Using the Rasch Model to Measure Comprehension of Fraction Addition
Marius Lie Winger1, Julie Gausen, Eivind Kaspersen
1Trygve Solstad, Department of Teacher Education, Faculty of Social and Eucational Studies, NTNU, Trondheim, Norway, trygve.solstad@ntnu.no.
Journal of Applied Measurement
|May 14, 2021
Summary
Transformations between mathematical representations effectively assess fraction addition comprehension. Difficulty levels vary based on the transformation type, offering insights into student understanding.
Area of Science:
- Mathematics Education
- Cognitive Science
Background:
- Assessing students' mathematical comprehension is crucial.
- Understanding fraction addition presents unique challenges for learners.
- Duval's theory highlights the role of representational transformations in mathematical understanding.
Purpose of the Study:
- To investigate if representational transformations can assess comprehension of fraction addition.
- To analyze the difficulty levels of fraction addition problems based on representational transformations.
Main Methods:
- 164 participants solved 20 fraction addition problems.
- Problems were designed based on Duval's theory of representational transformations.
- Rasch measurement theory and principal component analysis were employed.
Main Results:
- Items separated into three difficulty levels based on the transformation involved.
- Difficulty structure was consistent across gender and student subgroups.
- Diagrammatic representation production and type emerged as potential subdimensions.
Conclusions:
- Representational transformations are a viable tool for assessing fraction addition comprehension.
- Care must be taken to manage multidimensionality for accurate assessment.
- This framework offers a nuanced approach to evaluating student understanding of fractions.
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