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Learning to Solve Trigonometry Problems That Involve Algebraic Transformation Skills via Learning by Analogy and
1School of Education, University of New England, Armidale, NSW, Australia.
Frontiers in Psychology
|October 19, 2020
Summary
This study explores effective teaching methods for trigonometry, a challenging math subject. By comparing learning by analogy and learning by comparison, educators can improve student understanding of algebraic transformations in trigonometry problems.
Area of Science:
- Mathematics Education
- Cognitive Psychology
- Pedagogical Strategies
Background:
- Mathematics is a national priority, often perceived as purely theoretical and difficult to learn.
- Trigonometry presents unique challenges due to algebraic transformations and pronumeral placement (numerator vs. denominator).
- Existing research has not successfully addressed these learning difficulties.
Purpose of the Study:
- To investigate the effectiveness of learning by analogy and learning by comparison for teaching trigonometry.
- To elucidate and clarify two comparative pedagogical approaches for improving student comprehension of trigonometry problems.
- To counter the inherent difficulty of learning trigonometry problems involving algebraic transformation skills.
Main Methods:
- Learning by analogy: Juxtaposing linear equations with trigonometry problems (e.g., x/4 = 3 vs. sin30° = x/5) to leverage similar solution procedures.
- Learning by comparison: Identifying similarities and differences between trigonometry problems with varying pronumeral locations (e.g., sin30° = x/5 vs. cos50° = 20/x).
- Conceptual analysis of these two pedagogical approaches.
Main Results:
- The study proposes that combining learning by analogy and learning by comparison can enhance understanding of algebraic transformations in trigonometry.
- Learning by analogy facilitates understanding by drawing parallels between known and new problems.
- Learning by comparison deepens comprehension by highlighting similarities and differences in problem-solving.
Conclusions:
- The complementary strengths of learning by analogy and learning by comparison offer a promising pedagogical strategy for trigonometry.
- These approaches aim to improve students' ability to solve trigonometry problems involving algebraic manipulation.
- Further research can build upon these conceptual frameworks to develop targeted educational interventions.
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