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Three student tasks in a bestpractice classroom

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Active learning with messy data sets in a context that students can value ... Fathom Time in class and computer lab. Two week program, 4 *50 mins per week ... – PowerPoint PPT presentation

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Title: Three student tasks in a bestpractice classroom


1
Three student tasks in a best-practice classroom
  • Distribution

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2
What does statistics education research consider
best-practice?
  • Data concepts the big ideas of statistics
  • Active learning with messy data sets in a context
    that students can value
  • Culture and habits of enquiry and statistical
    process
  • Technology that allows exploration and
    visualisation
  • Assessment that genuinely measures learning

3
We did we want to get to?
  • Inference
  • Comparing two distributions
  • Making a decision, making a choice

4
Who we worked with
  • Extended mathematics Year 9
  • Co-educational
  • Motivated, capable students
  • Results may not be transferable

5
How did we get there
  • Pre-testing fractions and percentages
  • Fathom
  • Time in class and computer lab
  • Two week program, 4 50 mins per week

6
What we really tried to do
  • Develop intuitions and sense-making
  • Develop ability to communicate their
    understanding
  • Give students an informal and formal statistical
    vocabulary

7
GICSa framework
  • Global
  • Individual interesting data point
  • C Measures of centre
  • S Measures of spread
  • What???? A brief example may help explain

8
Murders in Chicago
9
The three tasks within this study I want to talk
about today
  • Task 1 Students height
  • Task 2 Weighing a small mass
  • Task 3 Reaction times

10
1st task Students heights
  • Informal formal vocabulary
  • Using the GICS framework
  • Whole class discussion
  • Introduce either side of mean

11
Task 1 Students height
12
A less sophisticated response
  • Presented the information as a series of
    disconnected facts
  • Statistics are quoted to an inappropriate number
    of decimal places e.g. 172.308 cm
  • Quote both median, mode and mean height but
    didnt explain which was the better measure

13
A more sophisticated response
  • This graph shows the height of our Maths class.
    In our class the range is 160 cm (the shortest
    person) 189 cm (the tallest). My height is 175
    cm and the average height is 172.3 cm. So I am
    over the average height. The mean is 172.5 cm and
    if we were to go 5 cm either side of that there
    would be 16 students heights, mine included.
    Therefore 88 of the class is 5cm above or below
    the mean. Only 4 students are shorter than 165 cm
    or taller than 180 cm

14
A more sophisticated response
  • Presented the data as an integrated whole
  • Described own height in relation to the data set
  • Used our informal percent either side of the
    mean as an informal measure of spread
  • 30 of students comprehensively described the
    aggregate in this manner

15
2nd task - Weighing a small mass
  • A classic statistical assessment task
  • 3.2, 3.0, 3.0, 8.3, 3.1, 3.3, 3.2, 3.15, 3.2
  • Need to determine the accurate mass of the small
    object.
  • Ask the students how they would do it.
  • Multiple choice response
  • About a 1/3rd students would discard outlier

16
3rd task Reaction times
  • Reaction times of male and female students
  • A raw data set, contained outliers
  • Students needed to interpret the raw data. What
    is reasonable?
  • Describe the distribution using GICS
  • Compare the two distributions

17
Reaction times - Male and Female students
18
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19
A less sophisticated response
  • Left the filter at the default setting
  • Statistics quoted to a meaningless six
    significant figures
  • Student hadnt engaged with data set

20
A more sophisticated response
  • Filter was set confidently
  • Rich description of data aggregate
  • Conclusion was tentative, cautious

21
Processing outliers
  • 23 did not consider the outliers at all, and
    included all the values in the data set.
  • 62 set a filter and excluded one or two outliers
    (1st task only 30).
  • 15 set filter CONFIDENTLY.

22
GICS framework
  • Used grudgingly
  • Hey! Writing about the distribution isnt the
    main gamewe want to know whether males or
    females have the faster reaction time.

23
Comparing two data sets
  • All used the mean or median to compare the two
    distributions.
  • None of the students compared the difference
    between the two means as a proportion of the
    actual means.
  • Students seemed obliged to provide a definitive
    answer i.e. find a difference between the two
    distributions when in fact there was no
    difference.

24
What did they think?
  • Hated it.
  • Didnt want to writethis is a math class!
  • Highly motivated by marks.
  • Maths lends itself to get right answers.
  • Not structuredmake the world simple, they were
    not comfortable with ambiguity and doubt.
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