Individual differences in conceptual and procedural knowledge: the case of algebra

Abstract

As children learn algebra, it is not certain whether they are learning both the procedural and conceptual aspects in a balanced way. Instead, students may be learning one of these types of knowledge more than the other. Previous research on children’s understanding of fractions have used cluster analysis to demonstrate that there are some students who rely more on conceptual knowledge, some who rely more on procedural knowledge, and some who rely equally on both. Using cluster analysis, the current study found that there are individual differences in the understanding of algebra in a sample of 104 grade eight students. Four clusters were found representing students who do relatively poorly on conceptual and procedural knowledge, those who do well on both types of knowledge, those who are relatively better conceptual problem solvers, and those who are relatively better procedural problem solvers. Furthermore, both conceptual and procedural knowledge are significant contributors to students’ overall performance in algebra, which suggests that both conceptual and procedural knowledge are important in algebraic learning.