No thinking allowed: DfE’s new times tables test for eight- and nine-year-olds aims to stop them using reasoning to work out answers

Nick Gibb refusing to answer times tables questions on Good Morning Britain in February 2018

The government’s new times tables test for year four pupils has been explicitly designed to rule out the possibility that they might think their way towards the answers, critics have highlighted as the assessments loom for children.

The new check gives eight- and nine-year-olds just six seconds to answer each of 25 questions on their times tables up to 12 – with the Department for Educating stating, in the assessment’s specification, that the short timeframe was set as such to deny children “enough time to work out the answer”.

The test is widely seen as the personal initiative of the rote learning enthusiast Nick Gibb, the former schools minister. It will be introduced in June – meaning that primary school pupils now face more assessments than they did before the pandemic – despite Gibb having lost his position last year.

There is controversy, too, about the pass mark for the new assessments. In advice for parents published last November, the DfE said that “there is no pass mark for the check”.

 However, the specification suggests that the key piece of information, to be passed on to organisations including Ofsted, will be the number and percentage of pupils who achieve full marks-implying the pass mark is 100 per cent.

And the new test seems not to have gone through Parliamentary scrutiny, despite this being stated as a pre-launch condition in its specification.

Overall, maths subject expects are said to be scathing about the new check. Gibb told an interviewer after announcing the test back in 2018 – though refusing himself to answer multiplication questions live on air -  that they would ensure that “every single child knows their times tables”.

The detail

The new times tables test was announced by Gibb back in 2018. During a round of media interviews in February of that year, he said that the phonics check for six-year-olds, introduced under the Conservative-led coalition government, had raised England’s reading results and that the prize of this new test was “huge”.

“The prize is knowing that every child leaving primary school will know their tables, will be fluent in arithmetic and they can then start secondary school really equipped to tackle the challenges of secondary mathematics,” Gibb said during an interview with Jeremy Kyle and Kate Garraway on ITV’s Good Morning Britain.

Gibb had also said that the test “enable[d] instant recall of these multiplication facts which frees the working memory to work on more sophisticated mathematics: long multiplication, long division, and prepares them for secondary school”.

The test was due to start in primaries in June 2020. But its launch was postponed with assessment cancelled during the pandemic. The current year four, then, will be the first to take them.

Controversy 1: no reasoning allowed

Critics are homing in, first, on the fact that this is explicitly a test of rote learning. The assessment has been designed to prevent children, who might not be able to remember instantly a number fact during the assessment, from filling that gap by thinking their way towards an answer.

This is clear from the specification, or the “assessment framework”, which was published by the DfE’s Standards and Testing Agency (STA) in November 2018.

It is clearly stated in the specification that this is a test of children’s ability to remember: “All questions in the MTC follow the same format and require the same recalling of facts from long term memory,” says the assessment framework under “cognitive domain”.

It adds: “The requirement to recall multiplication facts quickly will be the main source of cognitive demand for items in the MTC [multiplication tables check].

“The requirement to answer at speed is key to assessing fluent recall of multiplication tables. A time limit of 6 seconds per item has been set for the MTC. This allows pupils the time required to demonstrate their recall of multiplication tables, whilst limiting pupils’ ability to work out answers to the questions.”

In a footnote, the assessment framework arguably makes even clearer the fact that the test has been designed to prevent children using mathematical reasoning.

It states: “Six seconds was deemed the most appropriate time to allow children to recall and input their responses without allowing enough time to work out the answer.”

Arguing that children should not be able to think their way towards answers would appear to run counter to the approach of most assessment in school. It seems reasonable to wonder whether the public might struggle to understand why it would be so bad for someone, not recalling the content of one of their tables, to find another way to the answer.

Rebecca Hanson, who provides professional development for primary maths teachers and teacher educators and who has started a petition calling for the check to be delayed, argues that, while multiplication fact “fluency” is important, it is “extremely worrying” that children are to be assessed only on whether they can recall their tables “automatically” – without thinking.

In a blog, Hanson wrote: “Fluency and automaticity are different things. Someone who is fluent with their multiplication tables will automatically recall some results, but will still choose to check some results using appropriate mental strategies. For example, it is generally considered wise and appropriate that a child fluently calculates a result like 7 x 12 by adding 70 and 14 rather than by automatically recalling that the result is 84.

“While fluency with multiplication tables is an appropriate target for most children at the age of 9 or 10, the decision to assess for automaticity instead of fluency is extremely worrying, particularly as many of the children taking the test will only be 8 years old.”

Alison Borthwick, a mathematics adviser and lecturer who chairs the primary group of the Association of Teachers of Mathematics (ATM) and Mathematical Association (MA), said: “We are not saying that it’s not important for children to know their multiplication facts. But, if children are doing some really complex problems, and need to know that six eights are 48, clearly it’s helpful if they know the answer quickly. But if they can’t remember straight away, [in real life] they could still realise that they know what eight sixes are, and therefore get to the answer that way.

“So they need to know, but they do not necessarily need to know it instantly.”

Helen Williams, a primary mathematics consultant and author of the “Playful Mathematics” books, said: “There’s a misunderstanding that recall is the be-all-and-end-all.”

Ashley Compton, a senior lecturer at Bishop Grosseteste University who is an accredited professional development lead for mathematics, said that it was her opinion that it was useful for children to have automatic recall of multiplication facts.

But she added: “There is a danger that over-emphasising automatic recall by having national tests on this will result in schools prioritising pure memorisation over approaches which combine recall with a deep conceptual understanding of what is happening in multiplication and division.”

I asked the DfE what the evidence that automatic recall of multiplication facts was more important than being able to reason one’s way to an answer. The department, though, has yet to respond.

In a response to the DfE, after the check was proposed, the Advisory Committee on Mathematics Education (ACME) stated: “There is no authoritative research supporting the cognitive demand of recalling times tables in the way the MTC is designed.”

It added: “The MTC assumes that children will rely on verbal rote memory for their multiplication facts. Yet many children use the visual and structural components as well, or instead of, rote learning. This test does not allow for this.”

The ACME paper also points out that, while it is true that the current national curriculum – introduced in 2014 under Michael Gove as education secretary and Gibb as schools minister – does support “children learning facts fluently and quickly,” it does not specify that this must be through rote learning.

It added: “The NC [national curriculum] should not legislate particular pedagogical choices.”

This paper also raised questions about the detailed format of the new test. This consists entirely of questions in the format: x times y = ? Yet ACME argued: “Using verbal recall routines (e.g. 6 x 4 = ? ) is less useful in later mathematics than asking questions such as what numbers multiply together to give 24?”

ACME added that it was unnecessary to test 11 and 12 times tables, rather than just those up to 10, as the former were “not necessary for calculations”.

In a joint position paper on “the teaching and learning of multiplication bonds” – its term for times tables – the ATM and MA wrote that there were dangers in “pursuing a ‘learn the bonds in isolation’ model” of teaching, such as chanting times tables.

These included that doing so “promotes an image of mathematics as a subject focused on memorising rather than thinking. This may lead to an expectation of instrumental rather than relational understanding.”

Verbal memory alone was “not always reliable and it is subject to pattern interference,” added the paper, citing research from 2000 which had stated: “Despite many hours of practice, most people encounter great difficulty with the multiplication tables. Ordinary adults of average intelligence make mistakes roughly 10 per cent of the time. Some multiplications, such as 8 x 7 or 9 x 7, can take up to 2 seconds, and the error rate goes up to 25 per cent…the reason we have so much trouble is we remember the table linguistically, and as a result many of the different entries interfere with one another.”

The paper suggested that the ability to use reasoning in some cases to support the brain in coming to an answer – which of course is ruled out by these new checks – could in fact be useful. It stated: “Where multiplication bonds are learnt to automaticity through exploring the meaning of multiplication, connections [between numbers] become exposed. This supports learners in deriving multiplications at times when their memory proves unreliable.”

Controversy 2: The need for speed?

There is contention, too, about the emphasis, in this test, on recalling at speed. This could make the answers less reliable – which might be a particular problem given suggestions that the pass mark (see below) for this new assessment is effectively 100 per cent – and also increase maths anxiety, it has been argued.

The ATM/MA paper suggested that prioritising rote learning or instant recall “can result in negative attitudes towards mathematics because of an untimely and inappropriate focus on speed. It cited research from 2017 stating: “One of the challenges faced by the students in the first stages of elementary school is the task of memorizing the multiplication table…students who are challenged by such a difficult memorization task in the early years of school life develop a negative attitude towards mathematics in later years.”

Referencing two research papers, ACME’s paper stated: “Timed tests can increase mathematical anxiety, which blocks working memory and is linked to poor mathematics performance, particularly with girls.”

Williams said: “There is no research that says speed is effective or necessary, in fact quite the opposite- and what about the raised anxiety level for these children, and all for accountability.”

Ashley Compton told me: “Maths anxiety is a well-known phenomenon which many children and adults suffer. Fast recall under testing conditions is something that increases that anxiety and will contribute to putting many children off mathematics.”

She added: “There is a common belief that only some people can do mathematics. Failing the times table test can reinforce this belief in some children and could result in them seeing themselves as people who cannot do maths rather than encouraging them to work harder at it…Having to recall under pressure can result in people panicking, which then reduces your ability to recall quickly.”

Interestingly, Gibb refused to load such anxiety on himself when doing his media interviews to discuss the tests back in 2018.

There were at least two interviews in which he refused to answer multiplication questions when put to him by the interviewer. Asked by Good Morning Britain interviewer Jeremy Kyle what eight times nine was, Gibb – an accountant by training - had responded: “I am not going to get into this. I have learnt through bitter experience never to answer these questions.”

But Co-presenter Kate Garraway followed this up by saying: “You don’t want to get into it because you’re worried you might get it wrong…and yet look at you, a very successful person, who clearly can add up and do maths, so why is it so important for an eight-year-old to do it when clearly you feel vulnerable about it, and there you are a government minister?”

Gibb replied, smiling: “Well no eight-year-old or nine-year-old will be doing it on live television.”

Garraway came back: “It will be pressure for them [the children], though. And in the context of their world, that’s pressure.” Gibb simply smiled. The combative Kyle then added: “Perhaps more politicians would be successful if they connected with the people who elect them.”

Controversy 3: 100 per cent pass mark?

As mentioned above, the DfE has said that there is no pass mark for the check. However, educators have pointed, again, to the specification, which does seem to imply that only children gaining full marks will be counted.

It states: “The check will determine whether a pupil can fluently recall multiplication tables. Therefore, there is no standard for the MTC beyond the number and percentage of pupils who achieve full marks.”

Though no school league tables will be compiled based on the check, this information will feature in, for example, Ofsted’s systems.  

The specification states: “As is the case with the Phonics Check, school-level results will be available to selected users including Ofsted via the Analyse School Performance (ASP) data system.”

This system, the specification points out, allows the DfE, schools, local authorities, multi-academy trusts, Ofsted inspectors and school governors to access detailed school performance data.

Again, the above statement in the specification would appear to suggest that only the number and proportion of pupils gaining full marks on this test will be collected.

Both Hanson and ACME, in its response paper, have raised questions about this. ACME’s paper stated: “Children need to answer 25 out of 25 [questions] correctly to record a pass on the test. Are there any other tests that have a threshold of 100%”

Controversy 4: Lack of Parliamentary scrutiny?

The specification also included a caveat in relation to the check’s introduction. It would be statutory from 2019/20, said the document “subject to approval from Parliament”.

Yet there has, in fact, been no Parliamentary scrutiny. This is part of what drove Hanson’s petition. She said that the new tests were being introduced, as a statutory requirement in schools, via a statutory instrument, which was an amendment to the Education Act 2002. This was not required to be laid before Parliament.

This meant Members of Parliament were not notified of the order having been made, so MPs were not aware of its existence.

There has, said Hanson, therefore not been any public debate with the check – which was debated in 2018 but not, now, with its delayed introduction about to happen in classrooms.

In a Parliamentary written answer to the Liberal Democrat Munira Wilson , Robin Walker – Gibb’s successor as schools minister – said revealed that back in 2019 the government had amended legislation on key stage 2 assessments to introduce the check from 2020. The assessments, though, of course had then not happened in 2020 and 2021.

The amendment had the effect of introducing, for the first time, a statutory assessment in year four – to an order about key stage 2 tests taken in year six.

The combined effect of this seems to be that a new assessment, about which it seems many within the maths education community have reservations including over a lack of research base, is being introduced seemingly at the behest of a now-former schools minister without Parliamentary scrutiny.

Reactions in summary

Borthwick told me: “Everybody in the maths community is totally anti this multiplication tables check.”

Compton, despite being in favour of children being able to know multiplication facts quickly, said: “I think [the test] is a waste of time and resources. Schools are already testing their children’s multiplication table knowledge. We have students going into teaching placements across much of the East Midlands and I have yet to hear of a school that is not practising and testing multiplication tables. This test is not going to give the schools any additional information. This suggests that its purpose is more to check up on schools, showing a lack of faith in teachers and their professionalism.”

Hanson, like others I spoke to about this, describes the test as the personal project of Nick Gibb, who of course arguably sought to shape in great detail not just what children were taught, but how they were taught it during his lengthy spell as schools minister.

Her petition states: “This exam was created by one minister without meaningful consultation with the education community and, in its current form, is not fit for purpose.” A press release Hanson put out to publicise it stated: “The test was developed by ex-minister Nick Gibb, who proudly ignores evidence and people who understand education…[Nadhim Zahawi, the education secretary] now needs to start to deal with Gibb’s toxic legacy.”

I put points to the DfE on this, but have yet to have a response.

Postscript: my own experience of a version of the check

I was interested as to how I might fare myself with this assessment, or with something quite similar to it.

I loved maths at school, got an A grade at A-level, use numbers a lot for my job and find myself testing my primary-age children on their tables frequently.

But I found myself pausing, first, on reading the joint ATM/MA position paper on the subject, as I sought to test myself on one of the more notorious multiplication facts it references: 7 x 8.

I don’t normally fall down on these calculations, and thought “56” to myself. But, then I wondered, “was it not 54”? So I double-checked: I knew for certain that  6 x 8 was 48. So, I could check that my original answer of 56 was correct, by adding six to 48, to find out what one more set of sixes was.

It’s exactly this type of mathematical reasoning, building on other knowledge as support where pure memory might be unreliable, that this new check is designed to rule out. But is it really a problem that I used that method to reinforce my answer? Does the ability to use more than one method reflect, actually, some greater mathematical engagement?

I then decided to take a version of the test which has been made available via the group More Than a Score, which is campaigning against the check.

I ended up scoring 23 out of 25, which if the argument described above in terms of what data are recorded is right would be a fail.

I failed to answer the first question on time, though this was a factor of me not being familiar with the format of the answer-inputting process, and I guess could be rectified. But my other wrong answer might have been more instructive. Presented with the question “9 x 12”, my brain froze. I know the answer is 108. But, with that clock ticking, I could not find a way of remembering it in time.

Does that mean I have not mastered the tables? Well, I would argue against this. But, if the specification is correct and only 100 per cent is counted as “fluent”, then there I would be, labelled a failure at least for data collection purposes.

This is even without considering, for example, basic data entry problems such as pressing the wrong button by mistake.

I’m guessing that my experience would be far from unique. Ashley Compton told me: “I have tried doing some of the sample questions online and found that the technology also slowed me down, resulting in me just barely getting some answers in time. I also made a mistake with one because my concentration slipped and I misread the question. It was 3 x 12 and I put 4 because my brain decided to change it to 3 x 4 = 12 rather than 3 x 12 = 36.”

All in all, this may be presented as just a short new assessment of an aspect of mathematics which does indeed seem important. But this development does seem to raise many questions.