The Three Mathematics Worlds in the education of teachers that teach Mathematics: the calculation of the area limited by regular polygonal regions
DOI:
https://doi.org/10.5007/1981-1322.2021.e82694Abstract
This article aims to discuss the study of the Three Worlds of Mathematics (Embodied, Symbolic and Formal) by David Tall, in the process of initial or continuing education of teachers who teach Mathematics. It emerges as a broad, articulate and dynamic theoretical framework that outlines mathematical knowledge developing in the long term through human actions (teachers and students) in mathematical objects. Embrace three mathematical forms (practical, theoretical and formal) of conducting mathematical thinking in the course of teaching and learning processes in Mathematics are included, which are interrelated with three ways of mathematically abstracting (structural, operational and formal). A hypothetical situation is discussed with the calculation of the area of ??regions bounded by regular polygons as a function of the radius of the circumference that circumscribes it and based on the area of ??the region of any triangle, from the sine value of one of its angles internal. This is a bibliographic research. At the end, the discussions for the calculation of the area of ??the region limited by a circle are extended.
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