id: 06622170
dt: j
an: 2016e.00538
au: Zazkis, Rina; Kontorovich, Igor’
ti: A curious case of superscript ($-1$): prospective secondary mathematics
teachers explain.
so: J. Math. Behav. 43, 98-110 (2016).
py: 2016
pu: Elsevier, New York, NY
la: EN
cc: E40 F50 H40 I20
ut: inverse function; reciprocal; script writing; homonymy; polysemy
ci:
li: doi:10.1016/j.jmathb.2016.07.001
ab: 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.
rv: