Involvement of Algebraic-Geometrical Duality in Shaping Fraction’s Meaning and Calculation Strategies with Fractions

Abstract

Many mathematical concepts and processes, besides the algebraic form of their presentation, can be modeled as well geometrically through diagrams and graphics. Both these aspects of concepts demonstration (algebraic and geometrical aspect) are present on mathematical textbooks of pre-university education. In this paper we consider algebraic and geometrical aspect on 6 th grade math textbooks and in particular algebraic-geometrical duality, aiming that the fraction concept and the fraction calculation strategy to be assimilated better by the students. A study was made with 78 students to understand their abilities to express using algebraic symbols and to introduce mathematical situations with geometrical models for “Fractions” chapter. After the analysis of calculative strategies applied by students, in the article it is suggested that algebraic-geometrical duality must be included in teaching based on a complete framework. This will enable students to fully realize the deep understanding of concepts and the calculative strategies they are using.