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Transforming professional practice: Teaching numeracy across the curriculum

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Title: Transforming professional practice: Teaching numeracy across the curriculum


1
Transforming professional practice Teaching
numeracy across the curriculum
  • Merrilyn Goos

2
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.

3
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

4
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)

5
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)

6
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.

7
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)

8
21st century numeracy
Dispositions
Tools
Contexts
Mathematical Knowledge
9
21st century numeracy
Dispositions
Tools
Contexts
Problem Solving Estimation Concepts Skills
Mathematical Knowledge
10
21st century numeracy
Dispositions
Tools
Confidence Flexibility Initiative Risk
Contexts
Problem Solving Estimation Concepts Skills
Mathematical Knowledge
11
21st century numeracy
Dispositions
Tools
Confidence Flexibility Initiative Risk
Representational Physical Digital
Contexts
Problem Solving Estimation Concepts Skills
Mathematical Knowledge
12
21st century numeracy
Dispositions
Tools
Confidence Flexibility Initiative Risk
Representational Physical Digital
Contexts
Problem Solving Estimation Concepts Skills
Mathematical Knowledge
13
21st century numeracy
Dispositions
Tools
Confidence Flexibility Initiative Risk
Representational Physical Digital
Contexts
Problem Solving Estimation Concepts Skills
Personal and Social
Mathematical Knowledge
14
21st century numeracy
Dispositions
Tools
Confidence Flexibility Initiative Risk
Representational Physical Digital
Contexts
Problem Solving Estimation Concepts Skills
Personal and Social
Work
Mathematical Knowledge
15
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
16
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
17
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?

18
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
19
Changes in classroom practice Teachers
trajectories through the numeracy model
Tools
Dispositions
Contexts
Mathematical Knowledge
Critical Orientation
20
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)

21
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.

22
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
23
Changes in classroom practice Case study
  • I felt that my involvement in the project has
    changed who I am, both professionally and
    personally.

24
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

25
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.
26
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.

27
Transforming professional practice Teaching
numeracy across the curriculum
  • Merrilyn Goos
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