Published: 26th October 2026
Maths expert, David Pritchard, comments on the David Hume Institute briefing highlighting the importance of practical mathematical reasoning, confidence and real-world problem-solving.
A rapid uptake of a new Scottish mathematics qualification is helping more young people develop the skills to apply mathematical knowledge to real-world challenges, with implications for further education, employment and decision-making in an increasingly data-driven world.
A recent briefing from the David Hume Institute, Applications of Mathematics: A Revolution in Maths Education in Scotland?, highlights the significant growth of Applications of Mathematics at National 5 and Higher levels, and its potential to broaden mathematical participation while developing skills that are increasingly important in further study and work.
The growth raises important questions about how mathematical capability is understood, how young people are prepared for further study, and which skills they need to navigate a world increasingly shaped by data and artificial intelligence.
Mathematics for a changing world
Mathematician, David Pritchard, who helped to develop the curriculum for Higher Applications of Mathematics, challenges anyone who says it is an easy option. He said:
“When we developed Higher Applications of Mathematics, it was essential to create a course that was a Higher in its own right. It’s not a lesser version of Higher Mathematics, any more than Higher Chemistry is a lesser version of Higher Physics, or Higher Italian is a lesser version of Higher Latin.
“The aim was to create a qualification with its own intellectual challenge, rigour and value, developing a different but equally important set of mathematical capabilities.
“Mathematics is not only a set of technical tools, important as those are. It is also about choosing which tools to use, understanding what the results are telling you, and applying what you know to a situation you have not encountered before.
“That ability to transfer knowledge between contexts is a sophisticated skill. It requires robust number-sense, the confidence to tackle unfamiliar problems, and the judgement to recognise whether an answer is reasonable.”
Applications of Mathematics develops skills that are relevant to a wide range of further study and careers, including social sciences, nursing, financial services and other fields where people must interpret evidence, understand risk, work with data and make sound judgements under pressure.
These capabilities are not simply about making mathematics more accessible. They are about equipping learners to use it effectively in the situations they will encounter beyond the classroom.
The qualification also develops practical capabilities such as mathematical modelling, project planning, data analysis and the use of spreadsheets and statistical software - skills relevant across sectors, including financial services and healthcare.
Applications is part of Scottish Enlightenment tradition
The ability to assess whether a mathematical result makes sense is becoming particularly important in our rapidly changing world and as artificial intelligence tools become more widely used.
Pritchard said:
“As workers, as consumers, and most of all as citizens, our world is shaped by the use and misuse of numbers. We need people who can look at numerical statements, and ask: does this make sense?
Can you recognise when the assumptions are wrong, when the numbers are implausible, or when a claim simply doesn't follow from the evidence?
Can you apply what you know to test an answer rather than accepting it because it looks authoritative? We need people with the mathematical skills and confidence to see when the numbers don't add up, and to ask, why?
Higher Applications of Mathematics sits solidly in the Scottish Enlightenment tradition of “useful knowledge”. We need maths used critically, the way history or English or science might be used to interrogate the world around us and the claims people make about it. Applications of Mathematics helps develop that critical ability.”
Broadening participation in mathematics
The Institute’s research highlights the importance of connecting education with the skills people need throughout their lives. Applications of Mathematics offers an example of how curriculum design can broaden opportunities while maintaining meaningful academic challenge.
Susan Murray, Director of the David Hume Institute, said:
“The growth of Applications of Mathematics is an important development in Scottish education. It shows that there is a real appetite for mathematical learning that connects with the world young people inhabit and the futures they want to pursue.
“The ability to apply mathematical knowledge, interpret data and make sound judgements is essential for further study, employment and everyday life.
“As the economy changes and AI becomes more prevalent, these skills will become even more important. We need to ensure that parents, employers, universities and policymakers understand the value of Applications of Mathematics and the capabilities it develops.
“As Scotland considers how best to prepare young people for further education and a changing labour market, Applications of Mathematics provides an important example of how mathematical education in school is evolving to meet demand.
About Dr David Pritchard
Dr David Pritchard was born in Edinburgh and attended Balerno High School before studying mathematics at King’s College, University of Cambridge. He completed a PhD and postdoctoral research at the University of Bristol and the University of Cambridge. His academic research focused on applied mathematics, particularly environmental and geological fluid dynamics, sediment transport, non-Newtonian fluids and processes in porous media.
He joined the University of Strathclyde’s Department of Mathematics and Statistics in 2006. Alongside his university teaching, which includes teaching Mathematics and society, David has made a substantial contribution to the development of school mathematics education in Scotland.
Following his work on Higher Applications of Mathematics, he led a Scottish Funding Council-supported professional development module in mathematical modelling to help teachers prepare to deliver the new qualification. He has also contributed to online mathematics resources through the SCHOLAR project.
David’s work reflects a strong commitment to presenting mathematics as a discipline of reasoning, problem-solving and practical application. He believes that mathematical education should equip learners not only to perform calculations, but also to apply knowledge in unfamiliar contexts, interpret quantitative information and judge whether results make sense. His work on Applications of Mathematics has sought to broaden the mathematical opportunities available to young people while ensuring that the qualification maintains the academic rigour and standing of a Higher in its own right.
His wider contribution to mathematics education includes serving as Convenor of the Edinburgh Mathematical Society’s Education Committee from 2011 to 2015, representing the Society on the Joint Mathematical Council of the UK from 2014 to 2019, and serving as a trustee of the Council from 2017 to 2019. He was also a member of the Scottish Mathematical Council from 2015 to 2021 and contributed to the Royal Society of Edinburgh’s Learned Societies’ Group on Scottish STEM Education.
David has extensive experience in mathematical outreach and enrichment, including work with the UK Mathematics Trust’s Mathematical Circles, the Scottish Mathematical Challenge and Techfest-SetPoint’s Maths in the Pipeline programme. Across these activities, he has championed approaches that help young people experience mathematics as an engaging process of discovery and problem-solving.
His combination of mathematical expertise, university teaching experience, curriculum design and sustained engagement with teachers and professional bodies gives him a distinctive perspective on how Scotland can develop mathematical capability, strengthen pathways through education and help learners use mathematics confidently in further study, employment and everyday life.
