Seventh grade students' conceptual and procedural understanding of fractions : comparison between succesful and less successful students

Abstract

The aim of the study was to find the correlation between conceptual knowledge (CK) and procedural knowledge (PK) and the difficulties that less successful students have regarding fractions. The study was conducted with a mixed-methods approach using explanatory design which consisted of two phases. In the first phase of the study, a conceptual and procedural knowledge test (CPKT) was administered to 33 seventh grade students. In the second phase, interviews were conducted with two successful students (ST33 and ST24) and two less successful students (ST01 and ST03). The results of the CPKT showed a strong positive correlation between students’ conceptual knowledge (CK) and procedural knowledge (PK), r = 0.66 (p < .01). In addition, it was found that students’ school mathematics grade (mathematics GPA: grade point average) at the end of the sixth year was strongly related to both conceptual and procedural knowledge. In the second phase, the interview results showed that while successful students had combined conceptual and procedural knowledge, less successful students had orphaned procedural knowledge. It was concluded that students can benefit from having both conceptual and procedural knowledge in order to develop a good knowledge base in mathematics.