Individual Differences in Conceptual and Procedural Fraction Knowledge: What Makes the Difference and What Does it Look Like?

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.

The relationship between grade 11 learners’ procedural and conceptual knowledge of algebra

“…It agrees with Ho (2020), Chinnappan andForrester's (2014), andHuang et al's (2007) findings that learners displayed a better procedural than conceptual knowledge of fractions. However, it is contrary to Lenz and Wittmann's (2021) discovery that students were weaker on procedural than conceptual knowledge of fractions. It might reflect that they spent most of their time on understanding mathematical procedures than acquiring a deep conceptual understanding of mathematics.…”

“…Some studies (e.g., Lenz & Wittmann, 2021;Maulina, Zubainur & Bahrun, 2020;Khashan, 2014;Forrester & Chinnappan, 2010) focused on measuring learners' or preservice teachers' levels of procedural and conceptual knowledge of mathematics. Lenz and Wittmann (2021) discovered that grade 8 and 9 students in Germany had weaker procedural knowledge than conceptual knowledge of fractions.…”

“…Some studies (e.g., Lenz & Wittmann, 2021;Maulina, Zubainur & Bahrun, 2020;Khashan, 2014;Forrester & Chinnappan, 2010) focused on measuring learners' or preservice teachers' levels of procedural and conceptual knowledge of mathematics. Lenz and Wittmann (2021) discovered that grade 8 and 9 students in Germany had weaker procedural knowledge than conceptual knowledge of fractions. Khashan (2014) and Zakaria and Zaini (2009) discovered that trainee teachers had an average level of both http://journals.ums.ac.id/index.php/jramathedu conceptual and procedural knowledge of rational numbers.…”