The attainment of elementary algebraic reasoning capacities mediated by the instrumentation of ratio and proportion tables within the Excel computing platform

Abstract

Elementary Algebraic Reasoning (EAR) can be developed effectively from the early grades of school. This work focuses on the design, experimentation, and analysis of responses to teaching situations on proportionality, modeled using dynamic tables in Excel spreadsheets. The results obtained from students between 11 and 12 years old confirm that situations designed to drag help them transition from the numerical language, typical of static tables, to the symbolic language, an essential feature of a consolidated level of algebraization. We conclude that the use of spreadsheets has great potential for developing EAR, as it allows modifying arguments initially based on local generalizations to others that involve global generalizations. In that process, we also observe that spreadsheets promote an evolution in the language used, as their syntax is a bridge between verbal and symbolic languages.