Comparing the problem-solving, worked example, and analogy approaches for learning trigonometry: an element interactivity perspective across Australian and Malaysian students

This study applied the concept of element interactivity from cognitive load theory to differentiate the complexity of trigonometry problems and assess the effectiveness of three instructional approaches for solving them. The complexity of a trigonometry problem depends on the location of its pronumeral; for example, sin 32° = 50/x involves more solution steps than tan 75° = x/26 because the pronumeral appears in the denominator. A 2 × (Country) × 3 (Approach) design was used, involving Australian students (N = 48) and Malaysian students (N = 65). The problem-solving approach requires learners to search for a solution path. The worked examples approach provides a step-by-step solution procedure. The analogy approach emphasizes the concurrent processing of pairs of isomorphic worked examples. Results indicated that the worked examples approach was more effective than the problem-solving approach, demonstrating the worked examples effect. For Australian students, the worked examples approach proved the most efficient. However, for Malaysian students, the analogy approach was more effective. This may be attributed to Malaysian students’ stronger prior algebra knowledge, which likely reduced the element interactivity demands imposed by the analogy approach. However, because prior algebra was not directly measured, this interpretation should be treated with caution. Practically, the findings suggest that instructional approaches should be selected with consideration of students’ prerequisite knowledge. Worked examples may be more effective for learners with limited algebraic understanding, whereas the analogy approach may better support learners with stronger algebra prior knowledge.