Individual Differences in Conceptual and Procedural Fraction Knowledge: What Makes the Difference and What Does it Look Like?
Katja Lenz 1 * , Gerald Wittmann 1
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1 University of Education Freiburg, Kunzenweg 21, 79117 Freiburg, GERMANY* Corresponding Author

Abstract

There is a general consensus that both conceptual and procedural knowledge are essential for students’ mathematical development. A common argument is that differences in mathematical performance are caused by differences in conceptual and procedural knowledge. Therefore, it is important to investigate to what extent such differences in conceptual and procedural knowledge are empirically evident at the level of individual students. Accordingly, the aim of the present study is to describe individual differences in conceptual and procedural knowledge using the example of fractions and to analyze their relationship to the covariates grade level, school type, school, class, gender, and general cognitive abilities. Data from 377 students in grades 8 and 9 from 18 classes at four schools in Germany was examined. A hierarchical cluster analysis showed five clusters which reflected individual differences in conceptual and procedural knowledge. The clusters were characterized by (a) equal strengths in conceptual and procedural knowledge, (b) relative strengths in procedural knowledge compared to conceptual knowledge, (c) relative weaknesses in procedural knowledge compared to conceptual knowledge. Cluster membership was not related to gender or grade level, whereas the school type, school, and grade level were relevant for cluster membership. A stronger correlation between conceptual knowledge and general cognitive abilities could only be confirmed to a limited extent.

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, 2021, Volume 16, Issue 1, Article No: em0615

https://doi.org/10.29333/iejme/9282

Publication date: 28 Nov 2020

Article Views: 1809

Article Downloads: 1141

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