The field of Mathematical Cognition focuses on answering the question, “What is the best way to learn mathematics?” There are numerous techniques that have been shown to improve mathematical cognition, such as visual aids, self-explanation, or shuffling practice questions rather than grouping them by topic. “Mathematical cognition researchers are interested in how mathematical understanding and performance develops from infancy to adulthood, the factors which explain individual differences in mathematical performance and why some individuals find mathematics so difficult.” Gilmore, Göbel, and Inglis (2022)
One of the aims of this project is to give students an introduction to the process of engaging with research about mathematics that is not actual mathematical research. Students can also consider factors that would have a deleterious effect on learning mathematics, such as maths anxiety or learning disabilities, and how these factors might be ameliorated. The project will suit students who have an interest in education, pedagogy, or academic development.
The group project will be based on engaging with a range of maths cognition papers and interpreting their analysis, determining their validity, and presenting these findings to the group.
By the end of the project, students will have learned
This project will focus on the analysis of peer-reviewed literature to improve students’ understanding of maths cognition. Students will demonstrate their understanding by engaging with studies that have been carried out, interpreting and analysing these studies, and communicating their understanding in both written and oral formats.
Students will focus on one or more areas of mathematical cognition. This might involve a deep dive on a single approach, a comparison of multiple approaches, designing an experiment that takes into account trial design in detail (although there will not be time to run an experiment as part of the project), or consider a simpler trial where they simulate their own data.
Some topics that might be investigated would include
Common previous approaches to this project have included designing appropriate trials relating to maths cognition, the simulation and analysis of data for such a trial, and comparing and either contrasting or synthesizing multiple considerations and approaches to maths cognition. Students have also produced undergraduate level teaching resources designed to demonstrate and take advantage of theories within mathematical cognition. Alternative approaches to exploring maths cognition may be possible, but will require discussion with the supervisor early in the project.
Statistics I is a necessary prerequisite for the type of analysis that will be carried out in the Group Project, and additional statistical courses would be useful but not strictly necessary for the analysis used in the Individual Project.