How do we learn maths?

This project is offered jointly with Dr Ric Crossman.

Overview

There is a whole field of Mathematical Cognition dedicated to trying to answer the question “what is the best way to learn mathematics?”

Some of the ways in which we can try to answer this question include:

• investigating the role of visual aids in learning
• finding out whether we learn more when practice questions are shuffled together, rather than grouped by topic (spoiler alert: yes)
• looking into how established mathematicians use examples to understand a new idea, and then trying to teach students the same techniques

In this project, we will dig into some mathematical cognition research papers, asking ourselves questions like: are the authors testing the right thing? is the statistical analysis valid? can we use their conclusions to improve the way we learn maths? what even is a p-value?

Prerequisites:

This project will involve spending quite a lot of time thinking about statistical analysis that’s been done by other people. We will assume that you have met some statistical ideas before (for example, Statistics 1 is plenty).

Resources:

You might like to look into some of the following papers:

• The shuffling of mathematics problems improves learning (2007), D Rohrer and K Taylor – you can access the paper here.
• Mathematicians’ example-related activity when exploring and proving conjectures (2016), E Lockwood, A Ellis and A Lynch – you can access the paper here.