learning involves someone coming to know something something which the learner did not know before. Thus, it involves a transmission from not knowing to knowing. I suspect that this gives us a hint as to the nature of knowledge. I will finish with a note on how our understanding of knowledge might affect our pedagogy by noting how John Dewey's account, which is similar to the one I push for here, affected his pedagogy.
To learn something requires that one be able to do something with it. If I teach you the definition of a term, and you cannot apply the term accurately, I will not say that you have learned the term. Learning, then, whether learning a sport or learning an academic subject, involves the acquisition of capacities. Thus, knowledge is practical: it involves possessing abilities. Or, to put it another way: learning is practical: it involves gaining new capacities (I do not, at this point, make a distinction between an ability and a capacity).
The puzzles about knowledge which this helps us address are multiple. The first one I want to address, however, is about the nature of a state of knowledge. Given my claim that learning involves gaining capacities and that knowledge entails possessing such capacities, it is not entirely clear whether we gain the capacities and thus gain knowledge or gain knowledge which necessarily provides us with the capacities. To put it another way: are the capacities equivalent to the knowledge or merely a symptom of the knowledge?
Think about how we teach things. We may talk, and articulate propositions, and even expect the student to be able to regurgitate some of these propositions, but the end goal is always a kind of action. If we are teaching mathematics, we give students problems to solve, and we measure the students' understanding by their ability to solve the problems. The focus on abilities is even clearer in sports or languages, where the entire goal is to form certain capacities, not to have the students be able to regurgitate propositions on command.
This does not mean that knowledge just is the capacities we teach. However, it strongly suggests that knowledge is not chiefly knowledge of propositions, which it is frequently taken to be by those who think that knowledge merely results in abilities. The basic kind of knowledge, to use more technical terms, is more likely to be knowledge-how than knowledge-that.
This should help explain why a pragmatist like Dewey develops the kind of pedagogical approach he does. Pragmatists tend to hold that what matters about a proposition is its use-value: what one does with it. They thus tend to hold much closer to a view of knowledge as consisting in capacities than others. Dewey's pedagogy relies a huge amount on having students interacting practically with the subject matter, because he believed that the closer you can tie the point of an action--the capacities whose development is being developed in teaching the subject--to teaching it, the easier it is to learn. That is, he generalizes from the claim that one cannot learn to play baseball except by playing baseball to the claim that one cannot learn, for instance, biology, without actually doing biology, whereas the default mode of teaching is to teach the products of biology.
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