Skills Underlying Maths: The Role of Inhibitory Control in Learning Multiplication Tables

Good mathematical skills are important for success in modern life, but many children leave school without learning the mathematics they need. Understanding the skills involved in learning mathematics can help provide the right support to improve mathematics learning for all children. In particular, many children struggle to learn number facts, such as multiplication tables. Good recall of number facts helps individuals to be able to focus on other aspects of mathematical problem solving, such as understanding the conceptual relationships involved, or selecting an appropriate solution strategy. It is therefore unsurprising that individuals with good overall mathematics achievement tend to have good number fact knowledge. The importance of good recall of multiplication tables has been recognised by the UK Government, who have recently introduced a new national multiplication tables test to be taken by all children aged 8- to 9-years old from 2020.

There are a variety of approaches that can be used successfully to learn multiplication tables. To help children, many teachers and parents have increasingly turned to paper-based or computerised games and activities. However, at present we don't understand enough about the process of learning multiplication facts to know how to design these activities to be most effective in supporting learning. In particular, we don't know how features of these activities, such as whether children have to produce an answer or select from a range of answers, or whether there is a time limit or no time limit in producing answers, affect the process of learning and remembering multiplication facts. We also don't know if these features may increase anxiety levels for some children.

In order to make recommendations about the design of effective resources we need to understand more about the role of cognitive skills, such as inhibitory control, in number fact learning. Inhibitory control is involved whenever we need to ignore distracting information or suppress unwanted responses. Inhibitory control is likely to be important for learning multiplication facts because when recalling a number fact (e.g. 6 x 7) we need to ignore the answers to closely related facts (e.g. 6 x 6 = 36, 6 x 8 = 48). However, at present the role of inhibitory control in number fact learning is poorly understood.

We will conduct a series of studies that: 1) closely track the process of learning new number facts over time to identify when and how inhibitory control is involved; 2) identify how features of learning activities may increase or decrease the demands for inhibitory control and therefore impact the rate of learning; and 3) identify whether stand-alone inhibitory control training transfers from one context to another and could therefore support number fact learning.

This project will lead to improved understanding of the role of cognitive skills in number fact learning. This will allow the development of educational resources that incorporate design features to maximise the rate of number fact learning. More generally, this project will help to reveal the skills involved in mathematics learning and improve our understanding of why this subject is difficult for many individuals.

This project will identify the role of inhibitory control in learning multiplication tables and how features of learning resources affect this. This research has the potential for instrumental and conceptual impact on teachers, children, educational designers, policy makers and families, as well as building capacity in the educational community and beyond. Our impact plan was informed by focus groups with parents and children and interviews with teachers. Our Expert Panel includes representatives from two educational technology companies.

Teachers and children
The primary beneficiaries of this research are teachers and the children they teach. Working with intermediary and grass-roots organisations, we will increase teachers' understanding of the cognitive processes involved in learning multiplication tables, and mathematics more broadly. This will give them an insight into the challenges children face and an appreciation of the impact of their choice of classroom activities. In the medium- to long-term our findings will have the potential to change the way teachers teach multiplication tables and select resources for learners at different stages of proficiency, improving children's outcomes. Teachers will be able to make informed decisions about the value of different resources (including inhibitory control training) on mathematics learning and anxiety. The introduction of another national test for primary schools is likely to increase workload and stress for teachers, our findings will help mitigate this, and improve teachers' sense of efficacy and confidence, with evidence-based recommendations. More broadly, our research will contribute to national conversations about the value of cognitive psychology research for education and how psychologists and educators can work together for positive impact in the classroom. In the long-term children will benefit from this research by improved number fact learning. Not only will this raise achievement, leading to lasting benefits in employment opportunities, but it will also improve children's attitude to mathematics and reduce mathematics anxieties.

Educational resource developers
In the short- to medium-term, we will increase resource developers' understanding of the cognitive processes involved in learning multiplication tables so they have an appreciation that the way resources are designed impact more or less on these skills. In the long-term our findings will increase the effectiveness of resources to support multiplication tables learning by allowing resource developers to select optimal design features. This will provide a case study of how developers can improve resources by engaging with research and taking account of cognitive processes in learning. This will lead to more co-production of educational resources by researchers and developers.

Policy makers
Our research will support the implementation of evidence-based policy. In the short- to medium-term we will provide the Department for Education with evidence of how cognitive science can inform effective teaching practices, responding to their call for this (DfE, 2018). In the medium-term we will improve policy makers' understanding of what skills the national multiplication tables test is drawing upon, whether this matches the intention of the test and how to best assess fact learning.

Parents
In the long-term our research will help parents choose activities to support their child's multiplication tables learning. Providing parents with evidence-based recommendations will reduce parents' anxieties about helping their child with mathematics.

Research staff
Research staff will benefit by training in research methods, quantitative analysis, written and verbal communication to both science and general audiences, and working with children and schools. These are key skills that provide a firm foundation for a research career but are equally transferable to a wide range of employment sectors.