Teaching Problem Solving to Develop Algebraic Thinking: The Challenges to Move from Focusing on Operations to Representing Relationships

• In Event: Emerging pedagogies for powerful mathematics teaching

Proposal

Teaching mathematics using problems to solve is quite common around the world and quite well documented in the literature. In Chad, a country situated in Central Africa, the official curriculum proposes to use problem solving to develop mathematical competencies. The situational problems presented aim in fact to provide a context to support students to perform operations. Polotskaia and Savard (2018) named this vision of problem solving the operational paradigm. As opposed to this vision, the relational paradigm (Polotskaia and Savard, 2018) focused on the relationships between the data of the problem to develop a holistic view of the structure of the problem. The relational paradigm fosters the development of algebraic reasoning. This reasoning is defined by Polotskaia, Savard, Passaro & Anwandter Cuellar (2022) as an analysis of the relationships between different quantities (known, unknown or variable) and the producing logical inferences about other quantities or relationships.

As a consultant to support numeracy developers to design new mathematics textbooks for Grade 1 elementary school students, I introduced to them the relational paradigm to use it with students. After teaching it, some of numeracy textbook developers wrote lessons on problem solving. They were strongly encouraged to includes diagram to help students to see the relationships between the data within the situational problems.

In this communication, I will present how the implantation of this new paradigm in Chad brought up challenges for numeracy textbook developers. The results will show of this transition might be interpreted as a spectrum between the two visions.

References
Polotskaia, E. & Savard, A. (2018). Using the Relational Paradigm: effects on pupils’ reasoning in solving additive word problems. Research in Mathematics Education. 20 (1). 70-90.
Polotskaia, E., Savard, A., Passaro, V. & Anwandter Cuellar, N. S. (2022). Understanding practices fostering algebraic thinking in elementary school children. In C. Fernandez, S. Llinares, A. Gutierrez, & N. Planas (Eds.), The 45th conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 277–277). Universidad de Alicante, Spain.

Author

• Annie Savard, McGill University