Pre-service mathematics teachers’ knowledge of functions: a mixed methods sequential explanatory study

Abstract

It is common knowledge that teachers cannot teach students and help them learn and comprehend concepts they themselves do not understand. Thus, the purpose of this mixed methods sequential explanatory study was to examine knowledge held by pre-service secondary mathematics teachers in the topic of functions. The study attempted to characterize the depth of their subject-matter and pedagogical content knowledge of the concept of a function. In the first phase (quantitative) of the study, the investigation focused on categorizing pre-service teachers based on their level of knowledge of the concept of a function. In particular, the grouping was based on their Mathematical Pedagogical Content Knowledge perceptions, Common Content Knowledge, Specialized Content Knowledge, and Knowledge of Content and Students related to their knowledge of the concept of a function.