Secondary School Mathematics Teacher's Professional Knowledge: A case from the teaching of the concept of function

Abstract

This study examines the relationships between a secondary Mathematics teacher's pedagogical content knowledge and the dilemmas posed when teaching the concept of function. Alternative tools and procedures for analysing these relationships are used. The results illustrate the flexibility of her knowledge use in Mathematics teaching and how it is related to her knowledge of the pupils as Mathematics learners. In addition, it highlights the central role played by the teacher's knowledge about pupil comprehension in the content and organisation of her teaching agenda. The difference that the teacher establishes between exercise and problem shows her struggle with the two-fold understanding-memorisation of procedures as the content of a teaching dilemma. The results obtained suggest the need for secondary Mathematics teacher education programmes to adopt approaches that take into account the central role played by teacher knowledge about Mathematics learning, and the dilemmas generated when teachers have to reconcile objectives that are apparently contradictory during their teaching practice.