The Effects of Graduate Training on Reasoning Formal Discipline and Thinking About Everyday-Life Events

" The theory of formal disciplinenthat is, the view that instruction in abstract rule systems can affect reasoning about everyday-life eventsnhas been rejected by 20th century psychologists on the basis of rather scant evidence. We examined the effects of graduate training in law, medicine, psychology, and chemistry on statistical reasoning, methodological reasoning about confounded variables, and reasoning about problems in the logic of the conditional Both psychology and medical training produced large effects on statistical and methodological reasoning, and psychology, medical, and law training produced effects on ability to reason about problems in the logic of the conditional Chemistry training had no effect on any type of reasoning studied. These results seem well understood in terms of the rule systems taught by the various fields and indicate that a version of the formal discipline hypothesis is correct. A few years ago an article appeared on the Op-Ed page of The New York Times urging that Latin and Greek be taught routinely to high school students in order to improve intelligence (Costa, 1982). The justification given for this recommendation was a study showing that students who had taken Latin and Greek in high school scored 100 points higher on the verbal portion of the Scholastic Aptitude Test (SAT) than students who had not studied these languages. Although the editors of The New York Times apparently thought that this argument was worthy of consideration by its readers, it seems likely that most academically trained psychologists would be dubious on two different grounds. First, because of their methodological training, psychologists would be aware of the likelihood of substantial self-selection effects in any study of the kind described: High school students who take Latin and Greek are likely to be more intelligent than students who do not, and schools that include Latin and Greek in their curriculums are likely to have higher academic standards than schools that do not. Second, most psychologists are aware of the bad reputation of the "learning Latin" approach to teaching reasoning. Thus, they believe reasoning cannot be taught by teaching the syntax of a foreign language, by teaching principles of mathematics, or indeed by any "formal discipline" procedure whereby the rules of some field are taught and then are expected to be generalized outside the bounds of the problems in that field 9 Psychologists are, no doubt, right in their assertion that self-selection undercuts the argument for teaching Latin and Greek 9 Are they equally justified, though, in assuming that teaching foreign languages or any other formal discipline has no generalized implications for reasoning? The antiformal discipline view not only conflicts with what people have believed for most of recorded history, but its scientific support is far less substantial than most psychologists realize. The ancient Greeks believed that the study of mathematics improved reasoning. Plato urged the "principal men of the state" to study arithmetic. He believed that "even the dull, if they have had an arithmetical training 9 . . always become much quicker than they would otherwise have been" (quoted in Jowett, 1937, p. 785). Roman thinkers agreed with the Greeks about the value of arithmetic and also endorsed the study of grammar as a useful discipline for improving reasoning. The medieval scholastics added logic, especially the study of syllogisms, to the list of disciplines that could formally train the mind. The humanists added the study of Latin and Greek, and the curriculum for European education was set for the next several hundred years (Mann, 1979). The 20th Century Critique of Formal Discipline Although there were objections to the standard curriculum as early as the Enlightenment on the grounds that the rules of mathematics and Latin bear little actual resemblance to the rules necessary to think about most everyday-life events, it was not until the late 19th century that the view came under concerted attack 9 The attack came from psychologists, and it was utterly effective. In fact, it was one of the first policy victories of the new field. William James was withering in his critique of "faculty psychology," that is, of the view that mental abilities consisted of faculties such as memory, reasoning, and will that could be improved by mere exercise in the way that muscles could 9 Thorndike (1906, 1913) undertook a program of research, still impressive by modern standards, that showed little transfer of training across tasks, for example, from canceling letters to canceling parts of speech or from estimating areas of rectangles of one size and shape to estimating areas of rectangles of another size June 1988 9 American Psychologist Copyri8ht 1988 by the American Psychological Association, Inc. 0003-066X/88/$00.75 Vol. 43, No. 6, 431-442 431 and shape. Thorndike declared that "training the mind means the development of thousands of particular independent capacities" (Thorndike, 1906, p. 246). Hence, training in Latin could not be expected to improve people's capacities to perform other very different mental tasks. Similar conclusions have been reached by contemporary psychologists investigating the transfer of solutions of one problem to solutions of another formally identical problem, for example, between isomorphs of the "Tower of Hanoi" problem (Hayes & Simon, 1977), between homomorphs of the missionaries and cannibals problem (Reed, Ernst, & Banerji, 1974), and between slightly transformed versions of algebra problems (Reed, Dempster, & Ettinger, 1985). Learning how to solve one problem produces no improvement in solving others having an identical formal structure. The most influential student of reasoning in the middle of the 20th century, Piaget, reinforced already skeptical views of the value of formal training. Piaget believed that there were general rules underlying reasoni n g t h e formal operations and the propositional opera t i o n s b u t that these abstract rules were induced by everyone by virtue of living in the world with its particular regularities (Inhelder & Piaget, 1955/1958). Because learning is mainly by induction, via methods of self-discovery, formal training can do little to extend it or even to speed it up. It is important to note, however, that little research seems to have been conducted examining Piaget's dictum that abstract rules are difficult to teach. A still more radical view than Piaget's has emerged as a result of studying people's ability to perform certain logical operations. Wason (1966) and other investigators have established that people have great difficulty with abstract problems that follow the form of the material conditional, i fp then q. This has been done by examining how people respond to selection tasks that embody this logic. For example, subjects are shown four cards displaying an A, a B, a 4, and a 7; are told that all cards have letters on the front and numbers on the back; and are asked to turn over as many as necessary to establish whether it is the case that " i f there is a vowel on the front, then there is an even number on the back." Few subjects reach the correct conclusion that it is necessary to turn over the A (because if there were not an even number on the back, the rule would be violated) and the 7 (because if there were a vowel on the front, the rule would be violated). More generally, to determine the truth of a conditional statement, the cases that must be checked are p (because if p is the case, it must be established that q is We are indebted to Rebecca Collins, Elissa Wurf, and Dara Markowitz for advice and assistance and to Richard Catrambone, Patricia Cheng, and Keith Holyoak for comments on an earlier version of this article. The research was supported by NSF Grants SES85-07342, BNS8409198, and BNS-8709892, Grant 85-K-0563 from the Ott~ce of Naval Research, and Grant 87-1715 from NSERC. Correspondence concerning this article should be addressed to Darrin R. Lehman, Department of Psychology, 2136 West Mall, University of British Columbia, Vancouver, B.C., Canada V6T I Y7. also the case) and not-q (because if it is not the case that q, it must be established that it is also not the case that p). Yet subjects have no difficulty solving familiar everyday-life problems formally identical to the Wason selection task. For example, when asked to turn over as many sales receipts as necessary to establish that " i f the receipt is for more than $20, it has a signature on the back," subjects readily understand that large amounts and unsigned reverses have to be checked (D'Andrade, 1982). This fact has led some theorists to argue that people do not use inferential rules at all, but rather they use only those rules that are at a concrete, empirical level (e.g., D'Andrade, 1982; Griggs & Cox, 1982; Manktelow & Evans, 1979). This view would be consistent with the most extreme position derivable from Thorndike's findings: Learning does not transfer from task to task, and subjects do not generalize from a set of tasks to the level of abstract rules. Pragmatic Inferential Rules Recently, we and our colleagues have argued that the Thorndike tradition is mistaken in asserting the extreme domain specificity of all rule learning. We have identified several naturally occurring inferential rules that people use to solve everyday-life problems and have found that they are improvable by purely formal training (Cheng & Holyoak, 1985; Cheng, Holyoak, Nisbett, & Oliver, 1986; Fong, Krantz, & Nisbett, 1986; Holland, Holyoak, Nisbett, & Thagard, 1986; Nisbett, Fong, Lehman, & Cheng, 1987). These "pragmatic inferential rules" capture recurring regularities among problem goals and among event relationships that people encounter in everyday life. They are fully abstract in that they are not tied to any content domain (much like Piaget's formal operations), but they are not as independent of relationship types and problem goals as formal logical rules (which are included in Piaget's propositional operations) or the purely syntactic rule systems often studied by modern cognitive psychologists.