The symbolic world of mathematics

Abstract

In understanding upper secondary school students’ interpretations of information in symbolic representations of a distance-time-relation, little attention has been paid to the analysis of the condition of the conceptual development related to utterances. Understanding this better can help improve the teaching of attribute and information in symbolic representations of different phenomena. Two theoretical perspectives have been used to conduct the analysis: Tall and Vinner's theoretical perspectives on learning and Gray’s & Talls’s theory of three mathematical worlds. The findings provide evidence that a detailed analyse of student’s utterances show difference in quality related to student’s interpretations of a distance-time relation. The qualities were related to student’s concept images of functions and derivatives.