PRECISE MATHEMATICS COMMUNICATION: THE USE OF FORMAL AND INFORMAL LANGUAGE

Resumen

INTRODUCTION. When explaining their reasoning, students should communicate their mathematical thinking precisely, however, it is unclear if formal terminology is necessary or if students can explain or describe mathematical concepts using everyday language. This paper reports the results of two studies. The first explores the relation between students’ use of formal and informal mathematical language and procedural knowledge in mathematics; the second replicates and extends these findings using a longitudinal design over the course of an entire school year. METHOD. Study 1 uses a pre-test, intervention, post-test method across one unit of study. Study 2 uses the same pre-test, intervention, post-test method, however, it implements a longitudinal design across an entire school year using growth curve analysis. RESULTS. Findings show that students benefit most when they attempt to describe the targeted mathematical concepts, regardless of the type of language used. This finding is consistent with prior work showing that having students go through the process of self-explaining, independent of the quality of those explanations, yields benefits to learning (i.e. Chi, 2000). DISCUSSION. Although teachers should still use formal language in their classrooms; they should not be discouraged if students are initially unable to use formal language correctly. We suggest that teachers allow students to explain their reasoning using either formal or informal terms, especially while students are in the midst of developing an understanding the mathematical concepts.