Mathematical connections made in practice
Singletary, Laura Marie
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In this descriptive study, I examined the kinds of mathematical connections three secondary mathematics teachers made in their teaching practice, and I explored the teachers’ beliefs about mathematics. For each teacher, my primary data sources included six in-depth, semi-structured interviews and approximately two weeks of classroom observations. I used an inductive and iterative coding process to analyze the classroom data, and I developed the Mathematical Connections Framework to describe the explicit kinds of mathematical connections teachers made in practice. To analyze the teachers’ beliefs, I coded the interview and classroom data, drawing upon Green’s (1971) metaphorical interpretation of the structure of a belief system and Leatham’s (2006) theory of sensible systems of beliefs. These theoretical perspectives helped me understand the structure of the teachers’ beliefs about mathematics and how the beliefs were held as a sensible system. I present my findings through a series of narrative cases as well as a comparison across the cases. The teachers in this study made various kinds of mathematical connections for and with their students. Examining teachers’ beliefs about mathematics provided valuable insights into these teachers’ practices, helping me understand some of the reasons for the variation occurring among the mathematical connections the teachers made in practice. The mathematical connections each teacher made in practice were often related to the teacher’s beliefs about mathematics and, in particular, the teacher’s beliefs about the connected nature of mathematics.
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