Applied cognitive psychology--cognitive process instruction--speaks insistently of problems and of problem-solving strategies. This emerging approach to learning is a profoundly hopeful one, for it embraces the belief that the rational powers of our students are vital and dynamic ones susceptible to discipline and hence continuous growth. At a time when the reasoning skills possessed by many of our students appear to be woefully deficient, such affirmation of the intellect is more than merely welcome; it is downright necessary.
At the same time, it is easy to overlook some basic matters which must be borne in mind when we are speaking of heuristics, problem progressions and the like. Just what is a problem? How does a problem come into being and, as it were, live its life? How do students feel about problems of an intellectual nature? And I must add this question, perhaps the most elementary of all, since I am offering to look once more at well-trodden ground: just what is a student?
My answers to these questions might serve one of two functions: they might help to revive some old and fairly handy distinctions that have fallen out of use; or they might help to elucidate some of the psychological aspects of problem- solving activity. Problems, despite their being the stuff of everyday life, both academic and otherwise, are neither simple nor homogeneous. Of course, the same holds for students. If we can grasp more clearly the stages and the rhythms which characterize a student's growth as well as his efforts to meet the challenges inherent in all problems, we may well be on the way to becoming better teachers--shrewder, more sympathetic people better equipped to help our students grasp the richness and efficiency which are native to their minds. Students tend, specifically, to misunderstand the various ways in which their courage operates in problem-solving; by introducing the notion of what I call the "courage span," I hope to help alleviate the chronic self-shortchanging which sadly victimizes many of our students.
What is a "student"? We are accustomed, nowadays, to letting the term cover an astonishingly wide variety of meanings. It encompasses those who actively wish to be in our classrooms for instruction in our discipline; it encompasses those in our classrooms who would rather be elsewhere but have requirements to fulfill; it encompasses the reluctant who detest school generally, but feel unable to put it behind themselves for whatever reasons; and it encompasses that handful of devoted excitable people who have attached themselves to us because we