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.

[brilliotic]

See, IMO this may be true for some children but not for others. For some children it is more efficient to understand first.

But for most, I would expect understanding could and does quite efficiently develop alongside the memorising, and the memorising efficiently alongside the understanding, so why split the two?

Some children find memorising things really really hard. Memorising things that are completely random to them because they have zero understanding of it, must be even harder. Surely it is not more efficient to make a very hard task even harder for them? Also if you have zero understanding, there is more to memorise (e.g. you need to memorise 7x5 and then you need to memorise 5x7 as well, and then 35/7... ) so if your child struggles with memorisation, surely reducing the load is efficient?

It is great if young children can easily memorise TTs, I'm not advocating to prevent them. However in my experience most young children (e.g. pre-schoolers, reception age children) would probably find it pretty hard (and hence it wouldn't be efficient) to memorise the TTs.

Repeatedly chanting something with young children will help some memorise it without any problems, some will learn to recite an approximation of it (which surely is not a great idea, in maths) and some will not learn to recite anything at all. This is what happens e.g. with the Alphabet Song.

[Pratchet]

It matters which comes first in terms of efficiency of learning, that's all. It's not because one is more important or whatever. It's just more efficient to memorise when young and understand when older. It's not a value judgement on the merits of understanding vs memorising.

[brilliotic]

Noble, when you say this:
And certainly I’ve seen a few pennies drop when Y7 have been stuck on 12 x a number and I’ve said ‘12 lots of a number is just 10 lots of a number (which is easy) plus 2 lots of a number (which is easy)’. If they didn’t find 10 lots and 2 lots easy because they knew those tables, they’d have spent all their time with pen and paper slogging through repeated addition and missed the point.

I'm not quite sure I get what you are saying. To me the the example you make seems to be a case for 'understanding'. Your students knew their 2x and 10x timetables but weren't able to work out 12x ... because they didn't understand (until you explained) that 12x is just 2x + 10x. So all their TT knowledge didn't help them work out a multiplication beyond the ones they had memorised, because they lacked some basic understanding. They were not able to apply their TT because they didn't understand multiplication.

If they had already understood (or have now, after you explained, understood) that 12x is the same as 10x + 2x, but not known their 10x tables nor their 2x tables, it would obviously have been a lot harder for them. But equally it would have been harder for them to work out 12x if you hadn't told them that 12x is the same as 10x + 2x... no?

[brilliotic]

First of all, there are a very few posters on this thread who claim that memorising TTs is pointless/only necessary if you want to do something maths-y later. The vast majority here, I believe, agrees that 'knowing' your TTs makes a huge (positive) difference. Some very able people may get around memorising them without too much of a detrimental effect, but for the majority it is pretty much essential.
For some people, memorising them is easy, for others very very hard, but nevertheless, if at all achievable, it is worthwhile.

So what are we actually arguing about?

One dimension seems to be 'what is more important, understanding multiplication or memorising TTs?'
It seems to me that this is a pretty hypothetical question, as very few people/children will have a (permanent + complete) lack of understanding multiplication but yet be able to memorise TTs, and equally there will be very few people/children (completely and permanently) unable to memorise TTs (not even 10x) and yet able to understand multiplication.

A second dimension seems to be, what should come first?
Personally, I am not sure this really matters, as long as both are achieved at the end. I tend to believe that for most children, the two develop alongside each other. At times the understanding will aid the memorisation, at times the recall will aid the understanding. Some children will do more memorisation first, other children will achieve more understanding first. Does it really matter, as long as they achieve the end goal of understanding & memorisation? And are not completely put off maths in the process?

I don't think anyone on this thread is advocating that ALL children should (must be made to, if they like it or not) memorise TTs before they understand multiplication at all.
Nor do I think that anyone is advocating that all children must reach a certain level of understanding multiplication (what level exactly?) before they are 'allowed' to memorise.

So what are we arguing about?

[user789653241]

My ds was hyperlexic. He worked things out way before he can't possibly understand the concept, like, telling the time, how to decode the words, etc. Understanding always came afterwards.

[Pratchet]

If understanding comes first, learning may never come

[CuboidalSlipshoddy]

I once set a one mark “check you pen is working” question on a course for second year undergraduates which required them to do some simple conversion between base 2,8,10 and 16. I had been lazy formatting the paper so it was marked “no calculator”. It was a car crash. Aside from the fact that on this course they should have known powers of 2 up to 2^16 anyway, those that didn’t couldn’t reliably multiply or divide by 2 by hand. They all had grade a or better at a level maths, or equivalent. Claims you understand rather than “waste time” on rote practice? Yeah. Right.

[noblegiraffe]

just that if you are forced in that choice of spending time on understanding or learning, understanding should come first.

Nope. In maths, the best order of teaching depends on the topic. The evidence shows that in maths learning procedural fluency can support conceptual understanding.

And certainly I’ve seen a few pennies drop when Y7 have been stuck on 12 x a number and I’ve said ‘12 lots of a number is just 10 lots of a number (which is easy) plus 2 lots of a number (which is easy)’. If they didn’t find 10 lots and 2 lots easy because they knew those tables, they’d have spent all their time with pen and paper slogging through repeated addition and missed the point.

[sirfredfredgeorge]

Sir, I am quite curious. Without knowing times table, how can you do multi digit multiplication, fraction multiplication, decimal multiplication, factoring etc, etc. as fast as people who knows them?

I'm sure I wouldn't be anywhere near someone who actually knew them, but I can do fine on tt rockstars, but when I was at school we never had race to answer, it was just ask and write type tests, so you only needed to be fast enough to answer before the next question.

And on the more complicated questions, the other advantages made any difference in knowing vs calculating the times table irrelevant - yes I was probably gifted (although I had no real interest in maths, and my actual achievements are all elsewhere)

I've never been suggesting that knowing times tables isn't extremely useful, just that if you are forced in that choice of spending time on understanding or learning, understanding should come first.

Now it could be that actually that understanding requires some form of cognitive development stage, and learning TT's don't matter before, as the understanding wouldn't've been possible anyway, but I've never seen that suggested.

[noblegiraffe]

Not sure I see your point. You agree that learning to use logs is essential. We used to use paper look-up tables, now we use electronic ones.

[user789653241]

KeepOn, my ds loves Vi Hart. Brilliant stuff.

[SpicyTomatos]

There is a considerable difference between learning to use logs and learning to use log books. One is essential in maths and one is pointless.

[CuboidalSlipshoddy]

At first I thought it meant area

That would be 75 centimetres squared. or 75 square centimetres.

In general, it's ambiguous enough that if you write it when (say) setting an exam paper it would be queried. But "number, linear measure, square" such as "75 cm square" or "3 inches square" is such common idiom that it casual usage it is OK.

[Arkadia]

Cuboidal, English is not my first language, so I was confused by it. At first I thought it meant area, but then it couldn't because we are not given any further info. But if the meaning is clear, I am happy ;)
End OT

[KOKOagainandagain]

DS2 is not typical (how many DC are?) - he has ASD and is also 'gifted'. He learns on a 'need to know' basis - his need to know - he introduced me to YouTube videos by prof Vi Hart on sir pinski's triangle (?sp) at age 10.

He didn't realise the importance of TT (and can still work out the answer without having committed them to memory) until he could see the point when doing 'higher level' work with fractions, algebra, factorising, Pythagoras etc.

But this was only possible at internet school where he is able to work 2/3 years above chronological age. At brick school he had to master 'easier' TT and division facts before he could move on so he was stuck.

The abstract is not easier for him and says nothing about his ability or understanding. This had a huge impact on his sense of self as a learner and self esteem.

[CuboidalSlipshoddy]

Paving stones are 75cm square

Exactly what it says: that in plan, they measure 0.75m by 0.75m. Why do you think that is remotely problematic? What problem are you trying to invent? No, it doesn't mean they are 8.7cm x 8.7cm, if you're trying to claim it might be read to mean that they have an area of 75 square centimetres.

(And, to keep a previous poster happy, I worked out the square root of 75 using logarithms, owing to the limitations of the tool I had most immediately to hand).

[lunar1]

Both of mine knew their times tables and divides up to 12 by the end of year one. Both used different methods as they are quite different.

I can't tell you how much easier it makes everything for them both. All primary maths learning is so much easier for knowing them. They have both gone on to learn beyond their 12's and understand the meaning of the sums.

It's been ten mins a day, every day without fail-Birthday included. Little and often works wonders. I wish it had been taught to me in the same way.

[Arkadia]

Totally OT, but I don't want to start another thread.
What do you think this sentence means?
"Paving stones are 75cm square." (sic)

[CuboidalSlipshoddy]

Should we still teach kids to use log books

Yes, it would be a very good idea. You're using logarithms (or more particularly, discrete logarithms in a finite field) every time you log on to Mumsnet, and it would be lovely if more people who end up fiddling about with computers understood them. Logs are taught in the abstract as part of A Level (C1, noble?) but just knowledge of what a logarithm is and how they work would be extremely useful more broadly. Knowledge of how the "mean difference" column works would be really handy, too.

But then, computers and the web? Whoever might need to know how it works, eh?

[noblegiraffe]

Yeah, why should anyone have to learn anything when we can just Google it?

Or maybe employers want people who are basically literate and numerate and don’t have to look up every spelling in a dictionary and every calculation on a calculator? Because if they’re that ignorant, they’re likely to make mistakes even with technology.

[SpicyTomatos]

Should we still teach kids to use log books, or has the arrival of technology meant that they serve no use in real life? Most things that are taught do have meaningful uses.

[Alyosha]

They're irritating! arrgh

[Alyosha]

The whole "real life" brigade are annoying - the purpose of education is knowledge for its own sake, no one objects to History in the same way (who needs to know the when/what of WW2 for their day-to-day life?).

Secondly their irritating because they're wrong, any retail job needs a basic understanding of TT & arithmetic.

in the 28/63 example I can think of a lot of times when I have had to do something similar for my job, i.e. 28ml mini of 63ml product, how to price it?

Understanding how to get the original price of a £12 product with a 20% discount is 100% really about memorising the steps, when I first started in my job many moons ago I had completely forgotten how to do it. I taught myself and didn't understand "why" it worked, but it didn't matter. After 6 months of doing the calculation regularly I got it, knowing how to do it helped me to understand it; the calculation mechanics can come before the understanding.

[Pratchet]

Noble again 👆🏻

[noblegiraffe]

Simplifying 28/63 strikes me as a somewhat tedious question from which little of use can be learned, but exactly the sort of thing that gets asked in secondary school tests

Oh dear god save us from the ‘when am I ever going to use this in real life?’ brigade.