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Miconceptions with place value/rounding

Discussion in 'Mathematics' started by funkypete83, Jan 9, 2012.

  1. Hi
    I'm doing some research for a MAST course and was wondering if people could share their thoughts on the following:
    - When teaching place value/rounding what are the key things that you expect students to struggle with?
    - What are the implications of this for a Key Stage 3/4 course?

    Just to share my thoughts:
    I expect most students to understand the idea of 5 or more we round up but they cannot apply this between units, tens and hundreds etc.
    I put this down to them being taught a cheap trick at primary school that works in some cases but needs to be better understood in order to apply it. I believe this props up in many areas.

    I believe the implications are students not fully understanding the value of digits in numbers, e.g. 5, 157 not knowing that the 1 represents one hundred.
    This has a knock on effect for column addition, x 10 100 and 1000, rounding to nearest 10, 100 and 1000, rounding to decimal places and significant figures.

    I'm sure there are other areas and would love to hear your thoughts on this and why our students are failing to understand place value.
  2. This is the first year I've come across a tutee, Year 7, who has no understanding of place value. His Dad was so upset about this that he intended to tackle the problem over the Christmas holidays. I'm seeing the pupil tonight so it will be interesting to see how he has progressed, if he's still speaking to me!
  3. PaulDG

    PaulDG Occasional commenter

    The biggest issue I find is that the kids just don't like rounding - they don't like anything that looks like they're not going to get the "right" answer.

    From their point of view, rounding removes accuracy and they're suspicious of it.

    They then fear they're not going in the right direction and their work will be "wrong".
  4. bombaysapphire

    bombaysapphire Star commenter

    I would agree that understanding place value is usually the issue.
    If students can count up in thousands then rounding to the nearest thousand is much more straight forward. The fact that there are tens of thousands and hundreds of thousands seems to cause confusion for some.
    I try to teach my weaker students to read the number out loud before trying to round it.
  5. CarrieV

    CarrieV Lead commenter

    I would agree with PaulDG, it is the thought of "being wrong" that is the major problem when rounding, rather like estimating which my class also hate! They currently see maths as either right or wrong, rounding and estimating don't, to them, fall into either camp!
  6. strawbs

    strawbs Established commenter

    A strange one (but this is teenagers....) I've met recently is :
    Assuming that if they are not told to round, then just "cutting off" the number is absolutely fine
    eg if a calculation gives 2.738432 and says to round they will give 2.74; if it doesn't mention rounding they will give 2.73 because "you didn't tell us to round"
  7. The thought which strikes me is later on, students seeing 1.73205 as being more accurate than "sq rt 3". Similarly, preferring a long decimal than an answer in terms of pi.
  8. strawbs

    strawbs Established commenter

    and preferring decimals (inc rounded) to fractions
  9. PaulDG

    PaulDG Occasional commenter

    It's all part of the same "right answer" problem, though isn't it?

    They know that 1 divided by 2 is 0.5 and they'll get full marks for that answer.

    They're not sure if an answer of 1/2 will get them full marks or if they'll get the question "wrong" as they should have completed the question by doing that final division...

    They have the same fear about Pi. Leaving the Pi symbol in implies they haven't finished the question - and at least at KS3, they're right, aren't they? At GCSE they'd need to be very sure they'd read the question properly (which they don't do) to be certain of getting all the marks...

    (This is one reason why "levels" are such poor indicators in maths - it's not just the case that simultaneous equations are more difficult and require more technical skills than, say, basic addition, it's also the case that understanding both the explicit and implicit elements of any question in order to present the answer in the "correct" way is a huge conceptual leap and above the reading ages/comprehension level of many GCSE candidates. And then there's "functional skills"!!)
  10. I think this sums up most of the problems our students feel they face.
  11. Perhaps students struggle with concepts like place value because they have not been properly estbished doing other tasks that also require a proper understanding of place value - long multiplication and division.
    Other threads have discussed why or why not it is useful to do these "arcane" tasks. In my opinion, they are all part of understanding number and being able to round is another essential part.
  12. When teaching this topic to any secondary class I always make the point that rounding off is something that all pupils can do instinctively at a very high level before I start trying to 'confuse' them.
    I ask the class a series of random questions such as
    How long did you spend on facebook last night?
    How long did it take you to get to school?
    What is the distance to staffroom, town centre, local Town, London? etc.
    The point I then make to them is that in answering these qestions they have automatically assessed the context then rounded off to an appropiate degree of accuracy.
    All I have to do then is confuse them with a series of rules.

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