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Common Maths Misconceptions - let's make a list!

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

  1. bombaysapphire

    bombaysapphire Star commenter

    I agree. It also fits the properties for a parallelogram & trapezium as already mentioned. Not to mention being a regular quadrilateral.
    I am not expecting all students to enter KS3 understanding this. I do hope that they know that a square is a special rectangle. I don't mind whether or not the word oblong has come into it but I don't use it.
     
  2. Milgod

    Milgod Established commenter

    I would say it depends on what you classify as the properties of a kite. The definition I have read before is that a kite doesn't have parrallel sides.

    Then again, I have also seen a rhombus defined as having no right angles in some books/sites and other references only saying the opposite angles are equal (thus allowing for right angles).

     
  3. I'd be surprised if modern textbooks actually said that. According to Wikipedia, Euclid's original definition of a rhombus excluded the square, but the modern definition does not (see Wolfram MathWorld). I think you may be getting confused with books which have tables of the necessary properties of a shape. In that case, for the property "has two pairs of parallel sides", you would see a tick for a rhombus, parallelogram, rectangle and a square, but a cross for a kite and trapezium. But this does not mean that they cannot have two pairs of parallel sides; when a kite has, it becomes a rhombus as well. It's a challenging task for your more able Y6s to construct set diagrams for the quadrilaterals. For example, all squares are rhombuses; all rhombuses are kites; all rhombuses are also parallelograms - but not all kites are parallelograms (the only kites which are also parallelograms are the rhombuses)
     
  4. Milgod

    Milgod Established commenter

    I'm not getting confused over anything thanks. There are different definitions floating about in books and websites. This is the point many are trying to make. I prefer having more properties that mean a square can't be a rhombus (because of the right angle rule) or a kite (because it has parallel sides). By having more properties you don't as much silly confusion.
    Textbooks don't refer to oblongs much either which I think is a good thing.
     
  5. Milgod

    Milgod Established commenter

    I should add that those are the definitions that my school (well, maths leader) has given to each member of staff to make sure we are all teaching the same thing. I'll try and find out where they sources them from.

    I think these are small issues. The ones about ratio being used for probability are big ones.
     
  6. Can you find me one reputable website or textbook which says that a rhombus, in modern mathematical terminology, cannot have right angles?
    And the confusion is not silly - part of developing skills as a mathematician is working from definitions, and avoiding the trap of assumption. Do you really teach your children that a square is not a rectangle? or that a square is not a rhombus?
     
  7. Milgod

    Milgod Established commenter

    I teach them the differences between a square and a rhombus and tell them that depending on the definition you use sometimes a square is a rhombus. The school would like me to teach that they are completly seperate. All I would say is what benefit does using the inclusive definition have? Surely it makes things easier to use the exclusive definition.

    A square is certainly a rectangle. I don't think that was in doubt.
     
  8. Milgod

    Milgod Established commenter

    I also don't see the problem with placing bars next to each other on a bar chart (discrete data). If anyone can tell why this is needed then I am willing to listen. I haven't heard a good reason yet.
     
  9. Nazard

    Nazard New commenter

    It isn't in doubt. All squares are rectangles. Always.
    Sorry - no. If you are using the correct definition then all squares are rhombi.
    Well they are wrong, I am afraid.
    Um. But you are very happy to use an <u>inclusive</u> definition for a rectangle!
    It would make it easier, but wrong.





     
  10. bombaysapphire

    bombaysapphire Star commenter

    Statistics has rules designed to display data clearly. There are spaces between bars for discrete data to signify that things fall into one value or another. With continuous data a value right at the top of one category could be infinitesimally close to a value at the bottom of the next. The lack of space illustrates that.
    I agree with Nazard in the post above. Those shape definitions might make life easier but they aren't correct.
     
  11. Milgod

    Milgod Established commenter

    There is no other definition for a rectangle. The use of the word oblong is obsolete.
     
  12. Nazard

    Nazard New commenter

    ... and there is no other definition for a kite or for a rhombus. They are inclusive too.
     
  13. Thank you Nazard, that was my point to begin with. :)
    My question was not about whether a square was a rectangle or an oblong or whatever, it was the use of the word oblong. As I said I did not really see why an earlier poster was concerned about her KS2 pupils using the word rectangle instead of oblong because oblong is not used in KS3/4. So was it really an issue?
    I'd prefer KS2 teachers to concentrate on teaching pupils good basic arithmetic skills and avoid passing on the common misconceptions discussed on here, rather than worrying about pupils using the word rectangle instead of oblong.
     
  14. Sorry got mixed up here - my response was to Milgod (Post 141)

     
  15. Nazard

    Nazard New commenter

    And I am worried about 5-year-olds forming misconceptions. They think that rectangles and squares are different. They don't understand that the word rectangle can refer to that-4-sided-shape-with-4-right-angle-and-two-long-sides-and-two-short-sides and that it can also stand for that-4-sided-shape-with-4-right-angles-and-all-the-sides-the-same-length. The 5-year-olds will either get confused, or will claim that the second of these shapes is not a rectangle, but that it is a square.
    I appreciate why they might think that and wish that there was a way to avoid the problem.
    In hindsight I wish I had stopped there. My big mistake was in suggesting a possible solution to this problem.
    I know that the word 'oblong' is obsolete and therefore doesn't get used in any textbooks or at KS3 or KS4. I don't want it to be used at KS3 or KS4. I want 5-year-olds not to learn something that is very, very difficult to undo later.
    That's all.
     
  16. oldsomeman

    oldsomeman Star commenter

    Does all the arguement about the properties of shapes really matter?
    I would suspect most folks never get beyound basic definitions,or even care to try.Only the puritians care.......the rest of us dont.
    I understand its need if you are interested in maths,but i assume the vast majority are not(beyound maybe able to work out their wages).When teaching maths in Primary i an happy if they can firstly understand basic shapes and then understand some properties of those shapes..........its rare we get time to define,discuss or deliberate upon higher shapes and forms.
    This is not to say maths is not good,,or indeed to be able to take it to higher levels ...just lifes realities is that 50% of what we learn in most of our education is not always useful in real life,even if it might be in accademic circles.Yes it pushes the brain and develops some understanding(hopefully) but would kids really care?

     
  17. And when I was at school, this definition applied:
    1. Deviating from a square, circular, or spherical form by being elongated in one direction.
    2. Having the shape of or resembling a rectangle or an ellipse.That's what I understood by 'oblong'...Times do change, don't they?
     
  18. A fascinating thread ...
    However, I think the biggest problems are not when the terminology used is misleading because often using different language helps communication, but when what is expected is actually wrong. Let me give you a couple of examples:
    1. Always round numbers ending in .5 up. I understand that examiners mark this as correct except in accountancy exams but as a general principle we should only round .5 up half the time if we want the most accurate estimates.
    2. Providing approximate answers to the nearest 10 for (usually) additions by rounding the numbers to the nearest 10 and then adding.
    This causes the biggest problems for educated parents, so perhaps Maths teachers shouldn't worry because these same parents have to cope with about half the science that's taught being wrong - or at least based on oversimplistic models.
     
  19. My all time bug bear is that the equals sign means...thats where the answer goes !!

    NO !!!

    It means its EQUAL i.e. the same value on both sides of the = sign !!
    (true for adults and children i have found !)
     


  20. We are teachers, we are meant to be pedantic. If you are teaching maths to children your subject knowledge needs to be secure. I'm not saying all teachers need to be 100% correct 100% of the time but we have a responsibility to try to learn and not dismiss people who try to improve our knowledge as puritans.



    I don't spell well and often make grammatical errors, should I start telling the kids that it doesn't matter as they now what I mean? Luckily my students currently look out for my poor spelling and correct it, perhaps I should be telling them off for being puritans.
     

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