Comparing approaches through a reference epistemological model: the case of school algebra. (English)

Ubuz, Behiye (ed.) et al., CERME 8. Proceedings of the eigth congress of the European Society of Research in Mathematics Education, Antalya, Turkey, February 6‒10, 2013. Ankara: Middle East Technical University (ISBN 978-975-429-315-9). 2870-2879 (2013).

Summary: Luis Radford and Yves Chevallard, whose research programmes in mathematics education were awarded with the last Hans Freudenthal medals, have both given a prime place to the problem of teaching and learning elementary algebra. However, their approaches are far from being similar. Are they comparable? We are starting a dialogue considering how each approach, in a more or less explicit way, defines what algebra is and how it characterises ‘algebraic thinking’ or ‘algebraic activities’ with what we call a reference epistemological model (REM) of elementary algebra. The dialogue starts by assuming the point of view of the anthropological theory of the didactic, presenting our own REM, and the kind of questions addressed by this approach, in relation to the theory of knowledge objectification developed by Radford.