Towards validation of a rational number instrument: An application of Rasch measurement theory

Abstract

The rational number knowledge of student teachers, in particular the equivalence of fractions, decimals, and percentages, and their comparison and ordering, is the focus of this article. An instrument comprising multiple choice, short answer and constructed response formats was designed to test conceptual and procedural understanding. Application of the Rasch model enables verification of whether the test content was consistent with the construct under investigation. The validation process was enabled by making explicit the expected responses according to the model versus actual responses by the students. The article shows where the Rasch model highlighted items that were consistent with the model and those that were not. Insights into both the construct and the instrument were gained. The test items showed good fit to the model; however, response dependency and high residual correlation within sets of items was detected. Strategies for resolving these issues are discussed in this article. We sought to answer the research question: to what extent does this test instrument provide valid information that can be used to inform teaching and learning of fractions? We were able to conclude that a refined instrument applied to first-year students at university provides useful information that can inform the teaching and learning of rational number concepts, a concept that runs through mathematics curricula from primary to university. Previously, most research on rational number concept has been conducted on young learners at school.