Learning maths: research in the classroom

Geoff Wake, Professor of Education

As a maths teacher/educator/researcher we can find a lot in the literature in relation to student learning in general and learning maths in particular. Having worked as both a teacher and researcher over many years, I have witnessed much effort directed at building our knowledge base substantially. This has certainly added to what I know and understand of what, and how, students think when they are learning maths. Indeed, there is possibly more research into the learning of maths than of any other knowledge domain.  

We can find research that focuses on every topic of the maths curriculum from children’s early encounters with numbers, through spatial thinking, to the difficulties of understanding probability and risk, and on to calculus. We can turn to cognitive science to get an understanding of how we currently think the human brain processes information. On a different scale we can find survey responses about how much young people like or dislike maths, how resilient they might be in their learning of the subject and so on.  

 

In another direction our new Observatory for Mathematical Education will provide insight into students' pathway through mathematics by working with large and national data sets as well as tracking cohorts of students throughout different phases of their studies. We will have a lot of work on our hands to keep on top of so much research and knowledge. 

And an important question you might have: what might all this research tell me about what works in the classroom? This is also, of course, of crucial importance to students themselves, their parents, and society more widely. 

Classrooms are complex social spaces with many – some would argue too many – students coming together with their teacher(s) and mathematics in a multitude of different ways, expectations, and emotions. Research in classrooms that seeks to understand "what works" in face of this complexity is equally complex, as all manner of approaches are used by different teachers at different times and in particular circumstances. What can we do to research students’ outcomes in light of such complexity? 

That’s where research like our Mastering Maths research study sits. Central to the study is a very detailed and carefully designed professional learning programme that works with further education (FE) GCSE resit teachers. Teachers work on a modified lesson study programme that involves inquiry into their own practice in teaching with a mastery approach developed by and for GCSE resit teachers.  

The study is an Education Endowment Foundation effectiveness randomised controlled trial, which means that half of the participating teachers are allocated to a ‘business as usual’ group and aren’t involved in the programme of professional learning. Students’ scores and grades are compared between those taught by teachers who have been in the intervention programme and those taught by the ‘business as usual’ teachers. 

When the study is completed in 2025, we hope to find out not only about these outcomes, but also exactly the teachers’ and their students’ experiences of the Mastering Maths approach to teaching. 

The detail of the design of the Mastering Maths programme builds on much work of mine and numerous colleagues over many years. It brings together design of tasks, understanding of student learning, thinking about the structure of maths and its representation, consideration of teacher professional learning through lesson study, and much else. It embodies more than a lifetime’s work: it’s a synthesis of knowledge, understanding and expertise from the dynamic maths education community that has been active at Nottingham over many years.  

Why not join us on the next stage of our journey? You can find out more about the work of the Observatory for Mathematical Education on our website. 

Author information

Based in the Observatory for Mathematical Education at the University of Nottingham, Geoff is leading the Mastering Maths programme. 

Observatory for Mathematical Education team

Geoff Wake on X

Observatory for Mathematical Education on LinkedIn.

Mastering Maths.