A hypothetical learning trajectory for the construction of trigonometric equations with infinite solutions

In this research, we design and evaluate a hypothetical learning trajectory (HLT) for first-year university students of a Geometry course for the concept of trigonometric equations with infinite solutions. As the theoretical framework, we considered the instructional design heuristic of emergent models that guided our design of HLT and the interpretation of students' progress when we used HLT as a teaching tool. As a methodology, we used design-based research. The results provide evidence that HLT helped students understand the concept of trigonometric equations with infinite solutions. In particular, the results showed the students' progress from their model-of-solution set of trigonometric equations with finite solutions in bounded intervals toward a model-for-solution set of trigonometric equations with infinite solutions.