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

Francis Gilbert's picture
 22

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!)

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Janet Downs's picture
Mon, 04/01/2016 - 09:19

Barry - thanks for the link to ttrockstars. Was rather peeved there would be no chance of me ever becoming a Time Table Rockstar Goddess (or even a 'busker', the lowest level) because my factual recall of times tables is low.

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.

Janet Downs's picture
Mon, 04/01/2016 - 15:05

Barry - the examples you've described are not just factual recall of time tables. It's using number patterns (in this case multiplication by particular numbers) to explore maths. I'm all in favour of that.

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'.

Barry Wise's picture
Tue, 05/01/2016 - 09:14

Children who regularly play online games requiring split-second decision/reaction will not find TT tests 'torture' or even mildly stressful.

Time for adults to stop projecting IMHO.

Barry Wise's picture
Mon, 04/01/2016 - 17:38

But there is a problem this initiative is presumably designed to help redress: that of children arriving at secondary school ill-equipped to get on with the secondary curriculum and needing catch-up.

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.

Janet Downs's picture
Tue, 05/01/2016 - 14:20

But the parents of the children playing games aren't judged on their children's ability to play games. That's what this table test will be used for in relation to teachers. And it's likely this high-stakes test will cause teachers to be anxious (they are held 'accountable' if results aren't as high as the government says they should be). Anxiety then rubs off on the pupils.

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.

Paul Hopkins's picture
Mon, 04/01/2016 - 21:27

Hi Barry, I agree (see my previous comment) that access to the multiplication facts (as well as other things) and a deeper understanding of the relationship of these (e.g. commutativity) but I am not convinced that "total instant" recall is as important - I agree that there is some interesting work on working memory and maths but this is still not a huge body of work.

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?

Janet Downs's picture
Tue, 05/01/2016 - 14:09

Barry - I haven't said learning tables is undesirable. I said it was a means to an end. If the means don't work for particular children, then there are aids. Testing pupils on their instant recall does not test understanding. But saying this doesn't imply an opposition between understanding and 'rote learning' - it's saying committing tables to memory doesn't always bring understanding. (And I never used the term 'rote learning)'. And understanding isn't just demonstrated by instant recall (if that was true neither Francis nor I would have passed O level Maths).

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.


Janet Downs's picture
Tue, 05/01/2016 - 17:00

Thanks, Paul. I've just printed it out on a piece of card. I notice it says 'Keeping Kids Busy' on the bottom. That sums it up, I think!

Vanessa King's picture
Sun, 03/01/2016 - 14:32

Thanks for sharing. If an adult under pressure can fail, it's so much worse for children. An adult can rationalise the failure and know that they are not a bad person for getting the answer wrong. Children have a much harder time of doing that. I'm currently teaching GCSE resits at a six-form college and I feel like I'm undoing years of kids feeling bad about themselves because they can't answer a times table question fast enough for some faceless bureaucrats. And don't get me started on how kids are made to feel that getting a D in maths means they've failed....

FJM's picture
Mon, 04/01/2016 - 22:11

Being able to give almost instant answers to times-table questions is very useful for anyone studying a subject requiring numeracy, whether maths itself, the sciences or any others. For many, tables can be learnt without spoiling the fun of maths; for those who cannot get to grips with them, they must not be used as a form of torture. A pupil studying A-level maths will waste a lot of time if he has to reach for his calculator whenever faced with the likes of 6 x 7, whether in calculus, vectors, statistics, or so many other topics. I would never wish to make life hard for those who cannot manage this, but, as one who teaches chemistry, physics and maths to A-level, I can assure you that reflexive familiarity with the tables is very handy.

Paul Hopkins's picture
Mon, 04/01/2016 - 22:22

Hi FJM yes as an ex-teacher of Maths and Physics to A level and all the sciences (as well as maths and others to GCSE) I agree that this fluency is useful - but my worry is that by giving younger children the stress that they HAVE to pass this (as you say almost torture) will be counter-productive to the children and to the teachers and the schools (who this seems more aimed at).

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.

Michele -Lowe's picture
Sun, 03/01/2016 - 14:52

Take no notice of the TV people. It's the kind of thing they always do. In my brief spell in radio journalism I can't say I ran across many science or maths graduates. The dominant culture seemed to be - broadly- arts and politics. So the wrong-footing question is, by default, a typical sum kids get wrong. I'm sure I heard David Blunkett, then Education Secretary, getting caught out on R4 years ago answering 7x8, saying 54 when the answer is 56. I'm not arguing that quick recall of tables is not useful, especially in a time-pressed exam situation, but it's not the essence of understanding maths. Next time it happens (if), tell your inquisitor that this is the kind of public humiliation that puts a lot of kids off maths or at the very least inhibits them from exploring further its intricate possibilities. Or just refuse, pleading that Nicky Morgan doesn't so why should you.

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.

Paul Hopkins's picture
Sun, 03/01/2016 - 18:20

A few years ago I was at BETT (the education technology fest in London every Jan) and watched a bit of software for helping with calculation practice the emphasis was all on speed (if you got the answer fastest then your rabbit would run the race). When I asked the developer why it was based on speed he could only reply (my paraphrasing) "but look at the lovely graphics!".

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 ;-)]

Barry Wise's picture
Sun, 03/01/2016 - 20:33

My youngest children love times tables (and Maths generally) and both their classes are totally gripped by TTRockstars.

https://ttrockstars.com/page/features

Janet Downs's picture
Mon, 04/01/2016 - 09:25

Tables are a means to an end not an end in themselves. Children (and adults like me) who struggle with fast factual recall can overcome this by having tables on a reference sheet or, better, a multiplication square.

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.

Barry Wise's picture
Mon, 04/01/2016 - 10:35

Janet

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.

Michael Pyke's picture
Mon, 04/01/2016 - 13:41

Barry, the value of learning multiplication tables is an interesting debate (I'm broadly in favour) but I doubt if the latest government policy is based upon any serious research. It strikes me as a piece of cynical "dog whistle" politics, designed to appeal to the ageing core of Tory voters, who like to believe in a Golden Age of education - in their case, the early post-war years. Why else include 11 and 12 times tables when we have a decimal system? How long before we reintroduce the rod, pole and perch and all those other fascinating systems of ancient weights and measures that used to be printed on the rear of school exercise books?

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?

Michele -Lowe's picture
Mon, 04/01/2016 - 17:11

Michael, you put your finger on it. It is all about what are palatable messages to the sector of the electorate that voted for the current government. I await a return to inches and yards in maths measurements in text books. But on the serious side, I sense this is a political gimmick which will further deepen a sense of inadequacy in children who are not hands-up-first-to-the-answer types. And Janet my well be right about results used to hold schools 'accountable'. It would be an easy move, politically speaking.

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

Vanessa King's picture
Mon, 04/01/2016 - 23:07

I liken learning times tables to using a pair of scissors to cut paper. You want to think about cutting the paper and creating the thing you want to make, not put lots of energy and brainpower into actually controlling the scissors. You can use scissors without thinking so it becomes a delight to use them. Tables are the same thing. Learning them can be tedious and boring (although it doesn't have to be) but doing so makes other areas of maths much more pleasurable. I have explained this analogy to several of my students and it helps motivate them to learn. I despise the idea that kids should be tested on them and that teachers should be judged by them. Who cares whether you can open and shut scissors - what really matters is whether you can create what you want to create with them.

agov's picture
Tue, 05/01/2016 - 11:29

In ye olden days of the NuLab government there was a point when the unemployed were assumed to be in need of basic skills, including arithmetic (- now it's far worse). One person related how he had been asked a simple multiplication question and he gave the correct answer. He was told it was wrong. He said it wasn't. He was then told it was wrong because he hadn't used a calculator to get the result.

Another politician, another bright idea.

rogertitcombe's picture
Mon, 25/01/2016 - 12:42

 

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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