Learning, using and applying multiplication facts: Insights from research

NATASHA GUY, CENTRE FOR MATHEMATICAL COGNITION, LOUGHBOROUGH UNIVERSITY, UK

LUCY CRAGG, SCHOOL OF PSYCHOLOGY, UNIVERSITY OF NOTTINGHAM, UK

CAMILLA GILMORE, CENTRE FOR MATHEMATICAL COGNITION, LOUGHBOROUGH UNIVERSITY, UK

Knowing and using multiplication facts is a fundamental mathematical skill. Quick recall of these facts frees up valuable cognitive resources, allowing for faster and more accurate calculation of more complex problems. This helps children to tackle progressively more challenging content as they advance through the curriculum. The Year 4 multiplication tables check (MTC) requires children in England to master their multiplication facts up to 12 × 12. Inevitably this means that much time is dedicated to learning and practising multiplication tables, especially as children can find memorising them challenging. In this article, we explore some of the cognitive skills involved in acquiring multiplication facts and consider why some children struggle more than others to remember them.

The role of non-mathematical skills

Teachers observe notable differences in children’s ability to learn and recall their multiplication tables (van der Ven et al., 2015). Despite teachers adopting a range of teaching approaches and methods that help children to come to know their facts, some children continue to rely on inefficient calculation methods, such as skip-counting from zero, often resulting in mistakes and incorrect answers. The differences that children experience are not easily explained, as the specific processes involved in learning and recalling multiplication tables are not well understood. Recent research has therefore sought to understand more about the underlying skills involved (e.g. Burns et al., 2019; De Brauwer and Fias, 2009; Spiller and Gilmore, 2023).

Learning multiplication facts requires a range of non-mathematical, general cognitive skills, including language, attention, memory and executive function (Cragg and Gilmore, 2014). These skills are particularly required due to the way in which multiplication facts are stored in memory. Multiplication tables aren’t stored as a list of independent facts. Instead, as we learn multiplication facts, a network of information is created, with connections between related facts (Ashcraft,1992). As a result, each fact in this web-like network is associated with both the correct answer and a range of incorrect answers (De Visscher et al., 2016). This means that when recalling an answer to a particular question, it is necessary to suppress interference coming from other (often closely related) incorrect answers (De Brauwer and Fias, 2009). This requires cognitive skills such as executive function (Eaves et al., 2025; Megías et al., 2015). Learning to inhibit competing incorrect answers is a normal part of the learning process and something that children need to be able to do. Indeed, recent evidence from a study that we conducted with adults showed that even when learners knew their facts, they still experienced interference from closely related answers and made errors due to this interference (Eaves et al., under review). However, as with anything else, some children experience more interference from incorrect answers than others or are less able to deal with this interference, making the learning of multiplication tables more challenging (De Visscher and Noël, 2013).

Supporting struggling learners

Disadvantaged learners and those with special educational needs and disabilities are more likely to struggle with learning and recalling multiplication facts. There are many reasons for this – for example, differences in learner experiences, language ability or general cognitive skills, including executive function (Gilmore, 2023). Executive function skills underlie children’s ability to memorise, focus their attention and think flexibly, supporting the acquisition of new mathematics knowledge (Cragg and Gilmore, 2014). These skills develop throughout childhood at different rates and to different levels. Moreover, children from disadvantaged backgrounds are more likely to have lower levels of executive function skills, which may make focusing on, remembering or using their multiplication facts very difficult.

Considering different types of practice to support fact acquisition may be one way in which to support struggling learners. To ready children for the MTC, multiplication practice is often repetitive and requires speed. However, our recent work demonstrates that other forms of retrieval practice are just as effective (see www.sumproject.org.uk for information and updates to papers). Not all children enjoy learning under timed conditions or using rote learning practices designed to support memorisation. Where children are put off because the type of practice does not suit them, this can form a barrier to any practice happening at all. Consequently, interest and enjoyment are related to attainment (Fisher et al., 2012). The most important thing in improving fact acquisition is that some form of retrieval practice happens (Burns et al., 2019; Wong and Evans, 2007). Some children may prefer activities that provide them with a range of answers from which to select, instead of having to produce the answer, especially at the early stages of learning. Others may work more effectively without a constant reminder of how long they have to solve each problem. The MTC itself has an option for a pause between each item for children requiring additional support in their maths learning. With this option, children are still required to retrieve fluently, but the pause between questions may help them to gather themselves ready for the next item. This may build greater confidence and improve accuracy in their answers.

Prioritising understanding

Few would dispute that quick fact recall helps children to work at the pace and level required of them by the National Curriculum. However, the process of learning multiplication tables cannot be rushed. Children need to have a solid understanding of the meaning of multiplication (which begins with visual representations and verbal counting) and be taught how to use known information to develop reasoning strategies. Both elements need to develop alongside fast and accurate recall of multiplication facts (Cowan et al., 2011). The current expectation for children to memorise facts to 12 × 12 by the end of Year 4 means that this process is rushed for many, especially for struggling learners. Consequently, some children may be engaging in rote learning practices before they are developmentally ready or have good conceptual understanding of multiplicative reasoning. This may create misconceptions and gaps in learning, as well as frustration, for both the child and the teacher. An approach that builds on the necessary foundational understanding of numbers is much more likely to set children on the path to mathematical success. A curriculum that requires a reduced number of memorised facts and prioritises understanding of how to use them may be one way in which to steady the speed of learning expectations. Time must be allowed to not only give children the range of mathematical tools that they need but also provide sufficient instruction on how to use them.

Building mathematical connections

All children need to be taught conceptual understanding and the underlying meaning of multiplication alongside arithmetic facts. However, this is particularly the case for those that find recall more difficult. Timed practice is considered likely to benefit acquisition of basic arithmetic facts (Fuchs et al., 2016; Jay et al., 2019). However, strategy-based opportunities for learning are important to complement a focus on timed fluency (e.g. Brendefur et al., 2015; Woodward et al., 2006) – for example, understanding concepts like doubling and halving or gaining experience in noticing patterns when counting in fives or tens. Developing mathematical relationships supports children to build flexibility in the use of multiplication facts and provides them with a back-up strategy should memory fail them (Brendefur et al., 2015). Where children have difficulties in holding arithmetic facts in memory, not having an alternative method of finding correct answers blocks the path to success.

Yet there is a risk that increased focus on timed practice of multiplication tables may be separating this skill from other aspects of children’s maths learning. Tables are frequently taught during the fluency section of maths lessons, at registration time or at home. This lack of integration with broader maths activities may result in missed opportunities to support children in recognising the links between knowing multiplication facts and using them, which they struggle to make on their own. As children move through primary school, they are required to have higher levels of maths reasoning. Despite the benefits of being able to quickly access arithmetic facts, our recent work suggests that recall of multiplication facts does not necessarily mean improved reasoning or problem-solving skills. Children, especially those who find maths more challenging, need to be shown how to connect known facts to the underlying concepts of multiplicative reasoning and the different ways in which multiplication can be represented. For example, if a child can recall 4 × 3, can they also represent this using manipulatives or pictures, and can they identify where this fact would help them to solve contextual problems? While focus remains on memorising multiplication tables, those struggling to link mathematical concepts together may be spending less time learning to do so.

Conclusions

In summary, while good command of multiplication facts supports faster and more accurate calculation, it is far from the only skill that children require to succeed in maths. Moreover, learning multiplication facts does not automatically improve children’s multiplicative reasoning and problem-solving: emphasising fluency without context provides children with a tool but without an understanding of how to use it. Taking time to develop children’s conceptual understanding and build important mathematical connections between ideas is imperative, especially for those who find maths the hardest.