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Topic: My two cents
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Larry Sowder

Posts: 59
Registered: 12/3/04
My two cents
Posted: Jun 1, 1995 7:11 PM
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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 rule-then-examples (ruleg) vs
examples-then-rule (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.

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