Generative AI is reshaping mathematics education in profound ways. While much of the discussion around AI in education focuses on general applications, such as workload reduction for teachers and personalised learning for students, its specific contributions to mathematics deserve particular attention. Mathematics, often perceived as rigid and procedural, can be transformed by AI into a more exploratory and dynamic discipline.

At the heart of generative AI’s impact on maths education is its ability to model and generate mathematical explanations, examples, and problems. Traditional AI-driven tools, such as computer algebra systems, have long supported computation. However, generative AI goes beyond solving equations to helping students understand concepts through analogy, variation, and contextualisation. A simple request for an explanation of factorising quadratics, for example, can yield multiple interpretations, from technical descriptions to metaphorical ones, such as unlocking a treasure chest. The capacity to adapt explanations to different audiences makes AI a powerful tutor, capable of scaffolding student understanding in ways that conventional textbooks cannot.

One of the most striking uses of generative AI in mathematics is its ability to engage in structured dialogue. Unlike search engines or static resources, AI can role-play as historical mathematicians, engaging students in Socratic discussions. A student struggling with Pythagoras’ theorem might interact with ‘Pythagoras’ himself, being guided through the logical steps to discovery rather than merely receiving a formula. This conversational aspect, when well-implemented, fosters mathematical reasoning rather than rote learning.

Generative AI also enhances problem design. Teachers often invest significant time in crafting ‘theory of variation’ sequences of questions that promote deep understanding. AI can generate and refine problem sets based on variation theory, ensuring that questions build progressively on one another. It can provide contrasting examples, such as factorable and non-factorable quadratics, nudging students towards pattern recognition. Moreover, it can tailor problems to specific student misconceptions, offering targeted practice in areas where they need reinforcement.

Another powerful feature is AI’s ability to support visualisation. Mathematics is not just about numbers and symbols; it is also deeply conceptual. Generative AI can create interactive graphs, animations, and even code-generated visualisations to illustrate complex ideas. For example, an AI-generated slider tool might allow students to manipulate coefficients in a quadratic function and observe the changes to its factorisation. While not all AI-generated visualisations are pedagogically effective, the potential for dynamic representation of mathematical structures is significant.

Beyond direct student engagement, generative AI also plays a role in supporting teachers. Lesson planning, particularly for new or non-specialist maths teachers, can be challenging. AI-generated lesson plans provide a useful starting point, incorporating best practices while allowing for customisation. Similarly, AI can help generate real-world contextual problems, which are often difficult to design. While a quadratic equation about a garden’s dimensions may seem contrived, AI can rapidly generate a variety of plausible applications, some of which might be more meaningful to students.

There are, however, limitations. Generative AI, as it currently stands, is not inherently mathematical. It predicts text based on training data rather than performing true mathematical reasoning. While it can generate correct solutions and even proofs, it does not understand mathematics in the way a human does. It frequently makes errors, particularly with novel or non-standard problems, and may prioritise linguistic plausibility over mathematical accuracy. This makes its outputs useful for exploration but unreliable as definitive answers.

The ethical implications of generative AI in mathematics education also warrant consideration. While it can aid students in understanding concepts, it can also be misused to bypass learning. A student who asks AI to factorise a quadratic for them is not necessarily engaging in mathematical thinking. The distinction between seeking guidance and outsourcing problem-solving is critical. Encouraging students to ask AI to ‘teach them’ rather than simply ‘give the answer’ is a useful heuristic. Similarly, just as teachers have historically discouraged over-reliance on calculators, they will need to establish best practices for AI use.

Mathematics education has long evolved alongside technological advancements, from slide rules to calculators to dynamic geometry software. Generative AI represents the next frontier, offering new ways to interact with mathematical ideas. Used wisely, it has the potential to make mathematical learning more intuitive, engaging, and personalised. However, it remains a tool, not a replacement for human reasoning. The challenge for educators is not just in integrating AI, but in ensuring that it enhances rather than undermines mathematical thinking.

Based on my presentation at the Mathematical Subject Associations’ joint conference, 4 April 2024, Stratford Upon Avon.