História da Geometria para o ensino fundamentada na Ideografia Dinâmica

Abstract

This paper presents a reflective description of a research project focused on Dynamic Ideography as an integrative foundation between the History of Mathematics and Digital Technologies in the teaching of geometry. The study starts from the following central question: how can History, if used for teaching geometry based on Dynamic Ideography, contribute to a new understanding of the development and systematization of mathematics, promoting the teaching and learning of geometry? The general objective of the research is to explore Dynamic Ideography as a foundation that articulates the History of Mathematics and Digital Technologies, expanding the possibilities of teaching and learning in geometry. To this end, it was necessary to (i) identify the main trends, contributions and gaps in academic and scientific production – at national and international levels – related to the interactions between the History of Mathematics and Digital Technologies; (ii) understand the historical trajectory of technologies as cultural artifacts that influenced the cognition, representation and communication of mathematical ideas, from static to dynamic ideographies; (iii) to characterize the theoretical foundations of History for the Teaching of Mathematics and Dynamic Ideography; and (iv) to characterize the work of Oliver Byrne – with his colored diagrams applied to Euclid’s Elements – and the work of Jay Hambidge, with his approach to dynamic symmetry, highlighting how this type of historical material can be dynamized through GeoGebra and Manim. By integrating historical perspectives with technological approaches, the research seeks to support the premise that Dynamic Ideography can transform the teaching of geometry, promoting a more dynamic and interactive understanding of mathematical concepts. In this way, the study contributes to the reflection on new teaching methodologies, emphasizing the potential of dynamic representations in the development of geometric thinking and in the systematization of mathematics throughout history.