Prospective Elementary School Teachers’ Perception of Explanations by Counterexamples

Abstract

The purpose of this paper is to investigate the perceptions of prospective elementary school teachers about children’s explanations by counterexamples. First, based on a framework, a questionnaire survey was designed. Then, the author conducted a descriptive survey targeting prospective elementary school teachers, and analyzed the results of the survey. The results revealed that prospective teachers had their own criteria for judging the appropriateness of children’s explanations using counterexamples. The criteria were organized into three primary criteria, which were consistent across responses, and two secondary criteria, which applied to some responses. The primary criteria were as follows: 1) counterexample type (whether a counterexample is mentioned or not), 2) explanation type (whether there are some reasons how the counterexample is generated or not), and 3) a combined type (combined criteria of 1 and 2). The secondary criteria were classified into: a) letter/symbol type (whether the generality is indicated by letters or symbols or not) and b) (counter) example space type (whether a counterexample space or example space is indicated or not).