Using the many-facet rasch measurement to assess how pre-service mathematics teachers pose mathematical literacy problems

Abstract

This embedded mixed-method study aimed to determine the steps followed by pre-service mathematics teachers during the process of posing mathematical literacy problems and to analyze the processes of posing these problems. The participants consisted of 40 pre-service mathematics teachers enrolled in a course on mathematical literacy. They separated into seven groups. They first wrote mathematical literacy problems for four different content areas: "quantity", "uncertainty and data", "change and relationships", and "space and shape". They wrote down the steps they had followed in the problem-posing process, and then engaged in self-assessment on this problem-posing task. The steps followed by pre-service mathematics teachers were analyzed through the many-facet Rasch analysis method. Self-assessments were analyzed using the content analysis method. Based on the findings of the study, many-facet Rasch analysis identified 12 steps in the mathematical literacy problem-posing process, covering aspects such as context, mathematical content, considering the student level and interest, and evaluation (e.g., consulting an expert on the problem, working on the problem/solution, and revising the problem). The most difficult issues for them in the problem posing process were "clarifying/organizing the problem" and "determining mathematical values", while the easiest issue was "creating/determining the context". Also, it was determined that pre-service teachers were mostly inspired by their own lives and previous experiences when creating the contexts.