PROCEEDINGS OF THE 19TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2016
Pittsburgh, Pennsylvania
On symbols, reciprocals and inverse functions
Page: 1492
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 to this question of prospective secondary school teachers presented in a form of a dialogue between a teacher and a student. The data show that the majority of participants treat the symbol ☐!1 as a homonym, that is, the symbol is assigned different and unrelated meanings depending on a context. We exemplify how knowledge of advanced mathematics can guide instructional interaction.