Written Mathematical Reasoning in Two Different Content Areas in Grades 4–6

Abstract

In the context of a study on written mathematical reasoning, we investigated how students in grades 4–6 (N = 866) deal with two reasoning problems from different content areas (arithmetic and geometry). Moreover, we examined whether there are differences between the three age groups. So as to be able to describe the children’s reasoning skills comprehensively and with regard to central content-related features, we developed a category system by means of an approach that referred to theoretical considerations. The category system covers a broad range of mathematical reasoning skills as well as the content-related ideas that the children came up with and assesses these features in terms of their quality of application. The coding process resulted in satisfactory to good interrater reliability. In our paper, we present our findings both concerning the children’s demonstration of different mathematical reasoning skills and concerning their content-related ideas for solving the two reasoning problems. Our findings suggest that the content area plays a role with regard to the reasoning skills in various respects and that the three grades differ systematically from each other in several features of the reasoning process.