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Common Maths Misconceptions - let's make a list!

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

  1. oh nazard - i wasn't griping at you - i was griping at the universe in general[​IMG]
    i thought a circle wasn't an infinite sided polygon, but the infinite limit of an n-sided polygon, which isn't quite the same thing?
    i can do a division sign with the alt 0246 routine on sit-up-and-beg computers, but this laptop number pad and no number lock [​IMG]
    ÷ i've just copied and pasted it from the character map (all programmes - accessories - system tools - there's lots of handy symbols in those there maps) - but i can't tell till ippress 'post' if you'll be able to see it
     
  2. ooh yes - it works!!
     
  3. should have read 'this laptop has no number pad and therefore no number lock' - but you worked that out anyway, i'm sure!
     
  4. What?? Zero is a number; it's not a natural number, but it's a member of the integers, rational and real numbers. The symbol 0 is used as a place holder, but this was a development in notation, and is not relevant to the question of whether 0 is a number. And zero is an even number, given the definition of an even number as an integer which is a multiple of 2.
    As for the circle: well, it's possible to consider it as the limiting case of the n-gon as n tends to infinity, but as ever in mathematics, it's all down to definitions. What is a 'side'? A straight line edge? (then the circle has 0 sides) A continually differentiable boundary? Then the circle has 1 side. What answer would you want the KS1 teacher to give when asked about the sides of a semicircle?
     
  5. Regarding the issue between 'oblong' and 'rectangle', Can I just point out that as a KS3/4 maths teacher I cannot remember the last time I used the word oblong.
    This thread got me thinking, so I had a quick look through the (quite large) selection of textbooks I have on my shelf. Not a single one of them makes reference to an oblong.
    A rectangle is a four sided shapes, whose opposite sides are parallel and equal and all angles are 90 deg, (a special type of parallelogram), a Square is a Regular (all sides and angles equal) Rectangle.
    Why then are they called oblongs in primary school?

     
  6. Not all primary teachers use the word oblong, some only use rectangle unless pointing out it may be called an oblong by some, however oblong is not particularly mathematical.

    Do love writing the word parrallel though, perhaps the people who dress in white coats are coming for me as we speak.
     
  7. oldsomeman

    oldsomeman Star commenter

    trying to remember back to 1959 and before when i was in primary school.....never remember teachers worrying about terminology there.........strange that ......yet we survived all the years!
    I can remember a bit of secondary when we learnt some something about a village in Africa called TOASOHCAH?.......for tangets and co sines?Oh wonder how we managed with decimal log books and anti logs?
     
  8. nick909

    nick909 Star commenter

    I dread to think of the numbers of horrible deaths that must have ocurred as a result of the misconceptions identified in the thread.
     
  9. nick909

    nick909 Star commenter

    *this* thread.
     
  10. Nazard

    Nazard New commenter

    I am not sure "they" are called 'oblongs' much in primary school.
    In my experience the vast majority of Yr 7 pupils believe, wrongly, that a rectangle is a quadrilateral with four right angles, a pair of longer sides and a pair of shorter sides. It is unsurprising that younger children think this is the case, because when they see a triangle during a maths lesson they will receive reassurance that it <u>is</u> a triangle (the teacher will use the word, pupils will be praised for using the word, pupils will be corrected if they call it a 'circle', etc). If they see a regular quadrilateral they will hear it called a 'square'. If they see a non-regular quadrilateral that has four right angles they will hear it called a 'rectangle'.
    The shape that Yr 7 pupils almost all, wrongly, believe is called a 'rectangle' is actually an 'oblong'. If we start calling that shape, correctly, an 'oblong' when the children are very young, then we can introduce the word 'rectangle' to mean "a shape that is a square or an oblong" when the children are older.
    This would help the pupils to avoid a misconception, wouldn't involve any dumbing down and certainly wouldn't involve telling children something that is incorrect.
     

  11. hhhm!
    Looking at the definition of 'oblong' I can certainly see your point, however this does not really address my point that, most secondary texts and exams (in my experience) do not make reference to the shape in question being an oblong, so why is it such an issue at KS1/2?
    For that matter, I do not recall hearing the word oblong used very much to describe such a shape within the wider world outside the classroom - which is what we are supposed to be preparing children for isn't it?
     
  12. CB123

    CB123 New commenter

    Most KS2 text books also refer to rectangle rather than oblong. Im also certain the SATs do too
     
  13. Milgod

    Milgod Established commenter

    Well it isn't wrong though is it. An oblong is a type of rectangle, just like a square is.

    I note that a square is a type of rectangle, just like I say an oblong is. The children know exactly what I mean if I call an oblong a rectangle (as, let's face it, this is the more commonly used term).

    I think some of you are worrying too much about the small things that don't actually matter that much.
     
  14. Nazard

    Nazard New commenter

    My statement is correct! If I draw a square I can all it a 'square' (obviously!), or a 'rectangle'. Most children <u>don't</u> believe it is a rectangle. Most children believe that a rectangle must have two sides that are longer than the other two. The shape with this definition (4 sides, 4 right angles, 2 longer sides, 2 shorter sides) is an oblong.
    The children <u>do</u> know exactly what you mean if you call an oblong a rectangle, because they think (in the very vast majority of cases even up to and beyond Yr 7) that the two words mean exactly the same thing.
    <u>This</u> is the thing that children find difficult.
    I can't speak for anyone else, but <u>I</u> am worried about a misconception that has been held by almost every Yr 7 pupil I have ever taught!


     
  15. cdrr

    cdrr New commenter

    Sorry had to write, this mistake has come up twice now in this tread and if we as adults can't get it correct what chance have the kids got.
    The above should be 1/2, 1:1 and 0.5
    Another post was talking about probabilty and had the following example 1 in 3, 1:3 and 1 out of 3 as all being the same.
    The ratio should have been 1:2
    The poster also went on to state what can be used with probability. They were not quite correct. Yyou can use fraction, decimal or percentage for probability but you never use ratio. All the others are perfectly acceptable. Fractions are usually used as they best discribe the two parts.
    Expanation for the above ratios.
    1/2 or 0.5 split something into two equal parts. Each part is made of one, therefore the ratio is 1:1 The ratio 1:2 is actually denoting a split into two parts, one made up of one equal share and the other made up of two equal shares.
    Ratio can be complicated to understand and if the adults have difficulty, then the students definately will.
    The misconceptions spread further than just with the students.
    BTW I am a secondary school teacher and I am used to having to deal with misconceptions students have with regard to all different areas of maths.
    Sorry if I have offended anyone, that is not my intention.[​IMG]
     
  16. Milgod

    Milgod Established commenter

    Sorry, not to carry this on too long but you are wrong. You were implying that an oblong is not a rectangle. It is. My class are able to handle the fact that an oblong and rectangle don't mean exactly the same thing, even if I don't use the word oblong all the time.

    Once you have told children about a square being a special rectangle then there isn't too much need for the word oblong. You could even talk to the children about an oblong and tell them it's an old fashioned word that isn't used much anymore.
     
  17. Nazard

    Nazard New commenter

    Nope. I stated that:
    How about if I rephrase like this: The vast majority of pupils believe that a rectangle means the shape has to have two longer sides and two shorter sides (and 4 right angles). While all of the shapes that fit this description are indeed rectangles, the word rectangle also includes another set of shapes. Confusingly, for young children who are used to having a single word for all other shapes, they can call a square a 'square' or a 'rectangle'.
    Here's another way to rephrase it: The vast majority of children think the words 'oblong' and 'rectangle' are interchangeable.
    I am trying to suggest two things(*): (1) that it is a common misconception for Yr 7 to believe that squares are not rectangles and (2) that I fully understand why they have this misconception (all other shapes have a single name, etc - see my previous posts ...), so why not help 5 yr-olds out by using a word that means what they want it to mean, is correct and doesn't lead to misconceptions?

    [ (*) but obviously not doing a very good job of it ...]
     
  18. The problem with this approach is that the shape names for quadrilaterals do not describe disjoint categories. For example, a square is also a special form of a rectangle, a rhombus, a parallelogram, a kite, and a trapezium. A rhombus is also a parallelogram and a kite, etc.
    I think it is better to introduce the names rectangle and square at KS1, mention that a square is a special rectangle, and then in KS2 focus on why this is by looking at the defining properties of the shape names.
     
  19. Milgod

    Milgod Established commenter

    A square is not a type of kite or vice versa. It is also not a type of rhombus. Kites don't have any parrallel sides.
     
  20. Nazard

    Nazard New commenter

    A rhombus is a 4-sided shape that has four equal sides. The size of the angles is not mentioned. Therefore a square is rhombus that also has 4 right angles.
    A kite is a 4-sided shape that has two pairs of equal sides, where the
    equal sides are joined (rather than being opposite, as they are in a
    rectangle). A square, as well as being a special rectangle and a special rhombus, is also a
    special kite. [The reverse is not necessarily true - the only kites that
    are squares ... are actually squares!]
     

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