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Classroom Activities for Teaching the NCEA Level 1 and 2 Statistical Enquiry Standards

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There is currently a strong emphasis on teaching statistics within the context of the statistical enquiry cycle (PPDAC). This workshop will present a number of engaging activity formats that can be integrated into any statistical enquiry context in order to help students develop the skills required for AS 1.10, 1.11, 2.9 and 2.10. Ready-to-use resources set in particular enquiry contexts will be distributed to attendees as examples, but the main message of the workshop will be how the underlying activity formats can be used to enhance teaching in any statistical enquiry context. See also http://new.censusatschool.org.nz/resource/classroom-activities-for-teaching-the-ncea-level-1-and-2-statistical-enquiry-standards/
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Classroom Activities for Teaching
the NCEA Level 1 and 2
Statistical Inquiry Standards
Katrina McChesney
k.mcchesney@postgrad.curtin.edu.au
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This Session
Quick overview of AS 1.10, 1.11, 2.9, 2.10
Identifying ‘hotspots’
Teaching activities
Main messages:
Teaching, not assessing
Adaptable to different year levels & enquiries
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Statistical Enquiry Standards
AS 1.10: Compare
two population
groups using given
multivariate data
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Statistical Enquiry Standards
AS 1.11: Collect
(numerical) data to
investigate a
bivariate relationship
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Statistical Enquiry Standards
AS 2.9: Select
random samples to
make an inference
comparing two
population medians
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Statistical Enquiry Standards
AS 2.10: Conduct an
experiment to make a
suggestive inference
about an intervention
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For all the enquiry standards:
Achieved: Follow the process; make statements. “It
looks like boys tend to send more texts than girls.”
Merit: Justify what you said for Achieved!
“… because the median for the boys is 110 texts
and the median for the boys is 84.”
Excellence: Critique / evaluate findings. Does the
result make sense? What if …? Other variables
that could be investigated?
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Statistical Enquiry Standards
What are the
‘hotspots’
in these
standards?
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Some Possible Activities …
What ‘hotspots’ could they help with?
How could they be adapted?
To different standards
To different year levels
To address different ‘hotspots’
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Laminated Speech Bubbles
I notice … I wonder
… I worry …
Observations
Describing trends,
comparisons …
Conclusions
Posing questions
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Hedging our Bets
AS 1.10 multivariate data (comparing
two groups)
Common error in posing questions:
“Do Year 10 boys at my school send more
texts per day than Year 10 girls at my
school?”
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Hedging our Bets
AS 1.10 multivariate data (comparing
two groups)
Common error in posing questions:
“Do Year 10 boys at my school tend to send
more texts per day than Year 10 girls at my
school?”
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Hedging our Bets
AS 2.10 experiment
Common error in writing conclusions:
“Listening to classical music reduces people’s
blood pressure.”
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Hedging our Bets
AS 2.10 experiment
Common error in writing conclusions:
“The results of our experiment suggest that
listening to classical music may reduce blood
pressure”
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Hedging our Bets
Brainstorm “hedging” language
Practice writing questions and conclusions that
are appropriately “hedged”
Fix (hedge) given questions / conclusions
tend to
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Hedging our Bets
“Do Y11 girls in our class have lower pulse
rates than Y11 boys in our class?”
“The Y11 girls have lower pulse rates than
the Y11 boys.”
“Doing breathing exercises lowers
people’s pulse rates.”
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Quickfire Contexts
Brainstorming activity multi purpose
Sets of cards with enquiry contexts for L1 /
L2
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Quickfire Contexts
Linking to contextual knowledge:
What would you expect to happen?
Why?
What else could affect the results?
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Quickfire Contexts
Clarifying the requirements of each AS:
What kind of enquiry is this? How do you know?
L1: multivariate or bivariate?
L2: sampling or experiment? (exp type?)
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Quickfire Contexts
Writing suitable investigative questions:
Edit the statements to ensure that the population
groups are precisely identified (2.9, 1.10)
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Quickfire Contexts
Hedging our bets (again):
Edit to ensure that the question is ‘hedged’
appropriately
Write a (fictional but appropriately hedged)
conclusion
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Quickfire Contexts
One for teachers!
For L1, which context/s would your students
know enough about?
For L2, how would you provide the necessary
contextual knowledge?
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Jumbled Write-Up
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Writing Frames
(d)ISCUSS
for 1.10 comparisons / 2.9 inferences
TASGU
for 1.11 bivariate
PEEL / PEER
anywhere!
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Writing Frame: (d)ISCUSS
Initial impressions
What can you see? (Just look – don’t write yet – but don’t miss the obvious!)
Shape
Symmetrical? skewed? uni/bimodal?
Centre
Middle of the data median / mean
Unusual features
Outliers? gaps? bimodal?
Spread
IQR, middle 50%, quartiles, max/min
Shift / overlap
Boxes, medians, higher/lower on scale
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Writing Frame: TASGU
Trend
linear? curved? no relation?
Association
positive? negative?
Strength
strong? weak?
Groupings
any?
Unusual
outliers? change in trend?
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Writing Frame: PEEL / PEER
Point
“In my sample, I noticed that …”
“I can / cannot make a claim that …”
Explanation
“This means that …” (in context)
Evidence
Give values / statistics / refer to details of the graphs
Link (or Relevance)
Link back to population, context (why does this make sense),
expectations (“This was a surprise / I expected this because …”)
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Writing Frame: PEEL / PEER
Point
“In my sample, I noticed that …”
“I can / cannot make a claim that …”
Explanation
“This means that …” (in context)
Evidence
Give values / statistics / refer to details of the graphs
Link (or Relevance)
Link back to population, context (why does this make sense),
expectations (“This was a surprise / I expected this because …”)
Don’t POP in
your PEE!
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Using Writing Frames Ideas
Give students a template
students write for each section
Shared writing / koosh-ball
discussion in pairs / groups,
students take turns giving a
statement for one section (in
order)
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Using Writing Frames Ideas
Give students a (good)
exemplar students identify
(colour code or label) the parts
Give students a (not so good)
exemplar students check for
the parts and fix issues / add
missing elements
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Venn Diagrams
Comparing 2 groups
using 1 variable
BOTH
AS 1.10
Multivariate data
Relating 2 variables
for 1 group
AS 1.11
Bivariate data
Use PPDAC
process
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Venn Diagrams Big Picture
Dot plots /
box-and-whisker plots
BOTH
AS 1.10
Multivariate data
Scatterplot
Use graphs to see
the overall trends
AS 1.11
Bivariate data
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Venn Diagrams Big Picture
Given the data but
not the question to
investigate
AS 1.11
Bivariate data
BOTH
AS 1.10
Multivariate data
Given the question to
investigate but not the
data
Need data and a
question to
investigate
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Venn Diagrams Big Picture
Making inference
about what is
happening back in the
population
AS 2.10
Experiment
BOTH
AS 2.9
Sample
Making suggestive
inference only about
what happened in your
sample
Use sample results to
make an
inference
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Venn Diagrams Other Uses
Sample / population
IQR / middle 50%
Variation within sample / variation between
samples
• …
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Sources & Resources
http://www.nzqa.govt.nz/qualifications-
standards/qualifications/ncea/subjects/mathematics/levels/
https://www.facebook.com/Mathematics-and-Statistics-NZQA-
204205436382307/?fref=ts
http://seniorsecondary.tki.org.nz/Mathematics-and-statistics
https://drdalrymple.wordpress.com/
http://new.censusatschool.org.nz/resources/
https://www.facebook.com/groups/statsteachers/
http://teaching.statistics-is-awesome.org
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