Visualization of Algebraic Identities in R × R × R = R3 (in Space) at Secondary Education

Abstract

Algebraic identities, which are considered as one of the important subjects of mathematics and mathematics education, have important areas of use such as physics, chemistry, many branches of engineering, as well as calculating the distances among the earth, sun and stars and planning space travels. Algebraic identities play an important role in the mathematics curriculum and in mathematics in general. However, it is seen as one of the subjects that are difficult to learn by students in formal education. In this context, this study aims to convey the visual proofs of the identities to the researchers in an explanatory way by using the visualization approach in order to make it easier for students to understand some of the important identities in R³. In the teaching of proofs of algebraic identities in secondary education, teachers only give formulas or make algebraic proofs in lessons rather than showing visual proofs and relating them to daily life. This situation poses a problem for students with visual learning tendencies. For this reason, it is thought that showing the proofs of identities by making visual models or visualizations in lessons can be a solution to this problem. In this study, document analysis technique was used within the scope of descriptive analysis and it was designed as a compilation study. Visual proofs of some identities were made by using squares and rectangles from geometric shapes. In this context, in the light of the study, some suggestions were made to guide interested researchers in this regard.