Exploring the challenges of learning transformations of trigonometric functions by senior phase mathematics preservice teachers at a KwaZulu-Natal University.

Abstract

This study investigates the conceptual and procedural challenges that senior phase mathematics preservice teachers (PSTs) encounter in understanding and applying the transformations of trigonometric functions, within the context of a higher education institution in KwaZulu-Natal, South Africa. Grounded in a qualitative research design, the study involved 125 first-year PSTs who participated in a diagnostic assessment consisting of Eight analytical tasks focused on trigonometric graphs and functions. In addition, semi-structured interviews were conducted with a purposive sample of five participants to gain deeper insights into their reasoning processes and conceptual misunderstandings. Findings reveal a consistent pattern of difficulties and misconceptions among the PSTs in relation to core concepts such as amplitude, period, phase shift, and vertical shift. Many participants exhibited significant struggles in identifying and interpreting these features within graphical representations, particularly when asked to apply transformations such as vertical and horizontal shifts, reflections, and scaling. Furthermore, a prevalent issue was the misapplication of trigonometric identities, which resulted in errors when simplifying expressions or solving equations. A lack of fluency in transitioning between different representations, such as moving from algebraic equations to their corresponding graphs, or vice versa, further highlighted conceptual fragmentation in the PSTs’ understanding. Additional challenges included confusion in converting between radians and degrees, errors in determining the correct direction and magnitude of phase shifts, and difficulties in simplifying complex trigonometric expressions. These issues suggest that many PSTs are still operating at a procedural rather than a conceptual level, relying heavily on rote memorization without fully grasping the underlying principles of function behaviour and transformation. The implications of the study point to a need for significant pedagogical reform in the way trigonometric concepts are taught in teacher preparation programmes. Specifically, there is a need for instructional strategies that are both visual and interactive, incorporating tools such as dynamic graphing software, manipulatives, and contextualized problems that bridge abstract mathematics with real-world applications. Emphasizing multiple representations and encouraging metacognitive reflection may also foster deeper learning and retention. Recommendations for future research include exploring the impact of targeted instructional interventions, such as inquiry-based learning, collaborative problemsolving, and the integration of educational technology, on improving PSTs’ conceptual mastery of trigonometric transformations. By equipping future teachers with stronger foundational understanding and pedagogical content knowledge, this research seeks to contribute to broader efforts in revitalizing mathematics education and enhancing student outcomes at the senior phase level and beyond.