Abstract

MORENO-ARMELLA, Luis  and  RAMIREZ, Rubén Elizondo. The Encounter of Geometry with Learning. Educ. mat. [online]. 2017, vol.29, n.1, pp.9-36.  Epub Feb 14, 2022. ISSN 2448-8089.  https://doi.org/10.24844/em2901.01.

Conceiving of space as the space around us, and the inflexibility of Euclidean geometry to analyze physical space for over 20 centuries led to a crisis in the conception of mathematics. Eventually this created a tension between cognition and logic. We explain how such developments challenge learning paradigms and mathematical inquiry for learners today. We introduce this epistemological analysis to help us think about the nature of mathematical knowledge and hence learning today. The direct correspondence between physical space and mathematical structure was broken after the discovery of non-Euclidean geometry. Similarly, this is what is occurring with the implementation of dynamic mathematical environments that breaks the correspondence with static mathematical objects.

With our digital model of non-Euclidean geometry we focus on the affordances of new technological environments and the knowing of mathematics learners. This illustrates a representational re-description of mathematics and how it can modify our natural ontology to accommodate change and variation.

Keywords : epistemology; model; representation; intuition; learning.

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