Algebraic reasoning in primary school: A balancing act
Otten, M. (2020). Algebraic reasoning in primary school: A balancing act [doctoral dissertation]. Utrecht University
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.
Vollmuller, B., Veldhuis, M., Otten, M., Stuber, S., Anantharajan, M., & Keijzer, R. (2023). Developing functional thinking from teacher education to primary school: students walk along the number line. Presented at: CERME13 in Budapest, Hungary.
Understanding of, and reasoning about, descriptions of relations between quantities is an important aspect of mathematical learning and essential for anyone to function in society. Performing, guiding, and designing activities to support functional thinking is currently not part of the curriculum neither in primary education nor teacher education in the Netherlands. Activities for both primary education and teacher education are developed as part of the Erasmus+ Strategic Partnership FunThink. This poster shows how two preservice teachers translate activities on functional thinking from teacher education to practice. We concluded that these preservice teachers translate activities on functional thinking by mimicking most of the elements of the teacher education activity. The preservice teachers also make slight adaptations to the activity based on their own beliefs and interpretation of the activity and the perceived ability of their students.
Keijzer, R. (2023). Conceptueel kijken naar breuken. Volgens Bartjens – ontwikkeling en onderzoek, 42(5), 51-65.
Canjels, J.C. & Keijzer, R. (2023). Overtuigingen van leraren in groep 1 en 2 met betrekking tot het reken-wiskundeonderwijs. Volgens Bartjens – ontwikkeling en onderzoek, 42(5), 41-50.