Abstract

Developing conceptual understanding is a key goal of mathematics education at all levels. Unfortunately, compared to procedural understanding, it is much harder to reliably assess. Most efforts to measure students’ conceptual understanding involve the time-consuming development of a domain-specific concept inventory (e.g. Epstein, 2005) or the use of detailed clinical interviews (e.g. Piaget, 1959). Both of these methods are highly time-intensive, either in terms of development work or researcher time. These costs present a serious barrier to rigorously evaluating educational interventions that are designed to improve students’ conceptual understanding. In this talk I discuss an alternative approach to assessing conceptual understanding, based on Thurstone’s Law of Comparative Judgement from the psychophysics literature. I will explain the theoretical basis of the approach, and report a number of studies where my colleagues and I have employed it. These studies include assessing children’s understanding of fractions, assessing undergraduate students’ understanding of statistics, and the comparison of high-stakes examination standards over time.