:,J i THE aims of this paper are primarily constructive, that is, to conh-'' &quot;bute to the development of a scientific theory of concept formation., Bowever, before turning to this subject, there are two general aspects ' ~ of the teaching of mathematical concepts upon which I want to c0mrnent.l l to Teaching of Mathematical Concepts The first concerns the much heard remark that the newer, revisions of the mathematics curriculum are particularly signifìcant because of the ' emphasis they are placing on understanding concepts as opposed to the perfection of rote skills. My point is not to disagree with this remark, but urge that it is essentially banal. It is a good thing to understand; it is a bad thing to possess mere rote skill. The banality arises from not know-* ing what we mean by understanding. This failure is not due to disagree-ment over whether the test of understanding should be a behavioral one. i ' 1 am inclined to think that most people concerned with this matter would s admit the central relevance of overt behavior as a measure of understand-hgg The difficulty is rather that no one seems to be very clear about the exact specification of the behavior required to exhibit understanding. Moreover, apart even from any behavioral questions the very notion of understanding seems fundamentally vague and ill-defined
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