Pre-service Teachers’ Knowledge of Identifying and Clearing Pupils’ Misconceptions about Inverse and Composite Functions via Vignettes

Abstract

The purpose of this study was to investigate pre-service teachers’ knowledge of content and students vis-à-vis their ability to anticipate, identify and clear high school students’ misconceptions about inverse and composite functions. To accomplish this goal a case study research design was used to examine one fourth year mathematics education pre-service teacher from one of Zambia’s public universities. A case study strategy was preferred for this study because it enables the researcher to focus and have an in-depth investigation of an individual subject in a natural setting. As a data collection tool, the study used a questionnaire containing 7 vignettes comprising 4 inverse function vignettes and 3 composite function vignettes. Data were analyzed based on Ebert’s framework for characterizing the level of proficiency of functions and graphs. Findings revealed that the pre-service teacher’s level of proficiency of identifying and clearing students’ misconceptions was mostly good. Results suggest that vignettes might be useful in mathematical pedagogical courses in teacher education.