How Can We Track Our Students’ Progress Towards Becoming Mathematicians?

In this chapter we consider the question of how mathematics lecturers in classes that may be small, but are often quite large, can assess and track the views that their students have about mathematics and its uses. To answer the question, we describe the third stage in our overall project: the development and utilisation of a closed-form survey of students’ conceptions of mathematics. Our development of this survey was informed by the results of the previous two stages – the initial interviews and the open-ended survey. As well as structuring the questions around the conceptions we identified, we were able to make use of the actual words that our respondents had spoken or written. We present an initial closed-form survey, assess its statistical properties and use these to construct a shorter version, comprising a subset of the original questions, that can be utilised as a valid and reliable survey of students’ conceptions of mathematics and its uses (see Appendix 1). Such a survey can be used for various pedagogical purposes, in addition to its continued use as a research tool. Maybe the most important of these is for assessing and then tracking the views of groups of students in the typical tertiary mathematics lecture class. The survey can be administered early during a course to gauge the views of students, and thus to plan more effective ways of helping them towards broader conceptions. The survey can be used again during or at the end of the course, and a comparison with the previous results can indicate the extent of any change in views. Presenting the results to the students concerned and discussing the actual questions with them can be used as one way of introducing them to the full range of conceptions of mathematics.

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