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Sources of Individual Differences in Emerging Competence With Numeration Understanding Versus Multidigit Calculation
Lynn S Fuchs1, David C Geary2, Douglas Fuchs1
1Department of Special Education, Vanderbilt University.
Journal of Educational Psychology
|October 7, 2014
Summary
General cognitive abilities significantly impact understanding the base-10 number system more than multidigit calculation skills. Foundational math skills support both, especially through later math achievement, showing a reciprocal relationship.
Area of Science:
- Cognitive Psychology
- Developmental Psychology
- Educational Psychology
Background:
- Understanding number systems and calculation skills are crucial for mathematical development.
- General cognitive abilities and foundational math skills are known predictors of academic success.
- The distinct contributions of these factors to numeration understanding versus calculation skill require further elucidation.
Purpose of the Study:
- To investigate how general cognitive abilities and foundational mathematical competencies influence numeration understanding (base-10 structure) and multidigit calculation skill.
- To examine the developmental trajectories of these skills from 1st to 3rd grade.
- To determine the mediating role of early mathematical achievement.
Main Methods:
- Longitudinal study with 394 children assessed from 1st to 3rd grade.
- Measures included general cognitive abilities, foundational numerical competencies, numeration understanding, and multidigit calculation skill.
- Path-analytic mediation analysis was employed to examine predictive relationships.
Main Results:
- General cognitive abilities had a more direct and substantial impact on numeration understanding compared to multidigit calculation skill.
- Foundational mathematics competencies contributed to both outcomes, primarily mediated by 2nd-grade mathematics achievement.
- A mutually supportive relationship was observed between numeration understanding and multidigit calculation skill.
Conclusions:
- Cognitive abilities are foundational for understanding number systems, while calculation skills develop through practice and application.
- Early mathematical achievement plays a key role in bridging foundational skills to more complex mathematical abilities.
- Numeration understanding and calculation skill development appear to be intertwined and mutually beneficial.
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