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Predicting fraction magnitude knowledge and fraction arithmetic
Cecilia Björkhammer1, Ulf Träff1, Rickard Östergren1
1Department of Behavioural Sciences and Learning, Linköping University, Linköping, Sweden.
Journal of Experimental Child Psychology
|July 20, 2025
Summary
Numerical magnitude knowledge is key for learning whole numbers, fractions, and arithmetic. Part-whole knowledge aids magnitude understanding but not arithmetic skills, supporting the integrated theory of numerical development.
Area of Science:
- Cognitive Psychology
- Educational Psychology
- Developmental Psychology
Background:
- The integrated theory of numerical development posits that understanding numerical magnitude is foundational for mathematical learning.
- Prior research highlights the importance of number sense in early mathematical development.
Purpose of the Study:
- To empirically test the core assumptions of the integrated theory of numerical development.
- To investigate the predictive roles of whole number magnitude knowledge and part-whole knowledge in fraction understanding and arithmetic proficiency.
Main Methods:
- A cross-sectional study involving 379 fifth-grade students.
- Assessment of whole number and fraction understanding, including arithmetic skills and part-whole knowledge.
- Analysis using four structural equation models to examine relationships between variables.
Main Results:
- Whole number magnitude knowledge significantly predicted fraction magnitude knowledge and arithmetic proficiency.
- Part-whole knowledge was found to mediate numerical magnitude understanding.
- Part-whole knowledge did not directly predict arithmetic outcomes.
Conclusions:
- Findings support the integrated theory of numerical development, emphasizing the critical role of numerical magnitude knowledge in mathematical learning.
- Part-whole knowledge appears to function as a mediator for developing magnitude understanding, potentially bridging to more advanced concepts.
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