Professor Pauliina Ilmonen: Learning mathematical software in upper secondary school takes time away from learning the basics

Pauliina Ilmonen, Professor of Statistics at Aalto University, will step into the role of Dean of the School of Science at the beginning of June. She wants to emphasize the fundamentals in the study of mathematics.

‘We talk far too much about the advanced vs. intermediate tracks in mathematics, when the focus should be on the fact that the basics may be missing. You can’t learn to play the piano through phenomenon-based learning either. It takes repetition and practice.’

Insight comes only after routines are in place. For example, memorizing the multiplication table makes life easier. Once you have learned the techniques, understanding will follow.

In upper secondary school, a lot of time is spent learning mathematical software, but Ilmonen believes this takes time away from the basics. Problems already begin in comprehensive school if the foundation is weak. Students then learn to rely on various programs. Some even arrive at university without being able to compute with fractions.

‘In comprehensive school, studying mathematics mainly requires sitting down and doing the work. You practice and practice, because you can’t jump straight to more difficult topics.’

No to ability grouping — yes to enthusiasm

There has also been public debate about bringing back ability grouping. What does Ilmonen think about this?

‘There is no need for tracking or ability grouping. Children should have time to play and experience success.’

Tracking can increase the pressure to decide on a path too early. Instead of grouping, Ilmonen suggests offering extra challenges, STEM activities, and other hobby-based enrichment.

‘Ability groups can amplify differentiation based on family background. Parents with academic education tend to steer their children toward higher-level mathematics courses.’

Mathematics will continue to carry weight

Ilmonen believes that mathematics will continue to have significant weight in university admissions, despite changes now taking place in selection practices in Finland. Mathematics is closely linked to information processing, and alongside the first language, it predicts university success across many fields.

‘Mathematics teaches perseverance. It develops logical thinking and offers a strong indication of study readiness.’

Ilmonen’s list of essential basics includes: the four arithmetic operations, number sets, fractions and decimals, understanding parts and proportions and percentage calculations, the concept of a function, and at least the derivatives of polynomial functions.

‘These already provide a solid foundation for university studies. It’s also important to calculate with pen and paper so you can see what happens in between the steps.’

In Estonia, pen and paper are still used in learning mathematics. Estonian educators visited Finland when Finland topped the PISA rankings, and they applied what they learned here. Finland, meanwhile, changed its teaching methods—and the results began to decline.

‘One might draw conclusions from that.’

AI can be a great companion — or not

Ilmonen points out that we often forget how strong children’s and young people’s digital skills already are. We should also talk about AI and teach its responsible use. In addition, the world needs people who can develop these tools, not just use them.

‘If you know your stuff, AI is a really good companion. But some young people have a slightly distorted view of what AI can do. If we outsource thinking to AI, we lose problem-solving ability and our own reasoning. Learning remains superficial.’

According to Ilmonen, mathematical thinking develops especially when you fail to solve a problem despite trying. The brain grows from wrestling with difficult tasks.

‘We should congratulate ourselves regardless of the outcome.’