Teaching children as young as six to think through mathematical problems and understand the relationships between numbers can improve their maths attainment, according to the findings from a large trial published today by the Education Endowment Foundation (EEF).
Year 2 pupils who took part in the Mathematical Reasoning programme made the equivalent of one additional month’s progress in maths, on average, compared with similar pupils who continued with their usual maths teaching. The impact was larger for pupils eligible for free school meals, who made the equivalent of two additional months’ progress.
The findings come from a randomised controlled trial involving 238 schools and 6,291 pupils. The evaluation was commissioned and published today by the EEF and carried out by National Foundation for Educational Research (NFER).
The programme, developed by the University of Oxford’s Department of Education, is designed to help young children understand the mathematical relationships that underpin calculation and problem-solving. Rather than simply learning calculations, pupils are encouraged to think about quantities, numbers, and the steps needed to solve a problem.
How it works
Teachers and teaching assistants received online training in how to deliver the mathematical reasoning approach.
Over 12 to 15 weeks, teachers then replaced one maths lesson each week with a Mathematical Reasoning session.
The sessions focused on helping pupils develop their understanding of the relationship between quantities and numbers and use this understanding to reason through maths problems.
Teachers used manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). and whole-class discussion to make mathematical ideas visible. This included play activities that helped pupils explore quantities and explain their reasoning, for example:
- using blocks or counters to work out whether the number of marbles left in the bag was more or less than at the start, without knowing how many marbles there were to start with
- the caterpillar board game, where the children throw the die and predict where their counter will end by counting on, before moving the counter
- playing shop, using money and coins to practice counting and calculating amounts
In the second part of the session, the class split into two groups to reinforce what they had learned. The groups were flexible and teachers used their judgement to determine which pupils were allocated to each group:
- In one group, teachers taught and scaffolded further examples.
- In the second group, pupils played specially designed maths computer games under the supervision of a teaching assistant.
The trial and evaluation
The trial compared schools who delivered 12 – 15 weeks of the Mathematical Reasoning programme with a similar group of schools who continued with their usual maths teaching.
The findings received a ‘high’ security rating from the Education Endowment Foundation (EEF), which means there is a high degree of confidence in the results.
Mathematical Reasoning is an EEF Promising Programme, having previously demonstrated meaningful, cost-effective improvements in outcomes. This trial tested whether those benefits could be replicated when the programme was delivered at a larger scale using online teacher training.
Professor Becky Francis, CEO of the Education Endowment Foundation, said:
Professor Gabriel Stylianides, Professor of Mathematics Education at the University of Oxford and Professor Terezinha Nunes, Emeritus Professor of Educational Studies at the University of Oxford said: