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Multimedia Battery for Assessment of Cognitive and Basic Skills in Mathematics BM-PROMA
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Cross-notation knowledge of fractions and decimals
David W Braithwaite1, Jake McMullen2, Michelle A Hurst3
1Department of Psychology, Florida State University, Tallahassee, FL 32306, USA.
Journal of Experimental Child Psychology
|August 27, 2021
Summary
Understanding how fractions and decimals relate (cross-notation knowledge) is key for mastering rational numbers. This knowledge significantly boosts arithmetic skills, more than just knowing each notation separately.
Area of Science:
- Mathematics Education
- Cognitive Psychology
Background:
- Learning rational numbers involves understanding fractions and decimals separately (within-notation) and their connections (cross-notation).
- Multiple notations present learning challenges but also opportunities for deeper understanding.
Purpose of the Study:
- To test the hypothesis that cross-notation knowledge enhances rational number understanding.
- To investigate the predictive power of cross-notation magnitude knowledge on arithmetic skills.
Main Methods:
- Reanalysis of three published datasets from US and Finnish fourth- to eighth-grade students.
- Inclusion of measures for rational number arithmetic, within-notation magnitude knowledge, and cross-notation magnitude knowledge.
Main Results:
- Cross-notation magnitude knowledge significantly predicted fraction and decimal arithmetic performance, controlling for within-notation knowledge.
- Within-notation knowledge's relation to arithmetic was not notation-specific.
Conclusions:
- Cross-notation knowledge is a crucial predictor of rational number arithmetic skills.
- Findings have implications for assessing and teaching rational numbers, emphasizing the importance of inter-notation understanding.
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