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After all these years why don't they know........

Discussion in 'Mathematics' started by Maths_Mike, Mar 11, 2011.

  1. Maths_Mike

    Maths_Mike New commenter

    I cant understand the obsession with the grid method. Yes it is nice for algebra and can be linked to area of rectangles but I really dont think it has any benefits for long multiplication.

    I mean 243 x37 grid methods requires you to understrand that this is the same as (200+40+3) x (30 + 7). You still need to know your tables and then you makes mistakes with too many (or two few zeros) and with your adding up cos you dont keep the digits lined up.

    How is it any better than the "traditional" method - i.e 3 x 243 = 30 x 243?

    Sry - i get the benefit of undertand different methods and the link to algebra but algebra can be explained by linking to areas of rectangles any way.

    I just dont get it tbh
  2. Maths_Mike

    Maths_Mike New commenter

    How is it any better than the "traditional" method - i.e 3 x 243 + 30 x 243?
  3. I think there are two driving forces here in determining what is a good method.
    The first and most important is; Is it connected to a core primitive structure in mind of the student. So what I'm saying is; Can they clearly picture why the method they are using works? If so they will be able to regenerate or reconstruct that method when they forget it.
    Too many methods are transmitted as algorithms in ways which mean that students have not discovered those core structures and built their maths on it. So when they forget, they forget.

    The second it - is the method widely understood by the community around the child. Hence it's a good idea to ensure there is a calculation policy in place and that future teachers understand what previous teachers have done.

    So it ain't waht you do, it's the way you do it.
  4. anon2799

    anon2799 New commenter

    You make a good point.

    Yesterday I was chatting to the head of our huge secondary feeder, very experienced guy.
    He's also an ofsted inspector now (but we still speak to him) - he's recently been involved in primary inspections and it has really opened his eyes to what our expectations are and to what children are capable of.

    So much so that he is sending all his pupils over the next few years to spend a whole day in primary, to see what and how we teach, and just how much the children are capable of.
    He said he thinks the staff at his school "baby them".

    Ithink this will be an excellent way to start a dialogue with primary colleagues, a 2 way process, kind of ; this is what we do, what can we do to make it better, and how can it be continued and built upon without the usual dip,

    Possibly the first decent thing to result from ofsted.
  5. Lou
    Retention is shocking. Thats why I favour wrote learning and to distance numeracy from maths
    I dont think the grid method is better per se.
    Anecdotally its easier to teach as the requirement to fill boxes is more explicit than kids remembering the order of which numbers they are multiplying and using place holders
    My Y11s who are C/D border students certainly cant do either long mult or division, heck most cant do 'the freaking bus stop [​IMG] 'method. Unless its an integer answer (which they have had two or 3 stabs at) then "Its not a real number"
    Part 2 on the anecdotal front.......watch the MENA/EAL kids (who have just arrived) when you are teaching the grid method with a year 10 group [​IMG]
    They have already knocked out their long multiplication.......why?.......how? ...
    They are drilled at primary school...........
  6. Ahem

    I will re-iterate my oft repeated comment ... grid method - hate it and almost never teach it
  7. Raising numeracy standards eh? You might want to think about removing their surgically attached calculators for a year or two using non-calculator material. It's always seemed perverse to me why you would teach long multiplication, for example, and then hand the pupil a calculator.

    Actually we took the drastic step of introducing a 'No calculator' policy in Maths in year 7 so that we could concentrate on improving standards of basic numeracy and mental arithmetic. However, the LEA has now introduced annual testing using NFER tests, half of which are calculator questions, so we had better re-introduce them so that our students get the practice. You can't win!
    For those students who are prepared to do it, I find the grid method the most succesful. There are some kids who think they are too bright to use it who can't do long multiplication because they insist on using other methods - most of which demonstrate no understanding of place value. I suspect that most overseas students can do long multiplication because they are far more ready to follow instructions (an algorithm) than our pupils, who seem to question everything they are taught.

  8. afterdark

    afterdark Occasional commenter

    For me the problem is lack of retention amongst the student population. This varies from as a short as 10 mins ago to last year etc.
    I find it bizarre that children can and do segment their view of the world to such an extent that they make little connection between any 2 things.
    Why don't they know is probably an incomplete question.
    Better questions, for me, would be...
    Why do they no longer know their tables?
    Why do they forget so much?
    My current bane...
    Despite starting the lessons day after day with mental multiplication I have a year ... set who get multiplication in context wrong after getting it right in the starter. They were delighted to be shown how to use calculators to 'do' fractions. I am now trying to get them to remember to bring their calculators to school....

  9. The methods students use may involve:
    - know facts
    - algorithms
    - strategies based on robust flexible structures (primitives structures).
    So for example in division,
    to do 16 divided by 2 you may
    - just know the answer
    - us an algorithm like the bus stop method (algorithms usually apply to numbers not structures).
    - use a structural primitive, which for division is likely to be either splitting (16 things split in to two parts gives 8 things in each part) or chunking (there are 8 lots of two things in 16 things so the answer is 8).

    Whatever algorithms students learn, they are more likely to remember them if the also understand how they are connected to a structural primitive model. The structural primitive model helps them regenerate the alorithm when they forget it.

    So students are likely to remember grid multiplication well if it is well connected to the pictorial thinking behind it (they've done lots of counting and grouping of squares in rectangles as is done in Interact 7). They are likely to remember long multiplication which Mike prefers if they can clearly see how it breaks down into being repeated addition and are fluent in and have ownership of the construction of the algorithm.

    Is that any better? I know I'm geeky. I'm trying..... If it's still not clear please do ask.
  10. I hate the grid method, I never see it working well for students because there is too much scope for making errors. Remembering that eg 20 x 400 = 8000 (and for multiplying a 2-digit number by a 3-digit number, managing 6 such calculations, getting all those zeroes right, and then lining them up accurately to add up all the numbers in the grid - phew!)
    My daughter in Y5 immediately took to long multiplication when I showed it to her, and then last week had to perform 10 calcs using the method 435 x 7 = 400x7 + 30x7 + 5x7, plus an extension of 10 multiplications of 2-digit by 3-digit numbers, for her school hwk. She dragged herself through them using the teacher's preferred method, and got most wrong, then redid them using long multiplication and got them all right.
    I see the view that the grid method is based on understanding, but it's just so complicated to perform and needs organised neat writing etc. Whereas the long multiplication algorithm is not based on understanding but I think it's easier to learn, practise and perform for all abilities of kids. As long as you practise it enough, the algortihm will be there for you to use.
  11. gogojonny

    gogojonny New commenter

    It is a scandal in this country about how we force so many fluffy pretty methods on kids.
    Why can't they do vertical addition, vertical subtraction, short / long multiplication, short / long division?
    Which idiot invented chunking? I hate the grid method also - too much writing needed.
    Once kids master the basics they can tackle anything in Maths. Get that underlying confidence and they are away.
    I could add / subtract by Y2, times tables by Y4, multiplication and division by Y5. Isn't Vorderman meant to be on a task force to bring back some common sense to Maths?
  12. Surely chunking is just long division
  13. Chunking is about grouping objects or repeated subtraction. It gives the same same answer as splitting but it is a different route. Interestingly when two people do long division one may be picturing it as being splitting and another might picture it as being chunking while they're both doing the same thing!
    A third person following the same route may not picture it at all. For them it may just be an abstract algorithm applied to number.

    Chunking wasn't really invented it just kind of exists. Some argue there's a third primitive model for division which is scaling to one but this is harder to describe and use than splitting and chunking.
  14. DM

    DM New commenter

    A primitive model ...
  15. primitive in the sense of brains?
    timewise I would go for Twiggy as primitive.
  16. DM

    DM New commenter

    In the sense of considering smoking cool.
  17. I would love to guide my learner to do sum without using calculators. However, part of my learners' SOW is to learn how to use the calculator to check sum; even when I surfed the NCETM web and aware that it is essential to use the calculator.
    Therefore, I learn that we have to differentiate our learners their abilities towards their numeracy skills. Calculator will be good for the less able learner but it may be used and encourage to those lazy one to work out without their thinking.
  18. With regard to long division v chunking - how do your students cope with polynomial long division at AS level? Ours tend to be horrified that they are expected to be able to do division at all, let alone using algebra! (These are generally the same ones who can't believe they have to <u>learn</u> the quadratic formula.)
  19. DM

    DM New commenter

    Why do they need to do polynomial long division? The research shows that synthetic division is retained better by weak and medium ability students and leads on nicely to partial fractions etc (there is no difference in retention for strong students who are equally comfortable with either method).
  20. Would you like to present a coherent argument as to why it's a good idea Gove ignores his advisory committee on maths education which includes highly intelligent and experienced elected representatives from maths education in favour of a celeb who gets her books written by other people gogojonny?

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