@article {MATHEDUC.06622170,
author = {Zazkis, Rina and Kontorovich, Igor'},
title = {A curious case of superscript ($-1$): prospective secondary mathematics teachers explain.},
year = {2016},
journal = {The Journal of Mathematical Behavior},
volume = {43},
issn = {0732-3123},
pages = {98-110},
publisher = {Elsevier, New York, NY},
doi = {10.1016/j.jmathb.2016.07.001},
abstract = {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.},
msc2010 = {E40xx (F50xx H40xx I20xx)},
identifier = {2016e.00538},
}