Teaching numeracy across the curriculum

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Transforming professional practice:

Merrilyn Goos

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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.

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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

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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)

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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)

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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.

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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)

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21st century numeracy

Contexts

Tools

Mathematical Knowledge Dispositions

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Contexts

Tools

Problem Solving Estimation

Concepts Skills

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21st century numeracy

Contexts

Tools

Concepts Skills

Confidence Flexibility

Initiative Risk

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Contexts

Tools

Concepts Skills

Initiative Risk

Representationa l

Physical Digital

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21st century numeracy

Contexts

Tools

Concepts Skills

Initiative Risk

Representationa l

Physical Digital

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Contexts

Tools

Mathematical Knowledge

Personal and Social

Dispositions

Concepts Skills

Initiative Risk

Representationa l

Physical Digital

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21st century numeracy

Contexts

Tools

Personal and Social

Dispositions

Problem Work Solving Estimation

Concepts Skills

Initiative Risk

Representationa l

Physical Digital

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Contexts

Tools

Personal and Social

Citizenship

Dispositions

Concepts Skills

Initiative Risk

Representationa l

Physical Digital

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21st century numeracy

Contexts

Tools

Personal and Social

Citizenship

Dispositions

Concepts Skills

Initiative Risk

Representationa l

Physical Digital

Critical Orientation

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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 6-9

• 20 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?

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Research design

Time Activity Data sources

March Teacher meeting (1 day):

introduce numeracy model; try out numeracy teaching

strategies and tasks; plan for implementation

Surveys

• numeracy teaching confidence

• understanding of numeracy

June School visits (1 day per school):

observe and evaluate implementation

Lesson observations, interviews, teaching materials

August Teacher meeting (1 day):

evaluate implementation; share teaching resources and

strategies; plan for implementation

Octobe r

School visits (1 day per school):

observe and evaluate implementation

Lesson observations, interviews, teaching materials

Novem

ber Teacher meeting (1 day):

evaluate implementation;

reflect on professional learning

Surveys

• numeracy teaching confidence

• understanding of numeracy

Map trajectory through the numeracy model

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Contexts

Tool s

Mathemati cal

Knowledge Dispositio

ns

Changes in classroom practice: Teachers’

trajectories through the numeracy model

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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)

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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.

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Building an expressway

Contexts

Engineering NIMBY

Tools

Measurement Estimation

Number Confidence

Flexibility Authenticity

Protractors Rulers

Maps

Make decisions about cost vs most direct route

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Case study

“I felt that my involvement in the project has changed who I am, both professionally and personally.”

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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

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Changes in numeracy teaching confidence

Pre High Low Low

Post High High 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.

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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.

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Transforming professional practice:

Teaching numeracy across the curriculum

Merrilyn Goos