Three student tasks in a bestpractice classroom

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Three student tasks in a best-practice classroom

• Distribution

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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

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We did we want to get to?

• Inference
• Comparing two distributions
• Making a decision, making a choice

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Who we worked with

• Extended mathematics Year 9
• Co-educational
• Motivated, capable students
• Results may not be transferable

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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

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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

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GICSa framework

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

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Murders in Chicago
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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

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1st task Students heights

• Informal formal vocabulary
• Using the GICS framework
• Whole class discussion
• Introduce either side of mean

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Task 1 Students height
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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

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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

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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

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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

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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

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Reaction times - Male and Female students
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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

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A more sophisticated response

• Filter was set confidently
• Rich description of data aggregate
• Conclusion was tentative, cautious

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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.

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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.

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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.

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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.