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International Electronic Journal of Mathematics Education

International Electronic Journal of Mathematics Education
Individual Differences in Conceptual and Procedural Fraction Knowledge: What Makes the Difference and What Does it Look Like?
Katja Lenz 1 * , Gerald Wittmann 1
1 University of Education Freiburg, Kunzenweg 21, 79117 Freiburg, GERMANY
* Corresponding Author
AMA 10th edition
In-text citation: (1), (2), (3), etc.
Reference: Lenz K, Wittmann G. Individual Differences in Conceptual and Procedural Fraction Knowledge: What Makes the Difference and What Does it Look Like?. INT ELECT J MATH ED. 2021;16(1), em0615. https://doi.org/10.29333/iejme/9282
APA 6th edition
In-text citation: (Lenz & Wittmann, 2021)
Reference: Lenz, K., & Wittmann, G. (2021). Individual Differences in Conceptual and Procedural Fraction Knowledge: What Makes the Difference and What Does it Look Like?. International Electronic Journal of Mathematics Education, 16(1), em0615. https://doi.org/10.29333/iejme/9282
Chicago
In-text citation: (Lenz and Wittmann, 2021)
Reference: Lenz, Katja, and Gerald Wittmann. "Individual Differences in Conceptual and Procedural Fraction Knowledge: What Makes the Difference and What Does it Look Like?". International Electronic Journal of Mathematics Education 2021 16 no. 1 (2021): em0615. https://doi.org/10.29333/iejme/9282
Harvard
In-text citation: (Lenz and Wittmann, 2021)
Reference: Lenz, K., and Wittmann, G. (2021). Individual Differences in Conceptual and Procedural Fraction Knowledge: What Makes the Difference and What Does it Look Like?. International Electronic Journal of Mathematics Education, 16(1), em0615. https://doi.org/10.29333/iejme/9282
MLA
In-text citation: (Lenz and Wittmann, 2021)
Reference: Lenz, Katja et al. "Individual Differences in Conceptual and Procedural Fraction Knowledge: What Makes the Difference and What Does it Look Like?". International Electronic Journal of Mathematics Education, vol. 16, no. 1, 2021, em0615. https://doi.org/10.29333/iejme/9282
Vancouver
In-text citation: (1), (2), (3), etc.
Reference: Lenz K, Wittmann G. Individual Differences in Conceptual and Procedural Fraction Knowledge: What Makes the Difference and What Does it Look Like?. INT ELECT J MATH ED. 2021;16(1):em0615. https://doi.org/10.29333/iejme/9282

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.

Keywords

fractions individual differences conceptual knowledge procedural knowledge cluster analysis

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