Teacher beliefs and the didactic contract on visualisation.
journal contributionposted on 04.11.2011 by Irene Biza, Elena Nardi, Theodossios Zachariades
Any type of content formally published in an academic journal, usually following a peer-review process.
This paper explores secondary teachers’ views on the role of visualisation in the justification of a claim in the mathematics classroom and how these views could influence instruction. We engaged 91 teachers with tasks that invited them to: reflect on/solve a mathematical problem; examine flawed (fictional) student solutions; and, describe, in writing, feedback to students. Eleven teachers were also interviewed. Here we draw on the interviews and the responses to one Task (which involved recognising a line as a tangent to a curve at an inflection point) in order to explore the influence on the teachers’ feedback to students of: persistent images of the tangent line; beliefs about the sufficiency of a visual argument; and, beliefs about the role of visual arguments in student learning. We focus particularly on the influence on the didactical contract regarding mathematical reasoning that teachers with a variation of beliefs about the role of visualisation are likely to offer their students. We conclude with a concise description of a didactical contract which maintains a role for proof in the mathematics classroom that is not disjoint from the creative parts of visually-based classroom activity and that reflects an essential intellectual need. We also conclude with crediting the combination ‘task engagement-followed by-interview’ for the identification of subtle issues regarding the teachers’ pedagogical and epistemological beliefs and for the raising of their awareness of these issues.
- Mathematics Education Centre