Psychological Research (2007) 71: 495–502 DOI 10.1007/s00426-006-0046-6

O R I GI N A L A R T IC L E

Cynthia S. Koenig Æ Richard D. Platt Richard A. Griggs

Using dual-process theory and analogical transfer to explain facilitation on a hypothetico-deductive reasoning task

Received: 20 May 2005 / Accepted: 23 January 2006 / Published online: 4 April 2006 Ó Springer-Verlag 2006

Abstract Using the analogical transfer paradigm, the present study investigated the competing explanations of Girotto and Legrenzi (Psychological Research 51: 129– 135, 1993) and Griggs, Platt, Newstead, and Jackson (Thinking and Reasoning 4: 1–14, 1998) for facilitation on the SARS version of the THOG problem, a hypothetico-deductive reasoning task. Girotto and Legrenzi argue that facilitation is based on logical analysis of the task [System 2 reasoning in Evans’s (Trends in Cognitive Sciences 7: 454–459, 2003) dual-process account of reasoning] while Griggs et al. maintain that facilitation is due to an attentional heuristic produced by the wording of the problem (System 1 reasoning). If Girotto and Legrenzi are correct, then System 2 reasoning, which is volitional and responsible for deductive reasoning, should be elicited, and participants should comprehend the solution principle of the THOG task and exhibit analogical transfer. However, if Griggs et al. are correct, then System 1 reasoning, which is responsible for heuristic problem solving strategies such as an attentional heuristic, should occur, and participants should not abstract the solution principle and transfer should not occur. Significant facilitation (68 and 82% correct) was only observed for the two SARS source problems, but significant analogical transfer did not occur. This lack of transfer suggests that System 1 reasoning was responsible for the facilitation observed in the SARS problem, supporting Griggs et al.’s attentional heuristic explanation. The present results also underscore the explanatory value of using analogical transfer rather than facilitation as the criterion for problem understanding.

C. S. Koenig (&) Æ R. D. Platt Department of Psychology, St Mary’s College of Maryland, 18952 E. Fisher Rd., St Mary’s City, MD 20686, USA E-mail: [email protected] Fax: +1-240-8954436 R. A. Griggs Department of Psychology, University of Florida, P.O. Box 112250, Gainesville, FL 32611, USA

Introduction Peter Wason’s THOG problem (Wason, 1977, 1978; Wason & Brooks, 1979), a hypothetico-deductive reasoning task, has captured the attention of reasoning researchers for more than two decades because it is extremely difficult to solve. Koenig and Griggs (2004a) noted that correct performance on the standard abstract version of the task averages only 12% and ranges between 0 and 29% if no significant changes in task demands (e.g., Girotto & Legrenzi, 1993) or problem structure (e.g., Griggs & Newstead, 1982) have been made. In the standard problem, participants are shown four geometric figures; for example, a black square, a white square, a black circle, and a white circle. The participant is told that the experimenter has written down one shape (square or circle) and one color (white or black) and then is given the following exclusive disjunctive rule: ‘‘If, and only if, a figure includes either the color I have written down or the shape I have written down, but not both, then it is called a THOG.’’ One of the figures (e.g., the black square) is identified as a THOG, and the participant is instructed to decide whether or not each of the other three figures is or is not a THOG or if there is insufficient information to make a classification. In order to solve the THOG task, participants must first determine which color and shape combinations the experimenter might have written down that would result in the black square being classified as a THOG. Participants should hypothesize that either black and circle or white and square could have been written down because each of these combinations shares only one feature with the THOG exemplar. White and circle could not have been written down because this combination does not share any perceptual features with the THOG exemplar (i.e., black square). In addition, black and square could not have been written down because this combination shares both features with the THOG exemplar. Once the possible combinations have been hypothesized, a second

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step of reasoning is required. Participants must determine the ‘‘THOGness’’ of the remaining figures given the hypothesized combinations. If either white and square or black and circle were written down, the white circle would also be a THOG because it shares only one feature with either combination. The white square and black circle would not be THOGS, however, because each combination shares either both or neither of these features. Thus, the correct answer is that the white circle is a THOG and the black circle and white square are not THOGs. Several investigators using different experimental designs have determined that the task requirements of the THOG problem are not beyond the reasoning capabilities of most participants. Most participants understand the exclusive disjunctive rule (e.g., Wason & Brooks, 1979), can generate hypotheses for the possible combinations (e.g., Girotto & Legrenzi, 1989; Smyth & Clark, 1986), and are able to test the figures against these hypotheses (Wason & Brooks, 1979). The difficulty of the problem, however, results from the necessity of carrying out all of these tasks together. Girotto and Legrenzi (1989) suggested that participants have difficulty separating the features of the exemplar from the features that may have been written down. Newstead and Griggs (1992) elaborated on this explanation and labeled it ‘‘confusion theory’’. Specifically, when faced with the tasks of generating hypotheses for the possible color and shape combinations, holding this information in working memory, and testing each figure against these hypotheses, participants’ working memory capacity may be overwhelmed. To overcome this confusion, participants simplify the task by incorrectly assuming that the features of the exemplar are also the features that have been written down. Evidence for this failure in reasoning is derived from a preponderance of two typical error patterns that Wason and Brooks (1979) labeled ‘‘intuitive’’. Specifically, participants often identify the black circle and white square as THOGs and the white circle as not a THOG (labeled Intuitive error A by Griggs & Newstead, 1983) or they judge the THOGness of the black circle and white square as indeterminate but decide the white circle is not a THOG (labeled Intuitive error B by Griggs and Newstead). The ‘‘confusion theory’’ explanation for THOG task performance has garnered substantial support from investigations demonstrating the facilitating effect of separating the features of the exemplar from the features of the hypothesized combinations (Girotto and Legrenzi, 1989; Needham and Amado, 1995; O’Brien, Noveck, Davidson, Fisch, Lea, & Freitag, 1990), thus reducing the frequency of intuitive errors. Facilitating versions of the THOG task have typically involved the use of thematic content (e.g., Girotto & Legrenzi’s 1989 Pub problem and Needham & Amado’s 1995 Pythagoras problem). Thus, Girotto and Legrenzi (1993) developed an abstract version of the THOG problem (called the SARS problem) to determine if separation could lead to facilitation in the absence of

thematic content. In this THOG task version, they lexicalized the written down combination by labeling it SARS, arguing this would allow participants to separate the features of the exemplar (a THOG) from the features written down (the SARS). In addition, the SARS problem included the following hypothesis generation instruction before the THOG identification task: ‘‘Knowing for sure that the black diamond is a THOG, you have to indicate which one or which ones, among the remaining designs, could be the SARS’’ (Girotto & Legrenzi, 1993, p. 705). Following this task, participants were given the THOG identification instruction, ‘‘Could you also indicate whether, in addition to the black diamond, there are other THOGs?’’ (p. 705). Correct performance (70%) on the SARS problem was very high. Girotto and Legrenzi attributed this facilitation to the problem’s successful separation of the features of the THOG exemplar from those that were written down (those of the SARS) which led to problem understanding and the ensuing combinatorial analysis of the remaining design with respect to the hypothesized SARS combinations and the THOG rule. Griggs, Platt, Newstead, and Jackson (1998) attempted to replicate the facilitation for the SARS problem but reached a different conclusion regarding the source of facilitation. In their first two experiments, they failed to find significant facilitation for the SARS problem when the standard three-choice THOG classification instruction (i.e., is a THOG, is not a THOG, or insufficient information) was used. In Experiment 3, they used the classification instruction from the original SARS problem (i.e., ‘‘Could you also indicate whether, in addition to the black diamond, there are other THOGs?’’). With this instruction, significant facilitation was observed (48% correct). Why would this difference in correct performance have occurred? After classifying the two potential SARS (the white diamond and black circle) and being told that the black diamond is a THOG, participants are left with only one decision—determining whether or not the one remaining design (the white circle) is a THOG. In most cases, participants decided that it was. Therefore, Griggs et al. concluded that the ‘‘any other THOGs’’ instruction might have been interpreted to mean that there could be only ‘‘one other THOG’’. Indirect evidence for this interpretation was obtained in a fourth experiment in which substantial facilitation was achieved with a SARS problem employing a ‘‘one-other THOG’’ instruction (i.e., ‘‘In addition to the Black Diamond, one-other design is a THOG. Which other design is a THOG?’’), even in the absence of a hypothesis generation instruction. Griggs et al. (1998) concluded that an attentional heuristic explained the facilitation Girotto and Legrenzi (1993) observed for the original SARS problem. In the problem statement, the black diamond is identified as a THOG, and this initially draws attention to the features ‘‘black’’ and ‘‘diamond.’’ When instructed to determine which other designs might be the SARS, most participants (between 61 and 78%) correctly identified the

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black circle and white diamond as possibilities. Participants were then instructed to determine what they could say about ‘‘any other THOGs,’’ which appeared to be interpreted as indicating there was ‘‘one other THOG.’’ When faced with this instruction, participants likely focused their attention on the one remaining figure—the white circle. In doing so, they correctly solved the THOG problem. Thus, according to this interpretation, the SARS problem produces facilitation because of an attentional heuristic and not because its structural features lead to problem understanding. Recently, Koenig and Griggs (2004a, b) have begun to examine the validity of using facilitation as the criterion for inferring problem understanding, the abstraction of the THOG problem’s solution principle. They have suggested that the criterion for true understanding of this difficult task is successful transfer to the standard abstract THOG problem. Their investigations have explored the specific features in a source THOG problem necessary for demonstrating such transfer. Using this analogical transfer methodology with Needham and Amado’s (1995) Pythagoras THOG and O’Brien et al.’s (1990) Blackboard THOG, Koenig and Griggs (2004a, b) concluded that (1) a source problem entailing features that lead to separation or hypothesis generation may be sufficient to elicit facilitation but (2) both are necessary to produce analogical transfer. The results of the Koenig and Griggs (2004a, b) studies not only demonstrate that analogical transfer may be a better criterion for judging problem understanding but they also support dual-process accounts of reasoning, which emphasize two distinct cognitive systems. According to Evans’s (2003) dual-process theory, System 1 processes are ‘‘rapid, parallel, and automatic in nature (p. 454),’’ and are responsible for heuristic problem solving strategies such as an attentional heuristic that produce the intuitive errors on the THOG task. System 2, in contrast, is relatively slow, constrained by working memory capacity, and responsible for hypothetical thinking. Other differences between the two systems are that System 2 is volitional (rather than automatic), responds to verbal instructions, and is capable of overriding the default responses of System 1, such as an attentional heuristic, that may be involved in reasoning about the THOG problem. In the Koenig and Griggs (2004a, b) investigations of analogical transfer, the explicit instructions to generate hypotheses may have engaged System 2 processing, contributing to both the observed facilitation on the source problem and the abstraction of the problem’s solution principle. The present study was designed to investigate the facilitating features of the SARS problem within an analogical transfer paradigm in the context of dualprocess accounts of reasoning. Based upon Koenig and Griggs’s (2004a, b) previous findings of analogical transfer on the THOG task, it was concluded that two features of a source problem are necessary for eliciting transfer—separation and hypothesis generation. The SARS problem serves as a good test for this conclusion

because it includes an explicit hypothesis generation request and, according to Girotto and Legrenzi (1993), facilitates separation of the features of the exemplar from those written down. However, Griggs et al. (1998) argue that the facilitation for the SARS problem is the product of an attentional heuristic and not the problem’s structural aspects leading to problem understanding. By applying dual-process accounts of reasoning, two hypothesized outcomes can be derived from these competing explanations of facilitation. Girotto and Legrenzi (1993) would predict volitional System 2 reasoning (responsible for hypothetical thinking), which would lead participants to comprehend the solution principle of the THOG task and thus lead to analogical transfer. Griggs et al. (1998), in contrast, would predict more limited System 2 reasoning. Whereas System 2 would probably be engaged during the hypothesis generation stage of the task, participants would probably default back to System 1 when given the ‘‘any other THOGs’’ instruction and respond via an attentional heuristic. In doing so, the solution principle of the THOG task would not be abstracted, resulting in no analogical transfer.

Method Participants Eighty-four students enrolled in Introduction to Psychology courses at St Mary’s College of Maryland served as participants to fulfill an experimental participation requirement. Each participant served in only one transfer condition, and all testing was completed in groups of 20 or fewer. Materials Four problems were created for this experiment: (1) Standard THOG, (2) SARK, (3) SARK + one other THOG instruction, and (4) Dotted Cross Standard THOG. The first three problems served as source problems. All three problems entailed the same perceptual features for the figures in the problems (i.e., black square, white square, black circle, white circle). To reduce surface similarity with the source problems, a target problem (Dotted Cross Standard THOG) was created with two new shapes (hearts and crosses) and patterns (dots and stripes) that replaced the colors (black and white) and shapes (square and circle) of the figures in the source problems. The SARK problem was essentially the same as the SARS problem studied by Girotto and Legrenzi (1993) with the name used for the SARS changed to SARK. We made this change because the acronym ‘‘SARS’’ has been used recently in the media to signify ‘‘sudden acute respiratory syndrome’’ and thus is no longer meaningless. A second version of the SARK problem incorporated the one other THOG instruction. We included this problem to determine if the

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results for it would mirror those for the SARS problem when this instruction was examined by Griggs et al. (1998). Three figure orders were developed for each source and target problem. Additionally, the order of the figures differed in each pairing of source and target problems such that the remaining THOG figure appeared in different locations in the source and target problems. Examples of each source problem and the target problem are provided in the Appendix. Procedure Participants were told they would be working two deductive reasoning problems that had correct answers and that they could write on their problem sheets as they solved the problems. Each participant was then given a manila envelope with a source problem placed outside the envelope and a target problem placed inside the envelope. Participants were allotted 10 min to complete the source problem. At the end of this time period, the experimenter instructed participants to place the source problem inside the envelope and remove the target problem. A further 10 min was allotted for completion of the target problem. Following this time period, participants placed the target problem inside the envelope and removed a questionnaire that requested participants to (1) identify any similarities noted between the source and target problem and (2) denote if the source problem helped them solve the target problem. After completing the questionnaire, participants enclosed all materials in the manila envelope and submitted this to the experimenter. No participant reported that the 10 min time period was insufficient for completing either problem.

Results Data analyses The correct percentages for all source and target problems are given in Table 1. Correct performance on the SARK problem (68%) and the SARK + one other THOG instruction problem (82%) was significantly better than correct performance on the source Standard THOG problem (14%), v2 (1, N=56)=16.60, p<.001 and v2 (1, N=56)=25.82, p<.001, respectively. However, none of the source problems led to analogical

transfer, as indicated by the low levels of correct performance on the Dotted Cross Standard THOG problem in all three-problem conditions. Thus, participants appear to have failed to abstract the underlying solution principle of the THOG problem from any of the source problems. Error patterns Participants were presented with the Standard THOG three-choice instruction in the Standard THOG source problem and the three target problems. Thus, error patterns are reported for these four problems only (see Table 2). In the Standard THOG source problem condition, 50% of errors on the source problem were Intuitive A or Intuitive B. On the target problem that followed the Standard THOG source problem, Intuitive A and Intuitive B accounted for 52% of the errors. A similar pattern emerged in the SARK source problem conditions. For the target problem that followed the SARK source problem, 73% of the errors were Intuitive A or Intuitive B. In the SARK + one other THOG Instruction source problem condition, Intuitive A and Intuitive B accounted for 64% of the errors. Hypothesis generation In both SARK source problem conditions, participants were asked to provide hypotheses for the SARK before denoting the other THOGs (or one other THOG) from among the figures provided. In the SARK source problem condition, 96% of participants provided correct hypotheses for both. Of these, 70% correctly solved the SARK problem. In the SARK + one other THOG instruction source problem condition, 82% of participants correctly identified the two hypotheses. Among these, 91% correctly solved the SARK + one other THOG instruction problem. No participant who failed to generate at least one correct hypothesis was able to correctly solve either SARK problem. In the Standard THOG condition, this request was not included. Thus, no summary of hypothesis generation responses is provided for this problem. Of interest is the failure by most participants to transfer the hypothesis generation strategy (as indicated

Table 1 Percentages correct on source and target problems Problem condition

Standard THOG SARK SARK + one other THOG instruction

Source problem

Target problem

% correct

No. correct

% correct

No. correct

14 68 82

4/28 19/28 23/28

18 7 11

5/28 2/28 3/28

Table 2 Percentage of error patterns for problems with Standard THOG three-choice instruction Problem

n

Intuitive A Intuitive B Other

Standard THOG (source) Standard THOG (target) SARK (target) SARK + one-other THOG instruction (target)

24 23 26 25

33 43 57 48

17 9 16 16

50 48 27 36

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by notations on the problem sheets) to the target Dotted Cross Standard THOG problem after first solving one of the SARK problems. In their studies of the Blackboard THOG and Pythagoras THOG, Koenig and Griggs (2004a, b) noted high levels of notations on the source and target problems suggesting participants were abstracting elements of the solution principle from the source problem and transferring it to the target problem. In the present study, a transfer of the hypothesis generation strategy did not occur (at least as evidenced by participants writing the hypotheses on the target problem sheets). This suggests that the SARK problems did not lead to the abstraction of the underlying solution principle of the THOG problem.

Conclusions The results of the present study replicate previous findings of facilitation for the SARS problem and shed light on the basis for that facilitation. In particular, by looking at analogical transfer, it is possible to differentiate between the explanations for this facilitation proposed by Girotto and Legrenzi (1993) and Griggs et al. (1998). As noted earlier, Girotto and Legrenzi explained the facilitation by arguing that the labeling used in the SARS problem allows for easier separation of the features of the exemplar from the features that are written down, leading to an understanding of the problem’s logic and thus the correct solution to the problem. Their explanation of the improved performance relies on what Evans (2003) refers to as System 2 reasoning—deliberate consideration of the logical structure of the problem. If this explanation is correct, then participants should be able to demonstrate their understanding of the problem by exhibiting analogical transfer like that seen in studies examining the Pythagoras THOG (Needham and Amado, 1995; Koenig and Griggs, 2004a) and the Blackboard THOG (Koenig and Griggs, 2004b). In contrast, Griggs et al. (1998) argue that the facilitation is due to an attentional heuristic and, therefore, relies on what Evans refers to as System 1 reasoning—a lower level automatic perceptual process that is driven by surface characteristics of the problem. Specifically, the instructions in the SARS problem draw attention to the features of the identified THOG (black square) and the features of the possible SARS (black circle and white square). When asked to identify ‘‘any other THOGs’’ or ‘‘one other THOG’’, participants likely focus their attention on the one remaining figure—the white circle. In doing so, they correctly solve the THOG problem. If this attentional explanation is correct, then participants should not exhibit analogical transfer because they have not developed the correct logical understanding of the source problem necessary for transfer to the target problem to occur. The results of the present study clearly support the attentional explanation. While the majority of participants were able to correctly solve both versions of the

SARK problem, they did not demonstrate transfer to the target problems. The difficulty emanating from the THOG problem seems to occur in response to working memory overload. When participants are tasked with generating hypotheses and holding them in memory while testing the three possible THOGs, working memory capacity is exceeded and confusion results (Girotto & Legrenzi, 1989; Newstead & Griggs, 1992). In response to this confusion, participants may simplify the task by assuming that the features of the identified THOG are the features that have been written down. When participants rely on these perceptual features to reason about the THOG problem (System 1 processes) rather than considering the logical structure of the problem (System 2 processes), they are more likely to make intuitive errors (labeling the white circle as Not a THOG, and the other two figures as THOGs or as indeterminate). As Griggs and Newstead (1983) noted, ‘‘perceptual matching is the better explanation of intuitive errors on this task...used only when subjects are confused by the logic of the problem and have recourse to no other basis for responding’’ (p.451). In the present study, intuitive errors were the predominant error patterns in the Standard THOG and target problems (see Table 2). This suggests that because System 2 processes are constrained by working memory capacity, participants reverted to System 1 processes to solve the Standard THOG task. So far, we have argued that transfer did not occur because participants relied on System 1 processing in the source problem and as a result the solution principle was not discovered. However, transfer failure could occur for two other reasons even in cases where the solution principle was discovered in the source problem. Transfer failure could occur either because the transfer of System 2 processing was incorrect/incomplete or because the participant failed to recognize the analogy between the source and target problems and, therefore, did not transfer the relevant solution principle. We need to consider these two alternatives in turn to rule out these possibilities in the present situation. If the solution principle was discovered in the source problem, we might still see transfer failure if the target problem involved a different application of the solution principle or if other System 2 processing was required in order to solve the target problem. This might be likely to happen in a reasoning setting where a solution principle is learned on one type of problem but the transfer problem differs substantially in the underlying structure or the type of task so that the application of the solution principle would differ enough to prevent successful and complete transfer. For example, a participant might successfully reason regarding Modus Tollens in a conditional argument classification task while still failing to apply Modus Tollens in a more difficult application task like Wason’s selection task. The failure to correctly apply the principle of Modus Tollens in the selection task would not necessarily imply that the participant had not understood the principle in the classification task. However, this scenario seems unlikely to explain the

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present study since the source and target were isomorphs of one another and the types of decisions they were making in both tasks were the same. The other possibility is that the participants discovered the solution principle in the source problem but failed to see the analogy between the source and target problems. While the problems were isomorphs of one another, participants could have still failed to see the structural similarity if they focused instead on the superficial differences. For example, Gick and Holyoak (1980) found that most participants who discovered a solution schema in one problem solving scenario failed to apply it to an isomorphic problem in a different scenario unless they were given a hint that the solution from the first problem might aid their search for a solution to the second problem. In the present study, participants may not have recognized that the solution principle for the source problem could be applied to the target problem. However, this explanation seems unlikely given that Koenig and Griggs (2004a, b) have already demonstrated transfer from other versions of the THOG (e.g., Blackboard and Pythagoras problems) to the standard THOG. Given that the source problem in the present study in some ways has greater surface similarity to the target problem than the source problems in these previous studies, it is difficult to see how one might argue that the analogy would be noticed by participants in these past studies but not in this one. What remains to be explained is why other THOG problems like the Pythagoras and Blackboard problems produce transfer whereas the SARS problem does not. Koenig and Griggs (2004a) have proposed that for analogical transfer to occur two conditions must be met: (1) the source problem must result in separation of the exemplar from the combinations that may be written down and (2) the hypothesis generation strategy must be encoded. In the SARS problem, the labeling should fulfill the first of these requirements and hypothesis generation should be elicited when the participants generate the possible combinations for the SARS. Previous studies demonstrating transfer reveal that participants often transfer the hypothesis generation strategy as indicated by notations on the target problems (Koenig & Griggs, 2004a, b). That did not appear to be the case in the present study. This suggests that participants did not use a hypothesis generation strategy on the target problems even when they generated the possible feature combinations for the SARK (SARS) in the source problem. Thus, participants did not abstract the problem’s solution principle, and no transfer to the target problem was observed. Why? Evans’s distinction between two different reasoning systems provides an explanation for this transfer failure. Evans (2003) discusses the impact of competition between System 1 and System 2 processing. System 1 processes are believed to be automatic, occur without intention, and often involve the use of heuristics of a

perceptual nature. Therefore, when there is a conflict between System 1 and System 2, System 2 must ‘‘override or inhibit default responses emanating from System 1’’ (Evans, 2003, p. 456). However, Evans argues that suppression of System 1 is a high-effort process that only occurs when emphasis is placed on reasoning deductively, especially via verbal instructions. In the present study, participants were told they would be solving two deductive reasoning problems. Nevertheless, we do not believe this instruction caused participants to reason deductively and thus override System 1. The strongest evidence for this is derived from a comparison of correct performance on the source Standard THOG (14%) and the two SARK source problem conditions (68 and 82%). If this instruction produced System 2 processing, performance should be significantly improved on the Standard THOG problem. Further, in previous work on the THOG problem (Koenig & Griggs, 2004a; b), we have used this instruction for all problem conditions and differences in performance are accounted for by differences in other problem features. Evans suggests that belief bias effects may reflect this sort of competition between System 1 and System 2 processes. In a situation closely analogous to the present problem, Platt and Griggs (1993) found that performance on Wason’s four-card selection task could be facilitated by introducing an explicit rule that blocked matching bias (a System 1 reasoning heuristic) and by directing participants to provide reasons for the selections that they made (emphasizing System 2 processing). However when an explicit rule that allowed matching was introduced, facilitation was also reduced (Platt & Griggs, 1995). This result suggests that participants reverted to the default System 1 strategy when it was possible. A similar process may be occurring in the SARS problem. Whereas the SARS problem may provide an opportunity for both separation and hypothesis generation, the System 1 attentional heuristic may be more likely to guide performance. Because those attentional cues are not present in the target problem, no transfer occurs. If this analysis is correct, it suggests participants give the right answer to the SARS problem but for the wrong reason. The problem instructions guide the participant to believe that there is one other THOG, and since the other shape/color combinations have already been identified, attention is drawn to the remaining figure. The present results also point out the importance of using the analogical transfer paradigm to determine whether participants abstract the underlying solution principle of a problem. Without using this procedure, it appears that participants understand the solution principle of the SARS problem. They have a high rate of correct performance on it. However, the poor performance on the target problem in the transfer paradigm reveals that their correct selections are more likely attributed to System 1 processing and not a true understanding of the logical structure of the task.

501 Acknowledgements The authors would like to thank Vittorio Girotto and an anonymous reviewer for valuable comments on an earlier version of this paper.

SARK + one other THOG instruction problem Below are four designs: black square, white circle, white square, and black circle.

Appendix Standard THOG problem Below are four designs: black square, white circle, white square, and black circle.

By writing down one of the design colors (either black or white) and one of the shapes (either square or circle), I have developed a classification rule for the four designs. The rule is: ‘‘A design will be classified as a THOG if and only if it includes EITHER the color written down, OR the shape written down, BUT NOT BOTH.’’ I will tell you that the Black Square is a THOG. Using this piece of information and the classification rule given above, decide for each of the other designs whether or not it can be classified as a THOG. For each design, circle your choice: White circle IS a THOG IS NOT a THOG Can’t tell White square IS a THOG IS NOT a THOG Can’t tell Black circle IS a THOG IS NOT a THOG Can’t tell

I have defined one of these designs as a SARK. You do not know which design this is. But you do know that a design is a THOG if it has EITHER the color of the SARK OR the shape of the SARK, BUT NOT BOTH. I will tell you that the black square is a THOG. Knowing this, you have to indicate which one or which ones, among the remaining designs, could be the SARK. In addition to the Black Square, one other design is a THOG. Which other design is a THOG? Target problem Below are four figures. Each figure is either dotted or striped and cross or heart. By writing down one of these patterns (either dotted or striped) and one of these shapes (either cross or heart), I have developed a classification rule for the four figures. The rule is: ‘‘A figure will be classified as a THOG if and only if it includes EITHER the pattern written down, OR the shape written down, BUT NOT BOTH.’’ The figures are:

SARK problem Below are four designs: black square, white circle, white square, and black circle.

I have defined one of these designs as a SARK. You do not know which design this is. But you do know that a design is a THOG if it has EITHER the color of the SARK OR the shape of the SARK, BUT NOT BOTH. I will tell you that the black square is a THOG. Knowing this, you have to indicate which one or which ones, among the remaining designs, could be the SARK. Could you also indicate whether, in addition to the black square, there are other THOGs?

I will tell you that the Dotted Cross is a THOG. Using this piece of information and the classification rule given above, decide for each of the other figures whether or not it can be classified as a THOG. For each figure, circle your choice: Dotted heart IS a THOG IS NOT a THOG Can’t tell Striped heart IS a THOG IS NOT a THOG Can’t tell Striped cross IS a THOG IS NOT a THOG Can’t tell

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