Mathematics is more than exams

Katie Severn, Assistant Professor in Mathematics 

As a university maths lecturer, I often find myself repeating the phrase, “Maths is learnt by doing”, and it’s encouraging to see that incoming maths undergraduates tend to agree! Our recent survey of students preparing to start university mathematics courses revealed a strong preference for hands-on learning methods, with many highlighting the value of working through problems and tackling past papers as the most effective ways to master the subject.

 

The Power of Problem-Solving

This past September, the Observatory surveyed over 1000 students who had accepted firm offers to study mathematical sciences degrees in the UK. Students were asked to rate the helpfulness of various resources for learning maths, and the results were clear: working through maths problems and past papers stood out as valued methods, with 98% and 97% agreeing these were helpful resources, respectively. It’s no surprise that working through maths problems ranks so highly. This approach encourages active engagement with the material, and repetition and problem-solving are at the heart of learning maths. It’s through this iterative process of trial and error that students often experience those satisfying “aha!” moments where everything clicks.

The Double-Edged Sword of Past Papers

The reliance on past papers, however, presents a more complex picture. On the one hand, it’s clear why students find them so valuable. Past papers provide a concrete sense of what’s expected in assessments, helping students focus their preparation and build confidence. They’re also an excellent tool for practising problem-solving under realistic exam conditions. Of course, these students' responses are based on experiences at A-level, whether past papers remain such a valued resource as student’s transition to university is less clear.

A potential concern is that not all universities share past papers with students. For those in such institutions, a key resource is effectively off the table, creating a disparity in the tools available to learners. Even in universities that do provide past papers, there’s often some tension between educators and students in how they should be used. Educators want students to use past papers for practice, not to learn how to do an exam, and often will create assessments with unseen elements. The ultimate goal of a mathematics degree is to develop deep understanding, critical thinking, and problem-solving skills—not just to score well in assessments. Yet the reality remains that a student’s final grade is often derived primarily from exam performance, making past papers a tempting focal point for preparation.

To address this, universities need to offer students clear guidance on how to use past papers effectively but also perhaps should be rethinking assessment methods to reduce the dominance of traditional exams to encourage students to adopt a more comprehensive approach to their studies. Incorporating coursework, projects, or oral evaluations can provide alternative ways to demonstrate understanding.

AI as a tool

Unlike maths exercises and past papers, which are well-established learning resources, AI tools are a relatively new addition to a student’s toolkit. Despite the current buzz surrounding AI and the concerns universities have about its use raising questions around academic integrity, students in our survey did not rate AI tools as particularly helpful. In fact, many chose not to rate their usefulness at all, suggesting a lack of awareness or familiarity with these tools before arriving at university.

As tools like ChatGPT gain prominence, it's clear they have potential as learning aids when used thoughtfully and students’ limited engagement with them before university represents an opportunity. Universities can teach students how to use AI to support their learning, demonstrating how these tools can be used effectively, responsibly, and ethically to support their studies.

Equipping Students for Success

Educators play a vital role in equipping students with the skills and confidence to succeed in mathematics—whether in the classroom, exams, or real-world applications. Insights into how students learn and which resources they value allow teaching strategies to be tailored to their needs, addressing gaps in preparedness and building their problem-solving and critical thinking skills. By understanding students’ preferences and challenges, educators can create supportive learning environments that foster both academic success and readiness for the demands of mathematics beyond university.

What do you think? Are past papers overused, or are they an essential tool for success?

Author information

Katie (she/her) splits her time between the School of Mathematical Sciences, where she teaches statistics modules for undergraduate students, and the Observatory for Mathematical Education (where she is one of our data experts).  

Observatory for Mathematical Education team

Observatory for Mathematical Education on LinkedIn.