The association between conceptual understanding and reasoning ability in mathematics: An analysis of DNR-based instruction models

Abstract

Mathematical reasoning is a tool used to understand mathematical concepts. Mathematical understanding is the basic ability in learning mathematics which is a mental construction process that connects, makes generalizations and synthesizes internal and external representations of mathematical objects. It is suspected that these two abilities have a close relationship. Based on these assumption, this study aimed to describe and reveal if there was an association between mathematical understanding and mathematical reasoning of college students who were taught using the Duality Necessity Repeated reasoning (DNR)-Based Instruction in the Basic Mathematics Course. 107 prospective primary education students participated in the study. Data was collected using a test consisting of four problems related to two-variable linear equations. Association analysis was assessed using Spearman test. The result showed that there was a strong and positive association between the ability of mathematical concept understanding and mathematical reasoning. This implies that college students’ mathematical reasoning abilities are strongly influenced by their understanding of mathematical concepts.