I took this photo on a recent beach holiday - where was I?

Numeracy in the Australian Curriculum John Bleckly Curriculum Manager, Numeracy

Overview What does it mean to be numerate? Definitions How is numeracy dealt with in the AC? A numeracy model Numeracy and TfEL Where to from here?

Numerate citizens Describe a numerate person in our society? What do they have to know, be able to do and be?

Numerate citizens Consider any earlier time in Australia’s history Describe a numerate person? What did they have to know, be able to do and be?

Numerate citizens Consider the possible numerate lives of your students in 20 years time What will they have to know, be able to do and be? What does this mean for how we work with these students now?

Numeracy means … different things to different people PISA definition of mathematical literacy: An individual’s capacity to identify and understand the role mathematics plays in the world, to make well-founded judgments, and to use and engage with mathematics in ways that meet the needs of that individual’s life as a constructive, concerned and reflective citizen. An Australian definition of numeracy (AAMT, 1997): To be numerate is to use mathematics effectively to meet the general demands of life at home, in paid work, and for participation in community and civic life. Numeracy is a word used in some countries but elsewhere it is more common to speak of quantitative literacy or mathematical literacy. Internationally the best known definition of what we in Australia call numeracy is the PISA version you see here. In Australia, we have come to accept this definition (appears in national numeracy policy documents). 7

Distinguishing numeracy from mathematics Mathematics climbs the ladder of abstraction to see, from sufficient height, common patterns in seemingly different things. Abstraction is what gives mathematics its power; it is what enables methods derived from one context to be applied in others. But abstraction is not the focus of numeracy. Instead, numeracy clings to specifics, marshalling all relevant aspects of setting and context to reach conclusions. Steen, 2001 In fact it’s context that distinguishes numeracy from mathematics. Steen offered this elegant comment on the relationship between mathematics and numeracy. 8

Numeracy is an across the curriculum commitment Steen (2001, p. 18): To enable students to become numerate, teachers must encourage them to see and use mathematics in everything they do … Fortunately, because numeracy is ubiquitous, opportunities abound to teach it throughout the curriculum. Australian National Numeracy Review (2008, p. 7) recommended: That all systems and schools recognise that, while mathematics can be taught in the context of mathematics lessons, the development of numeracy requires experience in the use of mathematics beyond the mathematics classroom, and hence requires an across the curriculum commitment. The key idea in this project is that numeracy is developed not only in mathematics lessons, but in all curriculum areas. 9

Definitions In what ways are these similar/different? Implications? The ability to understand, analyse, critically respond to and use mathematics in different social contexts. (SACSA Framework) Numeracy is the capacity, confidence and disposition to use mathematics to meet the demands of learning, school, home, work, community and civic life. (Shape of Australian Curriculum) In what ways are these similar/different? Implications?

A model for numeracy A model for numeracy in the 21st century (Professor M. Goos) Citizenship Personal and social Work / Learning Contexts Dispositions Confidence Flexibility Initiative Risk Tools Representational Physical Digital Mathematical knowledge Problem Solving Estimation Concepts Skills

A model for numeracy A critical orientation or dimension – asking questions about The mathematics used to solve a problem Eg Did I use an efficient and/or accurate mathematical process? Is this result reasonable in this context? How mathematics is used to position and persuade Eg Is this data reliable? Is this an appropriate way to present this information? Who benefits? Using mathematics to inform ethical action Eg Using statistics (eg workers’ ages, salaries) to inform the purchase of a new pair of running shoes. Ethical behaviour involves students in building a strong personal and socially oriented ethical outlook that helps them to manage context, conflict and uncertainty, and to develop an awareness of the influence that their values and behaviour have on others. (ACARA)

A model for numeracy Critical orientation A model for numeracy in the 21st century (Professor M Goos) Critical orientation Citizenship Personal and social Work / Learning Contexts Dispositions Confidence Flexibility Initiative Risk Tools Representational Physical Digital Mathematical knowledge Problem Solving Estimation Concepts Skills

‘Much of Australia's agriculture and environment rely on the Murray-Darling river system. Yet the paltry 2,400 billion litres proposed to save it will only condemn it to a long, slow death.’ Chris Daley is Rivers Campaigner for the Wilderness Society NSW September 2011

Numeracy across the curriculum October 2010 Murray Darling-Basin Authority (MDBA) in its Guide to the Proposed Basin Plan ‘reducing water diversions in the Murray-Darling Basin by 3,856 gigalitres would give a “high uncertainty” of achieving the objectives of the Water Act 2007 and 6,983 gigalitres would give a “low uncertainty”. These numbers represented the culmination of decades of research carried out across the Basin.’

May 2011 ‘THE Murray-Darling Basin Authority is considering restoring much less water to the river system. ‘the scientific modelling used for the original draft plan to save the river was "coarse". The authority is now looking at "the most precise methodology". The authority confirmed that a figure of 2800 gigalitres was being considered. This falls well short of the 4000 gigalitres that scientists say is needed to revive the system.’ As reported on adelaidenow.com.au

Read the story Discuss each aspect of the numeracy model in relation to James’ experience and record on the proforma. Critical orientation

Learning Area examples

Teachers’ trajectories through the numeracy model Dispositions Tools Contexts Critical Orientation Mathematical Knowledge We asked teachers to annotate a copy of the model to show what their main concern was when they joined the project, and how they believed they successively explored and incorporated other elements of the model into their planning and teaching. Most teachers started with a concern for improving their students’ dispositions or their mathematical knowledge, and then moved from D to K or K to D. Some teachers linked use of tools with developing mathematical knowledge. Teachers then moved from dispositions to contexts or [knowledge-tools] to contexts. Only four teachers indicated that they considered critical orientation – and this was their end point. 20

Student Attitude Survey What do students say about the application of mathematics in other learning?

Yeah, where does numeracy fit? Numeracy in the AC How will my teacher help me develop my numeracy now we are using the Australian curriculum? Yeah, where does numeracy fit?

Numeracy in the AC General Capability Statements in all LAs The mathematics curriculum develops students’ mathematical knowledge and skills, enabling them to become confident and creative mathematical thinkers. Numerate students then apply their mathematical understanding in other learning areas … (to) achieve the intended outcomes for those learning areas. English When responding to or creating texts that present issues or arguments based on data, students identify, analyse and synthesise numerical information and discuss the credibility of sources and methodology. Many elements of numeracy are evident in science, particularly in Science Inquiry Skills. These include practical measurement and the collection, representation and interpretation of data from investigations. History Students need to organise and interpret historical events and developments and this may require analyses of data to make meaning of the past, for example to understand cause and effect, and continuity and change.

Numeracy in the AC General Capability Statements in all LAs When responding to or creating texts that present issues or arguments based on data, students identify, analyse and synthesise numerical information and discuss the credibility of sources and methodology. The mathematics curriculum develops students’ mathematical knowledge and skills, enabling them to become confident and creative mathematical thinkers. Numerate students then apply their mathematical understanding in other learning areas … (to) achieve the intended outcomes for those learning areas. Numeracy continuum Many elements of numeracy are evident in science, particularly in Science Inquiry Skills. These include practical measurement and the collection, representation and interpretation of data from investigations. Students need to organise and interpret historical events and developments and this may require analyses of data to make meaning of the past, for example to understand cause and effect, and continuity and change.

Developing numeracy School learning Numerate individual Other Learning Areas Other learning experiences Out of school learning

Numeracy in the LAs In each Learning Area, teachers identify the specific numerate demands of the learning area ensure students are equipped to meet the numerate demands. Would you expect numeracy to be most visible in the English, Science or History curriculum? Suggest a ranking?

Numeracy in English Numeracy can be addressed in English learning contexts across all year levels. Students select and apply numerical, measurement, spatial, graphical, statistical and algebraic concepts and skills to real-world situations and problems when they comprehend information from a range of sources and offer their ideas. When responding to or creating texts that present issues or arguments based on data, students identify, analyse and synthesise numerical information and discuss the credibility of sources and methodology.

Numeracy in English Foundation Year Year 1 Year 2 Year 3 Year 4 Year 5

Numeracy in English Could there be numeracy here? Year 3 Literature and context Create imaginative texts based on characters, settings and events from students’ own and other cultures using visual features, for example perspective, distance and angle Year 7 Literacy Plan, draft and publish imaginative, informative and persuasive texts, selecting aspects of subject matter and particular language, visual, and audio features to convey information and ideas

Discussion Handout: Numeracy in the content descriptors How does the filtering process represent numeracy in each learning area? What are the implications for teachers?

Numeracy in History Knowledge and skills in numeracy are evident in specific elements of the history curriculum. Students need to organise and interpret historical events and developments and this may require analyses of data to make meaning of the past, for example to understand cause and effect, and continuity and change. This requires skills in numeracy such as the ability to represent and interpret quantitative data.

Numeracy in History Handout of History scope for a year level. Select any one of the dot-pointed Elaborations What specific tasks might students actually be doing? What might be the numerate demands? Will students need support?

Numeracy in History Year 4 achievement standard By the end of Year 4, students place some of the key events and people they have studied in chronological sequence and they create simple timelines. Students pose questions about the past and locate relevant information from a range of historical sources. Students use a range of historical sources to examine the reasons for and impact of historical events. They use sources to identify different points of view in the past and the motivations of individuals and groups. Students explain the significance of events in bringing about change. Students compose historical texts, including narratives, using appropriate historical terms. They present their information using a range of communication forms (written, spoken, visual).

Numeracy in Science Many elements of numeracy are evident in science, particularly in Science Inquiry Skills including practical measurement and the collection, representation and interpretation of data from investigations. Students are introduced to measurement using informal units in the early years, then formal units; later they consider issues of uncertainty and reliability in measurement. As students progress, both qualitative and, later, quantitative data are collected, analysed and represented in graphical forms. Students learn data analysis skills, including identifying trends and patterns from numerical data and graphs. In later years, numeracy demands include the statistical analysis of data, including issues relating to accuracy, and linear mathematical relationships to calculate and predict values.

Numeracy as a General Capability General Capabilities Literacy Numeracy ICT competence Critical and creative thinking Ethical behaviour Personal and social competence Intercultural understanding General capabilities are a key dimension of the Australian Curriculum. They encompass skills, behaviours and dispositions that students develop and apply to content knowledge and that support them in becoming successful learners, confident and creative individuals and active and informed citizens.

Linking to TfEL framework Teachers create learning opportunities with students Domain 2 Create safe conditions for rigorous learning Domain 3 Develop expert learners Domain 4 Personalise and connect learning 2.1 develop democratic relationships 3.1 teach students how to learn 4.1 build on learners’ understandings 2.2 build a community of learners 3.2 foster deep understanding and skilful action 4.2 connect learning to students’ lives and aspirations 2.3 negotiate learning 3.3 explore the construction of knowledge 4.3 apply and assess learning in authentic contexts 2.4 support and challenge students to achieve high standards 3.4 promote dialogue as a means of learning 4.4 communicate learning in multiple modes How do you see numeracy connecting with TfEL?