Research in mathematics education and rasch measurement

Abstract

A glance through the titles of research reports in current mathematics education journals might cause one to wonder why researchers in mathematics education eschew the very Queen of the sciences in representing the results of their research. Why do qualitative approaches appear to dominate this field? Many could claim that it is because the usual quantitative methods lose the important qualitative aspects of good mathematics education research. But, what if one quantitative research methodology in education incorporated the same genuine scientific measurement principles that mathematicians routinely expect from the metric system of measures and, at the same time, remained sensitive to those significant qualitative aspects of good educational research? What if this technique was an analytical model in which Australians are world leaders? What if applications of the model to research in mathematics education were already showing very promising results – both in Australia and internationally? Rasch measurement is being used increasingly as a research tool by “mainstream” researchers rather than merely by the sophisticated psychometricians involved in large-scale achievement testing. Using the performance interactions between persons and items, it is possible to produce an ordered conjoint measurement scale of both people and items. This allows researchers to examine the behaviour of persons (e.g., students, markers, teachers) in relation to a particular set of items (e.g., test questions, curriculum outcome indicators, problem-solving methods, attitude surveys.) This permits the identification and examination of developmental pathways, such as those inherent in the development of mathematics concepts as well as the developing capacities of the students. In addition, the behaviour of sets of items can be examined in relation to particular sub-groups of persons (e.g., age cohorts of students) in order to identify the extent to which the chosen items measure the core mathematical constructs the researcher was intending to measure. However, the features of the family of Rasch models make them useful tools for other kinds of research in mathematics education. We might reasonably ask: Is this sequence of the mathematics curriculum appropriate for the children who learn it, and not just appropriate in the eyes of the consultants who wrote it? The Rasch rating scale model allows Likert scale attitude data to be thought about in developmental rather than merely descriptive ways. The Rasch partial credit model provides for the