Misconceptions in Vertical and Horizontal Shifts of Trigonometric Functions for Future Teachers

The study investigates specific misconceptions related to the vertical and horizontal transformations of trigonometric functions among pre-service teachers. It identifies common errors such as confusion between amplitude and vertical shifts, and misconceptions regarding the horizontal and vertical phase shifts. Using Duval’s (2006) framework, the research emphasises the importance of transitioning between different semiotic representations: symbolic, visual and algebraic. Through qualitative assessments of 125 pre- service teachers and detailed interviews with selected participants, the study uncovered graphing errors primarily with the cosine function. These include misrepresentations related to periodicity, amplitude and graph transformations. The findings highlight a need to shift educational focus towards diagrammatic and intuitive learning, linking this recommendation to observed errors. Emphasising this approach in curricula could enhance pre-service teachers’ understanding, improve their teaching skills and foster a holistic grasp of mathematical concepts.