Algebrization levels of school mathematics practices. Networking of the Onto-semiotic and Anthropological perspectives
DOI:
https://doi.org/10.35763/aiem.v1i8.105Keywords:
Algebraic reasoning, primary education, secondary education, onto-semiotic approach, teachers’ educationAbstract
Based on the onto-semiotic approach to mathematical knowledge and instruction a characterization of algebraic reasoning in primary education has been proposed, distinguishing three levels of algebraization. These levels are defined taking into account the types of representations used, generalization processes involved and the analytical calculation at stakes in mathematical activity. In this paper we extend this previous model by including three more advanced levels of algebraic reasoning that allow to analyze mathematical activity carried out in secondary education. These new levels are based on the consideration of 1) using and processing parameters to represent families of equations and functions; 2) the study of algebraic structures themselves, their definitions and properties. Furthermore, concordances and complementarities of this model with the three stages of algebrization proposed under the anthropological theory of didactics are analyzed
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