CENTRE FOR EDUCATIONAL DEVELOPMENT Developing practice around the realigned Mathematics and Statistics standards Workshop 2: Statistical inquiry Alison Fagan and Anne Lawrence Advisers in Secondary Numeracy & Mathematics

Set of four workshops Workshop 1:Achievement standard 1.1 Workshop 2:Achievement standard 1.10 Workshop 3: Other standards Workshop 4: Implications Exploring an assessment task for 1.1 A, M, E distinctions and the SOLO taxonomy

Review workshop one Statistics and Informal inference Develop understanding of A,M,E distinctions for AS 1.10 Consider implications for teaching and learning Objectives: Workshop 2

How did your students do on the Number Achievement Standard task? What do we need to do as teachers to enable students to deal with this sort of task? What does this mean for teaching and learning in our classroom? How could this task/schedule be improved? Review Workshop 1

What sort of rich learning task would be valuable to develop number thinking in your students? Reflection: Developing number thinking

AS Investigate a given multivariate data set using the statistical enquiry cycle Look at the standard: –What are the understandings required? –What do you think will be the step up from achieved to merit? merit to excellence? Statistics – Ach Std 1.10

Use your questions, data, graphs and summary statistics to complete the task: Describe features of the distributions comparatively; eg: shape, middle 50%, shift overlap, spread, unusual or interesting features and summary statistics; Write a conclusion summarising your findings. The conclusion should include an informal inference in response to the investigative question and be supported with relevant evidence. ’Get online’ task

What are some of the new ideas of this standard that you think are important? New ideas?

Statistical enquiry cycle Posing comparative questions Use of technology to select sample, draw graphs and calculate summary statistics Appropriate graphs Interpreting graphs: middle, shape, spread –Consideration of shift and overlap Informal inference –Making the call at Level 5 and 6 Key ideas

What is your understanding? Informal inference

We need to develop students’ understandings – from year 9 up Informal inference

For a sample size of 30 we will make the call if the difference between the medians is more than a third of the total spread. Why? What call can we make? –We can’t say there is no difference How can this be taught (as compared to told)? Making the call

Use the assessment schedule to mark your work on the task Discuss issues Use the assessment schedule to make decisions about N, A, M, E for the student work Marking the ‘Get online’ task

What are the implications for teaching and learning at Years 9 and 10? How does this fit with NZC? –What does Level 4 require? –What does Level 5 require? Discussion

Complete one statistical enquiry with one class at Year 10 or 11, involving sampling. Share with department Discuss student responses Discuss implications for years 9 and 10 teaching/learning programme. Homework