Meeting the requirements of both classroom-based and systemic assessment of mathematics proficiency: The potential of Rasch measurement theory

The challenges inherent in assessing mathematical proficiency depend on a number of factors, amongst which are an explicit view of what constitutes mathematical proficiency, an understanding of how children learn and the purpose and function of teaching. All of these factors impact on the choice of approach to assessment. In this article we distinguish between two broad types of assessment, classroom-based and systemic assessment. We argue that the process of assessment informed by Rasch measurement theory (RMT) can potentially support the demands of both classroom-based and systemic assessment, particularly if a developmental approach to learning is adopted, and an underlying model of developing mathematical proficiency is explicit in the assessment instruments and their supporting material. An example of a mathematics instrument and its analysis which illustrates this approach, is presented. We note that the role of assessment in the 21st century is potentially powerful. This influential role can only be justified if the assessments are of high quality and can be selected to match suitable moments in learning progress and the teaching process. Users of assessment data must have sufficient knowledge and insight to interpret the resulting numbers validly, and have sufficient discernment to make considered educational inferences from the data for teaching and learning responses.