Times Table - new government testing

[Blythe13]

My son is hopeless at times tables, he just can't remember them and I'm worried about the new government testing. Any good advice as it's making him feel really stupid and he's not.

"schools have finite resources and teaching time"
Yes, that's why children struggling need to practice out of school. Like I said on my first post.
My ds's school had bad results for phonics. They changed everything about phonics teaching.
Had bad results in reading in yr2 sats. They subscribed to bug club.
The school having difficulty children learning times tables need to prioritise their resources, since it's important. But if the school isn't, there are ways for parents to help as well. After all, knowing times table is for child's benefit. Not for school. I don't care about stats. But knowing times table will really makes difference for children in secondary school.

Finite resources should prioritise times tables and it shouldn't be one of the things left to parents, or you just embed privilege further

I'm not so sure about memorising first, then gaining understanding later. Well maybe for some children, but not for all.

There are things that need to be understood, and practised, about multiplication, e.g. that 6xA is the same as 5xA + 1xA (distributive law). Now if children know their 6x table off by heart, they will never work out 6xA in that way - they will just 'know' the answer. So in order to practise this and gain understanding from 'doing', they will have to start with more complex situations, rather than with small numbers and potentially concrete objects. Which might be overwhelming or confusing. Memorising TT early effectively means that the distributive law (for example) has to be understood as an abstract concept, rather than something that can be learned with concret objects and applications. (Because you're going to need a lot more chocolate buttons to demonstrate how distributive law works when the numbers you're multiplying are all 13 or over... you probably won't be doing that over and over until everybody has 'got' it... probably you'll skip the concret objects stage altogether, leaving some children with a very vague understanding of what is actually happening e.g. when they do grid/column multiplication)

Also children might gain the impression that multiplication is something you need to 'know' rather than something that you can 'work out'. So once confronted with problems beyond what they have memorised, even just 13x something, they might easily respond with 'I don't know that' rather than with 'give me a moment to work that out'.
For example, DS used to do divisions with remainders quite easily. Now he has memorised TT fact families and can recall divisions that result in whole numbers. However now when asked to do divisions with remainders, his immediate response is to start searching his memory, as if you were meant to memorise things such as 53/9= 5 R8. I've had to explicitly explain to him that these are not number facts to be memorised, but rather problems to be worked out, and using those number facts that he HAS memorised (e.g. in this case 5x9=45) should help him work it out more quickly/easily. Before he started memorising TT this would have been obvious to him. Now he needs constant reminders that maths is about working things out, not about memorising as many things as possible.

I think to some extent there is a similar problem with memorising number bonds to 10 before having properly grasped addition. As in, that you can put any two amounts together and then count them. Counting on, and/or using a number line, and later partitioning and colums etc, are techniques that help us work it out faster/more easily/more reliably. I think that young children should do lots of adding up, with and without using techniques, to get that practice in and to really understand addition. If they have memorised number bonds before having gained/secured that understanding, they will get less practice. E.g. my DD who is a pre-schooler has been memorising things. She'll ask me 'what's 3 and 4' and if I give her the answer, she'll remember it (she might ask a few more times over the next few days to re-inforce/check). She does this with other people too, it's like she's 'collecting' number facts for fun. Which is fine, I suppose, except that she'll never practise 'counting on' or using a number line with numbers 0-10 when she starts school in September, because she'll already 'know' all the answers. Then when they use a number line for bigger numbers for which she does not know the answers yet, she'll be stuck as she won't have learned how to use a number line. (Obviously, I am aware of this happening and am gently counteracting.)

So whilst I see that sometimes understanding develops over time, after memorisation, I'm not sure it is always a good idea to memorise before understanding has been achieved. I guess it depends on the child too.

See, that's all off putting, imagine how off putting it is to kids. By the time they've got through that they aren't going to want to learn anything by rote. Get it into them young then explain, is best. Another great thing for teaching kids patterns, is those 1 to 100 squares where you colour in the x3 x5 xwhatever, it gets children interested, and it all goes in the brain muscle memory.

I don't find it off putting at all, I found exploring numbers like that to be interesting and fun. My DS is the same. Luckily, DS completed most of his primary education in Australia and didn't have to memorise times tables until year 3 (2, 3, 5, 10x) and 4 (up to 10x). This was at age 8-10. Before this they explored and developed a sound understanding of multiplication. The PISA ranking for maths was slightly above that of the UK in 2015.

@Pratchet, it's interesting, that my ds learned times table from a poster when he is about 2/3 years old(that he demanded to buy a local library). He was obsessed with numbers, and I didn't teach him but he actually got the concept by himself and he got inverse operation(division) at the same time. I thought he was exceptional. But do you think many children are capable of understanding them?

I completely get what brill is saying and agree. The number of students I have when, in yr7, are asked to calculate what a x 15 is and they answer "you can't do that. You can only times up to 12 x 12" it was exactly as described - just rules learnt, but no understanding about what is happening.

If students in year seven think you can only do 12 x 12 that's nothing to do with learning them young. That's a failure of maths teaching in primary school, it's a failure to teach in years 2 3 4 what multiplication and division are. Maybe some kids can understand when they are three, I don't know. Your child sounds so bright! But there no disbenefitcand only benefit to learning them young.

In lreland we are the same as Australia. Only learn by heart at about 9 to 10. By then they know a lot like counting in 2s 3s etc so not too much to learn..My ds seemed to have been born knowing tables..he never learn them but he wasn't great at other kinds of maths but has a great memory for rote stuff.. but for others its torture.
In Secondary here they use calculators all through Maths so not knowing them completely by heart is not an issue.
I agree with Brill that knowing whats happening is more important.

duckling I know adults in their fifties who know their times tables up to 12 x 12 but still don't have that basic mathematical understanding.

Shrug if people don't want their children to learn times tables young when it's easy to do rote and singing, chanting and colouring in, not much anyone can do to persuade them

Rather do it then, than when they're six seven eight nine and find it unbelievably boring and could be using their brains to do something else like understanding them, and how they are used in fractions and algebra. Just me then

I actually think Pratchet has a point. My ds memorised times table as a kind of puzzle. We never done anything with it, just hang up a poster on the wall where he saw it at his eye level. So, I don't think it works for all, but it may work for some, if they are interested in numbers and puzzles, and the understanding of concept may come later, but tedious memorising is done already.

I don't know why memorising at age 3 should be any less or more tedious than memorising at age 8 or 9.

DS decided at age 7 to 'learn' the times tables, after having been working out all sorts of multiplications for a good while. For example, BEFORE he had memorised the TTs (but he was good at doubling), he could work out 6x12x8 mentally within 30 seconds (when playing the boardgame Plyt). He would do it by splitting the 6 into 2x3, then doing 3x12 by adding 12+12+12, then doubling the resulting 36 to reach 72 (for 6x12). In order to do 72x8, he would then double three times, so 72 ->144 -> 288 ->576.
Having this solid understanding of how multiplication works, and having worked out multiplications such as 3x12 numerous times, and being keen to do the memorising now (amongst other reasons, because of the realisation how instant recall of the 'easy' parts would help him work out harder multiplications faster) ... memorising the TT was quick and easy. There was not very much to learn, in fact, as quite a few 'multiplication facts' had already been memorised simply by having worked them out numerous times.

I believe the 'willingness' to learn them is probably what most influences the level of tediousness.

At nursery, learning to chant the TT is a bit like memorising the digits of Pi (for most children). Completely meaningless, a random string of sounds (many children will not even relate the word 'seventy-two' to 72 let alone have any concept of what that number is). If a child is happy (and able) to memorise these strings of sounds, then why not? But as soon as there is any pressure whatsoever (you need to chant with me now/you need to be able to reproduce these 'lines' before you start school/whatever) then it will feel 'tedious' (or worse) to the child, and I can't believe it would be good to insist on 'getting the memorisation out of the way'. My own DS could memorise whole story books word-perfectly at age 2, but did that entirely out of self-interest. He would have hated having to memorise something completely meaningless (to him, at that stage). And it would have been a lot harder, and a lot more tedious, than it was at age 7. Other children would have really struggled if someone had demanded for them to memorise the story books. I do not think it should be a requirement whatsoever, to memorise something/anything (before understanding) by a particular age such as 5.

And I still hold that if memorisation comes before understanding, you lose an opportunity for working on /developing the understanding.

Parents whose kids are bright usually think that way, in my experience

brilliotic, because ds wasn't trying to memorise them, he was just staring at it to look at the pattern, and learned it without any effort. That's why I said it may work for some children interested in numbers. Small children may not see it as something you need to learn, but pay enough attention to learn them without realising.

Irvine, I think what I mean is that it's a matter of 'stages not ages' in a way. Some children will happily learn TT without finding it tedious at an earlier age than others, but it is not the age of the child that makes it tedious. A child at 3, 7, 9 who is interested and keen will avoid the tedium. Memorising TT is not tedious at 7 because you're 7, not a happy activity at 3 because you're 3. It can be tedious at either age, especially for children uninterested and unwilling, who are made to memorise them. (And I would say also more likely to be tedious if basic understanding is missing: if someone demands of you to memorise this when you don't understand what it is about; this was not the case for your DS, it seems, for him it was more a matter of working out how multiplication works and memorising TT at the same time, out of his own drive/curiosity.)
Equally, it can be a painless thing at either age, especially if the child doesn't really have to 'work' at memorising but can just 'pick it up' eg from looking at a chart, from lots of working them out, from chanting/singing.

But for this, any of this, to work (as in, allowing a child to memorise TT without it feeling tedious) the child must be ready. A child that cannot 'read' numbers will not memorise TT by staring at a chart with lots of 'squiggles' on it. Also a child that doesn't know numbers beyond 10 yet will have a lot more memorisation work to do when chanting, as they will have to remember e.g. 'seventy-two' as a random string of sound, rather than a number. Whereas understanding reduces the amount of memorisation required, and if there is less to be memorised, chances are it will feel less tedious too.

Pratchett, my experience has been different: I have heard quite a few parents of very able children wanting their children to memorise TTs early, because they 'can'. Because they find memorising easy and effortlessly learn the TT and can then apply this to more interesting work. I have found myself in the minority when arguing, among people with able children, that just because a child can learn something easily does not mean it is the best thing for them to be doing. Just because some children are able to learn to read at age 2 does not mean it is necessarily in their best interest to teach them at age 2. Just because some children will easily memorise TTs at age 5 does not mean it is in their best interest to do so.
And if a child is not able to learn to read at 2, not able to easily memorise TTs at age 5, there is all the less reason to be doing it.

I think brigh

Whoops.

Very young children love repetition. Age very much matters. Repetition is a huge part of how they learn. Seems a shame to waste it.

I don’t think I like the implication that because a kid might find memorising times tables tedious that it should therefore be avoided for that age group. Who cares if it’s tedious when it needs to be done?

Sure you can jazz it up with games and songs but I don’t think children should be encouraged to have the view that everything in education should be fun or it’s not worth doing.

I don’t think I like the implication that because a kid might find memorising times tables tedious that it should therefore be avoided for that age group. Who cares if it’s tedious when it needs to be done?

But it needs to be done for a reason, learning without knowing the reason doesn't lead to good learning, there's no intrinsic reward in the learning, so you need something extrinsic.

And the reason is that knowing your times tables makes a bunch of other stuff much easier.

I’m not advocating times tables for 4 year olds, but people going ‘oh it’s tedious for a 7 year old’ aren’t presenting a good argument.

Sorry I have't RTFT but at our school they start teaching times tables using repeated addition.
Then they go to learning 2s, 5s and 10s by heart. I can't remember which one is next, but once you know a few, it is possible to fill in the gaps with addition and subtraction (sorry if this has already been mentioned up thread) so,

1 x 3 = 3
2 x 3 = 6
3 x 3 = (2x3) + 3
4 x 3 = (5x3) - 3
5 x 3 = 15
6 x 3 = (5 x 3) + 3
etc

Also in our school they do a couple of weeks in order followed by a couple of weeks mixed up. My children have all approached the mixed up list by looking through for 1 x, then 2 x, so doing them in the order they know them, rather than top to bottom of the list.

I agree with you noble, it needs to be done, but if the time is right, memorising is less of a chore and doesn't put kids off maths in the same way

Barbie, to me that approach is pointless and adds an extra layer of reasoning.
Times tables is purely a matter of memory and nothing else. Try to make them more "meaningful" is a waste of effort.
By all means, we can discuss on what strategy is best, but to think that 3x4=3*5-3 makes my head spin ;)