for the learning of mathematics

an international journal of mathematics education

Irene Biza ,  Elena Nardi ,  Theodossios Zachariades - Vol. 29 Num. 3 (2009)
 Teacher beliefs and the didactic contract on visualization


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 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.