Introducing the Australian Curriculum: Mathematics Consultation Version 1, ACARA, March 2010

1. Introducing the Australian Curriculum: Mathematics Consultation Version 1, ACARA, March 2010

2. Australian Curriculum Timeline Phase One – K-10 English, Mathematics, Science, History Shape May 2009; Consultation to May 2010; Online Nov 2010 11-12 Consultation to June 2010; Online Nov 2010 Phase Two – Geography, Languages, Arts Shape June 2010; Consultation to Online 2011 Phase Three - ICT; Design & Technology; Health & PE, Economics; Business, Civics and Citizenship Timeline to be advised.

3. ACARA Curriculum Development Process for Mathematics • National Mathematics Curriculum Framing Paper (NCB, November, 2008) • Shape of the Australian Curriculum: Mathematics (ACARA, May, 2009)

4. Curriculum Development Process Mid-2009 ACARA Writing Panel formed - • Preliminary Draft Australian Curriculum: Maths K-10 (ACARA, September, 2009) • Draft Consultation Version 1.0 K-10 (ACARA, March, 2010) • Year 11-12 Curriculum tracking about 3 months behind K-10 Mid-2010 Analysis of Feedback by K-10 Consultation and refinement of document in preparation for online publication by late 2010.

5. Considerations for Writers • nature of the learner and learning, including consideration of developmental changes in young people • whole curriculum and how learning areas relate • structural matters (K/T/P; Year 7; Senior Years) • inclusivity • general capabilities • cross-curriculum dimensions

6. Teaching & Learning Considerations Australian Curriculum will detail what teachers are expected to teach and students are expected to learn for each year of schooling. While written on a year-by-year basis, the curriculum acknowledges that, in any one year group, there will be a significant range of achievement.

7. Teaching & Learning Considerations Teachers will be required to understand the developmental diversity in the students they teach and are responsible for organising learning opportunities to meet individual learning needs. Curriculum documents will be written in a way that assists teachers to identify and respond to this range of achievement.

8. Teaching & Learning Considerations The curriculum should not predetermine the instructional approach to be taken by teachers. The curriculum should provide some flexibility for teachers to accommodate different levels of student development and achievement and approaches to learning.

9. General Capabilities The National Declaration on Educational Goals for Young Australians (Melbourne Declaration, November, 2008) identified important general capabilities that schools should help students develop, in addition to content of particular learning areas. It was required that these be incorporated into the Australian Curriculum.

10. General Capabilities (maths focus) • Literacy – writing, interpreting mathematical texts • Numeracy – application of mathematics • ICT – calculators, spreadsheets, dynamic geometry software • Thinking Skills – reasoning and problem-solving; critical thinking and justification; identifying questions to investigate

11. General Capabilities • Creativity – approaching problems in different ways • Self-management • Teamwork • Intercultural understanding (Indigenous perspectives) • Ethical behaviour • Social competence

12. General Capabilities The Australian Curriculum will ensure that young Australians will be provided with the opportunity to learn about, acknowledge and value: • the cultures of Indigenous peoples • sustainable patterns of living • Australia’s engagement with Asia.

13. Phases of Learning • Years K – 2 (5 – 8 years of age) • Years 3 - 6 (8 – 12 years of age) • Years 7 - 10 (12-15 years of age) • Years 11 - 12 (15+ years of age)

14. Phases of Learning Australian Curriculum will: • take Kindergarten (Preparation, Reception, Transition) as the first year of schooling and design curriculum for students who are between 5 and 6 years old in this first year • be designed for Year 7 as part of a K–10 sequence of learning for each of the learning areas. It will be written to be taught in either a primary or secondary school setting.

15. Australian Curriculum and NTCF Maths The renewed NTCF –Mathematics Learning Area was based on the National Mathematics Curriculum Framing Paper (NCB, November, 2008). Rationale and Aims of both the Australian and NTCF documents are consistent.

16. Australian Curriculum and NTCF • Essential mathematics knowledge and skills • Appreciate power and elegance of mathematical reasoning, importance of developing problem-solving • Links between components of mathematics and relationships with other learning areas • Recognition of digital technologies

17. Australian Curriculum and NTCF • Active and confident learners and users of mathematics • Numeracy Capability – Numeracy is the capacity, confidence and disposition to use mathematics to meet the demands of learning, school, home, work, community and civic life. p.5 Shape of Australian Curriculum: Mathematics p.1 NTCF Introduction to Mathematics Learning Area

18. ACARA Literacy & Numeracy Continua • Literacy and Numeracy Continua are being developed for Years 2, 4, 6, 8 and 10. • The continua will provide advice about appropriate attention to literacy and numeracy content to be included in the curriculum. • They will also serve to inform the NAPLAN.

19. Position on Numeracy Numeracy is fundamentally the responsibility of mathematics and is applied in other learning areas. It is crucial that the mathematics curriculum provides the opportunity to apply mathematical understanding and skills in context, both in other learning areas and in real world contexts.

20. Position on Numeracy • A particularly important context for the application of number and algebra is financial mathematics. • In measurement and geometry there is an opportunity to apply understanding to design. • The world in the 21st century is information driven and statistics and probability provide opportunities for students to interpret data and make informed judgements about events involving chance.

21. Australian Curriculum and NTCF Renewed NTCF and Australian Curriculum are ‘standards-based’ documents. Content organisation is different: NTCF - organised by developmental Key Growth Points and Bands, with related Achievement and Reporting Standards. ACARA – organised by year-levels with expected achievement standards that will be reported A-E.

22. ACARA Achievement Standards • The achievement standard will: • describe the quality of expected learning • be exemplified by annotated work samples that illustrates • the quality of learning • be accompanied by A-E descriptors to assist reports to • parents.

23. Year One Achievement Standard By the end of Year 1, Students are able to quantify collections to 20 and can count forwards and backwards to 100. They understand and are fluent with partitioning numbers to 10. They can read, write, order and model two-digit numbers and understand that these numbers are comprised of units of tens and ones. They are beginning to understand the relationship between addition and subtraction and use this knowledge to model and solve simple additive problems. Students collect data about themselves and their peers and represent these data in lists, tables and pictographs. They use everyday language to describe simple geometry and Measurement ideas and use uniform informal units to measure and compare length and capacity and use hours and half-hours to describe time.

24. ACARA Achievement Standards • Each K–10 achievement standard will be aligned with a ‘C level’ . • A ‘D level’ describes a quality of learning that is adequate for progression but may indicate the student will need additional support or assistance in progressing within the next level.

25. ACARA Achievement Standards • Additional work samples, which illustrate achievement well above and well below the achievement standard, will be provided to teachers to assist them to make on-balance judgements of A, B, D and E standards of achievement.

26. Content and Proficiency Strands

27. Australian Curriculum Three content strands (nouns): Declarative Knowledge ACARA NT DET - NTCF • Number and Algebra Number, Algebra • Measurement and Geometry Measurement, Space • Statistics and Probability Chance and Data

28. Australian Curriculum Expectations for proficiency (verbs) Procedural Knowledge • Understanding • Fluency • Problem solving • Reasoning Proficiency strands include and extend upon the NTCF’s Key Overarching Mathematical Outcomes: working mathematically procedural knowledge.

29. Proficiencies Understanding– building robust, adaptable, transferable mathematical concepts, the making of connections between related concepts, the confidence to use the familiar to develop new ideas, and the ‘why’ as well as the ‘how’ of Mathematics. Fluency– skill in choosing appropriate procedures, carry out procedures flexibly, accurately, efficiently, and appropriately, and, in also, recalling factual knowledge and concepts readily.

30. Proficiencies Problem-solving– the ability to make choices, interpret, formulate, model and investigate problem situations, and communicate solutions effectively. Reasoning– the capacity for logical thought and actions such as analysing, proving, evaluating, explaining, inferring, justifying and generalising.

31. Key Overarching Mathematical Outcomes • Appropriate and efficient application of skills, concepts and techniques in a range of contexts (Understanding, Fluency) • Effective and meaningful communication of Mathematical thinking (Problem-solving, Understanding, Fluency) • Appropriate and varied ways of working through Mathematical Investigations (Understanding, Reasoning) • Effective and appropriate use of technologies and other equipment (Fluency) • Generalisation (Understanding, Reasoning)

32. Teaching and Learning Proficiency strands describe ‘how’ content strands are explored… ie thinking and doing mathematics, and have been incorporated into the content elaborations.

33. Teaching and Learning • Challenging problems can be posed using basic content. • Content acceleration may not be the best way to extend students. • Choosing engaging experiences as contexts for a variety of tasks assists in making mathematics inclusive. * Enabling and Extending prompts * Open-ended questions / activities

34. Content Descriptions Content descriptions are available for each strand at each year level and represent a scope and sequence of what teachers are expected to teach. Year One - Number and Algebra 1. Counting Say, understand and reason with number sequences to and from 100 by ones from many starting point, and say number sequences of twos, fives and tens starting from zero.

35. The Australian Curriculum is attempting to reduce the ‘overcrowded curriculum’: • Recognises interrelationships between strands; number / algebra space / measurement (geometry) • Emphasises key mathematical ideas at a year level • Generally speaking, there is good alignment between the Content Descriptions (ACARA) and the key learnings of the NTCF in Mathematics.

36. Content Elaborations Provide additional illustrations and examples of content. Assist to develop a common understanding of what is to be taught. Integrate content strands to the proficiency strands.

37. Content Elaborations Year One - Number and Algebra 1. Counting Elaborations • saying number sequences emphasising 10 as a countable unit assists to develop an understanding of place value • developing fluency with forwards and backwards counting in meaningful contexts such as circle games (eg ‘I’m going to start at 24 and when I get to 13, everyone will be sitting in a circle’) • using a calculator to increase understanding of counting patterns (eg count by adding 2 each time, beginning with 0 and press +2 = = repeatedly) • understanding that skip counting (eg counting 5-cent coins) will also tell you how much money is in a collection and can assist with counting in a faster way

38. Hyperlinks Hyperlinks in the content descriptions will link to teaching resources and professional learning resources.

39. Time Allocations For Mathematics, ACARA have adopted the recommendation of the National Numeracy Review Report (COAG, May, 2008): That all jurisdictions should work towards a minimum of 5 hours per week of mathematics for students in all the primary Years K to 6/7 and a minimum of 4 hours per week in all the lower secondary Years 7/8 to 10. This time should include cross curricular learning. p. 18

40. Learning Design Model ACARA has provided for the Australian Curriculum: • a rationale and aims • content structure • pedagogy and assessment considerations, but has not recommended a learning design model.

41. Use NTCF Learning Design Approach Eight Learning Management Questions, Smith &Lynch, 2006

43. Feedback to ACARA Feedback from today’s session: • MTANT • AAMT • NT DET • Maths PLC (Top End / Central Australia). Individually: http://www.australiancurriculum.edu.au/Home http://www.aamt.edu.au/AAMT-in-action/Representing teachers/Curriculum

44. Carousel Brainstorm Topic Sheets • Achievement Standards / Content Descriptions • Elaborations (to Content Descriptions) • General Capabilities / Cross-Curriculum links • User-friendliness / Other Suggestions Facilitator Role ; focus; record; summarise Groups rotate through topic sheets and provide feedback. 10-15 minutes