Beyond linear proportionality
an epistemological framework for teaching area-volume relationships in contemporary mathematics education
DOI:
https://doi.org/10.23925/1983-3156.2026.v28.e74170Keywords:
Mathematics education, Proportional thinking, Epistemology of mathematics, Mathematical Modeling, Geometry teachingAbstract
This article proposes an integrative epistemological framework for teaching area-volume relationships in basic education, addressing the conceptual difficulties inherent in the transition from linear to multidimensional thinking. Grounded in complex proportional thinking, mathematical modeling, and contemporary mathematics education approaches, the proposal articulates theoretical principles with innovative didactic strategies. We critically analyze the “linear proportionality illusion” that permeates traditional geometry teaching, proposing instead an approach based on real phenomena and mathematical modeling. The presented framework offers significant contributions to teacher education and the development of complex mathematical competencies, positioning itself within the current debate on the epistemology of school mathematical knowledge.
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