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Common Maths Misconceptions - let's make a list!

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

  1. As maths co-ordinator, I want to compile a list of misconceptions for a staff meeting - to avoid all that awkward - "cringe - did she just say that?" moments
    So far I collected from some threads -


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    1. Try to avoid
    saying in subtraction - 7-5 = “We can’t take 5 from 7 or you can't take a
    big number from a small number” -
    instead


    “ at the moment we
    are taking away the little number from the big one because we haven't learned
    how to do it the other way yet .


    'Can we take a big number away from a little number?' 'No'


    'why not?'


    'because we haven't learned to do it yet'





    2. Avoid saying -
    add a zero when you times by 10 as this doesn't work when you x decimals

    I want it to be really non threatening for staff and supportive - Will post the final list for all

    Thanks

     
  2. As maths co-ordinator, I want to compile a list of misconceptions for a staff meeting - to avoid all that awkward - "cringe - did she just say that?" moments
    So far I collected from some threads -


    Normal
    0






    1. Try to avoid
    saying in subtraction - 7-5 = “We can’t take 5 from 7 or you can't take a
    big number from a small number” -
    instead


    “ at the moment we
    are taking away the little number from the big one because we haven't learned
    how to do it the other way yet .


    'Can we take a big number away from a little number?' 'No'


    'why not?'


    'because we haven't learned to do it yet'





    2. Avoid saying -
    add a zero when you times by 10 as this doesn't work when you x decimals

    I want it to be really non threatening for staff and supportive - Will post the final list for all

    Thanks

     
  3. inq

    inq

    1: Using the term sum rather than calculation so we hear children saying i can do the sum 3 - 2
    2: that the ratio 1:2 is the same as the fraction 1/2
    3: If you can stop them saying add a zero to multiply by 10 they then move onto move the decimal place right.
    4: that £5.01 and £5.1 are the same amount
    5: That 9/ 3 is the same as 3/9 (can't manage a divided sign on this computer!)
     
  4. Are you talking about childrens misconceptions or the language which staff use when teaching maths?
    If it is the second, from my own experience, I would say the use of the word "sum" can be confusing. It's used to describe calculations, "do these sums" as well as to mean add.
     
  5. Anonymous

    Anonymous New commenter

    How do you make 12?
    1 and 2
    This is what happens in pre school. And with my little boy. Trust me - he is great at using two numbers to make a third but he is getting a bit of a schock now to learn that 1 and 2 make 3.

    Borrow a ten - humm. We aren't going to pay it back.

     
  6. 1/2, 1:2, 0.5
    "all mean the same thing"
    ...
     
  7. Oh yes! This reminded me of another. In mental maths "what is the difference between 14 and 18?" Almost half the answers given related to the fact that one of them had a 4 in it and the other had an 8 - or the spelling!
     
  8. 'move the decimal point' instead of moving the digits
    talking about numbers to mean both numbers and digits

    Calling a rhombus a diamond - i have had months of trying to stop my TAs from using the word diamond and they keep telling that the last teacher thought it was an acceptable term [​IMG]
     
  9. I mean - misconceptions which the adults have and that they pass onto the children - language, concepts etc...

    Thanks so far, I've also been looking for ideas and found


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    3. Is 6 x 8 6 lots of eight ? It should be 6, 8 times to emphasis the repeated addition.
    Although it does the job, teaching the children that 'x'
    means 'lots of' is not entirely accurate because this terminology suggests that
    the calculation needs to be carried out in a certain order and multiplication
    is commutative.




    4. Shapes - To help children recognise Common
    regular shapes,
    draw them
    occasionally upside down, facing a different direction, or just tilted over, to
    force pupils to look at the essential properties? Avoid always drawing a square, right-angled or isosceles triangle
    in the 'usual' position. This will help to support their understanding that in
    maths, there's no such thing as a diamond! It's either a square or a rhombus.
    Hope I got x isn't lots of right - read a recent thread on it and seems to be a whole lotta debate on this issue!


     
  10. tiffster

    tiffster New commenter

    I had a lovely one with a Year 3 class. I drew an 8 and a 4 on the board and asked if anyone could tell me the difference between them.
    A little girl put up her hand and told me that the difference was that one was spikey and one was curly.

     
  11. trinity0097

    trinity0097 New commenter

    I've just been marking loads of KS3 tests, children are learning at some point that it is acceptable to write probaility in any of these forms...
    1 in 3
    1:3
    1 out of 3
    None of these are acceptable, the only thing that is is a fraction and at a push a decimal and at a real real push a percentage!

    Another one that bugs me is diamonds - there is NO such shape as a diamond
     
  12. Might be an obvious one but I've had a student who repeatedly [​IMG] used digit and number interchangably. I'm not a maths specialist by any means but that made even me cringe!
     
  13. Have compiled a little list for a quick staff meeting with whole staff. Let me know if anyone else has any other suggestions.



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    o\:* {behavior:url(#default#VML);}
    w\:* {behavior:url(#default#VML);}
    .shape {behavior:url(#default#VML);}



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    <ol style="margin-top:0cm;" start="1">
    <li class="MsoNormal">Try
    to avoid saying in subtraction (
    7-5) </ol>


    &ldquo;We can&rsquo;t take 5 from 7.&rdquo;
    or


    &ldquo;You can't take a big number
    from a small number
    .&rdquo;


    As you can take 7 away from 5
    = - 2


    Try instead to present it as


    &ldquo; At the moment we are taking away the little number from
    the big one because we haven't learned how to do it the other way yet.&rdquo;









    2. Avoid using &lsquo;add a zero when you times by 10&rsquo; as this doesn&rsquo;t work for decimals


    3.4 x 10 is not 3.40



    Suggest that the children move the digits to the next column
    along (left). This also supports the
    idea of divide by 10 when the digits move the next column along (right). The decimal point never moves - only the digits





    3. Multiplication - Is 6 x 8 6 lots of eight? Rather than use &lsquo;lots of&rsquo; , try
    instead to use &ldquo; it is 6, 8 times&rdquo;
    to emphasis the repeated addition. Although
    it does the job, teaching the children that 'x' means 'lots of' is not entirely
    accurate because this terminology suggests that the calculation needs to be
    carried out in a certain order and multiplication is commutative.





    4. Shapes - To help children recognise Common
    regular shapes,
    draw them
    occasionally upside down, facing a different direction, or just tilted over, to
    force pupils to look at the essential properties? Avoid always drawing a square, right-angled or isosceles triangle
    in the 'usual' position. This will help to support their understanding that in
    maths, there's no such thing as a diamond! It's either a square or a rhombus.





    <ol style="margin-top:0cm;" start="5"><li class="MsoNormal">Language! Sum refers only to addition
    calculations. You can&rsquo;t do a sum
    of 5-3. Instead there are addition
    calculations, multiplication calculations, division calculations and
    subtraction calculations. </ol>




    <ol style="margin-top:0cm;" start="6"><li class="MsoNormal">Formal
    Subtraction - avoid using &lsquo;borrowing&rsquo; from another column - this
    term is confusing, as we won&rsquo;t be &lsquo;paying it back.&rsquo; Use instead the word - exchange </ol>




    <ol style="margin-top:0cm;" start="7"><li class="MsoNormal">What&rsquo;s
    a digit and what&rsquo;s a number? A
    digit refers to the individual number 2 4 5. A number is the whole unit i.e. 345 So a 4 digit number is 4567.</ol>







    These a few errors which can be made, but more detail is
    given on the Count on site - see
    weblink





    http://www.counton.org/resources/misconceptions/pdfs/misconceptions1~22.pdf



     
  14. Agree with much of these. However, for number 6, the primary framework, does actually stipulate to use the terminology 'borrow from the 10' etc For example look under Year 5 Block A Unit 2:

    'The examples below work towards the decomposition method.
    Example: 563 - 248, adjustment from the tens to the ones, or 'borrowing ten'

    Not saying I agree with it but the strategy does direct teachers to teach it.
     
  15. Instead of saying add a zero, because adding zero to anything leaves you with the original number, you can introduce the idea of using zero as a place holder in the ones column which moves everything left by one space...ones become tens, tens become hundreds etc.

    Also emphasize that = means the same on both sides. I caught myself doing the wrong thing today when we were talking about numbers near 100. The question was 97 + 52. I wrote
    97 + 52 = 100 + 52 = 152 - 3 = 149 Clearly they are not equal.

    With the terms digit and number we talk about face value and place value. Face value being the digit and place value determining what it is worth so 4 (face value) can be 4, 40, 400, 4000 etc (place value).
     
  16. Had to convince my class to use methods taught in lessons to solve problems, why? They thought the grid method for multiplying was so easy it had to be cheating! I know this is not strictly on the subject, but amazed me!
     
  17. I am afraid that we will disagree on this one

    How do you intend to teach children WHY we use reciprocals when dividing by fractions if you are not going to start with their understanding of how many unit fractions are in a whole ?
     
  18. Having spent a number of years as a secondary maths teacher and recently moved into primary, I have found some very worrying misconceptions from other teachers. For instance I was told by a member of senior management at one primary school that it did not matter that the bars were joined on a bar graph when the data is discrete, which for the vast majority of data in primary school it is. I had to say to him that it did matter as it is not mathematically correct and was told I did not know what i was talking about as the maths scheme the school was using had the bars joined and they are not penalised in the SATs The SLT member was not a maths specialist!
    The other misconceptions I have heard and seen are the word diamond for rhombus and the moving decimal point.
    Rant over
    Sorry


     
  19. I'm a bit sick of year 7s tell me that I'm wrong when I tell them you can calculate 3 - 7 and that multiplication doesn't always make numbers smaller!



    And don't get me started on diamonds the whole class disagreed with me that day (three different primaries!) - they thought i was crazy with all this rhombus talk...



    Nothing wrong with borrowing in column subtraction, it does get paid back because the left number then "owes" less
     
  20. As an historian I've always my difficulties with maths. I remember one of those Eureka moments when a mathematician friend of mine explained (following my moan that I didn't understand why multiplying fractions made them smaller) simply said 'Well it's language, isn't it? Multiply means 'of'. And suddenly I understood why a half of a third or a third multiplied by a half equaled one sixth. Why had my maths teachers been so sloppy in their use of language?
     

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