## My TV humiliation shows that "traditional" maths teaching failed me

So it's the stuff of nightmare, total TV humiliation; a news presenter suddenly springs a quick maths test upon you -- and you get the wrong answer. Gavin Esler, who is a nice guy, asked me what 11 x 12 was. The lights were upon me, I fumbled in my head for an answer, 111, and it was, of course, totally wrong! He corrected me (the answer's 132) and then went on to suggest that this indicated that all children should learn maths the traditional way -- that is learn, as the government is now insisting, times tables by heart. But there's a slight problem. I did! I was tested in Year 6 on my times tables every week by a fearsome, old-fashioned teacher who scared me so much that I always got top marks. And yet, even though I did well, and went on to get a B grade at O Level Maths -- which puts me roughly in the top 10% of the population for Maths skills in 1984 when I took the exam -- I have to confess I am terrified of numbers and have virtually no interest in maths. I was taught maths the "traditional" way at every stage of my school career, learning multiplication tables off by heart, and completing reams of sums from text books. And yet for all that work, I have very little idea of how to think numerically, despite jumping through all the hoops. I went on, surpris I was on TV to argue that we need to nurture a generation who find maths a joyful experience. I never did. Perhaps for this reason, I always avoided watching Johnny Ball's 'Think of a Number'; numbers scared me, and still do! But seeing Ball on a TV programme recently about children's TV on the Beeb reminded me that he was trying to swim against the tide of maths teaching in the UK by putting the joy back into maths teaching, and encouraging children to think numerically, rather than see maths as endless rote-learning. If you are interested in examining the research which shows that high-stakes testing and rote-learning lowers standards in maths then I recommend you read Roger Titcombe's Learning Matters which explores the data in some depth. He has also blogged on LSN about the issue. Interestingly, the Education Secretary, Nicky Morgan, refused to take the very test she wants to force every child to take. (I have just been asked back by the BBC for another interview! Uh-oh! Expect more humiliation!)

## Comments

Nevertheless, the programme sounds fun (although cynical Year 7s might roll their eyes at the fancy dress element shown in one of the photos). However, I would argue with this statement on the website:

'By not having this basic building block [knowing tables off by heart), problem-solving later on in maths is always going to be light on solving and big on problems.'

It is understanding of multiplication that is important not necessarily knowing tables by heart. It's a useful skill to have and it's worth nourishing. But it's only useful if understanding is present. Slow factual recall of multiplication tables isn't a barrier to higher level mathematics if understanding is present. But lack of understanding definitely is.

But the test proposed by Morgan is on factual recall alone. It won't check that pupils know 3x4 is the same as 4x3.

I'm a great fan of spotting patterns - that's why I suggesting colouring in number squares such as multiplication or 100 squares. I also like investigating patterns using concrete methods (cuisenaire rods, uni-blocks etc). Then there are other methods of multiplication such as Napier's Bones. And I've seen multiplication tables produce intricate embroidered patterns. I would love to be able to use an abacus.

All that is exciting stuff. But in Morgan's world multiplication is reduced to that which can be easily tested - swift factual recall of times tables to 12. And then the results will be used to make schools 'accountable'.

Time for adults to stop projecting IMHO.

You seem to propose a false opposition between 'understanding' on the one hand and 'rote learning of tables' on the other. As if learning to recall times tables stopped you from understanding.

I can say that I have never seen a student arrive in Y 7 who demonstrates total instant recall of their multiplication tables but lacks understanding of multiplication (or related areas). By contrast, I have seen plenty who don't know their tables who don't exhibit proper understanding.

I simply don't believe that learning times tables hinders understanding. On the contrary, by freeing up mental space it seems to help develop it.

The requirement to learn tables was in the National Strategies (up to 10 X 10). The coalition made it up to 12 X 12. Ofsted declared it a necessary precursor to understanding multiplication in 2011.

All that's new here is a test. If everyone is already learning the tables - then that won't be a problem. If they're not, they should be.

Why not just relax, have fun. But if little Janet still can't recall 7x8 without a lot of scribbling than give her a multiplication square so she can get on with the mathematical problem without worrying whether her memory is reliable or not.

However I do not think that this new test is anything to do with learning - it is about making false judgements on teachers and schools. As you say all this was in the curriculum and has been for a long time (apart from the spurious move from x10 to x12 tables - for which there is no justification expect the one the is so common from politicians which seems to be the "this is what I did at school").

There is a purpose for testing as low stakes formative assessment but these high stakes, high stress tests (for the children, their teachers and the schools) can only further move the maths curriculum away from something which will inspire and excite children. We know maths already suffers in its perception as a subject which is "hard and dull" this has moved in primary schools with the change in teaching but I fear will move back if there are these kinds of emphasis.

However, I am interested in your observed correlation do you have wider data on this or are you aware of any wider studies?

That said, I had a go at times table quiz (free here) and was pleased I got 9/10 on my 7 times table. But I admit I was sloooooow and if I'd been working against the clock I would have failed (or typed in the first number that came into my head).

Reminder to self: download a multiplication square.

http://www.activityvillage.co.uk/sites/default/files/downloads/12_times_...

Paul

Jo Baoler talks a lot about the importance of confidence and attitude and I think that the student who will be studying (esp at A level) will become more and more confident when they are not having to answer under stress in time delineated tests - there is little published evidence that this is a essential maths skill.

I quite liked maths at school - particularly algebra - but never took it further than O level (1979). Since then, working in pre-school and early years education, it's one of the most enjoyable subjects to teach with very small children, because it's all games and exploring. We used to sit in the wendy house dishing out 9 biscuit bones into the bowls of 3 toy dogs and working out how to do it fairly. Time would fly by. We called it sharing. Having demonstrated the game I'd leave the kids to make up their own games and argue over/debate/resolve how to do it themselves with more of fewer bones.

I don't know how one keeps the joy of maths going in the older age group, however. Tests with time limitations start to kick in round about juniors and it's back to quick learning as opposed to deeper thinking which wins the day. As long as we have a relentless testing culture I fear this will be the order of the day.

There are some interesting arguments about the memorisation of number bonds and number facts and the use of working (short term) and storage (long term) memory and research in this area by the likes of Daniel Willingham and the knowledge of the relationships between numbers (e.g. that 7 x 8 is the same as 8 x 7 or indeed 7 x (2 x 4)) can be useful (Richard Skemp's work on this is very interesting) but there is little evidence that the ability to do this quickly - or under high pressure situations has benefit.

This is worry for me - rather than talking about why this might be an important or useful mathematically skill and thinking about ways we can develop and encourage this in children (and perhaps education secretaries) it has been put on as another pressure on children, their teachers and head teachers and linked again to the ongoing myth that cognitive development is the same as temporal development.

If readers are not aware of them the for the other side of the argument Conrad Wolfram and Jo Boaler and Dan Meyer talk about the limitations of rote learning times tables.

[There is perhaps a wonderful irony that in this blog I am asked to do a Maths calculation in order to be able to post ;-)]

https://ttrockstars.com/page/features

As I said to Barry above - fast factual recall of table is useful but only if understanding is present. Testing children on their fast recall as Morgan intends to do does not check understanding. It's just another test for demoralizing children and judging their teachers.

Much of the point of learning times tables is because the process of doing so itself helps to develop better number sense and fosters deep understanding.

One of my rockstars had homework assignments last term that involved finding patterns in the times tables. e.g. in the 9 times table:

- the digits all add up to 9 (18.....1+8=9; 27....2+7=9 etc)

- the units place counts down from 9 to 0 while the tens place counts up from 1 to 9

Children then notice things like how reciprocal the tables are (though they wouldn't use the word) but note that 3X4 comes out the same as 4X3

Once these patterns are noticed, teachers can get students to start investigating WHY.

But if people take a knee-jerk hostile 'never mind about times tables - it's all Gradgrind's facts and rote learning...' attitude, then children don't develop the confidence that comes from getting TTs right which then enables them to stay engaged.

I agree with you that imaginative teaching can make good use of tables but I bet that doesn't happen. It's worth re-iterating that all of my generation were relentlessly drilled in multiplication tables and their associated activities, such as "long" division, but there's no evidence that this produced a numerate adult population, and I do wonder to what extent the constant regime of drilling and testing helped to create the fear of mathematics that seems endemic in our culture?

The fear of maths in our culture which you refer to is acute. I've heard well-educated people confessing happily that they're no good at maths. But I haven't heard as many confess that they can't spell, string a sentence together coherently, write using the basics of grammar etc. It's commonly held that maths=arithmetic. Arithmetic is part of maths, but by no means the whole story. Sadly, though, given the framework within which we educate children, I can't see a way of escaping this paradigm

Another politician, another bright idea.

Numbers are slippery things. Who have thought that the whole vast scope of the field of mathematics has arisen from counting (eg pebbles). Who would have thought that there could be so many different kinds of numbers - integers, fractions, negative numbers, prime umbers, square numbers, triangular numbers, imaginary numbers even. Remembering multiplication tables is indeed useful. High stakes testing of such memory is not. Numbers begin to get very complicated very quickly. What would be the point of remembering all the prime numbers up to (say) 30? Could be useful certainly, but far more imporant to understand what a prime number is. Think about Chemistry. Should students be able to memorise all the elements of the Periodic Table along with their chemical symbols? Very useful certainly but would this help explain the patterns in the Table, how the patterns predict physical and chemical properties and how these are related to electrons, protons and neutrons? Not really. I suspect some Chemistry students can recall more facts about the Periodic Table than others but would this make them better organic, inorganic or physical chemists? Not necessarily.

As for chemistry, so for maths (and everything else worth studying).

This is the issue that 'The Titcombe Maths Test' explores.

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