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Common Maths Misconceptions - let's make a list!

Discussion in 'Primary' started by Blueowl99, Jun 2, 2010.

  1. Always ensure clear diction,,,,,,student introducing kilograms to class of Y! 'Oh dear! That's mot very nice. It's a bit scarey! Why do they have to call it a kill a Gran?'

  2. Drives me mad too. Especially when they do a long string of calculations..

    3 x 12 = 36 - 4 = 32 x 10 = 320

  3. Don't get too hung up about '='. Those in the computing industry numerically outnumber mathematicians and almost always use = for assignment and == for equality (in the absence of the traditional mathematical equality sign on our keyboards of 3 horizontal lines). In Chemistry = is used to separate the reactants and products in chemical equations (at least in school).
    Perhaps the real issue is that the NC uses = for both assignment (frequently in calculations) and equality (usually only in algebra) when purest would argue that they are different and we shouldn't try to pretend they are the same. It doesn't help that when we use English for a+3 = b - 2 we say 'equals' when we mean 'is the same as' and likewise for a=3 say a 'equals' 3 when we mean a 'is assigned a value' of 3.
  4. It would be great if Primary teachers didnt teach Volume = Length x Breadth x Height...EVER. Not even when it IS correct.
    This has to be the most difficult idea to overcome when teaching volumes of solids, other than cubiods. I know its easy (and lazy?) to do it this way at an early stage but when you have 15 year olds who still insist on randomly multiplying all the numbers on a diagram "'cos thats wot you do innit" its very frustrating.
    For solids with uniform cross sections, its easy to show how the volume relates to the area of the cross section and its height. I'm at a loss to understand why it wouldnt be introduced in this way at an early stage, saving my sanity years down the line.

  5. Andrew Jeffrey

    Andrew Jeffrey New commenter

    I think your great post highlights the problem that exists in what we teach children about mathematics generally.

    We often teach them something that 'happens to work at this level' but which does not hold volume, add a zero, multiplying makes things larger etc).

    This is as much to do with the pressure to get children through tests as anything else, and also the irritating need to 'demonstrate progress'.

    In our current system of inspection it is not important for children to make progress in their understanding - it is important that they can 'demonstrate progress' by 'getting answers right', however they get them.
    Unless all ofsted inspectors are trained mind-readers how can they know that ALL children have made progress?
    Sorry, end of rant. I'll get back in my box now. And contemplate its volume...
  6. jazz2

    jazz2 New commenter

    When did this change? I understood that .5 was supposed to be rounded up? How do you decide when not to round up? If it's "half the time" are you supposed to keep score??
  7. bombaysapphire

    bombaysapphire Star commenter

    As a secondary Maths teacher who also qualified as an accountant I have never heard of rounding up on 0.5 half the time.
    I would guess that this might be relevant in actuarial calculations but by the time a primary student has got to the stage of actuarial training they should be able to grasp the reason for applying a different rule in that case.
    This means that there is no problem teaching students to always round up on a 5!
  8. Brilliant post. HIt the nail right on the head.
  9. TaAPP I understood the three horizontal lines to be 'identity' i.e. applies for something that is always true, rather than equality.
  10. so - you are making a histogram of heights and you want to also calculate the mean height of your class
    what will happen if you round up all the .5's?

  11. Hmm. Calculating the volume of a cuboid was removed from the KS2 programme of study when the National Curriculum was revised in 2000. That said, I'm sure many schools still teach it, and will usually do so by constructing a cuboid with unit cubes, calculating the number of cubes in each layer (and making the link to calculating the number of squares when finding the area of a rectangle), then counting the number of layers and multiplying to find the total number of cubes. This is precisely the way the the KS3 program of study envisages volume of a cuboid being taught: <font size="2" face="Minion-Regular"></font><font size="2" face="Minion-Regular">find volumes of cuboids, recalling the formula and understanding the connection to counting cubes and how it extends this approach.
    So please don't blame primary school teachers for any confusion here.
    (And do you honestly believe that the children you are describing would be less confused if you taught them volume as you suggest? They are the ones who need the practical approach of counting cubes.)
  12. bombaysapphire

    bombaysapphire Star commenter

    I don't get the histogram point.
    Given that height is a continuous variable the chance of any student measuring exactly x.5cm is infinitesimal. A risk I am prepared to take! Not that I think I could measure heights accurately to the nearest mm anyway.
    In that situation would you really suggest to students that you round up on 0.5 half the time? Sounds like a recipe for unnecessary confusion to me.
  13. it's swings and roundabouts, i grant you -a statistician would say round 0.5 up and down to even numbers - that way you round up half the time and down half the time, so if you then calculate the mean, it won't be pushed up by the rounding (well - my friend's dad said so when he came to give us a talk at school - and he was a professor of stats)
    sorry - the histogram was a red herring - duh - i remember now, that is a counter-argument - rounding up and down half the time makes for a rubbish-looking histogram, not a good one
    will go and write a few lines by way of atonement

  14. Hi, Just found this- all very interesting and useful. Am looking forward to 'end'? result.
    I am a Numbers Count teacher and we have been advised not to use the term 'big' and 'small' as this can depend upon the physical size of the number written.
    Especially important in Foundation/ KS1
    There is also a very good reason for representing eg. The 2 x table as
    2x 1
    2x 2
    2x 3 not the other way around.

  15. I am confused- isnt that the point. Physically large numbers are "big"??? Or do you mean the size you write them on the board????
    What is the reason?
  16. This is the reason i've been a member for years and never posted before and wont again after this.
    No blame at all on any teacher who follows the method you describe as it is exactly the way it should be done. Count the number in the first layer ( the x-section) and multiply by the amount of layers (the height) Not just 'times all the numbers you can see together.'
    As for your last comment. Yes they would be less confused if they had the one method that actually works. I think you've made my point for me. It only works for cuboids. Try counting the cubes in a triangular prism or a cylinder and get back to me ...honestly...i'm interested. Hmm.
  17. Apologies if I offended you - that was not my intention. I should have expressed myself more clearly. My point was that the KS3 scheme of work says that children should be taught the formula, V = L x B x H. My guess is that the less able children will only half understand the explanation, and will seize onto the formula - just multiply all the dimensions. That gives them the right answer. Unless your teacher is lucky enough to have the time available to work with small groups of children to check on their understanding, they will just move on to the next topic. The gaps in understanding only become apparent when you attempt to generalise the formula to find the volume of a prism.
    Well, you can do it for a right angled triangular prism, and I would use the multilink cubes and half cubes to demonstrate this if working with a group that needed practical support. I agree with you in principle - we should strive as teachers to make sure that children understand why a formula works, and not just teach the formula. But I got the impression from your initial post that you would rather the formula was never taught.
  18. As promised, just a few months late...[​IMG]
    I've uploaded a sample powerpoint to use in a staff meeting to support TA staff with their support of KS1 and KS2.

    <h1>Staff Meeting PPT on common mistakes MADE BY STAFF in resources
    This idea basically stemmed from the idea of supporting TA staff in our school (who are wonderful of course) but whom have had very little training or input on how to support maths. This isn't an attempt to train staff to identifying misconceptions in children or discuss more detailed areas of that staff might have misconceptions.
    It is designed to be delivered in a brief staff meeting to highlight some key areas, with the idea that staff perhaps can discuss other common misconceptions and support each other with this initial staff meeting as the jumping off point.
    Any comments or glaring omision or mistakes, please let me know in the comments on resources.
  19. That sounds really interesting and I would like to see it. I searched for 'Staff meeting PPT on common mistakes made by staff' in the resources section but could not find it. Any suggestions/Whats the best way to find it?


  20. click on' Blueowl199'ss name and scan down his? her? resources
    wrt to the shapes slide - the not-a-diamond is a square on its side - i have seen this done in practise, which is why it grates - it means there are 2 separate areas for confusion here - referring to a rhombus as a diamond, and calling a square a diamond (or even a rhombus - yes, i know it is, but we classify it rather than call it that) because it's been rotated

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