Transforming professional practice: Teaching numeracy across the curriculum Merrilyn Goos

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.

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

Numeracy is an across the curriculum commitment 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. (Steen, 2001, p. 18)

Numeracy is an across the curriculum commitment Australian National Numeracy Review (2008) 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. (p. 7)

Numeracy in the Australian Curriculum Numeracy is one of 7 General Capabilities to be developed and used by students across all learning areas, in co- curricular programs, and in their lives outside school. In the Australian Curriculum, students become numerate as they develop the knowledge and skills to use mathematics confidently across all learning areas at school and in their lives more broadly. Numeracy involves students in recognising and understanding the role of mathematics in the world and having the dispositions and capacities to use mathematical knowledge and skills purposefully.

An Australian definition of numeracy 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. (Australian Association of Mathematics Teachers, 1997)

21st century numeracy Contexts Tools Mathematical Knowledge Dispositions

21st century numeracy Contexts Tools Mathematical Knowledge Dispositions Problem Solving Estimation Concepts Skills

21st century numeracy Contexts Tools Mathematical Knowledge Dispositions Problem Solving Estimation Concepts Skills Confidence Flexibility Initiative Risk

21st century numeracy Contexts Tools Mathematical Knowledge Dispositions Problem Solving Estimation Concepts Skills Confidence Flexibility Initiative Risk Representational Physical Digital

21st century numeracy Contexts Tools Mathematical Knowledge Dispositions Problem Solving Estimation Concepts Skills Confidence Flexibility Initiative Risk Representational Physical Digital

21st century numeracy Contexts Tools Mathematical Knowledge Personal and Social Dispositions Problem Solving Estimation Concepts Skills Confidence Flexibility Initiative Risk Representational Physical Digital

21st century numeracy Contexts Tools Mathematical Knowledge Personal and Social Dispositions Work Problem Solving Estimation Concepts Skills Confidence Flexibility Initiative Risk Representational Physical Digital

21st century numeracy Contexts Tools Mathematical Knowledge Personal and Social Citizenship Dispositions Work Problem Solving Estimation Concepts Skills Confidence Flexibility Initiative Risk Representational Physical Digital

21st century numeracy Contexts Tools Mathematical Knowledge Personal and Social Citizenship Dispositions Work Problem Solving Estimation Concepts Skills Confidence Flexibility Initiative Risk Representational Physical Digital Critical Orientation

Research study A one year action research study that investigated approaches to help teachers plan and implement numeracy strategies across all curriculum areas in Grades teachers in 10 schools – primary school teachers, secondary mathematics teachers, secondary non- mathematics teachers o To what extent did teachers’ classroom practice change over time as they engaged with the numeracy model? o How effective was the professional development approach in building teachers’ confidence in numeracy teaching?

Research design TimeActivityData sources MarchTeacher meeting (1 day): introduce numeracy model; try out numeracy teaching strategies and tasks; plan for implementation Surveys numeracy teaching confidence understanding of numeracy JuneSchool visits (1 day per school): observe and evaluate implementation Lesson observations, interviews, teaching materials AugustTeacher meeting (1 day): evaluate implementation; share teaching resources and strategies; plan for implementation OctoberSchool visits (1 day per school): observe and evaluate implementation Lesson observations, interviews, teaching materials NovemberTeacher meeting (1 day): evaluate implementation; reflect on professional learning Surveys numeracy teaching confidence understanding of numeracy Map trajectory through the numeracy model

Contexts Tools Mathematical Knowledge Dispositions Changes in classroom practice: Teachers’ trajectories through the numeracy model Critical Orientation

Changes in classroom practice: Case study First school visit: Investigating newspapers What is the percentage of different forms of “news” in a newspaper? (e.g., sport, local news, world news, feature articles, weather)

Changes in classroom practice: Case study Year 8 Society and Environment: Building an Expressway What is the best route for a new expressway to be built between Whyalla and Adelaide? Students provided with maps (1cm square grid) and grid references for start and end points. Route must only cross one river. Route must cross Gawler-One Tree Hill Road then rejoin Main North Road. Bends must be equal to or greater than 110 degrees. Must not pass nearer than one grid square to a quarry. Residents to be compensated at $150,000 per grid square for any land resumed. Crossing Uleybury vineyard to be kept to a minimum because compensation to residents is $500,000 per grid square. DESIGN FOR MINIMUM COST. USE A LENGTH OF WOOLLEN YARN TO MARK OUT THE ROUTE.

Building an expressway Contexts Engineering NIMBY Tools Mathematical Knowledge Dispositions Measurement Estimation Number Confidence Flexibility Authenticity Protractors Rulers Maps Critical Orientation Make decisions about cost vs most direct route

Changes in classroom practice: Case study “I felt that my involvement in the project has changed who I am, both professionally and personally.”

Changes in numeracy teaching confidence A survey was designed, based on Queensland’s Numeracy Standards for Graduates of Pre-Service Teacher Education Programs. The Numeracy Standards address three domains: Professional knowledge: knowledge of students, of numeracy, of students’ numeracy learning Professional attributes: personal attributes, personal professional development, community responsibility Professional practice: learning environment, planning, teaching, assessment

Changes in numeracy teaching confidence PreHighLow PostHigh Low Recognising the diversity of students’ numeracy learning needs. Understanding the nature of numeracy and its relevance to all curriculum areas. Understanding how students learn mathematics. Planning for numeracy learning and assessment. Using a range of effective numeracy teaching and assessment strategies. Using multiple representations and digital technologies to enhance students’ numeracy learning. Fostering risk taking and critical inquiry in numeracy learning. Catering for the diversity of students’ numeracy learning needs.

Conclusions We found encouraging evidence of teacher change and development. Teaching in context is difficult – mathematical knowledge may not transfer easily from one context to another. Recognising numeracy opportunities as they arise during a lesson is challenging for teachers The numeracy model can be used by teachers for curriculum planning and by researchers to track teacher development.

Transforming professional practice: Teaching numeracy across the curriculum Merrilyn Goos