Learning Geometric Polyformisms in Mathematics Education

Abstract

The renowned Russian mathematician, mathematics education methodologist, scientist, science popularizer, author of geometry textbooks, and lecturer at Moscow State University, Igor F. Sharygin, believed that geometry should primarily be geometric, rather than analytical or algebraic. The central character in this story should be the figure, with the triangle and circle dominating its surface, and the main means of learning should be the drawing and the image. Textbooks that focus on geometric content should not be limited to the development of geometric theories. The learning process of such content involves a wide variety of work formats, primarily through problem solving. A problem is not merely a skill exercise, but a component of knowledge. Students should become familiar with a sequence of sufficiently challenging geometric problems, following well-known models. Incidentally, this essentially constitutes the process of learning algebra as well.