From Formulas to Functions through Geometry: A Path to Understanding Algebraic Computations

The teaching of algebra at the secondary school level has faced a great revolution during the last 50 years. While previously, it was focused on technicisms and pure syntactic rules, the most modern trends recommend using a functional approach to algebra and giving more prominence to conversions among different representation registers than treatments as simplifications and expansions. Nowadays, the daily practice in teaching algebra is still influenced by the traditional approach, and there is a need to offer teachers examples of activities that can give meaning to algebraic computations. This study proposes a set of interactive activities for eighth grade students, with a functional approach to formulas in a geometric context. The goal of the study is to investigate how similar activities can help students to develop multiple approaches to problems, understand algebraic formulas, and discern which main problems they face. The activities were tested with about 300 students, and qualitative and quantitative data were analyzed to answer the research questions.