Abstract:

A qualitative case study was conducted to explore mathematics student teachers’ understanding of trigonometry as taught at secondary school level. Twenty two conveniently selected university mathematics major student teachers wrote a test which was developed to assess their content knowledge of trigonometric concepts. The student teachers were in their final year and had studied advanced university mathematics courses. After analyzing the test results using descriptive statistics, and based on their performance in the test, students were then categorized as high content knowledgeable and low content knowledgeable. Those who scored 50% and above were placed in the high content knowledge category while those who scored below 50% were in the low content knowledge bracket. A sub-sample of six students was then purposively selected for participation in follow up semi-structured interviews. In order to acquire rich data, three of the student teachers were selected from among the high content knowledgeable and the other half were sampled from among those in the low content knowledge bracket. The interviews explored the student teachers’ ability to explain comprehensively the trigonometric concepts and their ability to justify reasoning. An opportunity was also provided to the students to elucidate their solutions to particular test items. Analyses of students’ explanations and justifications were guided by the ideas of instrumental and relational understanding as espoused by Skemp (2006). Although the students could solve questions, and recite and use formulas to solve questions, content analysis of the interview transcripts revealed that more than 50% of them lacked the ability to explain coherently the trigonometric concepts or justify their reasoning. This result suggested that the study of advanced mathematics does not inevitably culminate in student teachers’ relational understanding of basic trigonometry as taught in secondary schools. In this regard, the view that during their training pre-service teachers of secondary school mathematics should be provided opportunities to study the subject matter which they are expected to teach upon graduation was augmented.

Keywords:

Content Knowledge, Secondary schools, Relational understanding, Instrumental understanding, Mathematics major student teachers, Pre-service teachers, Advanced Mathematics, Basic Trigonometry.