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Understanding how the brain works can transform how school students learn maths

School mathematics teaching is stuck in the past. An adult revisiting the school that they attended as a child would see only superficial changes from what they experienced themselves.

Yes, in some schools they might see a room full of electronic tablets, or the teacher using a touch-sensitive, interactive whiteboard. But if we zoom in on the details – the tasks that students are actually being given to help them make sense of the subject – things have hardly changed at all.

We’ve learnt a huge amount in recent years about cognitive science – how our brains work and how people learn most effectively. This understanding has the potential to revolutionise what teachers do in classrooms. But the design of mathematics teaching materials, such as textbooks, has benefited very little from this knowledge.

Some of this knowledge is counter-intuitive, and therefore unlikely to be applied unless done so deliberately. What learners prefer to experience, and what teachers think is likely to be most effective, often isn’t what will help the most.

For example, cognitive science tells us that practising similar kinds of tasks all together generally leads to less effective learning than mixing up tasks that require different approaches.

In mathematics, practising similar tasks together could be a page of questions each of which requires addition of fractions. Mixing things up might involve bringing together fractions, probability and equations in immediate succession.

Learners make more mistakes when doing mixed exercises, and are likely to feel frustrated by this. Grouping similar tasks together is therefore likely to be much easier for the teacher to manage. But the mixed exercises give the learner important practice at deciding what method they need to use for each question. This means that more knowledge is retained afterwards, making this what is known as a “desirable difficulty”.

Cognitive science applied

We are just now beginning to apply findings like this from cognitive science to design better teaching materials and to support teachers in using them. Focusing on school mathematics makes sense because mathematics is a compulsory subject which many people find difficult to learn.

Typically, school teaching materials are chosen by gut reactions. A head of department looks at a new textbook scheme and, based on their experience, chooses whatever seems best to them. What else can they be expected to do? But even the best materials on offer are generally not designed with cognitive science principles such as “desirable difficulties” in mind.

My colleagues and I have been researching educational design that applies principles from cognitive science to mathematics teaching, and are developing materials for schools. These materials are not designed to look easy, but to include “desirable difficulties”.

They are not divided up into individual lessons, because this pushes the teacher towards moving on when the clock says so, regardless of student needs. Being responsive to students’ developing understanding and difficulties requires materials designed according to the size of the ideas, rather than what will fit conveniently onto a double-page spread of a textbook or into a 40-minute class period.

Switching things up

Taking an approach led by cognitive science also means changing how mathematical concepts are explained... 


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The full article - by Dr Colin Foster, of Loughborough University's Department of Mathematics Education - can be read on the Conversation website. 

Notes for editors

Press release reference number: 24/28

Loughborough is one of the country’s leading universities, with an international reputation for research that matters, excellence in teaching, strong links with industry, and unrivalled achievement in sport and its underpinning academic disciplines.

It has been awarded five stars in the independent QS Stars university rating scheme, named the best university in the world for sports-related subjects in the 2023 QS World University Rankings – the seventh year running – and University of the Year for Sport by The Times and Sunday Times University Guide 2022.

Loughborough is ranked 7th in The UK Complete University Guide 2023, 10th in the Guardian University League Table 2024 and 10th in the Times and Sunday Times Good University Guide 2024.

Loughborough is consistently ranked in the top twenty of UK universities in the Times Higher Education’s ‘table of tables’, and in the Research Excellence Framework (REF) 2021 over 90% of its research was rated as ‘world-leading’ or ‘internationally-excellent’. In recognition of its contribution to the sector, Loughborough has been awarded seven Queen's Anniversary Prizes.

The Loughborough University London campus is based on the Queen Elizabeth Olympic Park and offers postgraduate and executive-level education, as well as research and enterprise opportunities. It is home to influential thought leaders, pioneering researchers and creative innovators who provide students with the highest quality of teaching and the very latest in modern thinking.