Introducing the Australian

Curriculum: Mathematics

Consultation Version 1, ACARA, March 2010

Australian Curriculum TimelinePhase One – K-10 English, Mathematics, Science,

HistoryShape May 2009; Consultation to May 2010; Online

Nov 201011-12 Consultation to June 2010; Online Nov 2010 Phase Two – Geography, Languages, ArtsShape June 2010; Consultation to Online 2011

Phase Three - ICT; Design & Technology; Health & PE,Economics; Business, Civics and CitizenshipTimeline to be advised.

ACARA Curriculum Development Process for Mathematics

National Mathematics Curriculum Framing Paper

(NCB, November, 2008)

Shape of the Australian Curriculum: Mathematics

(ACARA, May, 2009)

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.

Considerations for Writersnature 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

Teaching & Learning Considerations

Australian Curriculum will detail what teachers areexpected to teach and students are expected tolearn for each year of schooling.

While written on a year-by-year basis, thecurriculum acknowledges that, in any one yeargroup, there will be a significant range ofachievement.

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.

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.

General CapabilitiesThe 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.

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

General Capabilities

Creativity – approaching problems in different ways

Self-managementTeamworkIntercultural understanding (Indigenous

perspectives)Ethical behaviourSocial competence

General CapabilitiesThe Australian Curriculum will ensure that young

Australians will be provided with the opportunity to

learn about, acknowledge and value:

the cultures of Indigenous peoplessustainable patterns of livingAustralia’s engagement with Asia.

Phases of LearningYears 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)

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.

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.

Australian Curriculum and NTCFEssential 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

Australian Curriculum and NTCFActive 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

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.

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.

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.

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 andReporting Standards.

ACARA – organised by year-levels with expectedachievement standards that will be reported A-E.

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.

Year One Achievement StandardBy the end of Year 1,

Students are able to quantify collections to 20 and can countforwards and backwards to 100. They understand and are fluentwith partitioning numbers to 10. They can read, write, order andmodel two-digit numbers and understand that these numbers arecomprised of units of tens and ones. They are beginning tounderstand the relationship between addition and subtractionand use this knowledge to model and solve simple additiveproblems.

Students collect data about themselves and theirpeers and represent these data in lists, tables and pictographs.

They use everyday language to describe simple geometry andMeasurement ideas and use uniform informal units to measure andcompare length and capacity and use hours and half-hours to describetime.

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.

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.

Content and Proficiency Strands

Australian CurriculumThree 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

Australian CurriculumExpectations 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.

Proficiencies

Understanding – building robust, adaptable, transferablemathematical concepts, the making of connections betweenrelated concepts, the confidence to use the familiar todevelop new ideas, and the ‘why’ as well as the ‘how’ ofMathematics.

Fluency – skill in choosing appropriate procedures, carryout procedures flexibly, accurately, efficiently, andappropriately, and, in also, recalling factual knowledgeand concepts readily.

ProficienciesProblem-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.

Key Overarching Mathematical OutcomesAppropriate 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)

Teaching and LearningProficiency strands describe ‘how’ content strands are

explored…

ie thinking and doing mathematics, and have been

incorporated into the content elaborations.

Teaching and LearningChallenging 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

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 Algebra1. 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.

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.

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.

Content ElaborationsYear One - Number and Algebra1. 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

Hyperlinks

Hyperlinks in the content descriptions will link to

teaching resources and professional learning

resources.

Time Allocations

For Mathematics, ACARA have adopted therecommendation 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 theprimary Years K to 6/7 and a minimum of 4 hours per weekin all the lower secondary Years 7/8 to 10. This time shouldinclude cross curricular learning. p. 18

Learning Design Model

ACARA has provided for the Australian Curriculum:a rationale and aimscontent structure pedagogy and assessment considerations,

but has not recommended a learning design model.

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

Feedback to ACARAFeedback from today’s session:MTANTAAMTNT DETMaths PLC (Top End / Central Australia).

Individually:

http://www.australiancurriculum.edu.au/Home

http://www.aamt.edu.au/AAMT-in-action/Representingteachers/Curriculum

Carousel BrainstormTopic Sheets1.Achievement Standards / Content Descriptions2.Elaborations (to Content Descriptions)3.General Capabilities / Cross-Curriculum links4.User-friendliness / Other Suggestions

Facilitator Role ; focus; record; summariseGroups rotate through topic sheets and providefeedback. 10-15 minutes