Space of fuzziness: avoidance of deterministic decisions in the case of the inverse function

Abstract

We investigate responses of prospective secondary school teachers to a task related to the inverse function concept. We utilize ideas of fuzzy logic as a theoretical lens in analyzing the participants’ demonstrated avoidance of refuting the existence of an inverse to a quadratic function. The analysis is based on 29 responses to a scripting task, in which participants composed a hypothetical dialog between a teacher and students. The findings demonstrate three categories of fuzzy evaluations of a mathematical statement: (a) false blurred to be true; (b) almost false; and (c) almost true. We offer possible reasons for the prevalence of fuzzy thinking in general, and in discussing the inverse of a function in particular.