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UMA ORGANIZAÇÃO PRAXEOLÓGICA DA CONSTRUÇÃO DO FRACTAL ÁRVORE PITAGÓRICA UTILIZANDO O SOFTWARE GEOGEBRA
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UNIVERSIDADE ESTADUAL DO PARANÁ - UNESPAR
This research has as aim at investigating, through mathematics praxeology, skills and knowledge objects in Mathematics area and its Technologies mobilized by High School students during the construction of Pythagorean Tree fractal in GeoGebra software. Such objective was elaborated to answer the following research problem: which skills and knowledge objects present in the Mathematics area and its Technologies recommended in the National Common Curricular Base (BNCC in its Portuguese acronym) are mobilized by high school students during the construction of Pythagorean Tree fractal in GeoGebra software? As a theoretical-methodological contribution, this work is based on Anthropological Theory of Didactics - ATD principles, which allowed elaborating a praxeological organization for modeling the mathematical object focused on a didactic sequence. This work assumes methodological assumptions of Didactic Engineering that helped building and delineate this research. Analysis of such organization enabled an investigation on BNCC of skills and knowledge objects which might be developed during building and mathematical exploring of fractal. The research was implemented in a High School class in a state school of the municipality of União da Vitória – PR. A posteriori analysis made evident that students used technics to solve the subtasks that allowed the validation of the Mathematical Organization foreseen in our a priori analysis. In addition, it was identified that techniques used in Mathematical Organization direct to skills; similarly, the technologies used to justify the techniques may indicate mathematics knowledge objects; and finally, theories which conduct technologies lead to thematic units. Findings show that elaboration and choice of tasks that provide work with Fractal Geometry in Mathematics classes may contribute to teaching and learning this component in different teaching grades, integrating learning proposed by the BNCC, for example the knowledge objects Algebraic language: variable and unknown and Metric relations in the right triangle, and the skills Using algebraic symbology to express regularities found in numerical sequences and Solving and elaborating problems of application of the Pythagorean theorem or proportionality relations involving parallel lines cut by secants. These and other knowledge objects and other skills as well were possible to be developed by students during this proposal implementation.
Educação Matemática; Teoria Antropológica do Didático; Geometria dos Fractais; BNCC.