Sixty four preservice teachers taking a mathematics methods class for middle schools were given 3 math problems: multiply a three digit number by a two digit number; divide a whole number by a fraction; and compare the volume of two cylinders made in different ways from the same rectangular sheet. They were to a) solve them, explaining their solution, b) classify them as easy, of medium difficulty, or difficult, explaining the rationale for their classification, and c) explain how they would teach/help children to solve them. Responses were classified under three categories of subject matter knowledge, namely traditional, pedagogical, and reflective. Implications of these categories to effective math teaching are then discussed.
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