The Problematic Relationship between Theory and Practice

This chapter addresses the complex question of the relationship between theory and practice in mathematics education. After a brief introduction in which we recall the main conceptions of mathematics education as a scientific discipline, we express the different ways in which such relationship appears in the literature. We concentrate our attention on the most usual way of understanding such a relationship, i.e. between theory as the corpus of knowledge constituting mathematics education and practice as the act of teaching. Our idea of teaching acknowledges teachers as decision makers, influenced by important factors that the research should not neglect, such as knowledge, beliefs and emotions. This practice model has strong implications with theory itself and leads one to re-organize the quality criteria for research such as reproducibility and relevance. Consequently teachers' training -focused not only on knowledge but also on their beliefs, emotions and most of all on awareness- becomes an important fulcrum that grants the potential generalization of specific results and the feedback on practice. From this point of view, the Italian teacher-researcher - in particular within the international panorama of co-ordination typologies between teachers and researchers - has double significance: on one hand, it reduces the separation between theory and practice by making it evolve in a dialectic process between the two poles, on the other hand it gives life to a meaningful prototype of a high quality training process.