1. Statistics, teacher knowledge, and effective teaching Tim Burgess Massey University National Numeracy Conference Auckland 20 February 2008

2. Why is someone giving a keynote address about statistics at a numeracy conference? What is numeracy compared with mathematics? What about statistics - is it part of mathematics, numeracy, both, or neither? National Numeracy Conference

3. Outline NZ Curriculum Mathematics and Statistics learning area Statistics Teacher knowledge

4. Numeracy Conference Themes and Objectives Pedagogical content knowledge Effective professional development in mathematics Effective teaching of mathematics for diverse learners

5. Statistics in the curriculum in NZ 1969/72 1985/87 1992 2007

6. Mathematics vs. Statistics Mathematics π Deterministic; real life contexts may be useful for developing concepts but move towards the abstract Statistics µ ‘Reasoning under uncertainty’; real life contexts are essential to making sense of questions and issues µ Move towards statistical thinking and reasoning (and away from just skills and procedures) µ Most research on teacher knowledge has been conducted away from the classroom.

7. Statistical Thinking  Need for data "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." Sherlock Holmes in The Adventure of the Copper Beeches by Sir Arthur Conan Doyle.  Transnumeration changing the representation or form of the data  Variation  Reasoning with models eg. graphs: look for the distribution of the data: this includes features of centre, spread, density, skewness and outliers  Integration of statistical with contextual knowledge  Investigative cycle / Interrogative cycle  Dispositions

8. Mathematical Content Knowledge Common knowledge of content Specialised knowledge of content Knowledge of content and students Knowledge of content and teaching

9. Wild and Pfannkuch (1999): Statistical thinking Hill, Schilling & Ball (2004): Mathematical content knowledge Framework for examining teacher knowledge

10. Examples of common knowledge of content Left handed Right handed Total Whistler21517 Non- whistler 167 Total32124

11. Examples of specialised knowledge of content

12. Examples of knowledge of content & students

13. Examples of knowledge of content & teaching

14. Effective teaching A teacher needs: all four categories of teacher knowledge across all components of statistical thinking.

15. Missed opportunities in the classroom Gaps in the teacher’s knowledge will give rise to missed opportunities in the classroom. Listening to, interpreting, responding to students Posing questions for investigation Guiding students with handling category and numeric data Sorting data effectively, and moving from individual features to group features Students’ difficulties with data based statements Understanding variation, and development of inference

16. A solution What was the problem again? Pedagogical content knowledge Effective professional development in mathematics Effective teaching of mathematics for diverse learners One solution Engage and immerse teachers in investigations with real data - common knowledge of content Listen to students - real or video - specialised knowledge of content and knowledge of content and students Workshops - knowledge of content and teaching

17. Timperley et al.’s best evidence synthesis of the professional development literature showed overwhelmingly that no professional development that focused solely on general pedagogy was successful in raising the achievement levels of students, and conversely that the most successful professional development, in terms of student achievement, involved the development of both the content knowledge and the pedagogical content knowledge of teachers (and that this latter category was particularly critical). Timperley, H., Wilson, A., Barrar, H., & Fung, I. (2007 forthcoming). Teacher professional learning and development: Best evidence synthesis iteration [BES]. Wellington, New Zealand: Ministry of Education.

18. A challenge How can we meet the challenge of involving teachers (pre-service and in-service) in investigating real data so that all categories of teacher knowledge can develop to an adequate level? Investigations - physical manipulation of data - use of technology - eg Tinkerplots or Fathom - who should provide these resources?

19. A challenge - continued E-learning and pedagogy Information and communication technology (ICT) has a major impact on the world in which young people live. Similarly, e-learning (that is, learning supported by or facilitated by ICT) has considerable potential to support the teaching approaches outlined in the above section. For instance, e-learning may: … * enhance opportunities to learn by offering students virtual experiences and tools that save them time, allowing them to take their learning further. Schools should explore not only how ICT can supplement traditional ways of teaching but also how it can open up new and different ways of learning. p. 36: The NZ Curriculum