Meaning and understanding of school mathematical concepts by secondary students: The study of sine and cosine

Abstract

Meaning and understanding are didactic notions appropriate to work on concept comprehension, curricular design, and knowledge assessment. This document aims to delve into the meaning of school mathematical concepts through their semantic analysis. This analysis is used to identify and establish the basic meaning of a mathematical concept and to value its understanding. To illustrate the study, we have chosen the trigonometric notions of sine and cosine of an angle. The work exemplifies some findings of an exploratory study carried out with high school students between 16 and 17 years of age; it collects the variety of emergent notions and elements related to the trigonometric concepts involved when answering on the categories of meaning which have been asked for. We gather the study data through a semantic questionnaire and analyze the responses using an established framework. The subjects provide a diversity of meanings, interpreted and structured by semantic categories. These meanings underline different understandings of the sine and cosine, according to the inferred themes, such as length, ratio, angle and the calculation of a magnitude.