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Why do pupils need to know a written method for long division by the end of year 6?

Discussion in 'Mathematics' started by Anonymous, Feb 3, 2015.

  1. Violalass

    Violalass New commenter

    But that's not an argument for the long division algorithm, that's just an argument for thinking about what skills you want them to learn (neat layout etc). Your argument could be extended to include any algorithm, which still wouldn't necessarily make that algorithm useful per se.
     
  2. Vince_Ulam

    Vince_Ulam Star commenter



    If you are going to reduce arguments to absurdity then your own will, were it acceptable, invalidate arithmetical education and other significant portions of the curriculum. Think of all the time we could save if we abolished mandatory education and just sent kids to call centre training units or academies for ditch-diggers & shelf-stackers. Fortunately, we are not all so philistine.


     


  3. Well, yes...but then perhaps you could suggest an alternative algorithm to introduce to primary school children that allows them to build on their existing (limited) skill set and gives them an opprotunity to achieve competence, confidence and fluency in manipulating numbers?

    We're talking about a basic skill here - something that hundreds of millions of children have mastered successfully over hundreds of years, long before people started reading Child Development books and deciding that learning was too much like hard work! Teaching long division follows naturally from the work the kids have done on addition, subtraction and multiplication, and shows them how, and from where, the "machine" gets its answers when you type in something like 3751 / 233 and press Execute.

    Surely the aim of teaching is to show the kids that they can do something - not tell them that they're a bunch of mental cripples whose ambitions should never extend beyond a few simple operations because everything worthwhile in life can be performed by a machine?

    Or perhaps, as Vince suggests, we're making a terrible mistake educating the working classes. Perhaps we should reverse the Butler Education act, send the plebs back up chimneys, and leave elitist, white middle class concepts like long division, grammar, science and languages for the privileged public school few.


     
  4. Vince_Ulam

    Vince_Ulam Star commenter

    For the purposes of attribution and possibly continuity, it may be noted that the author of the opening post currently listed as Anonymous was Robyn147, and appears to have been banned for an infraction on the Opinion forum where, for the moment at least, she continues to post as spartacus123.


     
  5. Violalass

    Violalass New commenter

    Vince and Jeremy, your arguments seem to boil down to

    1. the children must learn something

    2. this is something

    Being able to find the square root of something using an algorithm is also 'something'. Doesn't make it useful. My point is not about difficulty, I don't think children are incapable, I just don't see why they must learn this skill in particular.

    What could they do instead? Basic algebra (properly), basic statistics (properly), plenty else out there.

    Your extension (both of you) to the thought that I therefore don't want 'plebs' educated at all is baffling and just stupid (and does not explain why this skill is vital) but I imagine it's what you've moved on to after 'they should learn it because then they'll be able to do it' didn't work on me.
     
  6. Anonymous

    Anonymous New commenter

    I don't know why you felt the need to mention that.

    And you have got your facts wrong - but don't let a little thing like evidence get in the way.

    I was not banned. I was put on moderation because of an altercation.

    I chose to leave. Want to know why? Because of people like you. Who are incapable of real mature debate but decide to argue and be abusive.

    I am sure this debate will continue. But I am sure people are glad you've informed them of the reason why you think I left (banned you say) and the username as well.
     
  7. bombaysapphire

    bombaysapphire Star commenter

    This is more than something. It is one of the four main operations. We teach pupils methods for addition, subtraction and multiplication which can be scaled up to any size of number, it feels like an omission not to do that for division.
     
  8. Not at all.

    There are 4 fundamental arithmetical operations

    Having given children the opportunity to master three of those, it is natural (for the teacher and the children) to extend this approach to give them a method for mastering the fourth.

    That doesn't mean "test it to destruction" or "force the kids to practise daily"! It's about empowerment, it's about showing that something can be done, it's about allowing them to be creative and practise their number management skills with a limited set of 'ingredients' before you start distracting them with higher level concepts like algebra.

    Frankly I find your comments about algebra and statistics absolutely baffling. Are you really suggesting that 8 or 9 year old children should be trying to do formal algebraic reasoning when their number sense isn't even fully formed typically? One of the big problems I'm seeing at the moment is teenagers trying to do A level Maths and failing miserably because they can follow a rule that says "bring down a power and decrease it by one" but they can't even add 2 fractions together confidently or multiply 2 numbers together!

    It's absolutely vital that the basics are mastered first - then you can move on to the more sophisticated stuff. At the moment secondary school teachers, employers and universities are having to repair the mental damage inflicted on children by generations of trendy primary school nonsense about chunking, thunking, whunking, gridding and other stuff that provides limited and insufficient practice and confidence in number manipulation. Sadly, Primary School teachers don't have to suffer the consequences of their actions - they can just get on with the business of producing drooling simpletons and leave someone else to pick up the pieces.




     
  9. It's a pity that this has turned into an attack on primary school teachers. My experience of what goes on in primary schools these days is quite limited, like most of us in this thread I suspect. I do know however that my local primary regularly sees year 6 leave with a couple at level 6, a couple at level 3 and the rest 4s and 5s. None of them are drooling simpletons. Nearly all of them can add, subtract, multiply and divide reasonably large numbers.

    I don't think anyone suggested starting 8 and 9 year olds on algebra and statistics before the basics are in place.

    Some of those primary leavers move on to secondary school and very soon find themselves being asked to factorise quadratic expressions, solve problems involving compound interest and solve problems using Pythagoras' theorem, before they're halfway through year 7.

    Perhaps the problems of A level students are not entirely the fault of primary teachers.
     
  10. Bensusan

    Bensusan New commenter

    Why not teach a more efficient algorithm for multiplication then?

    1. Multiply the units digit in each number and write the units digit in far right place, tens digit is carried.

    2. For the tens digit, multiply the 10's digit in first number with units digit in other then unit digit in first number with 10's in second and add them together with the carry. Write the unit in the tens place and carry the tens.

    3. For the hundreds digit, you need to repeat 2 for the HxU, TxT, UxH

    4. For the thousands digit, repeat for ThxU, HxT. TxH. UxTh.

    etc.

    This is the method I use for "long" multiplication. Scales up to any size numbers. Uses less paper than long multiplication and gets me the answer quicker.

    If I can do it, then anyone can do it, given enough practice.

    With smaller numbers, I can perform this algorithm mentally.

    So why not this algorithm instead of the traditional long multiplication?

    Going by your previous arguments it fits the criteria for inclusion into a basic skill. It's efficient and it's quick and it can be done by anyone with enough practice.
     
  11. Vince_Ulam

    Vince_Ulam Star commenter



    Why should Primary children learn algebra or statistics? Handheld electronic calculators can easily do these things. It seems you believe that





    Any argument made against long division may be made against any other part of mathematics or arithmetic. Why teach addition, subtraction and multiplication?



    It is not clear what you think is involved in teaching Primary children:





    I doubt that many Primary teachers can even themselves handle the basics of these never mind teach them to children. If long division is too much of a chore for Primary teachers then their practical regard for algebra and statistics does not bear thinking about.


     
  12. Vince_Ulam

    Vince_Ulam Star commenter



    Read the first eight words you which quoted.


     
  13. Vince_Ulam

    Vince_Ulam Star commenter



    Why not? It does not work, that is why not. To be generous, it looks like you may be attempting to parse 'Vedic' multiplication but you have failed. If this is how you multiply for your own purposes then it is to be hoped that somebody helps you balance your personal budget, nor should you be teaching arithmetic in schools, you should certainly not be teaching this rubbish.



    N.B. I think I speak for everyone in favour of teaching long division in Primary when I say that none of us are attacking Primary teachers in general. Speaking for myself, I think that many of them should formally upgrade their arithmetical and mathematical skills.


     
  14. Vince_Ulam

    Vince_Ulam Star commenter



    Please see the N.B. in my previous post.


     
  15. Bensusan

    Bensusan New commenter

    Yes it works, and no it's not a failed Vedic multiplication attempt. It uses my understanding of number, multiplication and place value. It works. lol.

    To get the units digit in your answer, you multiply the units digits together.

    To get the tens digit, you multiply TxU and UxT and add.

    To get the hundreds digit you multiply the HxU, TxT and UxH and add.

    All the while remembering your carry.

    Can't understand why you think it wouldn't work given that it does!!

    It's basically long multiplication but with the addition step incorporated into the multiplication. It requires accurate mental addition skills for 2 digit numbers, but that's well within the capability of most people, isn't it?



    Surely someone of your experience would be able to understand this very simple algorithm?
     
  16. Why the insults? That's no way to behave in a serious discussion.

    The method may not have been described perfectly but it certainly works and is OK for those who can cope with the demands on their short term memory. I wouldn't suggest teaching it in school though.

    I agree that some primary school teachers would benefit from upgrading their maths skills but this is true for some secondary school teachers too.
     
  17. Vince_Ulam

    Vince_Ulam Star commenter



    It is no insult in any kind of a discussion to say that somebody needs help with arithmetic, while serious conclusions can only be reached if all parties understand what is needed and what is at stake.





    The process Bensusan described in algorithm does not work. This is why it should not be taught in school and why it is to be hoped that anyone using it has help balancing their personal budget.





    Yes, although to a far lesser degree than Primary. Secondary Maths departments tend to show more discernment in their recruitment for specialisms than do Primary schools.


     
  18. Bensusan

    Bensusan New commenter

    It does work vInce and I've been using the method for years without a problem. See my follow up post for a clearer explanation of why it works.

    It's not easy to describe numerical algorithms using text in a forum.

    If you still don't understand I might draw you some pictures to help.

    It's an arithmetically sound method, and your lack of understanding of the method is not a sufficient argument for dismissing it as wrong, so be a sensible boy and take a little more time to understand the method before dismissing it as rubbish ;-) because if (as I know) it's not rubbish then you'll just end up looking silly. Lol.
     
  19. Then why use it as an insult?

    I read it, understood it and was able to use it to get correct results. Admittedly I have seen it before so I didn't read in very carefully. Why do you say that it doesn't work?
     
  20. Vince_Ulam

    Vince_Ulam Star commenter

    Bensusan, if you cannot explain a process in words then it has no algorithm.


     

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