Algebraic reasoning in primary school: A balancing act

Abstract

The research described in this PhD thesis focuses on stimulating fifth-grade students’ algebraic reasoning about linear equations. The importance of including algebraic activities in the primary school mathematics curriculum is increasingly being emphasized. Starting in the elementary grades with solving informal algebra problems that build on students’ intuitive understanding and natural ways of thinking can provide students with a conceptual basis for the study of more formal algebra in the later grades. Although there is abundant evidence available that primary school students are capable of algebraic reasoning, within the Dutch primary school mathematics curriculum algebra currently is virtually absent. This is a missed opportunity because stimulating young students’ reasoning on mathematical topics such as algebra in primary school has the potential to foster higher-order thinking (HOT). The main goal of this PhD project was to gain insight in whether, in what ways, and to what extent primary school students’ early algebraic reasoning could be fostered. Within this research, we specifically focused on students’ reasoning about linear equations.

The first aim of this PhD project was to investigate the role of the balance model, an often used model for fostering students’ understanding of linear equations in teaching linear equation solving, as reported in the international research literature. The second aim was to investigate the potential of various representations of the balance model for supporting primary school students’ understanding of linear equations. To this end, we developed and six-lesson teaching sequence on linear equations in which the balance model played a key role. The lessons of this teaching sequence were taught in various fifth-grade classes and the effect on students’ algebraic reasoning was evaluated. The final aim of this thesis was to investigate whether stimulating primary school students’ algebraic reasoning related to solving linear equations could also promote students’ reasoning in a distinct but related mathematical domain: graphing motion. For this, we looked into the effect of our teaching sequence about linear equation on students’ graphical reasoning.