Analysis of Mathematics teachers’ level of understanding of the objects f’(a) and f’(x)

Abstract

This paper describes the level of understanding of the relation between f’(a) and f’(x) among five Mathematics teachers who were teaching classes to 16-18 year olds in different schools in Colombia. The analysis is based on the APOS framework, in this case with the addition of certain semiotic aspects. The five teachers responded to an indirect questionnaire about their understanding of f’(a) and f’(x), and were subsequently interviewed in relation to a series of vignettes. Results illustrate how the comprehension of these two macro-objects, f’(a) and f’(x), can be related to the structure of both graphic and algebraic schemes and the associated semiotic conflicts.