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

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

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

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Implementing the AustralianImplementing the Australian Curriculum for Mathematics F to 10

Judy Anderson

The University of Sydney

Judy.anderson@sydney.edu.au

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

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.

Which tasks (Cockcroft, 1982): would support these proficiencies?

Examine the types of questions and tasks you use during mathematics lessons.

Gould, 2006 (Cockcroft, 1982):

✔

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

✔

Which tasks (Cockcroft, 1982): would support these proficiencies?

Examine the types of questions and tasks you use during mathematics lessons.

Bloom’s Taxonomy (Cockcroft, 1982):

- Understand
- Remember
- Apply
- Analyse
- Evaluate
- Create

Higher order thinking

Problem solving

Reasoning

Thinkers (Cockcroft, 1982):Bills 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

Approaches to teaching problem solving … (Cockcroft, 1982):

Approaches to teaching problem solving … (Cockcroft, 1982):

Approaches to teaching problem solving … (Cockcroft, 1982):

Approaches to teaching problem solving … (Cockcroft, 1982):

S (Cockcroft, 1982):uccessful 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

Which tasks or problems (Cockcroft, 1982):?

Types of problems??? (Cockcroft, 1982):

- Open-ended
- Rich tasks
- Real-world problem
- Challenge
- Investigation
- Inquiry
- Problem-based
- Reflective inquiry

Which tasks or problems (Cockcroft, 1982):?

Content specific questions requiring a range of levels of thinking

Area and Perimeter in Year 5/6 (Cockcroft, 1982):

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

Which card is better value? (Cockcroft, 1982):

Please explain your thinking.

Deep mathematical

knowledge

General reasoning

abilities

Communication

skills

Heuristic

strategies

Number (Cockcroft, 1982):andAlgebra

Make up an equation where the answer is (Cockcroft, 1982):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.

NumberandAlgebraDeep mathematical

knowledge

General reasoning

abilities

Communication

skills

Helpful beliefs

eg orientation to ask

questions

Abilities to work

with others

effectively

Number and Algebra (Cockcroft, 1982):

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

Number and Algebra: (Cockcroft, 1982):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

Constructive alignment (Cockcroft, 1982):(Biggs, 2004)

- Curriculum
- Instruction
- Assessment

Planning for Implementation (Cockcroft, 1982):(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

Favourite (Cockcroft, 1982): 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.

Resources: (Cockcroft, 1982):

- 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???

Key messages … (Cockcroft, 1982):

- Balance is important
- Evaluate the types of questions and tasks used during mathematics lessons
- Assessment, assessment, assessment!!!
- Alignment between curriculum, teaching and assessment