1. Conducting statistical investigations to develop learner statistical thinking

2. Rethinking Junior Statistics
What do we wish students understood better in the senior school?
We don’t have time in the senior school to teach big foundational ideas.
Not so assessment driven
Opportunity to teach BIG IDEAS
A lot more freedom and flexibility

3. Key statistical concepts:
types of variables (science department)
shape and distribution
strong interpretation skills of dot plots and box-and-whisker plots
samples and populations, sampling variability and making an inference
develop insight into the process of conducting a statistical investigation

4. Senior learners need to be able to:
conduct their own investigation/ experiment
make insightful comments about the results of others' investigations.
It is difficult for learners to make insightful comments without first appreciating the complexities of conducting an investigation.

5. I am keen for the junior learners to work in groups to conduct their own investigations to help them realise that there are different ways of collecting and recording data and that decisions made in the planning stage will impact on the results found.

6. Assessment task want them to learn big ideas
learners focus on what’s assessed and how it’s assessed
assessment-for-learning
learners show us the best work they can produce

7. Teaching progression 9Maths? 10Maths 1 group “typical” 2 groups
“compare”
data collected from population
9Maths?
data collected from sample, inference about population
10Maths

8. Year 9 to focus on 1 group of learners
what they can see about that 1 group of learners
what is “typical”
make an inference about the rest of Year 9s in context
eg. My class is really sporty so our results will be better than the general Year 9 results

9. Year 10 to compare 2 different groups of learners
samples need to come from 2 different populations
Year 8 learners vs Year 10 learners
make an inference about the populations in context.

10. Teaching sequence
PPDAC – where everything fits in. I like to see big picture first
Start with categorical. Bar graphs or pictograms
Shape/ distribution is a key focus of this topic
Need to teach shape before calculations
Pip Arnold’s stuff on Census at Schools

11. Graphs - in Context
want learners to realise that each dot on the dot plot represents something within that context
eg. someone’s shoe length,
the number of countries one learner has visited

12. Number of Letters in Your First Name Teaching Activity
each student works out number of letters in their first name
define variable – possible issues
write data value on paper
physically form a line ordering data values
find 5 point summary

13. First Name Teaching Activity
draw dot plot and box-and-whisker
each dot is the number of letters in a particular learner’s first name
median is the number of letters in Jaeden’s name
every dot has a story!

14. Teaching and Learning time
9Maths: 4 weeks
10Maths: 4 weeks → 5 weeks this year
more time for sampling variability

15. Teaching sequence 2 & 3 weeks teaching: PPDAC Shape Writing questions
Analysis
Sampling variability

16. Investigations Start investigations Split lessons
First half: working in groups to decide what to investigate, variables, write their questions
Second half: continue teaching analysis

17. Investigation conditions
Problem and Plan written collaboratively in groups
Data collected collaboratively in groups
Analysis and Conclusion written individually under test conditions, open book
Learners show us their best work!

18. Choose a Question
Spend a few minutes trying to come up with some examples of questions students might choose
Identify any issues they would face in trying to collect appropriate data
Decide whether or not these issues could be addressed

19. Questions How old are you? What type of music do you like?
How much time do you spend playing sport?
How long can you hold a wall sit for?
What is the length of your foot?
How many windows do you have in your house?
How sporty are you?

20. 9Maths: Data collection
Collected data from their own class in groups
Group Stations

21. 10Maths: Data Collection
Needed to collect data from 2 different Year levels
Organised a timetable where each Year 10 class paired up with a Year 8 class
Year 10’s practised collecting data from their own class first
Even if not fully ready to complete assessment task, still stick to timetable
Group Stations for collecting data

22. Analysis Hand-drawn graphs
no technology or use technology?
Absent students were given data by their group members

23. Conclusion Answer your initial question
Make inference about the populations of all Year 8 and Year 10 learners at Whangaparaoa College
Consider whether your sample reflects the population/ reflect on investigation process/ is this what I expected

24. Comments A lot of buy-in from learners High quality work
Contextual writing
Insightful comments
Does this make sense to me?
Not enough time on sampling variability

25. Questions

26. Probability No test – not assessment focused
Fun and challenging activities

27. Graphs
Historically taught abstract concepts and then contextual problems as applications
After teaching coordinates for years, taught party preparations
Number of sausages for a party – intuitive – don’t need to teach
Now straight into context and later draw out abstract
Linear Algebra projects

28. 9Maths Linear Graphs Project
Students:
designed their own linear pattern
drew shapes
constructed a table
constructed a graph
wrote the formula

29. 9Maths Linear Graphs Project
Excellence
made a change to their pattern
drew the graph of this adapted pattern on the same axes
commented on how the change to the pattern had affected the line graph
(gradient, y-intercept)

30. 10Maths Linear Graphs Project
Students choose their own type of contractor – interest factor (Hitman), challenge concept of mathematics not being creative interesting
3 different contractors to choose from
(given some constraints at a Merit + level) such as graphs need to intercept.
Construct tables, draw line graphs on same axes, write formulae

31. 10Maths Linear Graphs Project
Interpret the lines graphs – very similar to Level 1 Linear Graphs assessment but as a project
Which contractor do they recommend
Very good exam results months later
From the contextual work, later draw out the abstract: y = mx + c
investigate the gradient and y-intercept in context first, later draw out the abstract

32. Questions

33. Thank you!