The influence of theoretical tools on teachers’ orientationto notice and classroom practice: a case study

Assumptions about the construction and the transmission of knowledge and about the nature of mathematics always underlie any teaching practice, even if often unconsciously. I examine the conjecture that theoretical tools suitably chosen can help the teacher to make such assumptions explicit and to support the teacher’s reflection on his/her previous as well as future educational practice. In particular, I show how an epistemological vision of mathematics in resonance with a model of cognitive dynamics can work as a powerful tool to support a teacher’s stable and autonomous attitude of noticing. To support this argumentation, I present some experimental data concerning a case study of one teacher. Through a methodological frame suitably arranged I try to describe how the teacher’s ability to rely on this particular theoretical frame affects: the choice of the global goals in mathematics education; the design of educational interventions; the interpretation of learners’ cognitive behaviours; and the assessment.