This Unit is under construction, material will be uploaded gradually.
Credits : all modules, except module 0, are presented and have been filmed by Anna Sfard herself. Module 0 has been prepared in collaboration with Jean-Luc Dorier, who presents it and has been film at the university of Geneva.
Great many stories of mathematics learning have been told, and they may sometimes be seen as competing with each other. While each one of us may favor one of these stories and call it “the best”, there is no single version that can count as the story of mathematics learning – as the one that is superior to all the rest in some absolute way.
The version to be presented in this unit is called commognitive. Explaining this approach will require engaging with the fundamental questions of what is learning, what is mathematics, and what we mean when we put these two words together and speak about learning mathematics. All this will be done in the modules that follow. This brief introductory talk evolves around the preliminary query: Why should we spend our time trying to define things as basic and obvious as learning or mathematics? In response, it is claimed that the way we speak impacts the way we act.
This module introduces the commognitive definition of learning. To clarify it fully and to explain why it was chosen from among many existing alternatives, the presentation of the definition is preceded by a brief historical account of research on human development.
Ever since its beginnings, the study of human learning has been fueled by the relentless tension between two desires: the researchers’ wish to capture human learning in all its uniqueness and their wish to do it scientifically, whatever this word meant for them at that time. Because of the conflicting nature of these two desires, it was difficult to attend to both of them at the same time. Whenever a story of learning was told that seemed to satisfy one of them, the resulting research would eventually be criticized for the neglect of the other one. The history of these zigzagging attempts is organized in this talk around the widely differing answers given by various schools of thought to the question “If learning means change, what is it that changes when people learn?” The response adopted by the commognitive researcher seems to constitute an effective tool for capturing the uniqueness of human learning, the goal that can now be pursued without compromising the scientific quality of the endeavor.
MODULE 3 - Mathematics as discourse
MODULE 4 - Mathematical objectsas discursive constructs
MODULE 5 - Mathematical routines
MODULE 6 - Historical development of mathematical discourse
MODULE 7 - Ontogenetic development of mathematical discourse
MODULE 8 - Cultural embeddedness of mathematics leanrning
MODULE 9 - Identity of mathematics learner
MODULE 10 - Teaching mathematics
MODULE 11 - Commognitive research and its methods