A purpose-built model for the effective teaching of trigonometry: a transformationc of the van Hiele model

There is widespread acknowledgement that students in second and third level education have diffculty with trigonometry. This is not only the case domestically in Ireland, but also internationally. Evidence exists that trigonometry is not being taught well at second-level. The fact that many teachers have not studied mathematics to degree level is contributing to this issue. Therefore, students are unprepared in trigonometry upon entering third-level education and fall further behind in their undergraduate mathematical studies. In addition, the teaching and learning of trigonometry is an under-researched issue worldwide. The purpose of this research was to examine ways of improving the teaching of trigonometry, and to develop a purpose-built model of how to teach it effectively. The author developed a purpose-built model for the effective teaching of trigonometry in two stages. He first extended the van Hiele model of geometric thought to the specific branch of trigonometry, leading to a learning model for trigonometry. The second stage was to elaborate on this learning model to make it applicable to teaching trigonometry. A systematic teaching structure for trigonometry was developed with the use of APOS theory and genetic decomposition. Essentially, the author adapted a model of how people learn geometry, to a model of how to teach trigonometry. This purpose-built teaching model was applied in the form of a teaching intervention with a group of 19 pre-service secondary mathematics teachers in order to investigate whether or not the model could aid in the development of trigonometric understanding. The research was guided by an Educational Design Research methodology which incorporated a proof-of concept approach. The teaching model and its incorporated teaching strategies were shown to have a positive effect on teaching trigonometric concepts for understanding. Pre and post-test ndings indicate that the teaching intervention led to significant increases in understanding with reference to the teaching model. Through the proof-of-concept approach, the fndings indicate that the teaching model could contribute towards better teaching of trigonometry at second-level.