What is transference and does it really happen?
If there’s one major theme in my postings or at least my I-should-post-about-that-ings, it is my struggle with the idea of prerequisites. In a broader context, this becomes a struggle with one motivation for much of the higher-ed curriculum: transference. By this I mean the idea that learning about method M in course C will prepare a student to apply method M’ in life-scenario C’ where the allowed differences between M and M’, and C and C’ are subject to debate. For example, in a math class we study word problems, using whatever course relevant math methods we wish to reinforce (e.g. implicit differentiation in related rates problems) and when we connect this course to the university-wide general education outcomes, we check of the box for ‘Problem Solving’. The implication being, I think, that having passed our course, which required some (specific) problems to be solved, that the student has grown in his or her ability to solve problems in general.
Here’s my take: I don’t think transference happens much, if at all. I think when it is observed, it comes from very deliberate and possibly long-term practice in learning to identify or look for similar contexts and in generalizing methods. It also shows when there’s an underlying skill that gives the student either an advantage in carrying over a method to very similar problems (e.g. factoring quadratics to factoring cubics with no constant term), or a skill that is both basic and has a natural, commonly occuring context (e.g. addition).