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Pie Chart Misconceptions

Discussion in 'Mathematics' started by noodledoodle, Dec 20, 2008.

  1. Hi
    I am in the middle of my PGCE, for my next assignment I have to write and teach a scheme of work. As part of the write up I have to comment on the misconceptions held by students about the topic and also ensure I address these within teaching the subject.

    My topic is Pie Charts, I have searched the internet for common misconceptions but not coming up with a huge amount of information, could any of you let me know of misconceptions you have come across when teaching this subject previously.

    I am teaching a year 9 set 4.

    Many thanks

     
  2. I know you're looking at secondary, but this very useful book for primary may offer some pointers for you. hope it helps.
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    <tr id="ctl00_content_trw_Title">
    <td class=">
    <h2>Children's Errors in Maths: Understanding Common Misconceptions In Primary Schools</h2></td></tr>
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    <tr id="ctl00_content_trw_ISBN">
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  3. tafkam

    tafkam Occasional commenter

    Pie Charts is a very precise topic. Does it not form part of a wider data unit?

     
  4. maths126

    maths126 New commenter

    Drawing pie charts - students often forget to convert frequencies to angles. A good way to prevent this is to consider the pie chart as a whole split up into fractional parts. Commonly these sectors will be drawn in advance. For example, a circle with four equal sectors, or ten equal sectors, even 20 equal sectors. If your class size is 28, provide the students with several pie charts with 28 sectors pre-drawn (Excel can do this easily). Students can then colour in enough sectors to match the class survey ("The green sectors show the students who walk to school" etc.)
    Angle measuring - when you come on to calculating angles, be aware that many students will have physical difficulties doing this accurately, not least because of the perennial confusion between one angle scale and the other. The successive errors are likely to compound as they go round the circle, leaving the last sector very inaccurate. One way to prevent this is to use 360º protractors, and prepare a "cumulative angle" column before drawing the chart. For example, rather than draw 43º followed by 36º, show these as 43º and 79º before marking them on the chart.
    Interpreting the pie charts - a common idea tested in the old KS3 tests was the conceptual understanding between NUMBER and PROPORTION. Questions of the type "Mary's sector is bigger than John's sector. Mary says this shows more people in her class like sprouts than the number of people in John's class. Explain why Mary is WRONG" (based on the fact that John's class is twice the size of Mary's class).

     
  5. A huge annoyance to me used to be that other subjects (ok, geography) used to always use percentage pie charts. They were taught to multiply the frequency by 3.6, but had no understanding of why they should do this.

    They then carried back to maths class that ALL pie charts should be multiplied by 3.6 to find the angle. Grrrrrrr.

    Thankfully that doesn't happen now (but probably more because Geography doesn't really DO pie charts anymore rather than wonderful across the curriculum collaboration!).
     
  6. It is part of a wider topic of data handling butfor my asignement we have been recommended to focus on a smaller topic, the SoW is for 6 lessons. We are doing concept of pie charts, how to draw them, read data from them, collecting real data outside of the classroom, ICT and an assessment.

    Given the skills at drawing scattergraphs we have just done the drawing part will be torturous!

     
  7. Thanks manon and Math126, loads of useful things to consider for this piece of work and within my planning of the lessons.
     
  8. Can't compete with the completeness of 126's post .... but the interpretation misconception he identifies is the key - students assume that a bigger slice in one pie chart means a greater frequency that a smaller slice in another pie chart.

    One lesson that I use to try and overcome this is a card matching activity where I have several cards with pie charts on, several frequency tables and several bar charts. There are the same number of each but, teh sneaky bit, is that they do not match up 1 to 1 to 1. I have designed them so that some pie charts match with more than 1 frequency table and bar
     
  9. sorry - hit post while sneezing!

    [continues]

    chart. Once pupils fathom this I get them to draw their own multiple 'possible' frequency tables/bar charts for the unmatched pies.
     
  10. Maths_Mike

    Maths_Mike New commenter

    If they are the same area of sector then they should infact represent the same frquency. It is the AREA of the SECTOR not the ANGLE that actually should represent the frequency (as in the difference between bar charts and histograms.



    Therefore to suggest that 2 circles the same size represented classes with differing numbers of pupils would be wrong. Just something you need to be aware of.
     
  11. Maths_Mike

    Maths_Mike New commenter

    so from maths 126 post he maybe should have said the angle is bigger which would not necessarily indicate more students for the reasons he elluded to, but if the area was bigger then infact it would!
     
  12. Maths_Mike

    Maths_Mike New commenter

    so from maths 126 post he maybe should have said the angle is bigger which would not necessarily indicate more students for the reasons he elluded to, but if the area was bigger then infact it would!
     
  13. I know in GCSE Stats they have 'comparative pie charts' where the total area of the circle represents the total frequency of the population (and hence you can compare frequencies directly between 2 different pie charts by finding sector areas).

    I have always treated comparative pie-charts as a more sophisticated use of the core pie-chart principle - whereas, I think, that Mike is suggesting that pie-charts (at GCSE where total frequency is not explicitly related to pie radius as they only occur one at a time) is actually just a 'simplified' version of pie charts.

    There clearly is an important difference between these statements as I was thinking that my pie charts were 100% legit but that you could do some clever stuff beyond them to make them even more useful whereas, if Mike is right (and I have no reason to doubt him) then I've been teaching a "fix" previously which I don't like.

    I think I'll have to do some extra homework!


     
  14. ian60

    ian60 New commenter

    I've never really liked a pie chart on its own, it does not show as much information as a bar chart or histogram, and I'm not sure that comparative pie charts are that much better.

    Has there been any work on how well we perceive differences in area as opposed to, say, differences in height?
     
  15. But in the questions it does state that the numbers are different. Students are expected to recognise that pie charts show proportions,and this is a difficult concept to understand.

    There is also no way of showing a frequency of zero, except by default. There may also be a problem with rounding so that the angles do not add to 360 , this can lead to a discussion on do we always round up on xx.5? Pie charts (albeit percentage ones) in papers often mention this.


     
  16. maths126

    maths126 New commenter

    The questions I had visualised when I wrote in my previous post were:
    • Comparing insects found on a beach before and after a clean-up operation
    • Comparing trees in a wood before and after a disease killed a lot of them off.
    • (Can anyone please give year and tier on these two?)
    I think the KS3 question did admittedly draw them to the appropriate size, but since this was not a GCSE Stats question there was no suggestion about them being comparative pie charts. It really was a test simply about whether the student knew the difference between frequency and proportion.
    Sorry if that part of the post was unclear and thanks to those who picked it up.

     

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