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Multimedia Battery for Assessment of Cognitive and Basic Skills in Mathematics BM-PROMA

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Published on: August 28, 2021

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.

Keywords:

Arithmetic Cross-notation knowledge Decimals Fractions Integrated Theory of Numerical Development Magnitude knowledge Numerical development

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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.