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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. Vince_Ulam

    Vince_Ulam Star commenter



    I did not.



    If you follow Bensusan's given algorithm, you do not get correct results. In your second post on page six you said that the 'method' had not been described perfectly, that is to say no method of multiplication had been described. You yourself accept that the given algorithm does not work.

     
  2. Bensusan

    Bensusan New commenter

    I described the algorithm clearly in words in a subsequent post once I found time in the day to give it justice. Give it a read and let me know how you get on. As I said, I'm prepared to give a visual description of the method if it helps you to understand this simple algorithm.
     
  3. The method was recognisable. The method, which I recognised, works.

    What's wrong with the word "method"?
     
  4. Vince_Ulam

    Vince_Ulam Star commenter



    Bensusan suggested teaching his explicit algorithm to children as a method of multiplication. You may recognise what he intends, but how do both you and he expect children to recognise a method of multiplication they have not yet learnt? They have only your instructions - your algorithm - to guide them.





    A method of multiplication produces correct results. Not every process produces correct results, as many children's exercise books testify.


     
  5. Bensusan

    Bensusan New commenter

    But how can you say an algorithm that has been used successfully by many people is wrong? It works. I use it to get quick results. Others have too. The longer you take to accept this the more ridiculous your stance looks.

    But that aside, the point of stating the algorithm was to illustrate that an algorithm without an understanding of the ideas involved puts a lot of people off. Your response just confirms that.
     
  6. Vince_Ulam

    Vince_Ulam Star commenter



    An algorithm must specify every step needed to achieve the desired outcome. Your algorithm does not outline the steps needed to achieve multiplication.




    You gave the algorithm as an 'efficient' method of multiplication to be taught to Primary schoolchildren. It is no such thing.



    The point of an algorithm is to circumvent understanding. An algorithm for making a cup of coffee does not require understanding of agriculture, dairy farming, economics, fluid dynamics. thermodynamics, electrical engineering, metallurgy or ceramics.


     
  7. Bensusan

    Bensusan New commenter

    Because I had limited time to do that. You try writing out the algorithm for long division using text, post it here and see how that works eh? Like most taught algorithms, a teacher will demonstrate the algorithm on the board rather than write up a generic set of instructions on the board, right?



    I simply asked WHY NOT teach the algorithm? Is it any more difficult than long division? If you like long division for its efficiency, then why not appreciate this algorithm for ITS efficiency? You seem to be confusing rhetoric for statement of fact.

    If a pupil in primary school can do long division, then there is no reason not to expect that same pupil can follow this algorithm. All that the pupil needs to be able to do is multiply within the tables and add some numbers. Is that MORE difficult than trying to see how many times 56 goes into 464? Explain why you think that ALL pupils should be able to follow the long division algorithm to divide by a 2 digit number, yet NOT be able to follow this simple algorithm for multiplication. Don't simply STATE that they cant do it. EXPLAIN WHY you think they wouldn't be able to do it.
     
  8. Vince_Ulam

    Vince_Ulam Star commenter



    Then you admit that your algorithm does not outline the steps needed to achieve multiplication. Well done.





    No, the first line of the post where you introduced your algorithm, your first on page six, claimed it was 'a more efficient algorithm for multiplication'. In reply I pointed out that it is not an algorithm for multiplication. You have accepted this in the last point to which I responded, as you can see above. Do you know what 'efficient' means?



    I have. Your algorithm is not a method of multiplication. No special mathematical knowledge is required to account for this, no understanding of number or category theory. If the steps of your algorithm are followed as you have given them, they do not work.



    The overarching problem here is that there are some primary teachers who cannot carry out basic arithmetic &or explain how to perform it.


     
  9. Bensusan

    Bensusan New commenter

    Whether you understand it or not, my post was RHETORICAL in nature. It put forward for sake of argument an algorithm which was just as easy for pupils to cope with as long division and I wanted to find out if there was any reason why it shouldn't be taught.

    The reason for doing that was to point out that the same reasons you give for arguing AGAINST using the algorithm would be similar to the reasons that others give against using the long division algorithm. But you knew that, didn;t you, which is why you tried to deflect away from what I wanted you to answer.



    As for your lack of understanding of the method, does this help?

    [​IMG]



    Perhaps now you can explain why you think that this method is

    (a) inefficient

    (b) unsuitable for primary children

    (c) rubbish

    yours, lolster ;-)
     
  10. Bensusan

    Bensusan New commenter

    If you can't understand the above diagram, I know some primary teachers who could maybe do a video for you or something? Just a thought.
     
  11. Vince_Ulam

    Vince_Ulam Star commenter



    I have no doubt that children can follow the steps you gave in your first post on page six, as reproduced from that post below, but this would not allow them to multiply correctly. You said plainly that these steps were 'a more efficient algorithm for multiplication' so you should not be surprised if people take you at your word.





    You are tying yourself in knots. You have already admitted that your given algorithm, reproduced below from your first post on page six of this discussion, will not work. Now, moving on to your image:





    This is 'Vedic' multiplication. Skip back to my fifth post in page six of this discussion, in response to your given algorithm there:





    Now read your response, in your second post on page six:





    Bensusan, the algorithm you gave in your first post on page six:





    Does not describe the process you followed in your image. If we follow your algorithm 56 * 78 = 868. I suppose I must tell you that this is not the correct answer.



    As to the merits or otherwise of Vedic multiplication, these are irrelevant. The algorithm you gave and have been defending for hours was a failed algorithm for Vedic multiplication - as I pointed out hours ago - therefore wrong, inefficient, unsuitable for Primary schoolchildren and rubbish.



    As I said, also in my first post on page six:




     
  12. Bensusan

    Bensusan New commenter

    You seem to twist my posts to fit your own twisted, unbending refusal to back down when you know you have no real way to defend your stance. I explained that my initial description of the algorithm was rushed and fixed it so that it was clearer for you yet you still refer to the flawed one as if the subsequent improvements have no effect on your opinions. I've demonstrated that the method works and asked you the simple question WHY DO YOU THINK A PRIMARY PUPIL WOULD NOT BE ABLE TO DO THIS. You still haven't answered it.
     
  13. Bensusan

    Bensusan New commenter

    Oh and if it IS vedic multiplication (didnt realise it had a name, I just remember the algorithm) then it must be a valid and reliable method for multiplication rather than, as you so thoughtfully said "RUBBISH" lol
     
  14. googolplex

    googolplex Occasional commenter

    The only comforting aspect from the latest skirmish in this ridiculous debate is that, unlike the previous battle from around 3rd Feb, it has taken place during the half term break and, hence, outside of the working day. It follows, this time, that the kids presumably aren't missing out. Quite what was going on earlier in the month, and what your bosses thought they were paying you to do at the time, who knows...

    Really, both of you, bang your heads together in shame...
     
  15. Vince_Ulam

    Vince_Ulam Star commenter


    [​IMG]
     
  16. Vince_Ulam

    Vince_Ulam Star commenter



    Yes, I use the occult practices of reading English and the ancient mysteries of keyboards to respond forensically to the stuff you have actually posted e.g. you might like to try some English yourself and work out how something can be simultaneously twisted yet not bent.



    My position on long division is uncontroversial.





    Both your first and second posts on page six of this discussion give the same algorithm. You build to n columns from the right but neglect to reduce from the right after reaching n. It fails as an algorithm for multiplication.





    The method in the image is not the algorithm you gave.





    Some are able to handle the trick of Vedic multiplication but few retain it as a method, finding it difficult to cross multiply and keep track of all the partial products and sums. None should be given your failed algorithm for Vedic multiplication as it does not result in correct products.


     
  17. Vince_Ulam

    Vince_Ulam Star commenter



    It has several sources but Vedic is the name best known.



    I said that it was your 'failed algorithm' for Vedic multiplication which was rubbish, not the method itself. You may check the post again if you do not believe me, it is my fifth on this page.



    The method itself should not be taught to primary school children because it is a trick - it does not reinforce the fact that multiplication is repeated addition which is what we wish primary children to know. Look at your image - neither 48, 86 or 43 are multiples of 56 therefore it makes no sense to anyone learning how to formally multiply. Conventionally, for the same multiplication, both partial products prior to summation are multiples of 56, as will be their sum which is the final product.



    Vedic multiplication should not be taught to children as a 'valid and reliable' method.


     
  18. Bensusan

    Bensusan New commenter

    Ok your last post makes it clear now what I'd suspected. I came here for serious discussion, whereas you just troll and abuse. I won't waste my time any further.
     
  19. DM

    DM New commenter

  20. Vince_Ulam

    Vince_Ulam Star commenter



    You can't find a bar and get drunk like everyone else?


     

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