The teaching and learning of trigonometry

A major desire of many African nations today is to be technologically developed. In South Africa there tends to be an acute shortage of skilled manpower in the field of science, engineering and technology. The fundamental importance of mathematics to humans could be explained in terms of the interrelationship between mathematics and the development of humans to advance the cause of humanity. Science and technology rely on the application of trigonometry in real life situations which affect the daily lives of people. In this paper, we report on a qualitative study which explored the mental constructions made by Grade 12 learners when solving for the unknown properties of triangles in trigonometry. The study was carried out at a school in KwaZulu-Natal (n=30) in South Africa. The data were collected from written responses of students to a structured activity sheet consisting of questions on 2-dimensional shapes, and subsequently analysed using Action, Process, Object and Schema (APOS) theory. Findings emanating from the data analysis informed a modification of the initial genetic decomposition, which raised some didactical implications for basic education, specifically for the learning and teaching of trigonometry.