lew@ihuxr.UUCP (08/26/83)
There was an article in Physics Today once about Piaget's idea of concrete vs. abstract reasoning. The article applied this idea to physics instruction, but the recent coin problem discussion reminds me of this dichotomy. The basic concept is that the abstract reasoner is aware of his or her reasoning process. The AR is able to collect concrete reasoning patterns and organize them under a single structure. The concrete reasoner, by contrast, is stuck at the anecdotal level. If a particular argument or technique "clicks" in a particular case, he or she will happily solve the problem, but will otherwise be left at a loss. The CR is unable to take charge of his or her own reasoning process. Many explanations of the coin problem sought to break the 50-50 mental block by providing different mental images of the problem. This is a strategy which appeals only to concrete reasoning. Bayes' Theorem is the abstract collection of all imaginable variations of the coins-in-the-cabinets problem. Whoever can understand Bayes' Theorem can conquer an entire realm of problems at once. Those who reject an analysis based on abstract reasoning in favor of concrete explanations are, in my opinion, misguided. Lew Mammel, Jr. ihuxr!lew