New geometries, new spaces: The discussion about the origin of the geometry at the beginning of the XX century and its impact on teaching
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In this contribution we reconstruct the discussion, that developed from the end of the XIX and the beginning of the XX century, regarding the meaning of the axioms in geometry. In such a discussion, psychological and cognitive considerations played a relevant role. The actors involved in the debate recognized their clear educational implications. In this perspective, the historical case we are analyzing can also help to frame the always significant relationship between mathematics education and the other disciplines that support it in the understanding of teaching and learning processes.
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