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My two cents
Posted:
Jun 1, 1995 7:11 PM


I'm starting to realize that my advancing age is responsible for all my deja vu feelings!
1. Whether 'discovery learning' is better or not can hinge on what criterion you have in mind. Some netters seem to have in mind standardized tests; others, an implied focus on processes involved in mathematical approaches and/or, for some students at least, the excitement of figuring something out for oneself.
2. At least one study several years ago suggested that there are individual differences (surprise!) on dealing with rulethenexamples (ruleg) vs examplesthenrule (egrul).
3.Unfortunately, at that time there wasn't much of a distinction between concept definitions (conventional usage of words, so correctness relies on an external authority) and principles (statements making assertions about concepts, and subject in many cases to student testing for correctness). So one person's 'discovery' lesson might involve figuring out what a polygon is (a definition), and another person's might involve figuring out an expression for the angle sum of a polygon (a principle).
4. It is my impression that psychologists now think/know/have evidence that most routine/natural human thinking is based on examples, sometimes a very special example, instead of on some sort of mental checklist of definitional attributes. The rub is that a deductive mathematical development *is* based on definitions. Part of learning in mathematics, at least at some point, involves coming to appreciate the latter.



