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Mathematics teacher's Specialised knowledge and the mathematical working spaces of a linear algebra's teacher

Abstract:

In this study, we approach the possible relationships between the analysis results of a classroom session with two different theoretical models: The Mathematics Teacher's Specialized Knowledge (MTSK), and the Mathematical Working Spaces (MWS). We also discuss the specialized knowledge that an university teacher of Linear Algebra deploys in a session about matrix product, and the ideal MWS of the teacher in this session. The knowledge showed explains the different genesis that the teacher prioritizes in the mathematical work he proposes. Thereby, the analysis with both models allows us to understand in depth the mathematical activity that the teacher fosters and how it is sustained by his knowledge.