Implementing the Austra lia n Implementing the Australian Curriculum for Mathematics F to 10

1. Implementing the AustralianImplementing the Australian Curriculum for Mathematics F to 10 Judy Anderson The University of Sydney Judy.anderson@sydney.edu.au

2. Key messages … • Balance is important • Evaluate the types of questions and tasks used during mathematics lessons • Assessment, assessment, assessment!!! • Alignment between curriculum, teaching and assessment

3. Mathematics teaching should include opportunities for (Cockcroft, 1982): • exposition by the teacher; • discussion between teacher and pupils and between pupils themselves; • appropriate practical work; • consolidation and practice of fundamental skills and routines; • problem solving, including the application of mathematics to everyday situations; and • investigational work.

6. Which tasks would support these proficiencies? Examine the types of questions and tasks you use during mathematics lessons.

8. Gould, 2006 ✔ Because three is a larger number than 2 ✖ Because four is a larger number than three ✖ Because six is a larger number than 3 ✖ Because 5 & 6 are larger numbers than 2 & 3 ✔ Because 12 & 13 are larger numbers than 9 & 10 ✔

10. Which tasks would support these proficiencies? Examine the types of questions and tasks you use during mathematics lessons.

12. Bloom’s Taxonomy • Understand • Remember • Apply • Analyse • Evaluate • Create Higher order thinking Problem solving Reasoning

14. ThinkersBills et al. (2004) • Give an example of … (another and another) • Open-ended • Explain or justify • Similarities and differences • Always, sometimes or never true • Odd-One-Out • Generalise • Hard and easy

15. Approaches to teaching problem solving …

16. Approaches to teaching problem solving …

17. Approaches to teaching problem solving …

18. Approaches to teaching problem solving …

19. Successful problem solving requires Deep mathematical knowledge General reasoning abilities Personal attributes eg confidence, persistence, organisation Skills and Attributes Heuristic strategies Communication skills Abilities to work with others effectively Helpful beliefs eg orientation to ask questions Stacey, 2005

20. Which tasks or problems?

21. Types of problems??? • Open-ended • Rich tasks • Real-world problem • Challenge • Investigation • Inquiry • Problem-based • Reflective inquiry

22. Which tasks or problems? Content specific questions requiring a range of levels of thinking

23. Area and Perimeter in Year 5/6 Which shape has the largest perimeter? Please explain your thinking. Design a new shape with 12 squares which has the longest possible perimeter. Deep mathematical knowledge General reasoning abilities Communication skills Heuristic strategies

24. Which card is better value? Please explain your thinking. Deep mathematical knowledge General reasoning abilities Communication skills Heuristic strategies

25. NumberandAlgebra

26. Make up an equation where the answer is x = 2 Make up an equation where the answer is x = 3 Make up an equation where …. Another idea: Change one number in the equation 4 x – 3 = 9, so that the answer is x = 2. NumberandAlgebra Deep mathematical knowledge General reasoning abilities Communication skills Helpful beliefs eg orientation to ask questions Abilities to work with others effectively

27. Number and Algebra • Explain the difference between particular pairs of algebraic expressions, such as and • Compare similarities and differences between sets of linear relationships, eg.

28. Number and Algebra:Fractions Deep mathematical knowledge • Explain why is less than • Explain why General reasoning abilities Communication skills Abilities to work with others effectively Informal and Formal Proof

29. Constructive alignment(Biggs, 2004) • Curriculum • Instruction • Assessment

30. Planning for Implementation(including Problem Solving and Reasoning) • Identify the topic (mathematical concepts) • Examine curriculum content statements • Use data to inform decisions on emphasis • Select, then sequence, appropriate tasks/activities • Identify the mathematical actions (proficiencies) in which you want students to engage • Design assessment for ALL proficiencies

31. Favourite Sources MCTP (Maths300 through www.curriculum.edu.au) Bills, C., Bills, L., Watson, A., & Mason, J. (2004). Thinkers. Derby, UK: ATM. Downton, A., Knight, R., Clarke, D., & Lewis, G. (2006). Mathematics assessment for learning: Rich tasks and work samples. Fitzroy, Vic.: ACU National. Lovitt, C., & Lowe, I. (1993). Chance and data. Melbourne: Curriculum Corporation. Sullivan, P., & Lilburn, P. (2000). Open-ended maths activities. Melbourne, Vic: Oxford. Swan, P. (2002). Maths investigations. Sydney: RIC Publications.

32. Resources: • MCTP (Maths 300) – Curriculum Corporation website http://www.curriculum.edu.au • ABS – http://www.abs.gov.au • NCTM – http://www.nctm.org • NRICH website – http://nrich.maths.org.uk/primary • Others???

33. Key messages … • Balance is important • Evaluate the types of questions and tasks used during mathematics lessons • Assessment, assessment, assessment!!! • Alignment between curriculum, teaching and assessment