Alex Corner

Mathematics Education

Along with Peter Rowlett, I am collecting data for a project concerned with students' perception of their own identities as mathematicians/learners of mathematics. Together we have shared interests in motivating learners through puzzles and games.

I am also interested in students' understanding of the role of assumptions in pure mathematics and how this can be compared to their understanding in a more applied setting, such as that of mathematical modelling.

Publications

1. Steckles, K., Ketnor, C., Porter, R., Shukie, A., & Corner, A. S. (2025). Lecturers don't know everything: students watching the thought processes of lecturers on unfamiliar ground. Teaching Mathematics and Its Applications, 44(1), 68-92.

Due to the nature of the teaching environment, students may often develop perceptions of their lecturers’ ability as mathematicians, based on the pre-prepared and well-rehearsed content they present. In reality, performing mathematical calculations and solving problems is a difficult skill, and students may compare their own experiences unfavourably with the ease they see lecturers display. To interrogate this disparity, an exercise was included in an undergraduate maths session during which lecturers attempted unseen problems from A-level maths papers, so the students could see them model the process of problemsolving - including making istakes, applying helpful strategies and techniques, correcting their own errors, and identifying gaps in their knowledge. As well as modelling these positive behaviours for students, the session aimed to develop the students’ understanding that their own experiences of struggling with maths are normal and healthy. The activity formed part of a broader session on making mistakes in maths, which also included some advice and opportunities to find mistakes in mathematical working-out. The students were invited to participate in questionnaires and focus groups to explore their perceptions and attitudes towards their lecturers’ knowledge and capacity to make mistakes, and in this paper we analyse these responses and consider how this relates to teaching, and to students’ personal development.

2. Rowlett, P. and Corner, A. S. (2022). Flexible, student-centred remote learning for programming skills development. International Journal of Mathematical Education in Science and Technology, 53(3), 619-626.

During the COVID-19 pandemic, the teaching of programming for undergraduate mathematicians was moved online. This was delivered asynchronously, with students working through notes and exercises and asking for help from staff via online messages as needed. Staff delivery time was redirected from content delivery into a formal system of formative assessment, which replaced informal discussion and feedback during in-person classes. Formative tasks were submitted and feedback was provided via GitHub Classroom. Students were broadly positive about the formative feedback system and mixed about the need for live delivery. Formal formative feedback highlighted that students may hold incorrect views about the accuracy of task completion, making formal formative submission an effective use of staff delivery time.

3. Rowlett, P. and Corner, A. S. (2021). Topics of interest to the MSOR community: evidence from the first 20 years of MSOR Connections. MSOR Connections 19(2), pp. 55-74.

Topic modelling, an automated literature review technique, is used to generate a list of topics from the text of all articles published in previous issues of MSOR Connections. There are many topics of consistent popularity, including assessment, employability, school-university transition and the teaching of specific subjects and skills with the mathematics, statistics and operational research disciplines. We identify some topics that have waned in popularity, especially following the demise of the MSOR Network, including organised book and software reviews, conference and workshop announcements and reports, and articles focused on staff development. In its present form as a fully peer-reviewed practitioner journal, there appears to be a shift in focus from personal reflection to evidence-based research. There is a high focus on innovative practice using technology in the publication, though with less focus on specific software over time. Similarly, more nuance appears to be entering the discourse over maths support and e-assessment as these topics mature. We note a rise over time in student-centred approaches and a sudden rise in the previous issue of digital and remote learning due to the COVID-19 pandemic. We speculate about future trends that may emerge, including an increased focus on digital and remote learning and an increase in content on equity, equality, diversity and inclusion.

4. Rowlett, P., Smith, E., Corner, A. S., O’Sullivan, D., & Waldock, J. (2019). The potential of recreational mathematics to support the development of mathematical learning. International Journal of Mathematical Education in Science and Technology, 50(7), 972-986.

A literature review establishes a working definition of recreational mathematics: a type of play which is enjoyable and requires mathematical thinking or skills to engage with. Typically, it is accessible to a wide range of people and can be effectively used to motivate engagement with and develop understanding of mathematical ideas or concepts. Recreational mathematics can be used in education for engagement and to develop mathematical skills, to maintain interest during procedural practice and to challenge and stretch students. It can also make cross-curricular links, including to history of mathematics. In undergraduate study, it can be used for engagement within standard curricula and for extra-curricular interest. Beyond this, there are opportunities to develop important graduate-level skills in problem-solving and communication. The development of a module ‘Game Theory and Recreational Mathematics’ is discussed. This provides an opportunity for fun and play, while developing graduate skills. It teaches some combinatorics, graph theory, game theory and algorithms/complexity, as well as scaffolding a Pólya-style problem-solving process. Assessment of problem-solving as a process via examination is outlined. Student feedback gives some indication that students appreciate the aims of the module, benefit from the explicit focus on problem-solving and understand the active nature of the learning.

5. Corner, A. S., & Cornock, C. (2018). Applications and props: the impact on engagement and understanding. MSOR Connections, 17(1), 3-15.

Problems based on applications or objects were added into a first year pure module in gaps where real-life problems were missing. Physical props were incorporated within the teaching sessions where it was possible. The additions to the module were the utilities problem whilst studying planar graphs, data storage when looking at number bases, RSA encryption after modular arithmetic and the Euclidean algorithm, as well as molecules and the mattress problem when looking at group theory. The physical objects used were tori, molecule models and mini mattresses. Evaluation was carried out through a questionnaire to gain the students' opinions of these additions and their general views of applications. Particular attention was paid to the effect on engagement and understanding.