### Abstract:

This was a qualitative case study that explored Zambian mathematics student teachers? content knowledge of functions and trigonometry in secondary schools. The students were in their final year of study and had studied advanced university mathematics and had completed Mathematics Education courses. Content knowledge was investigated as Common Content Knowledge (CCK) and Specialised Content Knowledge (SCK). Data was collected in two phases: Phase 1 utilised a mathematics test to gather CCK and SCK data from 22 conveniently chosen University of Zambia student teachers majoring in mathematics. Phase 2 used semi-structured interviews to collect SCK data from a sub-sample of six purposefully selected students.
Descriptive statistics and qualitative techniques were used to analyse the test data and content analysis to analyse the interviews. Although the students achieved a mean score of about 52% in the CCK of functions, an item by item analysis suggested that they were not proficient therein. They had a shallow understanding of composite functions, domains and ranges, extreme values, and turning points. They also had a superficial understanding of the definitions of concepts. While the students managed to identify functions, the majority could not coherently explain concepts and justify their reasoning. The students showed a limited understanding of the Cartesian plane representations of functions and the algebraic representation of quadratic functions.
The students achieved a mean score of approximately 53% in the CCK of trigonometry, and 68% of the sample achieved scores above 50%. An item by item analysis suggests that most of the students were proficient in CCK. However, the students could not comprehensively explain concepts and justify their reasoning. While most of the students could apply rules and formulas, they could not coherently explain and prove these. Similarly, they could not translate algebraic trigonometric functions to the Cartesian plane. Generally, there seemed to be a disconnection between the students? CCK and SCK of trigonometry. These findings suggested that the study of advanced mathematics does not automatically result in students? comprehensive understanding of school mathematics. While the students had studied advanced UNZA mathematics, it was found out that they had not acquired an in-depth understanding of the functions and trigonometry required at secondary school level.