비정형 그래프에 대한 예비 중등 수학교사 세 명의 교수를 위한 수학적 의미 분석

Abstract

The informal graph is ‘a graph showing real-life contexts and irregular changes without being bound by the definition of a function or algebraic equation’, and is a new concept that was introduced in the first year of middle school by the 2015 revised Korean mathematics curriculum. According to previous studies, some teachers do not have a high level of understanding of informal graph. This raises the need to analyze in detail how teachers understand informal graph and reflect it in teacher education, given that the way teachers understand mathematical ideas closely influences the way students form mathematical ideas. The present study analyzes the mathematical meaning for teaching of prospective mathematics teachers on the informal graph to provide specific implications for one area of school mathematics taught in pre-service teacher education. Specifically, we examined three of the 15 prospective participant teachers' ways of reasoning with two items all of which required them to draw and interpret informal graph through questionnaire and semi-structured interview. We paid attention to mathematical meaning for teaching of each the three teachers, who were chosen due to the distinctive ways they coordinated two quantities, brought forth in reasoning with informal graph. Finally, the conclusions and the implications for teacher education were discussed.