This is the topic I’m offering to supervise for final-year BSc students at Durham, in 2024-25. It’s a joint project with Sam Fearn. In it, we will learn how to use modern automated assessment tools to prepare materials for courses in higher mathematics.
It is often said that one of the best ways to gain a deep understanding of a topic is to teach it to somebody else. In this project, we will apply this maxim to a 3H mathematics course, designing automated assessment materials suitable for other students to use to help them learn the course. We will use a topic drawn from one of your third-year modules as a focal point. You can choose which module to use, or we’ll have some suggestions of our own.
Automated assessment is a powerful teaching tool, enabling learners to test their own understanding without requiring an external marker. This allows students to get feedback at a pace that would be infeasible without the use of such tools. This in turn allows for students to immediately test whether they have understood the feedback and hence better understood the material – this is sometimes known as closing the feedback loop. This style of assessment is known as formative assessment (or assessment for learning), as opposed to summative assessment (or assessment of learning). However, producing automated assessments can be challenging, requiring both the pedagogical skills to know what sorts of errors to check for and what feedback to give, as well as the technical skills to produce an assessment capable of checking for these errors.
In this project we will use a tool called STACK, which in turn uses a computer algebra system known as Maxima, in order to assess students’ answers to the questions we design, and to produce feedback which the students can then use to help develop their knowledge. We will consider what makes for an effective formative assessment, as well as how to provide useful feedback to a student – pedagogical skills which are important in teaching, beyond producing automated assessments. Students taking this project will choose a topic from third-year mathematics to learn about, and produce an assignment designed to support other students in learning about this topic.
This project will involve spending quite a lot of time writing code in Maxima. You don’t need to know any Maxima to start with, but you should be prepared to learn it.
You’ll also be expected to have a good understanding of linear algebra.
You might like to look into some of the following papers: