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Building fraction magnitude knowledge with number lines: Partitioning versus analogy
Alexandria A Viegut1, Percival G Matthews2
1Department of Psychology, University of Wisconsin-Eau Claire.
Developmental Psychology
|September 28, 2023
Summary
Using analogy to teach fractions significantly improved children's understanding of fraction magnitudes compared to traditional partitioning methods. This approach, leveraging whole number knowledge, showed lasting benefits for fraction comprehension.
Area of Science:
- Cognitive Psychology
- Educational Psychology
- Mathematics Education
Background:
- Understanding fraction magnitudes is crucial for mathematical development.
- Traditional partitioning methods for fractions may not fully utilize students' existing knowledge.
- Number line representations generally support fraction magnitude understanding better than area models.
Purpose of the Study:
- To investigate the effectiveness of an analogy-based lesson for teaching fraction magnitudes.
- To compare analogy-based learning with traditional partitioning on number lines and area models.
- To determine if analogy enhances fraction understanding, particularly with large denominators and over time.
Main Methods:
- An online experiment with 84 second and third graders.
- Random assignment to three groups: analogy lesson, partitioning lesson on number lines, or control (area models).
- Lessons focused on representing fraction magnitudes on number lines, with a key analogy group example provided.
Main Results:
- The analogy lesson was more effective than the control lesson and as effective as the partitioning lesson.
- The analogy group showed superior performance on large-denominator fractions at delayed retention and transfer tests.
- Partitioning on number lines was more effective than on area models, with some sustained advantage.
Conclusions:
- Domain-general analogy is a powerful tool for supporting mathematical development in fractions.
- Analogy-based instruction can enhance fraction magnitude understanding, especially for complex fractions and long-term retention.
- Leveraging prior whole number knowledge through analogy offers a promising alternative to standard fraction instruction.
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