DIGITAL LEARNING
Secondary school mathematics in an AI world
Dr Paul Parham , Second in Mathematics
AI has recently shown tremendous improvements in different subject examinations up to undergraduate level , typically outperforming the majority of students ( Scarfe et al ., 2024 ), though its mathematical ability has progressed comparatively more slowly ( Kiela et al ., 2023 ). Since AI learns from experience , its capabilities depend on the extent to which it has been trained on similar problems , and to help benchmark performance , large databases of mathematics questions have been created ; GSM8K consists of approximately 8000 questions up to Year 9 standard ( Cobbe et al ., 2021 ), while MATH consists of around 12500 harder competition-level problems ( Hendrycks et al ., 2021 ). The best-performing AI can now achieve 97.1 % on GSM8K ( Zhong et al ., 2024 ), an improvement from 74.4 % in April 2022 ( Wang et al ., 2022 ), and 87.9 % on MATH ( Lei et al ., 2024 ), an improvement from 64.9 % in June 2022 ( Lewkowycz et al ., 2022 ). These developments not only raise important questions about mathematics teaching and learning , but also pose deeper philosophical questions about mathematics education .
One problem with current mathematics curricula can be encapsulated by the student question about why they are learning a topic . In some cases , this is relatively easily answered by relating the material back to real-world applications , the foundation for future concepts , or career relevance . This is more challenging for other topics where it is hard to argue beyond simply benefitting the next standardised assessment , the structure and format of which are often unrelated to how the underlying mathematical skills may be valuable beyond school . Indeed , as Wolfram ( 2020 ) argues , this is an example of the cart leading the horse , with assessment driving syllabus content . Our current assessment approaches do not lend themselves well to evaluating students ’ abilities to solve real-world problems , presumably for reasons of perceived difficulty devising standardised assessments , though essay-based subjects have successfully achieved this for many years . It could be argued that future mathematics assessments should assess knowledge , understanding , and problemsolving skills in situations closely mimicking real-life ; this may include establishing the right questions to ask , working with complex noisy and / or incomplete data , and deciding between methodologies to approach the problem , which may include computational and AI tools . These mathematical skills are undoubtedly teachable in the school environment , yet current standardised assessments predominantly assess student muscle , despite the superior power and efficiency of today ’ s computational and AI machinery . To be clear , this is not suggesting there is no merit in teaching students mathematical methods by hand . On the contrary , one of the most powerful ways of evaluating deep understanding is to teach it to others and who better than to computers that interpret instructions verbatim ; as such , I am a strong advocate for teaching students computational thinking , problem-solving , and programming .
In essence , the problem with today ’ s mathematics education in the era of AI is mistaking proficiency at completing mathematical calculations by hand with calculations by an appropriate methodology as the crux of the subject ; paraphrasing Wolfram ( 2020 ), we need students to be first-class problem-solvers , not secondclass competitors in a race against computers they have little chance of winning . Thus , we need students to be educated in AI-augmented computational thinking to solve problems using the latest technological tools to reduce the discrepancy between school mathematics and the increasing demand for technical jobs requiring these skills , particularly as the number of industries adopting AI-based technologies increases ( Howarth , 2024 ). One solution to this disparity is the four-step process in Figure 1 proposed by Wolfram ( 2020 ), who suggests that school mathematics curricula be replaced by a wider framework based on computational and mathematical thinking , which mimics real-life problemsolving : define the question of interest ; abstract by translating the human-language form of the question into a form ready for computation ; compute the
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