Conversations boost pupils’ maths skills

It is Friday morning and division is on the timetable for Class 4B. Perhaps not the most ideal time of day, according to teacher Nicolas Leal. The pupils have just come from craft, art and music lessons and are, as he puts it, “a bit restless”. Concentration often starts to wane just before lunch.

But this is no ordinary maths lesson. After a brief introduction, the pupils form groups of three, standing in front of their own whiteboards along the classroom walls. The maths books remain on the desks. Concepts such as numerators, denominators and ratios are to be understood through the pupils talking, reasoning and solving problems together. Soon the classroom is filled with chatter, laughter and the sound of thick pens moving across the boards.

Leal walks around the classroom, listening, observing and helping where needed. After the exercise, he gathers the class together again, follows up and lets the pupils test their knowledge on their own using mini-whiteboards.

Talking to others

Ten-year-old Tova Bringsäter doesn’t think the tasks were particularly difficult – her group managed all the levels.

“I find maths quite easy, she says. But you learn by talking to others and understand the concepts better. And we get to move around a bit – it’s easy to get bored sitting still all the time otherwise.”

Classmate Walter Steurenthaler agrees:

“I think I learn more. The maths book is good for the basics, but it’s more fun with the whiteboard.”

“And if you can’t do it yourself, there are two others who can help,” adds Dylan Twerin.

The idea behind the approach is to engage the pupils and help them stay focused. It is intended to complement the more traditional teaching approach using maths books and independent work. According to the school’s evaluations, the method has yielded results – the pupils’ knowledge has improved, as evidenced by various maths tests, amongst other things.

Pupils’ attitude

Leal became aware of the approach when he wanted to develop the communicative aspect of maths teaching, in line with the curriculum. Through Haninge Municipality, he came into contact with Eva Hartell , a research director and docent, who is in charge of the K-ULF research project (see fact box), a collaboration between KTH and several school authorities.

Together with several teachers involved in the project, he developed his new teaching method, drawing on research findings from Peter Liljedahl, a professor of mathematics education. So far, Leal is pleased with how the teaching has developed – not least in terms of the pupils’ attitude.

– The children seem happy. They can say “yes, let’s do this!”. They are motivated and excited.

Grouping also plays an important role. Three pupils per group, chosen at random, works best. In pairs, it’s easy for one to take over, and in groups of four there’s a risk of ending up with two groups of two, he explains.

More productive

He clearly notices that the pupils have become more engaged and productive.

– Everyone gets more done. Those who find maths difficult still manage to solve something, and those who are strong get to practise explaining and communicating.

Maths is also a subject that evokes strong emotions.

– Many people talk about maths anxiety. It really is an emotional subject, says Leal.

– My goal isn’t for everyone to love maths – but for it to feel possible to learn.

Text and photo: Christer Gummeson ( gummeson@kth.se )

From research to the classroom

Mathematics teaching using vertical whiteboards is an example of how educational research can be put into practice within the K-ULF project. It is the result of collaboration on practice-oriented research between KTH’s Department of Learning and primary schools in Haninge.

“Above all, the collaboration is about developing teaching and conducting relevant research for practising teachers,” says docent Eva Hartell, research leader at the Education Department, Haninge Municipality, and an affiliated researcher at KTH.

The idea for the maths method arose during a project meeting within K-ULF (Compensatory Teaching for Learning and Research), which Nicolas Leal then developed and refined.

Having all pupils participate at whiteboards means they can quickly test solutions, see how they work and receive feedback.

"By eliciting information about whether pupils have understood or not, the teacher can fine-tune the teaching accordingly. This requires planning and conscious choices on the part of the teacher," says Hartell.

The teaching method is based on so-called formative assessment and draws on science of learning.

"If students get stuck, the teacher can adapt the teaching immediately. It is better to identify this during the lesson than in an exam at the end of the course."

K-ULF, which focuses on STEM subjects and is part of a national initiative for practice-oriented research, is now in its sixth year. The collaboration is based on mutual exchange between schools and academia, emphasises Hartell.

"We learn from one another. The researchers learn from the teachers, the teachers from us, and we generate new knowledge – so it becomes a joint development process with long-term impact."

The initiative has been made permanent by the government and will continue at least until 2035.

Text: Christer Gummeson ( gummeson@kth.se )

Some terms: Science of Learning is a field of research into learning, based on insights from psychology, neuroscience and education. STEM = Science, Technology, Engineering, Mathematics. Nicolas Leal practises explicit mathematics teaching, a teaching method in which the teacher clearly explains, step by step, how to solve mathematical problems.