The Development of a Reference Framework for Measuring Students' Understanding in a First Year Calculus Course

Abstract

This thesis investigates the development of an instrument, a reference framework, for measuring students' understanding of mathematical concepts in a first year calculus course at the University of the Western Cape (UWC). The reference framework is a detailed method for analysing students' written and oral responses to non-routine questions. Criteria for constructing the reference framework are established within the context of a theoretical framework developed to model understanding, and based on analysis of empirical data collected by the author and those gleaned in relevant literature. A "fuzzy" measure of the level of students' understanding is also implemented.