
06622170
j
2016e.00538
Zazkis, Rina
Kontorovich, Igor'
A curious case of superscript ($1$): prospective secondary mathematics teachers explain.
J. Math. Behav. 43, 98110 (2016).
2016
Elsevier, New York, NY
EN
E40
F50
H40
I20
inverse function
reciprocal
script writing
homonymy
polysemy
doi:10.1016/j.jmathb.2016.07.001
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.