How The 3D Geometrical Patterns Can Be Used To Develop The Algebraic Thinking.

Abstract

This paper presents a teaching method that aims to restore the meaning and dynamism to the study of the remarkable transition from the geometric to the algebraic thinking in the learning of mathematics. The aim is to provide a geometric framework for the development of algebraic thinking. To this end, and in order to facilitate the links between theory and practice, our research is based on some activities that can be carried out in the classroom, assessment tools and student productions using didactic and IT tools. Our key idea it to ask  a sample of middle-school scientific students to use some 3D shapes (volumes), and to try proposing some remarkable identities of order three, that generalize that of order two. This enables us to have some first answers to our main research problematic: “How the 3D geometry can be used to develop the algebraic thinking”.