The study of pictorial sequences as a support to the development of algebraic thinking

• Main Author: Branco, Neusa
• Publication Date: 2012
• Other Authors: Ponte, João Pedro da
• Format: Article
• Language: eng
• Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
• Download full: http://hdl.handle.net/10451/22609
• topic: Algebra; Algebraic thinking; Equations; Sequences

The purpose of this article is to study the contribution of a teaching unit that introduces algebra through pictorial sequences and problem solving with an exploratory and investigative approach towards the development of the algebraic thinking of grade 7 students. The study focuses on the work of a student, Joana, in different algebraic tasks. Data were collected by means of two interviews, audio recording and a research journal. Prior to the teaching unit, working with a pictorial sequence, the student fails to recognize the algebraic language except in a simple situation. During the teaching unit, the work in the classroom promotes the analysis of different strategies and justifications and the use of the algebraic language. After the teaching unit, the student decomposes the pictures in a sequence and identifies the relation between the order of the picture and the number of its elements, expressing it algebraically. Besides, she uses different strategies to solve equations, showing aunderstanding. She also recognizes the meaning of unknowns and generalized numbers in the symbols that appear in different contexts. Joana’s performance suggests that the teaching unit promoted the development of essential aspects of algebraic thinking like the ability to generalize in pictorial sequences, the understanding of symbols, expressions, and equations, and the use of informal and formal strategies for solving equations.