Scotland’s Enlightenment Legacy Inspires a New Approach to Maths Education

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.

Scotland’s Budget: Focus on What Spending Delivers, Not Just How Much It Costs

The David Hume Institute has called for a more strategic approach to Scotland’s economic spending, arguing that public investment must be judged by the economic capacity it creates, not simply the amount of money spent.

In its submission to the Scottish Parliament’s Economy, Tourism and Energy Committee’s pre-Budget scrutiny for 2027–28, the Institute argues that constrained public finances make it more important than ever to prioritise investment that strengthens productivity, encourages business investment and innovation, supports employment and improves living standards.

With public spending under pressure and funding for the economy, tourism and energy portfolios expected to fall in real terms, the Institute argues that across-the-board reductions risk overlooking investments that could deliver significant long-term benefits.

Instead, the Government should assess major programmes against clear criteria: what problem are they intended to solve, why is public intervention necessary, what would happen without it, and what lasting economic benefits will they generate?

The submission identifies five priorities:

• Improving productivity and business investment

• Developing infrastructure that enables economic activity

• Making better use of people’s skills

• Strengthening innovation and economic resilience

• Ensuring Scotland’s energy transition creates lasting benefits for domestic businesses and workers.

It also calls for a more rigorous approach to evaluating public spending. Counting businesses supported, projects delivered or visitors attracted tells only part of the story. Policymakers must also establish what changed as a result of spending, whether benefits would have occurred anyway, and how much economic value was retained in Scotland.

Crucially, the Institute argues that economic performance cannot be considered in isolation from other policy areas. Housing, transport, skills, financial wellbeing, energy and planning all influence productivity and investment.

The submission’s central message is that Scotland needs a longer-term perspective on public finances, recognising the trade-offs between immediate spending pressures and investments whose benefits may take years to emerge.

As the Institute concludes, the question for Scotland’s 2027–28 Budget should not simply be how much the country can afford to spend, but what can Scotland afford not to invest in?

Rapid growth of learners in Scotland embracing real world skills

Attainment in National Progression Awards has more than doubled since 2022, prompting calls for more awareness about new qualifications.

Wednesday 23rd September 2026

A new briefing from The David Hume Institute shows a significant shift in how learners in Scotland build practical work-ready skills alongside traditional exams. 

The paper, “The Changing Landscape of Education in Scotland: A New National Progression?” reveals that attainment of National Progression Awards (NPAs) - qualifications typically assessed continuously throughout the year rather than in a final high stakes exam, has more than doubled from 19,640 in 2022 to 44,0303 in 2026. 

NPAs now span more than 267 subject areas including cyber security, data science, sports leadership and health care. They are increasingly being delivered in-house by secondary schools across Scotland to broaden choices and learning in the senior phase. 

This growth reflects the recommendations of the Hayward Review which was commissioned by the Scottish Government and published in 2023.  The trend mirrors that in other countries highlighted in the OECD’s 2026 report, A Skills First Labour Market which calls on education systems across the globe to focus on practical, transferable skills that directly support employability and economic opportunity. 

Susan Murray, Director of the David Hume Institute, said:

“The rapid growth of National Progression Awards means thousands more young people are now gaining skills and qualifications through a different model of learning and assessment, often alongside traditional National 5s and Highers. 

“This is a significant change that more people, especially employers, need to understand. NPAs are helping develop practical skills and are part of the changing education landscape in Scotland. This development seems to have gone largely unnoticed in public discussion about education and youth employment in a rapidly changing jobs market.

“Continuing to develop NPAs raises important questions about how we recognise skills, how we design the senior phase and how qualifications connect young people with continuing education and employment.”

The new briefing identifies curriculum flexibility, the growing relevance of practical and job-ready skills, and increased delivery of NPAs directly within secondary schools as factors behind their growth.

The briefing also highlights challenges accompanying the expansion of NPAs. Access to particular subjects varies across Scotland, while employers and recruiters will need to understand an increasingly diverse qualifications landscape. Schools and colleges are using approaches such as cluster-school provision, college partnerships and online tutoring to broaden access.

The growth of National Progression Awards is highly relevant to the upcoming Milburn Review publication because it shows that changes to how young people develop skills, are assessed and connected to future jobs are already underway in Scotland.

Susan Murray, Director of The David Hume Institute added

“The Milburn Review is considering how we can better prepare more young people for further education, employment and a changing labour market. NPAs provide an important part of the jigsaw in Scotland, with a focus on practical skills with standards set by trade and professional bodies.

“This development should not be overlooked. Whatever conclusions the Milburn Review reaches, it is important to understand the rapid change already underway in Scottish schools.”

Quotes from the briefing

Mr Meikle, Headteacher at Craigmount High School said:

“Our school delivers a wide range of NPAs both in-house and in partnership with the local college. Last year pupils at Craigmount achieved over 4000 qualifications - 7% were NPAs and 176 were Level 6 NPAs.

“NPA courses are popular with pupils because they can see their progress with regular assessment and choose subjects directly related to careers they wish to pursue or new subjects that interest them.  Subjects range from business and marketing to web design and cyber security, and give a good grounding in developing skills required for life after school.”

A 2026 NPA Student said:

“I did mainly Nat 5's, and one NPA. Doing the NPA was just as much work, but it was spread out more during the year, so I had one less subject to worry about at exam time. I really enjoyed the NPA, partly because I liked the subject, and also because you could really get into something rather than constantly revising previous topics for an exam at the end of the year so I got really immersed in it.“ 

A 2026 NPA Parent said:

“My son chose an NPA because he was interested in the subject, rather than because it was an NPA. But being an NPA was a real positive. The work was assessed during the year, which felt much fairer than basing the assessment on one exam at the end. And it reduced the pressure a bit, when he was sitting his Nat 5 exams, as he had one less to revise for.”

Thumbnail photo credit: X on Unsplash, downloaded free on 17.9.26