2134/9034
Irene Biza
Irene
Biza
Elena Nardi
Elena
Nardi
Theodossios Zachariades
Theodossios
Zachariades
Teacher beliefs and the didactic contract on visualisation.
Loughborough University
2011
untagged
2011-11-04 14:06:22
Journal contribution
https://repository.lboro.ac.uk/articles/journal_contribution/Teacher_beliefs_and_the_didactic_contract_on_visualisation_/9369818
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.