What Subject Matter Knowledge do second-level teachers need to know to teach trigonometry? An exploration and case study

This study reports on the level of trigonometry Subject Matter Knowledge (SMK) of third and final-year pre-service second-level mathematics teachers ((Formula presented.)) at an Irish third-level institution. The aim of the study was to determine if this sample of prospective teachers has an appropriate level of SMK to teach second-level trigonometric concepts. The development of an instrument to measure teachers’ SMK of trigonometry with respect to teaching trigonometric concepts at second level is detailed in this report, and the subsequent findings from its administration to the sample are discussed. The findings indicate that the sample has gaps in their SMK of trigonometric concepts that are on second-level syllabi and are underprepared to teach those concepts for understanding. This study reveals that the majority of the sample has enough SMK to teach the early years of second-level trigonometry but does not have enough SMK to teach the later years. The strengths and shortcomings of the sample in relation to their SMK of trigonometry are presented. The authors conclude that second-level trigonometry content should be taught in initial mathematics teacher education in order to combat this issue.