Cognitive models for the concept of angle

Tese de doutoramento em Filosofia

The instructional models taught in class were similar to the students' models. The teachers addressed angle as a basic-level category, discussed its submodels, clarified the boundaries, and established cognitive reference points. They gradually increased the use of complex metaphors and of several models. The study enriched the characterization of the first two levels of van Hiele theory and demonstrated the value of categorization theory in understanding how our comprehension of mathematics is rooted in basic human attributes pertaining to the material and social conditions of human life. The embodiment of mathematical ideas by the material world, including our bodies, needs greater emphasis in all facets of mathematics education.