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3. Improving classroom assessment in primary mathematics education

Author

Veldhuis, M. and Veldhuis, M.

Abstract

The main goal of this PhD research was to provide insight into primary school teachers’ classroom assessment practice in mathematics in the Netherlands. Classroom assessment is assessment that teachers can use to get access to their students’ skills and understanding, in an effort to tailor their instruction to students’ needs and thus move learning forward. The common departure point of the studies in this thesis was that such use of classroom assessment integrated in teachers’ teaching practice to determine where students are in their development could lead to an improvement in students’ mathematics performance. Whether supporting teachers in the use of classroom assessment in mathematics education indeed had an incremental effect on students’ mathematics achievement was the main research question of this thesis. After establishing teachers’ current assessment practice in primary mathematics education through a large-scale survey study, a number of classroom assessment techniques for mathematics in Grade 3 (groep 5) were developed, piloted, and quasi-experimentally evaluated. Teachers and students reported that they liked the classroom assessment techniques and found them useful in daily practice. The quasi-experimental evaluation of learning effects on mathematics achievement showed that students of teachers using classroom assessment techniques progressed notably more from pre- to posttest than other students.

Published
2015

5. Algebraic reasoning in primary school: A balancing act

Author

Mara Otten, Heuvel - Panhuizen, M.H.A.M. van den, Heinze, A., Veldhuis, M., and University Utrecht

Subjects
Primary (chemistry), Computer science, Higher-order thinking, Mathematics education, ComputingMilieux_COMPUTERSANDEDUCATION, Early algebra, algebraic reasoning, linear equation solving, embodiment, physical experiences, balance model, representations, higher-order thinking, motion graphs, Early Algebra, Algebraic reasoning
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.

Published
2020

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