Pre-service teachers’ understanding of sine and cosine functions and their inverses based on the unit circle trigonometry

Abstract

We applied Action-Process-Object-Schema (APOS) theory to study pre-service secondary mathematics teachers' understanding of the concepts of sine and cosine functions and their inverses based on the unit circle approach. We used a model (genetic decomposition) of mental constructions that students may do to understand these notions and designed research-based didactical materials and implemented them in two countries, Czech Republic and Iran. Eighteen pre-service teachers (nine from each country), who were studying a bachelor's degree of mathematics, participated in our research. The study involves three phases: initial interview, instructional intervention, and exit interview, which were separately carried out in each country.We discussed the teachers' understanding in both initial and exit interviews.