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Common Maths Misconceptions - let's make a list!

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

  1. What are your thoughts on rectangle versus oblong? A square is a special rectangle but an oblong always has adjacent sides of different length.

    I think it is acceptable to say 'lots of' for multiplication as well as thinking of it as repeated addition.
  2. I usually ask the children regarding the above: IS it the same to divide 9 bars of chocolates between 3 kids or 3 bars between 9 kids? When do they get more chocolate to eat?

  3. I think you have to introduce and discuss 6 lots of 8 and 6 8 times to show their relationship and why you'll still get the same total even though each requires you to do something different. Very interesting to hear that 'lots of' helps with later algebra, and it would. Arrays offer a brilliant visual/iconic image to show the difference between the two and why there is the same total.
  4. Nazard

    Nazard New commenter

    I would much prefer pupils in KS1 to use the word 'oblong' where they currently use rectangle.
    I assume that many pupils, when getting to grips with the names of
    shapes in Foundation/Y1/Y2 understand that:
    • this round shape is a circle - it can't be called a triangle or square, etc
    • that three-sided shape is a triangle - if I call it a circle or a rectangle then it is wrong
    • that space where the classroom door is open, it's called a rectangle - if I call it a square or a circle then I am wrong.
    But I betcha that <u>no-one</u> at that level would then go on to say: "hey, but this shape with four equal sides and equal angles can't be called a circle or a triangle but it can be called a square or a rectangle." !
    Children at that stage need to be able to distinguish between the shapes. Call it an oblong and then they can. Later, introduce the word "rectangle" as the set of shapes that are either squares or oblongs (the union of the two sets, if you like).
  5. using 'rectangle' as synonymous with 'oblong' is just WRONG - why set kids up with an untruth?
    would you say 'plant' is synonymous with 'vegetable' just cos it's simpler and cuts down the number of words/concepts?
    i need a good night's sleep [​IMG]
  6. The problem is that these children are not taught only in school. They will hear the word rectangle used outside school, and if asked we have to agree that that is right ("yes, that's an oblong rectangle"). We get into further difficulties because oblong is an adjective (elongated), and can refer to an ellipse, although that is not a likely usage in KS1.
    Personally, I think we should use both terms, and later on in KS2 use the mathematical definition to clarify that we have oblong rectangles and square rectangles, both being complementary subsets of the quadrilateral rectangles. (and then we get my MAT Y6 last year who asked about rectangular triangles - and yes, they exist)
  7. I knock on the IWB and say, 'Knock next door and borrow one' even in year 6 in my efforts to teach to different learning styles and Multiple Intelligence profiles, and have to say none of the KS2 students have yet struggled with the notion of not paying back to digits on a board or page, but I think the metaphor and action helps some.
  8. Be careful sum means addition, what is the sum of 9 and 3.
  9. Nazard

    Nazard New commenter

    I am not suggesting that for a moment. Sorry I wasn't clear in my previous post.[​IMG] I'll try to do better this time:
    I believe that young children are likely to associate a single name with a shape. When referring to the colour of a particular set of shapes in their classroom there is a single right answer and all the rest are wrong (it's either yellow, or it's red, or it's green, etc, but it won't be all of them at once).
    For the actual shape, every other situation has a single correct answer. It's a circle. It's a triangle. Etc. The only awkward name is 'rectangle'.
    Most pupils I teach in Yr 7 (and above) believe that a shape called a 'rectangle' has two equal shorter sides and two equal longer sides (and 4 right angles too). What they are calling a 'rectangle' is actually an 'oblong'.
    I am suggesting that we teach young children to call this shape (4 right angles, two shorter sides, two longer sides) an 'oblong' - which is correct. They won't be making any mistakes then. Later, when they are ready for the idea that a 'rectangle' means a 4-sided shape with 4 right angles, we can introduce that word.
    I hope that is clearer!
  10. Surely continuous data should be temperature or speed etc where any point has a value?
  11. My pet hate is teachers (and text books) which teach area and perimeter together. The only message the kids get is that for one you have to "times it" and the other you have to "plus it". They usually have no concept of the idea of area as a separate entity from linear measurement.
  12. gitmath

    gitmath New commenter

    (And Reedle) Thank heavens someone pointed that out!!
  13. One of my colleagues has also been compiling such a list for her Maths specialist teacher qualification.
    I asked my Year 3 pupils what a fraction is. The response was interesting.
    "It's something you move the table."

    I questioned the respondant further.

    "Well, when you say could we please move the table back a fraction, we do it"

    and that's after one bite at the new maths framework, let's hope the next session is more successful!
  14. I completely agree with you!
    I even dared to voice this opinion to an advanced maths teacher, but was put down in no uncertain terms.
  15. Just what, in your opinion, IS an acceptable way to refer to probability?
  16. Off topic
    It will be interesting to see how much longer the obelus (&divide;) will remain in use given the difficulty of access on computer keyboards compared to the slash ( / ). I notice that the calculator supplied on my mobile phone uses the latter.
    If you need to type an obelus without using a Symbol lookup, then (in Windows) holding down Alt while typing 246 on the numeric pad will display &divide; on releasing the Alt key. (It must be on the numeric pad - using the keys over the alpha pad will not work.)
    Ooh! An &divide;, how quaint.
  17. Two that particularly annoy me ....
    <ol>[*]"A circle has one side" (KS1 teacher) ... no it doesn't! It has infinitely many and belongs at the end of the sequence of regular polygons, rather than at the beginning (nicely illustrated by the mirror trick - know it?). There are child-friendly ways of putting this, or leaving it as a possibility to discover later.[*] "Is 0 and odd or even number?" (KS2 teacher) .... 0 is a placeholder, NOT a number.</ol>(If you need to bump up your liste, there are several books with ready made lists of children's errors and misconceptions in maths, many of which survive into adulthood and make it into the staffroom ... e.g. "Children's Errors Mathematics: Understanding Common Misconceptions in Primary Schools" edited by Alice Hansen and "Children's Mathematics 4-15: Learning from Errors and Misconceptions" by Julie Ryan & Julian Williams.)
  18. Please use "sum" to represent addition not subtraction


  19. I am a little torn with this post. I agree to an extent that being ale to do it might be enough but at some point you will need the conceptual understanding.

    I have taught adults for the last 8 years or so and have to undo the rules they apply blindly that they remember from school with no understanding as why they are doing it. Case in point being the zeros example not working with decimals.
  20. Nazard

    Nazard New commenter

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