PLENARY PANEL PAPER
Michèle Artigue
Université Paris-Diderot

INTRODUCTION

Mathematics education has been developing as a research field for more than four decades now and has accumulated results, but the usefulness of these for practice remains a debated issue. Many authors point out the gap between research and practice, reflect on its possible sources, and try to learn from the successful examples that nevertheless exist. This was for instance the purpose of Boaler (Boaler, 2008) in the lecture she gave in Roma last March at the Symposium organized for celebrating the centennial of the International Commission on Mathematical Instruction (ICMI). Moreover, the conflicts generated in many countries by curricular changes evidence that even when research is considered influential, the positive character of this influence is frequently a matter of discussion. Making clear what research offers teachers and student teachers for enhancing teaching practices remains thus a non trivial enterprise.

In this contribution, reflecting on my personal experience, I will try to contribute to this panel, discussing what didactic research can offer teachers to help improve mathematics teaching and learning. I will focus on a specific mathematical topic: elementary algebra. Since the early nineties, I have been involved in different research projects about algebra (Artigue & al., 2003). I have organized training sessions for student teachers and teachers when professor at the IUFM (Institut Universitaire de Formation des Maîtres) of Reims, and then in the frame of my activities at the IREM (Institut de Recherche sur l’Enseignement des Mathématiques) of the University Paris Diderot - Paris 7. I hope that this reflection will offer valuable insights for the discussion, illustrating different ways through which research can impact practice as well as the potential and limits of these. In order to situate this contribution, I feel necessary to briefly describe the French educational context.

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