Transforming professional practice: Teaching numeracy across the curriculum

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Transforming professional practiceTeaching
numeracy across the curriculum

• Merrilyn Goos

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Numeracy means different things to different
people

• PISA definition of mathematical literacy
• An individuals 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 individuals 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
Dispositions
Tools
Contexts
Mathematical Knowledge
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21st century numeracy
Dispositions
Tools
Contexts
Problem Solving Estimation Concepts Skills
Mathematical Knowledge
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21st century numeracy
Dispositions
Tools
Confidence Flexibility Initiative Risk
Contexts
Problem Solving Estimation Concepts Skills
Mathematical Knowledge
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21st century numeracy
Dispositions
Tools
Confidence Flexibility Initiative Risk
Representational Physical Digital
Contexts
Problem Solving Estimation Concepts Skills
Mathematical Knowledge
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21st century numeracy
Dispositions
Tools
Confidence Flexibility Initiative Risk
Representational Physical Digital
Contexts
Problem Solving Estimation Concepts Skills
Mathematical Knowledge
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21st century numeracy
Dispositions
Tools
Confidence Flexibility Initiative Risk
Representational Physical Digital
Contexts
Problem Solving Estimation Concepts Skills
Personal and Social
Mathematical Knowledge
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21st century numeracy
Dispositions
Tools
Confidence Flexibility Initiative Risk
Representational Physical Digital
Contexts
Problem Solving Estimation Concepts Skills
Personal and Social
Work
Mathematical Knowledge
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21st century numeracy
Citizenship
Dispositions
Tools
Confidence Flexibility Initiative Risk
Representational Physical Digital
Contexts
Problem Solving Estimation Concepts Skills
Personal and Social
Work
Mathematical Knowledge
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21st century numeracy
Citizenship
Dispositions
Tools
Confidence Flexibility Initiative Risk
Representational Physical Digital
Contexts
Problem Solving Estimation Concepts Skills
Personal and Social
Work
Mathematical Knowledge
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
• To what extent did teachers classroom practice
  change over time as they engaged with the
  numeracy model?
• 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
October School visits (1 day per school) observe and evaluate implementation Lesson observations, interviews, teaching materials
November 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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Changes in classroom practice Teachers
trajectories through the numeracy model
Tools
Dispositions
Contexts
Mathematical Knowledge
Critical Orientation
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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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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.

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Building an expressway
Dispositions
Tools
Confidence Flexibility Authenticity
Protractors Rulers Maps
Contexts Engineering NIMBY
Measurement Estimation Number
Make decisions about cost vs most direct route
Mathematical Knowledge
Critical Orientation
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Changes in classroom practice 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 Queenslands
  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 practiceTeaching
numeracy across the curriculum

• Merrilyn Goos