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.

I suppose in the end, either you find it easy to learn and memorise, or you don't.
I still know the times tables that I had to learn as a child and the only two that I have to think about are 11 x 11 and 11 x 12. All the rest are instant recall. [smug]
My year 3 children have really struggled and were getting in a flap about not being able to remember them all, so the approach above was a way of working around that and taking the stress of the test away.

Arkadia , I think "getting" 3 x 4 = 3 x 5 - 3 or not makes the child ,athematically able or not. You can use this methods to do more complicated mental calculation with bigger numbers if the child knew this works.

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

Not really, it allows you to do calculations either faster, or more importantly which would otherwise exceed your working memory.

I never learnt times tables, had no interest in doing so, some of them arrived by repeated experience, but I could always work them out sufficiently fast, I would've been described as highly able in maths if in school today, but I never saw the point of learning times tables, it never made anything easier for me.

So easier is individual, but of course it's not a negative to know them, however which is more important, knowing times tables, or understanding the underlying maths concepts. I think the underlying concept is much more important, so if you've not got that, spending time on tables isn't going to help you - the only things it makes easier is more maths you're not going to understand anyway.

Without times tables, fractions and algebra are much harder. You have to think about the arithmetic instead of the principle.

Yes, irvine, but that's two different things altogether.

I think the underlying concept is much more important, so if you've not got that, spending time on tables isn't going to help you

It really is. Bright people who can work out times tables in a flash may not appreciate that.

noblegiraffe How does it help you? It might help you get an answer to a particular question by learning tricks - but learning tricks is not understanding. So how does instant recall of 4x7 help understand the question we had the other day:

35 in the class, 4/7ths of the class are girls, how many boys?

But if you haven't got a clue that 5 x 7 = 35, you have no hope solving the question, however way you decide to do this, imo.

Not directed at me, I know, but knowing the 7 times table means that you can look at 35, divide by 7 to give 5 and then multiply 5 by 4 to give the number of girls (20) which you then take away from 35 to give 15 boys.
(That would be how I would use times tables knowledge in the example given)

Completely agree with Noble

but knowing the 7 times table means that you can look at 35, divide by 7 to give 5

No, knowing that you could or should divide 35 by 7 is quite distinct from knowing the times table, it requires understanding, all that knowing the times tables does is make that stage faster (and may make it possible to answer it in your head due to working memory demands)

I think at our school, times table are taught as a fact family, so if you know 5 x 7 = 35, they should know 35 / 7 = 5 etc. So knowing times table should equal knowing division fact as well.

In Japan, kids learn the kuku song. It's awesome. They learn the tables so much quicker than in the UK.

It's considered fine to to have them learn the song before they understand what multiplication means. It doesn't stop them understanding the concept long term. I have no issue with rote memorization preceding understanding for this kind of thing.

We need an English equivalent!

Noble I don't think anyone was saying TT shouldn't be learned because it is tedious to do so. The disagreement between Pratchett and myself was merely if age determines tedium, and had nothing to do with the question if they should be learned at all.

IMO if they can be learned without tedium, that is better than if it does involve tedium, and in some cases this can be achieved. In various ways. Which should IMO be explored before going for the tedious route.

But if all else fails, then rote memorisation, however tedious it is, will be necessary.

Regarding the understanding multiplication vs TT memorisation: I agree with sirfred that knowing that 5x7=35, and even knowing that 35/7=5, does not help you solve the 4/7 of a class of 35 problem if you do not understand multiplication and division. If someone asked you 'what is 35/7?' and then 'what is 5x4? you would be able to answer, but if you didn't understand multiplication, you would never even know that that is the operation required in this scenario.

If you DO understand multiplication, knowing your TT will reduce the load on your working memory and so will make the question much more solvable. If you do understand multiplication and do not know your TT, the question is still solvable given enough time and perhaps pen & pencil, and a good working memory. But if you do not understand multiplication, the question is not solvable.

irvine you can divide 35 by 7 without knowing that 5x7=35. You simply count how many 7s fit into 35. 7 (1), 14 (2), 21 (3), 28 (4), 35 (5 -> there's your answer).
But if you do not understand multiplication and division, you will not know that 4/7 of 35 requires dividing 35 by 7 and then multiplying by 4.

Yes, algebra and fractions are MUCH harder if you don't know TTs. You waste a lot of brain space on arithmetic. You might reach the end of your working memory capacities.

That doesn't to me equal that it is more important to memorise TTs than to reach understanding of multiplication. If only one of the two can be achieved, I'd go for understanding.

If even basic understanding can be achieved, then memorisation should be very strongly encouraged.

I also think the fact that some children struggle to memorise the TTs (when they are actually a rather limited number of 'fact families') means that there comes a point where you stop telling the child 'try harder' but instead find ways to 'try differently'. And in some cases that might involve working on increasing understanding. Some children just aren't very good at memorising and retaining 'number facts'. Demanding them to become better at memorising won't make them better at memorising. These children need to be shown ways of working around their lack of memorisation skills.

Divide by the bottom, times by the top. Do you think that they don’t get taught how to find 4/7s of a number?

I work in a numbers job and every day I curse the fact that I don't know TT it makes my life so much harder.

I don't think understanding is necessary, at some point it will "click" and you will understand that knowing 5*7=35 helps you to understand that 35/7 = 5 or to help you simplify fractions such as 35/70.

There's a weird fetish for trying to get kids to understand before they learn anything, just teach them how to do it - the understanding will come later and if you don't teach the operations you'll have people like my colleagues who still don't know how to find the original price of a product priced at £12 with a 20% discount.

The grid method is great for children who are more big picture thinkers
(as are many dyslexics)
If you google "times tables grid method" a great one appears which is a fantastic tool for learning. Seeing patterns and understanding the relationships between the numbers helps many children, and is better than rote learning for long term understanding of mathematical concepts.

Yyy aloysha - that

Pratchet, as you say worst case scenario they never understand but at least they can do the calculation.

If you focus on understanding they might never understand AND never know how to do the calculation!

Noble, that is a technique. Children can be taught techniques without understanding. This can take you quite a distance but has limits. Applying techniques without understanding also burdens working memory and means that as soon as the question is phrased slightly differently, you get stuck (or you have to memorise every phrasing for which this technique applies).

Alyosha, people like my colleagues who still don't know how to find the original price of a product priced at £12 with a 20% discount. Well presumably they are now allowed to use calculators. If they still can't work that out, it has nothing to do with lack of TTs knowledge (as they can replace that with the calculator) but has everything to do with a lack of understanding, meaning they don't know what multiplications to type into the calculator.
Presumably they were once taught a technique to solve % discount problems but not the whys, and have now long forgotten the technique and are not even able to re-create it by reasoning their way through it because they do not understand what it all means.

I've never understood why people still learn times tables up to 12. I know dozens exist, but they are fairly rare now.

I'm also not sure that having to resort to a calculator really holds anyone back in life.

Finally, the only numbers in maths at a higher level are 0, 1 and infinity.

Indeed they can be taught techniques, brilliotic which is why you were incorrect to say But if you do not understand multiplication and division, you will not know that 4/7 of 35 requires dividing 35 by 7 and then multiplying by 4.

They can be taught to divide by the bottom and times by the top. But if they don’t know their times tables they can’t do times tables or fractions of amounts. Or loads of other things.

I also don't understand why things like long division are still taught. There are so many other more useful things that the time could be spent on.