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Question 5:
Posted:
Feb 27, 2001 6:51 PM
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"Should school mathematics in the future be taught more formally or more
informally."
It is my belief that the most important tool that any mathematician has is
an "intuitive feel" for mathematics. How, then, can we better develop this
intuitive sense in our students? It is my belief that the most formal
approach (theorem, corollary, proof) is also the least intuitive for most
students.
In the extreme, I have known students who can capably manipulate a variety
of formulas but do not understand what they are doing or why it is supposed
to work. These students will often do well in their courses, yet they
vocally hate mathematics.
As a teacher, I attempt to merge concrete models and strong informal
reasoning with the underlying concepts. In the end, it is easier to turn a
logically correct (but informal) argument into formal language than it is to
build an intuitive understanding of a formal "line" proof.
Best wishes,
-Ted Fischer
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