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Children learn spurious associations in their math textbooks: Examples from fraction arithmetic
David W Braithwaite1, Robert S Siegler1
1Department of Psychology, Carnegie Mellon University.
Summary
Children often struggle with fraction arithmetic due to relying on learned associations rather than conceptual understanding. These associations, linking specific number patterns to operations, are mirrored in textbooks and influence mathematical strategy choices.
Area of Science:
- Cognitive psychology
- Mathematics education
Background:
- Fraction arithmetic is a critical yet challenging topic in K-12 mathematics.
- Students' difficulties may stem from associative knowledge rather than conceptual understanding.
- This associative knowledge might be learned from the structure of practice problems.
Purpose of the Study:
- To investigate the hypothesis that associative knowledge influences fraction arithmetic strategy selection.
- To examine if children's learned associations mirror textbook problem structures.
- To compare these learning patterns in the United States and China.
Main Methods:
- Conducted experiments with middle school students in the U.S. and China.
- Assessed children's associations between operand pairs and arithmetic operations.
- Analyzed textbook materials for similar associative patterns.
Main Results:
- Children in both countries associated equal denominators with addition/subtraction.
- Students linked whole numbers and fractions with multiplication/division.
- These associations were consistent with patterns found in textbooks.
Conclusions:
- Children learn associations between number structures and operations from practice problems.
- This associative knowledge impacts fraction arithmetic strategy.
- Cross-cultural differences in these effects and their educational implications warrant further study.
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