The idea that formal study of abstract systems of rules develops habits of mind that are useful in reasoning about concrete problems has been around for a long time. Plato, for example, argued that study of arithmetic and geometry was effective in improving reasoning, and that improving the arithmetical and geometrical skills of its leaders would serve a state well. Other formal systems, grammar, logic, and languages, were added to arithmetic and geometry, resulting in the classical college curriculum of the nineteenth century—a curriculum that did not include chemistry or other natural sciences.

The incorporation of science into the curriculum that began in the late nineteenth and early twentieth centuries was based to some extent on experimental evidence that cast doubt on Plato's idea that formal training in reasoning would carry over into all aspects of a person's intellectual and practical life. Thorndike, on the basis of empirical research on transfer of training effects, argued that there are no general inferential rules that apply to all disciplines (2). Instead there are highly specific empirical rules that deal with concrete events and apply to other events only to the extent that the two have identical elements in common. Piaget agreed with Plato that people use inferential rules, but argued that these cannot be taught to any significant extent (3). Every individual develops such rules in the normal course of maturation, but instruction cannot alter that development. Both of these positions argue against the classical, one-size-fits-all curriculum.

Nisbett et al. take an alternative view that is closer to Plato's: people do use inferential rules, and such rules can be taught, sometimes by abstract means. However, Nisbett et al. argue that the rule systems people use naturally (and that can be taught) are pragmatic and are induced in the process of solving recurrent everyday problems. With respect to training in statistical reasoning they found that either teaching statistical rules or teaching by having students solve example problems would work. With respect to training in conditional logic, they found that neither abstract logical training nor showing subjects how to use rules to solve problems would work alone, but when these two approaches were used simultaneously, students learned.

To me the most interesting aspect of the Nisbett paper is also the most disturbing. Chemistry was one of four disciplines within which they studied the effect of two years of graduate work, both on statistical and methodological reasoning and on applying conditional logic to solve problems. Two years of graduate study did not significantly improve chemistry students' abilities in either area, although it did improve the abilities of medical students and psychology students in both areas and the abilities of law students in conditional logic. It appears that reasoning can be taught, but we are not doing it! (Of course the data might also imply that our students' abilities are already at such a high level that they cannot be improved, and we could argue that the types of reasoning ability the psychologists were looking for are not needed by chemistry students.)

It is certainly true that in most undergraduate chemistry curricula students are much more often confronted with problems that have definite, deterministic answers than they are with problems that may have several answers or no answer at all. The chief exception to this is undergraduate research, which does involve students in questions to which their experimental answer is not going to be checked against the back of the book. Since undergraduate research has obvious benefits in the maturation of young chemists, wouldn't it make sense to try to make some of the same benefits available to students in nonresearch courses? But how?

Nisbett et al. provide some ideas for us to try. In some cases using examples alone, or teaching general logical rules alone, will suffice. We are at that stage in the textbooks and teaching methods of many of our undergraduate courses now. Books are full of very specific examples of how to solve relatively simple problems. Indeed, some students don't bother to read the book at all, because concentrating on the examples will make them successful on our tests. I think that there are many cases in chemistry teaching where we need to go much farther than the excellent examples we already have, and Nisbett et al. reinforce that belief. More important than either a formal discipline of logical rules or examples of applying those rules is the combination of the two: abstract training closely coupled with concrete, real-world examples (very different from the textbook examples just mentioned) of how to apply the abstract ideas in a variety of situations.

I ran the Nisbett paper by a psychologist friend of mine, and he took it one step farther. The really hard trick, after knowing abstract rules and being familiar with examples of applying them, is to know which set of abstract rules will work in a new situation. (Or, from a more discipline-chauvinistic perspective, to know to which kinds of new situations chemistry's abstract rules will apply. Fortunately there are a great many.) We need to present students with a broad range of situations where they can practice skills of choosing and applying abstract sets of rules to unfamiliar problems. Concentrating too much on the standard, relatively simple "problems" in most textbooks and examinations is not enough. So let's work to go beyond that in creative and effective ways!

Literature Cited

1. Nisbett, R. E.; Fong, G. T.; Lehman, D. R.; Cheng, P. W. Teaching Reasoning"; Science 1987, 238, 625­631.

2. Thorndike, E. The Psychology of Learning; Mason-Henry: New York, 1913.

3. Brainerd, C. Piaget's Theory of Intelligence; Prentice-Hall: Englewood Cliffs, NJ, 1978.