Thinking with Objects in Mathematics: the Case of Geometry

Thinking with Objects in Mathematics: the Case of Geometry. Research report by Evgeny Zaytsev at “Psychology and technology in mathematics education” conference.
March 18-21, 2019, Moscow, Russia.
education.yandex.ru/pme/
Evgeny Zaytsev, Moscow, presents the results of the study conducted together with Sergey Bychkov (Moscow Pedagogical State University).
The emphasis laid upon the skills of numerical calculations and algebraic transformations, which dominated the pre-computer era, is gradually losing its significance. Today mathematical education is viewed as aiming at the formation of scientific thinking skills. The paper suggests an approach to mathematical education based on the concept of object-oriented mediation. The characteristic feature of this approach consists in that the student is placed in conditions similar to those that historically led to the formation of new sections of mathematics.
The authors propose to introduce elements of geometric algebra as a propaedeutic complement to the ordinary course of symbolic algebra. The mastering of the diagrammatic reasoning at an earlier stage will allow students better understand the geometric origins of algebraic technique and increase motivation for its study. Geometric solutions of algebraic problems can be found by drawing diagrams with pencils and markers of different colors, or with the help of computer graphics, which will make the study of this technique more attractive for modern students.
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Это видео можно посмотреть на русском: www.youtube.com/watch?v=eKId2... A