{"id":1034,"date":"2025-11-26T11:57:28","date_gmt":"2025-11-26T11:57:28","guid":{"rendered":"https:\/\/blog.lboro.ac.uk\/cmc\/?p=1034"},"modified":"2026-01-07T15:34:41","modified_gmt":"2026-01-07T15:34:41","slug":"more-than-facts-why-understanding-of-multiplication-matters","status":"publish","type":"post","link":"https:\/\/blog.lboro.ac.uk\/cmc\/2025\/11\/26\/more-than-facts-why-understanding-of-multiplication-matters\/","title":{"rendered":"More than facts: why understanding of multiplication matters."},"content":{"rendered":"\n

Camilla Gilmore is a Professor of Mathematical Cognition in the Centre for Mathematical Cognition. Lucy Cragg is Professor of Developmental Psychology at the University of Nottingham. Natasha Guy is Research Assistant in the ESRC Centre for Early Mathematics Learning. This post summarises research conducted as part of the Skills Underlying Maths project<\/a> funded by the ESRC.<\/em><\/p>\n\n\n\n

What\u2019s seven times nine? Quick, you\u2019ve got six seconds to answer.\u202f <\/p>\n\n\n\n

Learning to recall multiplication facts has always been part of mathematics in upper primary school. But over the last few years this has received more time and attention due to the\u202fmultiplication tables check\u202f(MTC), a statutory assessment of multiplication fact recall.\u202f <\/p>\n\n\n\n

The MTC was introduced in 2022 with the aim of driving up standards in mathematics. It\u2019s an online test that children take on a tablet or computer, made up of 25 questions with six seconds per question. It\u2019s therefore not surprising that in a survey of UK primary school parents we found that almost 90% reported that their children had been asked to practise multiplication tables at home. <\/p>\n\n\n\n

Being able to quickly recall multiplication facts is valuable. Not having to think about seven times nine, just knowing that it\u2019s 63, frees up a child\u2019s mental thinking space. This means they can focus on different aspects of the mathematics they are doing, such as completing multi-step problems or using reasoning to solve context-based problems.\u202fAutomaticity of multiplication facts also provides a foundation for more advanced mathematics topics that children will encounter at secondary school.\u202f <\/p>\n\n\n\n

However, many have suggested that the MTC is unnecessary, and that it places too much emphasis on fact recall at a cost to other areas of mathematics. There are also concerns<\/a>\u202fthat it disadvantages some children for reasons such as digital accessibility.\u202fNevertheless, the recent report of the Curriculum and Assessment Review<\/a> (CAR), and the government\u2019s response<\/a> to it, make clear that the MTC is here to stay. So, what does research tell us about the MTC? <\/p>\n\n\n\n

Assessing multiplication fact recall<\/strong> <\/p>\n\n\n\n

Our research<\/a> has investigated whether the MTC is a good way of testing children\u2019s recall of multiplication facts. We found that children\u2019s scores on a computer test equivalent to the MTC are strongly related (r = 0.8) to a more traditional paper-and-pencil timed fact test.  <\/p>\n\n\n\n

In our study, there was no evidence that any children were particularly disadvantaged by the computerised test. However, we did find that children\u2019s attention skills and how quickly they could enter numbers into the tablet they were using did influence their scores.\u202fThis suggests that, for it to be a fair test, it is important that children are familiar with the technology they are using to complete the test. Some children may have particular difficulties accessing the test and the CAR report rightly suggests that accessibility of the test should be explored.  <\/p>\n\n\n\n

Multiplication fact recall and multiplicative reasoning<\/strong> <\/p>\n\n\n\n

The purpose of introducing the MTC was to improve children\u2019s broader mathematics attainment by improving their multiplication fact recall. But performance in the Year 6 SATs tests, which assess a range of mathematical skills,\u202fshows little change and there is some evidence<\/a> that MTC scores are not correlated with SATs outcomes. Of course, this may relate to the nature of the SATs tests as much as the nature of the MTC.  <\/p>\n\n\n\n

Our studies may suggest an important distinction between knowing multiplication facts and understanding how to use them. Multiplicative reasoning involves understanding and using relationships based on multiplication facts and applying this to solve problems. In our recent work, we found that children with good fact knowledge also did well on a test of multiplicative reasoning (r<\/em> = 0.7). However, in a training study we found little association between improvements in fact recall and improvements in multiplicative reasoning (r<\/em> = 0.2). This suggests that although the two skills are related, recalling multiplication facts doesn\u2019t automatically help children to apply their knowledge. Working towards the multiplication tables check can support fact recall, but children will need extra support in knowing how to use and apply these facts. <\/p>\n\n\n

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Image taken from The Sum Project<\/a>.<\/figcaption><\/figure>\n<\/div>\n\n\n

The CAR report suggests that the new curriculum should have an increased focus on multiplicative reasoning in Key Stage 2. An important aspect of this will be to help children link automaticity of facts with understanding of multiplicative structures.  <\/p>\n\n\n\n

Time pressure<\/strong> <\/p>\n\n\n\n

The timed nature of the MTC is a particular concern to many. However, having a time limit per question \u2013 which is only possible with a computerised test \u2013 is essential to assess recall, rather than fast calculation. <\/p>\n\n\n\n

Because the MTC is a timed test, teachers and parents may use\u202fsimilar time-pressured approaches\u202fto prepare children and help them improve their multiplication fact\u202frecall. But our research<\/a> showed that while practice with a computerised game can support children\u2019s fact recall, the benefits to learning are the same whether or not children are encouraged to answer as quickly as possible. This suggests that doing some regular multiplication fact retrieval practice is more important than the type of\u202fpractice.\u202f <\/p>\n\n\n\n

We did find that children who were anxious about mathematics learnt less when practising with time pressure compared to children without mathematics anxiety. Without time pressure, anxiety levels were not related to the amount of learning. Even though the MTC is a timed assessment, it doesn\u2019t mean that children only need to do timed practice to prepare for this. Some children may benefit more from less time pressure when practising. <\/p>\n\n\n\n

Multiplication fact recall is just one\u202felement of mathematics\u202fand so having a good balance is important. Fact recall and testing should go hand in hand with other areas of mathematics learning such as understanding concepts, choosing strategies and solving applied\u202fproblems.\u202f <\/p>\n\n\n\n

Find summaries of our research and infographics for teachers and parents on our website<\/a>.<\/p>\n\n\n\n

This article is republished from The Conversation<\/a> under a Creative Commons license. The image was supplied by the University of Nottingham. Read the original article<\/a> here.<\/p>\n","protected":false},"excerpt":{"rendered":"

Camilla Gilmore is a Professor of Mathematical Cognition in the Centre for Mathematical Cognition. Lucy Cragg is Professor of Developmental Psychology at the University of Nottingham. Natasha Guy is Research Assistant in the ESRC Centre for Early Mathematics Learning. This post summarises research conducted as part of the Skills Underlying Maths project funded by the […]<\/p>\n","protected":false},"author":769,"featured_media":1038,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"lboro_blog_alternative_thumbnail_image":"","footnotes":"","_links_to":"","_links_to_target":""},"categories":[143],"tags":[151,224,138],"class_list":["post-1034","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cognitive-research","tag-mathematics-education","tag-multiplication","tag-primary-education"],"_links":{"self":[{"href":"https:\/\/blog.lboro.ac.uk\/cmc\/wp-json\/wp\/v2\/posts\/1034","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.lboro.ac.uk\/cmc\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.lboro.ac.uk\/cmc\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.lboro.ac.uk\/cmc\/wp-json\/wp\/v2\/users\/769"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.lboro.ac.uk\/cmc\/wp-json\/wp\/v2\/comments?post=1034"}],"version-history":[{"count":11,"href":"https:\/\/blog.lboro.ac.uk\/cmc\/wp-json\/wp\/v2\/posts\/1034\/revisions"}],"predecessor-version":[{"id":1071,"href":"https:\/\/blog.lboro.ac.uk\/cmc\/wp-json\/wp\/v2\/posts\/1034\/revisions\/1071"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blog.lboro.ac.uk\/cmc\/wp-json\/wp\/v2\/media\/1038"}],"wp:attachment":[{"href":"https:\/\/blog.lboro.ac.uk\/cmc\/wp-json\/wp\/v2\/media?parent=1034"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.lboro.ac.uk\/cmc\/wp-json\/wp\/v2\/categories?post=1034"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.lboro.ac.uk\/cmc\/wp-json\/wp\/v2\/tags?post=1034"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}