Conducting statistical i nvestigations to develop learner statistical t hinking

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 towork 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

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 NameTeaching 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 NameTeaching 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 • https://prezi.com/eyqqtt9jphvh/

32. Questions

33. Thank you!