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A GEOMETRIC APPROACH TO DEFINING …
A GEOMETRIC APPROACH TO DEFINING MULTIPLICATIONPETER F. MCLOUGHLIN AND MARIA DROUJKOVAThe set-theoretic construction of the real numbers in the 1870s marked a shiftin emphasis from GEOMETRIC to algebraic reasoning (see [3]). This shift in reason-ing may have inadvertently created some problems in the lower-level mathematicscurriculum (in the at least). Let us clarify what we mean by this. Currently,prospective K-12 math teachers and Science, Technology, Engineering, and Math-ematics (STEM) students can graduate from university without ever seeing thefollowing:(1) A rigorous definition of multiplication ;(2) A proof that two triangles have the same angles if and only if the lengths oftheir corresponding sides are proportional;(3) A pro
A GEOMETRIC APPROACH TO DEFINING MULTIPLICATION PETER F. MCLOUGHLIN AND MARIA DROUJKOVA The set-theoretic construction …
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