Analysis of preservice teachers’ understanding of solving trigonometric equations: A perspective through actions, processes, objects, and schemas theory

This study analysed first-year preservice teachers’ understanding of trigonometric equations at a South African university in the Eastern Cape province. We employed the Action-Process-Object-Schema (APOS) framework to analyse the mental constructions made by preservice teachers in solving trigonometric equations. A qualitative case study design was employed to analyse test scripts from 223 preservice teachers, complemented by follow-up interviews with eight of these participants. Findings show that the success rate in the two analysed items was low. Students who had not developed specific mental structures could not solve the given problems. Only 15.5% of the participants reached the Object level, while 76% remained at the Action or Process stages. Conversely, 8.5% of the participants were at the pre-Action stage, having not shown evidence of action mental structures conjectured in the genetic decomposition. Challenges encountered include difficulties with algebraic manipulations, reference angles, angle relationships across quadrants, and conversions between degrees and radians. The analysis further revealed a lack of understanding of the periodic nature of trigonometric functions and the general solution derivation. Contribution: These findings reflect global trends in mathematical struggles across various educational levels, particularly in solving trigonometric equations. The study highlights the importance of assessing preservice teachers’ mathematical knowledge both at the entry and exit points of their training programmes. Such dual assessments could improve their content mastery and teaching effectiveness. This suggests that adjusting educational strategies to address these identified gaps could foster significant growth.