The University of Montana

Department of Mathematical Sciences

Technical report #5/2011

New Perspectives on the Didactic Triangle: Teacher-Student-Content

**Simon Goodchild,** University of Agder, Norway

**Bharath Sriraman**, The University of Montana

**Abstract**

What constitutes development when applied to the teaching of mathematics? Responses to this question might focus on the nature of the tasks and activities in which teachers engage their students. The introduction of ’inquiry’ tasks, problem solving activities, and open, rather than closed tasks can all be taken as evidence of teaching development, indeed there has, over the past couple of decades, and recently been considerable attention on the nature of tasks in the literature of mathematics teaching development. In classrooms tasks are a ‘mediating artefact’ used by the teacher with the intention of leading students to develop new understanding or knowing, that is tasks are used in a wider context of teaching. This special issue of ZDM brings together leading researchers and thinkers in the field of mathematics education to address, from the perspective of their own research the relationships between mathematics, student and teacher.

*How does/can the introduction of inquiry or investigational tasks impact upon the relationships within the didactical triangle?**How does/can the development of a problem oriented approach to mathematics teaching and learning affect the relationships within the didactical triangle?**How does/can the introduction of digital technologies to teaching and learning mathematics affect the relationships within the didactical triangle? Does the technology introduce another ‘vertex’ such that it is necessary to refer to a didactical quadrilateral?**How do/can teachers transform the relationships between mathematics, students and themselves?**How can those working in teaching development projects influence teaching so that teaching, and the didactical relationships are accommodated to new artefacts (inquiry tasks, problems, ICT, etc?).*

**Keywords:** Didactic Triangle; Didactical Transpositions; Mediation between Teacher-Student-Content; Mathematics Education Theory

**AMS Subject Classification:** 97