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A curious case of superscript ($-1$): prospective secondary mathematics teachers explain. (English)
J. Math. Behav. 43, 98-110 (2016).
Summary: In mathematics the same symbol ‒ superscript ($-1$) ‒ is used to indicate an inverse of a function and a reciprocal of a rational number. Is there a reason for using the same symbol in both cases? We analyze the responses of prospective secondary school teachers to this question. The responses are presented in a form of a dialogue between a teacher and a student and are accompanied with participants’ commentary on their choices of instructional approaches. The data show that the majority of participants treat the symbol $\square ^{-1}$ as a homonym, that is, the symbol is assigned different and unrelated meanings depending on a context. We discuss how knowledge of advanced mathematics (or lack of it) can guide instructional interaction.
Classification: E40 F50 H40 I20
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