were native English speakers, none had received formal training in logic, and none had taken part in Experiment 1 . Materials and procedures Participants were run in small groups of up to four people. Each participant was presented with four experimental tasks. First, the same two syllogistic reasoning tasks as in Experiment 1 were run, one to determine strategy and one to measure reasoning performance. Two measures of ability were then completed, the Vandenberg Mental Rotation task (spatial ability) and the Shipley Institute of Living Scale (verbal ability). Shipley Institute of Living Scale (SILS). The SILS is a selfadministered pen and paper task comprising two subtests, a 40 item vocabulary test, and a 20 item test of abstract reasoning. It has also been widely used as a measure of general intellectual ability, and the well-established Wechsler Adult Intelligence Scale (WAIS-R; Wechsler, 1989) has served as one of the basic criterion measures for validating SILS in predicting individual IQ scores. The two tasks correlate highly, r = .8, and WAIS-R full-scale IQ scores c a n be estimated from SILS data (Zachary, 2000). The abstraction test items each comprise a 17


sequence of numbers, letters, or words with the final element in each sequence omitted. The task is to complete the sequence. For instance, if the sequence was, knit in spud up both to stay_______ the correct response would be to finish the sequence with the word ‘‘at’’. This task relies partly on long-term memory, but also on attentional abilities, abstract concept formulation and cognitive flexibility. SILS can be used as a measure of cognitive impairment in which case a 10 minute time limit is imposed for each subtest. However, for a student population, this time proved excessive and no time limits were imposed in the present study, all participants finished both SILS tests in well under 10 minutes. Although the SILS yields six major summary scores, only four were used for the present purposes: (a) vocabulary score, (b) abstraction score, (c) combined total score, and (d) estimated WAIS-R IQ score. The other two scores (the conceptual and abstraction quotients) are derived from these but are generally utilised in assessing cognitive impairment in clinical settings and hence were not appropriate for current purposes. For more information on these, see Zachary (2000). In the present study, SILS performance was treated as an indicator of verbal/abstract reasoning ability, and the estimated WAIS-R score as a measure of a more general intellectual ability. It was predicted that verbal reasoners would score more highly than spatial on SILS, especially on the abstract reasoning subtest. Vocabulary may be more concerned with educational attainment and would be assumed to be similar for all of the undergraduate population. Vandenberg Mental Rotations Test (VMRT). The VMRT (Vandenberg & Kuse, 1978) is a pen and paper test of spatial visualisation ability developed from the classic Shepard and 18


Metzler (1971) mental rotation task, as used by Cooper and Mumaw (1985) described earlier. Vandenberg and Kuse presented significant correlations between the VMRT and 20 other established and validated tests of spatial ability, r=.32-.68. Internal reliability of the test was high, r=.88, and test-retest reliability has been shown to be between .7 and .83. The test has been associated with spatial working memory ability on various cognitive tasks. The VMRT comprises 24 items, each consisting of a criterion figure, presented with two correct alternative representations and two incorrect distractors. The figures are three-dimensional drawings of cubes stacked in various arrays. In each case, the task is to identify the two alternative representations which are identical to the criterion object, but presented rotated about the vertical axis t o varying degrees. A 5 min time limit was imposed for the task and participants were instructed to work both quickly and accurately. Participants scored 1 point if they identified both correct alternatives for an item. Performance on the VMRT was treated as an indicator of spatial ability. It was predicted that if a spatial reasoning strategy were indeed a reflection of enhanced spatial abilities or preference for working with spatial representations, then spatial reasoners would outperform verbal on this task.

Results Strategies were first identified from written protocols as in Experiment 1. In this case, 69 participants (63%) presented evidence of using a verbal strategy throughout and 35 participants (32%) a spatial strategy. Six participants (5%) produced either mixed or indeterminate protocols. Figure 2 presents typical examples of protocols produced by verbal and spatial reasoners in Experiment 2. The protocols typically show the characteristics previously reported. In the verbal protocol, the participant indicated an understanding that bookbinders equal drivers from Premise 1. Her arrow and annotation clearly show how she has therefore inserted the term ‘‘drivers’’ for ‘‘bookbinders’’ in Premise 2 to arrive at the correct conclusion, 19


‘‘Some of the drivers are not poets’’. In the spatial reasoner’s protocol, the first premise has been represented by placing a circle representing bookbinders inside a larger one representing drivers (because all bookbinders are d r i v e r s ). The third term (labelled NP for not poets) has then been added to the initial representation as a further circle, partly overlapping with the bookbinders circle and hence also with that representing drivers. From this the participant concludes, ‘‘Some drivers are not poets’’. Syllogism:

All of the bookbinders are drivers Some of the bookbinders are not poets

Correct conclusion given in both cases: Some of the drivers are not poets

Verbal reasoners Participant 62

BOOKBINDERS = DRIVERS (Instead of bookbinders) Some drivers are not poets

Spatial reasoners Participant 64

D BB NP

Figure 2. Experiment 2: Typical written protocols produced by verbal and spatial reasoners.

In line with previous research, verbal and spatial reasoners performed similarly on the syllogistic reasoning task (verbal mean=48% correct, SD= 14.6; spatial mean=51% correct, SD=18.7)*very similar scores to Experiment 1. Table 4 presents their performance on the verbal and spatial ability measures, and the correlation between each of those measures and syllogistic reasoning. For the verbal measure (SILS), scores for each of the subtests, total score, and estimated WAIS score are shown. For the Vandenberg Mental Rotation task, an index of spatial ability has 20


been computed from the number of items correct divided by number of items attempted in the 5 min allowed for this task. As the means suggest, t-tests indicated no significant differences between verbal and spatial reasoners on any of these measures (p>.05 in every case). This suggested no differences in ability per se across the strategy groups. However, differences in correlations between groups on t h e Vandenberg suggest this measure of spatial ability predicts syllogistic reasoning performance to a noticeably greater extent for spatial reasoners, compared to verbal. The difference between correlations for the two groups is significant, z=1.97, p=.05, and is in line with the prediction that the two strategy groups draw differentially on spatial cognitive resources. Conversely, the correlation between performance on the verbal measure (SILS) and reasoning performance did not differ across strategy groups, p>.05. TABLE 4. Experiment 2: Descriptive statistic for all measures, by strategy group SILS vocabulary SILS abstraction SILS total Est. WAIS score Vandenberg

Verbal Spatial

Mean

SD

Mean

SD

Mean

SD

Mean

SD

Mean

SD

29.33 30.14

3.46 3.59

31.30 30.34

4.57 3.77

60.64 6.74 60.48 5.67

104.96 104.54

6.92 5.67

0.53 0.47

0.25 0.24

Correlation of ability with syllogistic reasoning Verbal .22 .27* .30* Spatial .37* .24 .40*

.30* .40*

.15 .49**

*Significant at .05 level, **significant at .01 level.

To test this further, a multiple linear regression was conducted, with syllogistic reasoning performance as the dependent variable. Five predictor variables were included, strategy grouping, Vandenberg, and WAIS scores (both converted to z-scores), and two interaction variables computed from the products of these and strategy grouping. We used WAIS as it is directly derived from both SILS subtests and provides a useful indicator of 21


overall performance on the verbal ability measure. Moreover, intelligence has been shown to be related to both reasoning ability and working memory capacity (e.g., Kyllonen & Christal, 1990; Suß, Oberauer, Wittmann, Wilhelm, & Schulze, 2002). Overall, the predictor variables accounted for a significant proportion of the variance in syllogistic performance, R2=.20, F=6.19, p < .001. The statistics are presented in Table 5. TABLE 5. Experiment 2: Results of multiple linear regression on syllogisms, with cognitive ability measures as predictors.

Strategy WAIS Vandenberg WAIS*Strategy Vandenberg*Strategy

b

t

Sig.

.16 .24 .04 .15 .32

1.81 1.99 0.28 1.41 2.8

.07 .05 .78 .16 .01

A main effect of WAIS score (and hence by implication the verbal ability measure, SILS) suggests this significantly predicts reasoning performance in both verbal and spatial reasoners. The spatial measure however (Vandenberg), significantly predicts reasoning performance in an interaction with strategy. This suggests differences between the strategies in terms of the influence of spatial ability on reasoning performance. Separate regressions on the two strategy groups show a significant effect of WAIS in both cases: verbal =.28, t=2.02, p < .05; spatial =.40, t=2.95, p< .01. Performance on the Vandenberg spatial ability task, however, was only predictive for the spatial reasoners: spatial =.50, t=3.7, p=.001; verbal .04, t=.28, p >.7.

GENERAL DISCUSSION The rationale for this research was based on the growing body of 22


evidence to suggest individual differences in strategies spontaneously adopted for a range of reasoning tasks. These strategies seem to be either verbal- propositional or visuospatial in nature. However, the cognitive basis for strategic differences remains uncertain. Two related factors, working memory and verbal-spatial abilities, have repeatedly been associated with reasoning performance and the two experiments presented here investigate the role of these factors in determining strategy choice. Importantly, verbal and spatial strategies were clearly identified in both Experiments 1 and 2 with written protocols indicating characteristics closely in line with those reported in previous research. Experiment 1 aimed to examine whether verbal and spatial strategy users draw differentially on verbal and spatial working memory resources. When the strategy groups were identified and compared, they were found to perform comparably on all measures. Their reasoning ability appears similar, as does their working memory capacity. In confirmatory factor analysis, a two-factor multigroup model fitted the data well and clearly suggested that verbal reasoners drew primarily on verbal resource, and spatial drew similarly on both verbal and spatial resources. The verbal and s p a t i a l factors were correlated, indicating the additional contribution of higher order processes for both strategy groups. This may reflect the loadings on Capon et al.’s (2003) third factor, where all measures loaded and which they suggested showed the influence of shared central executive resource and reflected variations in processing efficiency (see also Baddeley & Logie, 1999). Given that the problems were presented in written form, and participants asked to provide written conclusions, it is unsurprising that both groups present evidence of using verbal resources. The important factor is the use of spatial resource by those reasoners who employed a spatial strategy. It is worth contrasting these findings with those from many dual- task studies, described 23


earlier, which find little or no involvement of visuospatial working memory in syllogistic reasoning. Gilhooly et a l . (1993) noted that most participants in their studies used superficial heuristics which placed little demand on working memory. Their methodology, involving computerised sequential presentation of premises, places a significant load on the memory slave systems, and makes logical reasoning difficult for many people. They add that spatial working memory involvement would likely be observed if participants were using more complex strategies. This seems to be the case in our Experiment 1 where participants were allowed the cognitive space and time in which to ‘‘work out’’ their conclusions. There is accumulating evidence for a further fractionation of spatial working memory resources into distinct visual and spatial subcomponents (e.g., Della-Sala, Grey, Baddeley, Allamano, & Wilson, 1999; Pickering, 2001). The dissociation is further indicated by the distinctiveness of visual and spatial developmental trajectories (e.g., Logie & Pearson, 1997) and numerous neurological studies that indicate independence of brain activation (e.g., Courtney, Ungerleider, Keil, & Haxby, 1996; Smith, Jonides, & Koeppe, 1996) or selective impairment following brain injury (e.g., Luzzati, Vecchi, Agazzi, CesaBianchi, & Vergani, 1998; Wilson, Baddeley, & Young, 1999). Spatial and verbal strategies have also been shown to be neurologically distinct (e.g., Reichle et al., 2000). Investigation of strategies with regard to the relative involvement of visual and spatial subcomponents may offer further explanation about how spatial reasoners especially use their abilities. Further research might usefully explore how spatial reasoners perform if they are prevented from using a spatial strategy, either by instruction or by task demands which prevent them from successfully drawing on their spatial abilities and visual and/or spatial memory resources. 24


Experiment 2 investigated the relationship between verbal and spatial ability and reasoning strategy. The strategy groups were not found to differ in terms of syllogistic reasoning performance, spatial and verbal ability, or general intelligence (as measured by estimated WAIS score). However, spatial ability (as measured by the Vandenberg mental rotation task) significantly predicted syllogistic reasoning performance for the spatial strategy users. No differential effect of verbal ability was observed. These findings are consistent with those in Experiment 1. Together these two studies provide further converging evidence for the differing involvement of verbal and spatial systems in reasoning and that those differences are related to strategy usage. Individual differences in verbal and spatial working memory systems have been associated with cognitive flexibility and the ability to draw effectively on verbal and spatial resources (Schunn, Lovett, & Reder, 2001). This flexibility may mask underlying differences resulting in similar results on verbal and spatial ability measures, regardless of syllogistic reasoning strategy preference. Similarly Cooper and Mumaw (1985), described earlier, showed that strategies are associated with individual cognitive aptitude, rather than reasoning performance. This suggests that it is not verbal and spatial abilities per se that underpin strategy choice, but rather the ability to draw on verbal and spatial resources, including those within the working memory system. This is just what the present findings indicate. Verbal reasoners draw on verbal memory resources and use their verbal abilities during reasoning. Spatial reasoners, on the other hand, draw on verbal plus spatial resources. Accordingly, strategy choice was not reflected in differences in accuracy. This lack of differentiation in explicit ability further suggests that strategy choice is unlikely to have resulted from conscious metacognitive awareness of personal strengths and weaknesses. 25


Further research might consider how manipulation of problem content might lead some reasoners to perform better than others as a function of strategy. For instance, a commonly observed reasoning phenomenon is that of belief bias, the tendency to endorse conclusions which are believable, irrespective of their logical validity. We (and Ford, 1995, previously) deliberately presented problems with belief neutral content. With more belief-laden problems, spatial reasoners, with their more explicit representation of the premise meaning, might be expected to be more immune to such biases than verbal reasoners (whose strategy is more linked with the structure of the problem). Similarly, problem content which is explicitly spatial might also elicit performance differences between groups. Overall, it must be acknowledged that some of the variance in reasoning performance within and between the strategies remains unexplained. The current findings are preliminary and cannot account unequivocally for differences in strategy. However, they do indicate that individual differences in abilities and working memory resources (especially spatial components) do relate to strategy choice. Our results also indicate the importance of spatial working memory in syllogistic reasoning, at least for some individuals, challenging dual-task studies which suggested little involvement for the spatial working memory component. Although we have observed no differences in reasoning accuracy as a function of strategy, any fully comprehensive theory of reasoning will need to take strategic differences into account. This may be particularly challenging for accounts which propose the ubiquity of verbal representations and processes (e.g., Polk & Newell, 1995; Rips, 1994). An in-depth discussion of theoretical accounts and implications is beyond the scope of this paper, but the issue is discussed elsewhere (Bacon et al., 2003; Ford, 1995; Roberts, 2000). Overall, strategy groups do not differ in terms of working memory capacity, verbal or spatial ability, or 26


intelligence. However, they do draw differentially on working memory subcomponents and their ability to work with spatial information. As such, these findings present significant additional evidence for the existence of fundamental cognitive differences between the two groups of individuals that we (and Ford, 1995, previously) have termed verbal and spatial reasoners.

REFERENCES Ackerman, P. L., Beier, M. E., & Boyle, M. O. (2005). Working memory and intelligence: The same or different constructs? Psychological Bulletin, 131(1), 30-60. Bacon, A. M., Handley, S. J., & Newstead, S. E. (2003). Individual differences in strategies for syllogistic reasoning. Thinking and Reasoning, 9(2), 133-168. Bacon, A. M., Handley, S. J., & Newstead, S. E. (2004). Verbal and spatial strategies in reasoning. In M. Roberts & E. Newton (Eds.), Methods of thought: Individual differences in reasoning strategies (pp. 81-105). Hove, UK: Psychology Press. Baddeley, A. D., & Logie, R. H. (1999). Working memory: The multi-component model. In A. Miyake & P. Shah (Eds.), Models of working memory: Mechanisms of active maintenance and executive control (pp. 28-61). Cambridge, UK: Cambridge University Press. Capon, A., Handley, S., & Dennis, I. (2003). Working memory and reasoning: An individual differences perspective. Thinking and Reasoning, 9(3), 203-244. Colom, R., Rebollo, I., Abad, F., & Shih, P. (2006). Complex span tasks, simple span tasks, and cognitive abilities: A reanalysis of key studies. Memory and Cognition, 34(1), 158171. Cooper, L. A., & Mumaw, R. J. (1985). Spatial aptitude. In R. F. Dillon (Ed.), Individual differences in cognition (Vol. 2, pp. 67-94). New York: Academic Press. Courtney, S. M., Ungerleider, L. G., Keil, K., & Haxby, J. V. 27


(1996). Object and spatial visual working memory activate separate neural systems in human cortex. Cerebral Cortex, 6, 39-49. Daneman, M., & Carpenter, P. A. (1980). Individual differences in working memory and reading. Journal of Verbal Learning and Verbal Behaviour, 19(3), 450-466. Daneman, M., & Merikle, P. M. (1996). Working memory and language comprehension: A metaanalysis. Psychonomic Bulletin and Review, 3(3), 422-433. Della Sala, S., Gray, C., Baddeley, A., Allamano, N., & Wilson, L. (1999). Pattern span: A tool for unwelding visuo-spatial memory. Neuropsychologia, 37, 1189-1199. Egan, D. E., & Grimes-Farrow, D. D. (1982). Differences in mental representations spontaneously adopted for reasoning. Memory and Cognition, 10(4), 297307. Ford, M. (1995). Two modes of mental representation and problem solution in syllogistic reasoning. Cognition, 54(1), 1-71. Gilhooly, K. J., Logie, R. H., Wetherick, N. E., & Wynn, V. (1993). Working memory and strategies in syllogistic reasoning tasks. Memory and Cognition, 21(11), 115-124. Gilhooly, K. J., Logie, R. H., & Wynn, V. (2002). Syllogistic reasoning tasks and working memory: Evidence from sequential presentation of premises. Current Psychology, 21(2), 111-120. Handley, S. J., Capon, A., Copp, C., & Harper, C. (2002). Conditional reasoning and the Tower of Hanoi: The role of spatial and verbal working memory. British Journal of Psychology, 93, 501- 518. Johnson-Laird, P. N., & Byrne, R. M. J. (1991). Deduction. Hove, UK: Lawrence Erlbaum Associates Ltd. Just, M. A., & Carpenter, P. A. (1985). Cognitive co-ordinate systems: Accounts of mental rotation and individual differences in spatial ability. Psychological Review, 92(1), 137-172. Just, M. A., & Carpenter, P. A. (1992). A capacity theory of comprehension: Individual differences in working memory. 28


Psychological Review, 99(1), 122-149. Klauer, K. C., Stegmaier, R., & Meiser, T. (1997). Working memory involvement in propositional and spatial reasoning. Thinking and Reasoning, 3(1), 9-47. Knauff, M., Mulack, T., Kassubek, J., Salih, H., & Greenlee, M. (2002). Spatial imagery in deductive reasoning: A functional MRI study. Cognitive Brain Research, 13, 203212. Kyllonen, P. C., & Christal, R. E. (1990). Reasoning ability is (little more than) working memory capacity?! Intelligence, 14, 389-433. Logie, R. H., & Pearson, D. G. (1997). The inner eye and the inner scribe of visuo-spatial working memory: Evidence from developmental fractionation. European Journal of Cognitive Psychology, 9, 241-257. Luzzati, C., Vecchi, T., Agazzi, D., Cesa-Bianchi, M., & Vergani, C. (1998). A neurological dissociation between preserved visual and impaired spatial processing in mental imagery. Cortex, 34, 461-469. MacLeod, C. M., Hunt, E. B., & Mathews, N. N. (1978). Individual differences in the verification of sentence-picture relationships. Journal of Verbal Learning and Verbal Behaviour, 17, 493-507. Miyake, A., Friedman, N., Rettinger, D., Shah, P., & Hegerty, M. (2001). How are visuospatial working memory, executive functioning, and spatial abilities related? A latent-variable analysis. Journal of Experimental Psychology: General, 130(4), 621-640. Oakhill, J. V., Yuill, N., & Parkin, A. J. (1986). On the nature of the difference between skilled and less-skilled comprehenders. Journal of Research in Reading, 9(1), 8091. Pickering, S. J. (2001). Cognitive approaches to the fractionation of visuo-spatial working memory. Cortex, 37, 457-473. Polk, T. A., & Newell, A. (1995). Deduction as verbal reasoning. Psychological Review, 102(3), 533- 566. Reichle, E. D., Carpenter, P. A., & Just, M. A. (2000). The neural bases of strategy and skill in sentence-picture 29


verification. Cognitive Psychology, 40(4), 261-295. Rips, L. J. (1994). The psychology of proof. Cambridge, MA: MIT Press. Roberts, M. J. (2000). Individual differences in reasoning strategies: A problem to solve or an opportunity to seize? In W. Schaeken, G. de Vooght, A. Vandierendonck, & G. d’Ydewalle (Eds.), Deductive reasoning and strategies (pp. 23-48). Mahwah, NJ: Lawrence Erlbaum Associates, Inc. Roberts, M. J., Gilmore, D. J., & Wood, D. J. (1997). Individual differences and strategy selection in reasoning. British Journal of Psychology, 88, 473-492. Schunn, C. D., Lovett, M. C., & Reder, L. M. (2001). Awareness and working memory in strategy adaptivity. Memory and Cognition, 29(2), 254-266. Shah, P., & Miyake, A. (1996). The separability of working memory resources for spatial thinking and language processing: An individual differences approach. Journal of Experimental Psychology: General, 125(1), 4-27. Shepard, R. N., & Metzler, J. (1971). Mental rotation of three dimensional objects. Science, 171, 952-954. Smith, E. E., Jonides, J., & Koeppe, R. A. (1996). Dissociating verbal and spatial working memory using PET. Cerebral Cortex, 6, 11-20. Su¨ ß, H.-M., Oberauer, K., Wittmann, W. W., Wilhelm, O., & Schulze, R. (2002). Working memory capacity explains reasoning ability*and a little bit more. Intelligence, 30, 261-288. Toms, M., Morris, N., & Ward, D. (1993). Working memory and conditional reasoning. Quarterly Journal of Experimental Psychology, 46A, 679-699. Vandenberg, S. G., & Kuse, A. R. (1978). Mental rotations, a group test of three-dimensional spatial visualisation. Perceptual and Motor Skills, 47, 599-604. Vandierendonck, A., & de Vooght, G. (1997). Working memory constraints on linear reasoning with spatial and temporal contents. Quarterly Journal of Experimental Psychology, 50A(4), 803-820. Wechsler, D. (1989). WAIS-R Manual: Wechsler Adult 30


Intelligence Scale-Revised. San Antonio, TX: Psychological Corporation. Wilson, B., Baddeley, A. D., & Young, A. W. (1999). LE, a person who lost her ‘‘mind’s eye’’. Neurocase, 5, 119-127. Zachary, R. A. (2000). Shipley Institute of Living Scale: Revised manual. Los Angeles: Western Psychological Services.

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APPENDIX The 16 syllogistic reasoning problems presented in Experiments 1 and 2. No. 1

2

3

4

5

6

7

8

Syllogism

No.

Syllogism

Some of the bankers are managers All of the bankers are chefs Some managers are chefs None of the journalists are pilots Some of the journalists are divers Some of the divers are not pilots None of the farmers are clowns All of the butchers are clowns None of the farmers are butchers None of the journalists are pilots All of the divers are journalists Some of the divers are not pilots All of the pilots are journalists None of the journalists are divers None of the pilots are divers None of the farmers are clowns Some of the clowns are butchers Some of the butchers are not farmers All of the clowns are farmers Some of the butchers are clowns Some of the butchers are farmers Some of the athletes are singers All of the singers are dancers Some of the athletes are dancers

9

Some of the managers are bankers None of the bankers are chefs Some of the managers are not chefs None of the bankers are managers Some of the chefs are bankers Some of the chefs are not managers None of the athletes are singers Some of the dancers are singers Some of the dancers are not athletes Some of the pilots are journalists None of the divers are journalists Some of the pilots are not divers All of the managers are bankers None of the chefs are bankers None of the managers are chefs Some of the singers are athletes None of the dancers are singers Some of the athletes are not dancers Some of the clowns are farmers Some of the farmers are not butchers None of the clowns are butchers All of the singers are athletes Some of the singers are dancers Some of the athletes are dancers

10

11

12

13

14

15

16

32