Emergences and affordances as opportunities to develop teachers’ mathematical content knowledge

Teachers’ mathematical content knowledge has been under scrutiny for some time. This development is in the wake of learners’ unsatisfactory performance in national examinations and international achievement tests. A widely held belief is that one, if not the most important, of the efforts to improve and enhance the performance and achievement in mathematics of learners is addressing teachers’ mathematical content and pedagogical content knowledge through continuous professional development initiatives. The focus of this article is on the former. It describes how emergent and affording opportunities are brought to the fore from classroom observations and interactions in workshops and institutes with practising teachers. It concludes that this in situ dealing with mathematical content knowledge holds much promise for buy-in by teachers because it addresses an immediate need related to their practice

The French Didactic Tradition in Mathematics

This chapter presents the French didactic tradition. It first describes theemergence and development of this tradition according to four key features (role ofmathematics and mathematicians, role of theories, role of design of teaching andlearning environments, and role of empirical research), and illustrates it through two case studies respectively devoted to research carried out within this traditionon algebra and on line symmetry-reflection. It then questions the influence of thistradition through the contributions of four researchers from Germany, Italy, Mexicoand Tunisia, before ending with a short epilogue