Towards a Didactic Model for Assessment Design in Mathematics Education

Abstract

In this chapter we compare and contrast the didactic and psychometric models of assessment design. We begin with background information and an introduction to assessment, and then the relationship between the goals of mathematics education and assessment is presented. This relationship is made explicit by exhibiting two assessment problems, each reflecting a different way of thinking about mathematics education. The primary objections to the current way of assessing students, and alternatives that have been developed for it, are next presented. We then present a theoretical perspective on the psychometric approach, followed by some recent developments regarding this assessment model. Here we arrive at the crucial issue in this chapter, namely, the need to extend assessment design in mathematics education via a didactic model. The consequences of the psychometric requirements and assumptions for mathematics education are presented and discussed. Importantly, we discuss how we can overcome certain misconceptions that inhibit an approach to assessment which is aligned with the new way of thinking about mathematics education. Finally, we present examples of assessment problems that represent a didactic model of assessment design. The chapter concludes with a reference to Freudenthal and his concept of mathematics as a human activity. The approach to assessment in the chapter, and the examples that exemplify it, are identified as consistent with Freudenthal’s thinking.