The Four-card Problem and the Generality of Formal Reasoning

Looking behind: Turning cards in the selection task

Wason's selection task requires that one imagine which of four cards, each of which has a letter on one side and a number on the other, one would have to turn over to determine whether a statement about the cards is true or false. For example, one might see four cards showing T, H, 6, and 4 and be asked to say which card or cards one would have to turn over to determine whether a statement in the form of If a card has T on one side, it has 4 on the other is true. In the great majority of experiments with this task no cards are actually turned. This limits the conclusions that can be drawn from experimental results. In two experiments participants actually turned (had a computer turn) virtual cards so as to show what they contained on their originally hidden sides. Participants were given a monetary incentive to do well on the task, and they performed it, with trial-by-trial feedback, many times. Performance was much better than is typically obtained with the more common way of performing the task. Results also demonstrate the importance of the precise wording of the statement to be evaluated and how a misinterpretation could help account for a tendency for people to turn only a single card even when the turning of two is required. Results prompt several questions of a theoretical nature and are discussed as they relate to recent theoretical treatments of the selection task.

Toward a Statistical Theory of Reasoning

It is argued that the observed variability of responding in reasoning tasks might usefully be described by mathematical models based on stochastic processes. The data of a number of experiments employing Wason's selection task are reanalysed and it is shown that selection probabilities of individual cards are statistically independent. This is consistent with a class of simple stochastic models and renders conventional “insight” explanations of the data unparsi-monious.

A provisional stochastic model is formulated and subjected to a limited parametric test with reasonably satisfactory results. Some general directions for future research along these lines are suggested.

On the Strategies that Blacks Employ in Deductive Reasoning

Over the past two decades, Wason's Four-Card Selection Task has attracted such a large amount of research and has generated such varied, interesting, and controversial results that it has come to be regarded as a standard paradigm for looking at how people reason deductively. Nevertheless, this article, which replicates Griggs and Cox's (1983) second experiment with a sample of 192 undergraduate college students, reports the first systematic study of the strategies that Black Americans use in the selection task. The results largely parallel those reported by Griggs and Cox as well as those that have been reported by other researchers. Still, the present results do differ in a number of ways from prior findings. We report an atypically high rate of accuracy for the standard version of the selection task. Also, the effect of problem content on processing strategy is curiously small, and its structure is unprecedented. On balance, the results of this study challenge monolithic notions of cognitive development that universally ascribe deficits in reasoning ability to Blacks. Some Blacks, notably those researched here, appear to acquire conceptual rules for logical reasoning that are as powerful and as fallible as any developed by people in Western, literate societies. Future research should explore the etiology of individual differences in reasoning ability and proclivities among Blacks.

Performance of Adolescents Following Instruction in Conditional Reasoning: A Six-Month Follow-up

One of the more controversial subjects in adolescent research is the ability of instruction to affect performance and ability of a formal operational task. This study investigated the ability of instruction to improve the development of conditional reasoning skills in younger adolescents. Participants (N= 61) were instructed in conditional reasoning utilizing two 50-minute question and answer periods and concrete materials. Adolescents in the rule group were given the conditional syllogism while adolescents in the discovery group were not given the syllogism until they had "discovered" the inherent syllogism based on concrete materials presented. Performance was measured prior to, immediately after, two weeks after, and six months following instruction. When compared to non-instructed children's performance (N = 32) instructed subjects made significant performance gains until the six month follow-up when performance reverted to pre-instruction levels. Implications include the interaction of instruction and reasoning development. Discussion centered on the attentional capacity and mental effort required in conditional reasoning.

Deductive Reasoning with Prose Passages: Effects of Age, Inference Form, Prior Knowledge, and Reading Skill

This study applied knowledge about inference-making from the deductive reasoning literature to the drawing of specific inferences from prose passages. It explored the effects of age, inference form, prior knowledge, and reading skill on inferential comprehension. In Experiment 1, fourth-grade, seventh-grade, and college students read three prose passages, each containing six inferential questions based on premises expressed in the passages. Premise information was either true, false, or neutral with regard to subjects’ prior knowledge. To answer the questions correctly, subjects were required to make deductive inferences with six different inference forms. Content (true, false, or neutral) and form interacted differently depending on the age of subjects, but content affected performance with at least some forms for all age groups. When reasoning with conditional forms, subjects’ use of more advanced reasoning patterns with true content decreased with false and neutral content, where less advanced reasoning patterns were shown. In Experiment 2, the relationships among reading skill, inference form, and content were explored with seventh-grade and college students. For college students, reading skill had a positive main effect, but did not interact with form or content. For seventh-graders, skilled readers were better able than less skilled readers to reason from false and neutral premises with determinate inference forms.

A neglected window on hypothesis testing in adolescence: explicit standard order conditional selection tasks

The paper reported four experiments on explicit standard order conditional selection tasks, which permit more direct inference of subjects' strategies than do other conditional selection tasks. The experiments allowed plausible rational support-seeking strategies to be reduced from nine to three, disproof strategies from six to three. The main strategy in early adolescence was either (1) models-based deduction, as suggested by Johnson-Laird and Byrne in 1991 or (2) rules-based deduction, as suggested by Rips in 1994, with a factual attitude to hypothesis and offered information. In late adolescence a substantial minority adopt a hypothetical attitude to both these things, which may be applied with either of these strategies or with (3) the nondeductive strategy suggested by Langford and Hunting in 1994. This general picture of developmental possibilities can be extended to Inhelder's and Piaget's problems requiring information search to test conditional and biconditional hypotheses, in particular their chemicals, pendulum, and rods problems. This extension is obtained by assuming that adolescents acquire a range of strategies for problems requiring more or less focussed information search, conditional selection tasks requiring the former, Piagetian formal operations tasks tending towards the latter. Current evidence does not indicate whether strategies (1) or (2) are dominant in younger adolescents or whether strategies (1) or (2) or (3) are dominant in older adolescents. Thus, the Piagetian argument that formal operations thinking passes from factual rules-based deduction to hypothetical rules-based deduction is only one of several styles of theory that can readily accommodate current evidence in this area.

Transfer of conditional reasoning: effects of explanations and initial problem types

Transfer of reasoning on Wason's (1966) selection task was explored in three experiments. Experiment 1 tested the effects of problem explanations and verbalization instructions on transfer from abstract or thematic problems to abstract problems. Explanations facilitated transfer only when the initial problems were abstract; verbalization did not produce transfer between problems. Experiment 2 explored the effects of problem similarity and explanations on transfer between problems. Although transfer occurred following explanations, no effect of similarity was found for thematic problems. In both of these experiments, the thematic effect (Wason & Shapiro, 1971) was observed. Experiment 3 examined the effects of explanations to abstract or thematic problems on transfer to subsequent abstract or thematic problems. Transfer of reasoning occurred from both initial problem types, particularly to problems of the same type; however, transfer occurred to a greater extent from abstract problems than from thematic problems. The results are discussed in terms of problem similarity and Cheng and Holyoak's (1985) pragmatic reasoning schema hypothesis.