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Abstract
Students‚ conceptions of mathematical induction in a
standard teaching approach were found to be largely
manifestations of deficient proof schemes, such as the
authoritative and the symbolic non-quantitative proof
schemes. On the other hand, when a fundamentally different
instructional treatment of mathematical induction was
implemented in an elementary number theory course taught to
prospective secondary teachers, students‚ conception of
mathematical induction developed as a transformational proof
scheme--a mathematically mature way of thinking. The
alternative instructional treatment was guided by a system
of learning-teaching principles, called the DNR system,
which was developed and in turn implemented in a sequence of
teaching experiments on the concept of mathematical
proof.
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