Concrete or Abstract?

Concrete examples or abstract examples? I have struggled with this issue in lectures and in writing. Usually, I opt for concrete example first followed by the more general, abstract case.

My rationale for this approach has been the results from the Wason Selection task. That logical problem (If P then Q, if Not P then Not Q is the solution to both cases) is solved much, much more often in its concrete form (~75% of the time) than in its abstract form (~5% of the time). Here is a site that explains this problem.

However, recent research from the Ohio State University (as reported in the New York Times) in mathematics education suggests that teaching the abstract first is far superior to teaching the concrete first in mathematics problems. This research was recently reported in the journal Science. The authors are Jennifer A. Kaminski, Vladimir M. Sloutsky, and Andrew F. Heckler.

To me, the discrepancy between the Wason Selection data and the Kaminski et. al data indicates that further research is needed. I agree that flying by the seat of one's pants is not a good idea here. It would be nice for teachers to know, once and for all, which strategy is best.

By the way, I sometimes use an abstract first strategy. Recall my earlier post on the Mastermind game. There I use an abstract first-first strategy to teach about main effects and interactions.