How Do Mathematics Students Think of Mathematics? – A First Look
In this chapter we begin our investigation of the process of becoming a mathematician. The first step in this inquiry is based on a series of interviews that we carried out with a small number of students studying mathematics as a major at an Australian university. In these interviews we asked students about their ideas of mathematics as a discipline, their learning of mathematics, and their future use of mathematics in their studies and professional life: in this chapter we will focus on the first of these aspects. We found that students’ views could be described in three levels – from narrowest to broadest, focusing on the techniques and components of mathematics, mathematical models and mathematics as an approach to life. These levels showed a hierarchical relationship: students who viewed mathematics as an approach to life were also aware of the modelling aspects and the technical components of the discipline. However, those who viewed mathematics in terms of its techniques seemed unable to appreciate the broader views, the modelling and the approach to life. In this chapter, we describe the research that we carried out to arrive at these conclusions, and illustrate the levels that we discovered using our students’ own words taken from the interview transcripts. We discuss the place of these results in our overall project and put forward some initial thoughts about their implications for our teaching and our students’ learning.
KeywordsBroad Conception Broad View Mathematical Science Deep Approach Broad Level
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