An epistemological reference model for primary-level algebra research

The anthropological theory of the didactic sets out the questioning of mathematical knowledge as playing a decisive role, and proposes the development of reference epistemological models (REMs) as an analytical tool. We present a REM of the development of school algebra that fits into a broader model connecting arithmetic, algebra, relative numbers, functional modeling and differential calculus. This model takes “calculation programs” as a starting point, viewing algebra as a structured modeling process in three stages. We illustrate the potential of this model for creating and analyzing didactic sequences in the first stage of the algebrization process.