They don't teach long division anymore...!

[ElaClaw]

My dd is in the first year of secondary and during some revision work came across a sum where long division would be useful. She swore that she has never done long division and I was adamant that she would have done it in Primary school.

Fast forward to parents' evening. I asked the (young) maths teacher and he says that long division is no longer part of the curriculum (he even said he didn't even know how to do it until a couple of years ago when he taught himself for personal interest.

Apparently they just use a calculator.

I have often wondered about this worldgonecrazy. I remember being taught methods without the slightest understanding of the reason behind them all and I floundered badly in secondary as a result. I specialise in teaching maths to infant level now and I really believe it IS better taught in primary than it was. You should find that your dd is taught the old fashioned methods as well as modern ones (I think this is often an overstated difference tbh). This would have been the case in every school I have taught in, but this is only a sample of four!

I am often rather bemused by the discussions in the media about maths teaching. It is often implied that children no longer learn times tables by heart. This is not my experience. It is implied in the media that teaching fractions in year 1 is a new initiative when I have always taught fractions (half and quarter) in year 1.

So the question remains, where is it all going wrong? IS it going wrong? What surveys are they that imply we are all going to hell in a handcart? Does bruffin's ds only not remember the written method of long division and could he manage a calculation doing it a different way?

I have no experience or understanding of teaching above primary, I would love to hear from someone who has that insight.

My ds is obviously using a method that suits him. All i know is that he cant do long division. He doesnt retain that method but has still managed to do very well in maths. I never liked the way my dcs were taught times tables ie i was taught to say 2 2s are 4, 3 2s are 6 etc and i still have install recall of all my tables. My dcs were taught to count up ie 2,4,6,8, it seems a long way of remembering them. My dd is also very good at maths and probably more a natural mathematician than DS is, she seems to think in numbers, so i have left them to get on with it and do it whatever way suits them best. They are not struggling and dont seem to have any problems working out every day maths ie DS very good at working out how much his shares are worth and how much they have made using mental arithmatic

worldgonecrazy, I think she meant he was doing long division intuitively, rather than using the old fashioned written method. PRobably he was chunking, but didn't know what it was called.

The whole point of the modern methods is to show there's lots of ways to solve a problem, rather than one rigid method. When I read about chunking, because my DS was doing it at school, I realised I'd been doing it all my life, to solve problems in my head, but just didn't have a name for it. Things that I struggled over at primary school, because I was trying to follow a method set out by the teacher, came naturally as I got older because I thought about them in a different way that made sense to me. That is what intuive mathematicians do naturally, and its what modern primary maths is meant to teach (though clearly more successfully in some cases than in others).

So not remembering the bus stop method of long division has not harmed his understanding/numeracy understanding at all.

When you teach a class of children you realise that all them come at learning from their own angle. What worked for one child, or the OP who is recollecting their experience, will not be the ideal method for another child. What IS done very well now is encouraging children to find the mental method that works for them.

I think he uses another method Humphrey I dont know how he does it but I dont get involved in his homework nowadays, but someone bought up long division at home the other day and DS said he still didnt know how to do it. They have non calculator papers in GCSE and I am sure in A level as well.

sorry a few cross posts

"they don't teach long division anymore" Thank God for that!!!!!

But they do teach it, just not neccesarily in the way you did it - i have never been able to do it and i have A level maths. I have never EVER used it though.

I agree - the methods my dss' have been taught are methods I have used myself when doing mental arithmetic. I do object to them being a way of writing things down to show your working, though - it's not so much chunking as chunky and clunky if you're forced to write it down like that. I think something like: 14,567/27 is just going to look neater and be done quicker using the bus stop method if you need to show your working out. But then, I'm old fashioned.

I agree, some dc can cope with bus stop method but most are taught the grid method for long � and long ÷. alot dont seem to know tables.

I find these new methods more confusing.

I'll quickly outline the method I would use, I would write it in a sort of grid:

74100 divided by 300 (ok I know you could simplify this but supposing we did it the long way)

I would think to myself, lets try 100 times 300, so subtract 30000 from 74100 which gives me 44100.

Ok, lets subtract another 100 times 300, giving us 14100. Lets now take away 30 times 300, so 14100 - 9000 is 5100.

Then we could subtract 10 times 300 from 5100 giving us 2100. We can then see that 7 times 300 is 2100 so subtract that from 2100 bringing us down to 0.

Then I would add up how many 300 I took away from 74100 to give us 0. 100+100+30+10+7=247.

So 74100 divided by 300 is 247.

I learnt this method in Primary 6 in Scotland in the late 80s. I would probably take a few mental shortcuts from what I have written down, but this is what I was trying to show dd.

Using long division i would have done

  <span class="underline">_2 4 7</span><span class="underline">_</span><span class="underline">_</span>

300/74100

• 60000 2300 = 14100 - 12000 4300 = 2100 7*300

if that makes sense

sorry thats not clear i didnt mention bringing down the noughts

I would turn 74100/300 into 741/3 personally.

I've always taught long division but that's in secondary school. We teach a method that's effectively long division but isn't written in a standard column form that you might be used to. I'd teach the long written way with a higher class.

Its definitely in column form on the A-Level syllabus when they come to dividing two polynomials although normally I have to start with some numerical examples as they all deny all knowledge of ever having to divide two numbers before

could you do 741 /3 to get same answer? or something along those lines

Yes, I would turn it into 741/3, and then turn it into (600+120+21)/3, and then the answer would be 200+40+7.

Mind you, it's still easier to do 3s into 7 for the hundreds column (2, remainder 1 which adds 10 to the next column), 3s into 14 for the 10s column (4 remainder 2 which adds 20 to the next column) and 3s into 21 for the units column (7), which is what you end up doing with the bus stop method. Is it really past the wit of teachers to explain why this works?

After all, it is doing what raspberryYoghurt described, really, isn't it?

In other words, rounded down to the nearest 100, how many hundreds of 3s are there in 700 (because this is the biggest number that can go in the hundreds column in your answer, given that 3 will go into numbers less than 300 less than 100 times...) - answer 2, with 100 remaining. So, how many tens of 3s are there in 140 - answer 4, with 20 remaining. And how many 3s are there in 21 - answer 7 with nothing remaining, so no need to go into decimals.

(the bit in brackets should go after the "answer 2, with 100 remaining" to make more sense!). Anyway, the bus stop method makes sense to me, so I'm sure a teacher could work out a way of explaining why it works.

Kids aren't asked to do long division at GCSE in my memory of papers. By long division I mean something like 8314/27.
They all know the bus stop method for short division (by decimals, and single digits).

They need to do long division of polynomials at AS level, the kids never remember the method because it just doesn't come up at secondary, unless in a contrived way. But they usually can divide polynomials perfectly well once shown.

Chunking is, IMO, a far better and intuitive method for long division than the tedious figuring out how many 27s are in 83 and working out remainder paper method.

Yes, to work out 83/27 I would immediately think 20x3=60 and 7x3=21 and 60+21=81 therefore the answer is 3 times, remainder 2. I wouldn't want to go into decimals, though.

... unless I was writing it all out using the bus stop method, to remind me of where I had got to. The bus stop method doesn't stop you needing to know times tables and basic mental arithmetic, it just keeps track of where you've got to.

yes bus stop every time

"I would turn 74100/300 into 741/3 personally." Me too, and I did show her that too, which she did know.

"as they all deny all knowledge of ever having to divide two numbers before " so it's quite common then?

bruffin, that does make sense, and is fairly similar. I think that's how my mum does it.