Title: Three student tasks in a bestpractice classroom
1Three student tasks in a best-practice classroom
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2What 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
3We did we want to get to?
- Inference
- Comparing two distributions
- Making a decision, making a choice
4Who we worked with
- Extended mathematics Year 9
- Co-educational
- Motivated, capable students
- Results may not be transferable
5How did we get there
- Pre-testing fractions and percentages
- Fathom
- Time in class and computer lab
- Two week program, 4 50 mins per week
6What we really tried to do
- Develop intuitions and sense-making
- Develop ability to communicate their
understanding - Give students an informal and formal statistical
vocabulary
7GICSa framework
- Global
- Individual interesting data point
- C Measures of centre
- S Measures of spread
- What???? A brief example may help explain
8Murders in Chicago
9The 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
101st task Students heights
- Informal formal vocabulary
- Using the GICS framework
- Whole class discussion
- Introduce either side of mean
11Task 1 Students height
12A 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
13A 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
14A 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
152nd 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
163rd 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
17Reaction times - Male and Female students
18(No Transcript)
19A less sophisticated response
- Left the filter at the default setting
- Statistics quoted to a meaningless six
significant figures - Student hadnt engaged with data set
20A more sophisticated response
- Filter was set confidently
- Rich description of data aggregate
- Conclusion was tentative, cautious
21Processing 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.
22GICS framework
- Used grudgingly
- Hey! Writing about the distribution isnt the
main gamewe want to know whether males or
females have the faster reaction time.
23Comparing 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.
24What 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.