Subject-Matter Knowledge and Pedagogical Content Knowledge: Prospective Secondary Teachers and the Function Concept

Abstract

This article investigates teachers' subject-matter knowledge and its interrelations with pedagogical content knowledge in the context of teaching the concept of function. During the first phase of data collection, 152 prospective secondary teachers completed and open-ended questionnaire concerning their knowledge about function. In the second phase, an additional 10 prospective teachers were interviewed after responding to the questionnaire. The analysis shows that many of the subjects did not have a modern conception of function. Appreciation of the arbitrary nature of functions was missing, and very few could explain the importance and origin of the univalence requirement. This limited conception of function influenced the subjects' pedagogical thinking. Therefore, when describing functions for students, many used their limited concept image and tended not to employ modern terms. In addition, many chose to provide students with a rule to be followed without concern for understanding.