New tools, new learners new numeracies

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New tools, new learners new numeracies?

• Merrilyn Goos
• The University of Queensland

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Some questions

• What is meant by numeracy in the 21st century?
• What repertoire of numeracy practices do young
  people demonstrate in life outside school?
• How can we develop numeracy practices at school?

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What is numeracy?

• Numeracy involves
• A numerate person can
• A numerate person knows
• A numerate person is

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What is numeracy?

• Some lay views of numeracy
• numbers (doing sums, arithmetic)
• the basic maths people need in order to survive
  in the real world
• the name for primary school maths
• the name for the vegie maths subject in secondary
  school

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Early definitions of numeracy

• The mirror image of literacy, but involving
  quantitative thinking.
• Crowther Report, 1959 (UK)

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Early definitions of numeracy

• Possessing an at homeness with numbers and an
  ability to use mathematical skills to cope
  confidently with the practical demands of
  everyday life, together with understanding of
  information presented in mathematical terms.
• Cockcroft Report, 1982 (UK)

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Elements of quantitative literacy
culturalappreciation
numbersense
symbolsense
confidence withmathematics
logicalthinking
practicalskills
quantitativeliteracy
makingdecisions
mathematicsin context
interpretingdata
prerequisiteknowledge
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Mathematical literacy

• Mathematical literacy is the capacity to
  identify, understand and engage in mathematics,
  and to make well-founded judgments about the role
  that mathematics plays in an individuals current
  and future private life, occupational life,
  social life with peers and relatives, and life as
  a constructive, concerned and reflective citizen.
• PISA, 2001

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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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20th century 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.
• Numeracy, A Priority for All
• (DETYA, 2000)

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21st century numeracy
Mathematical knowledge
Contexts
Tools
Dispositions
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21st century numeracy
Mathematical knowledge
Skills Concepts Estimation Problem solving
Contexts
Tools
Dispositions
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21st century numeracy
Mathematical knowledge
Skills Concepts Estimation Problem solving
Contexts
Risk Initiative Flexibility Confidence
Tools
Dispositions
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21st century numeracy
Mathematical knowledge
Skills Concepts Estimation Problem solving
Contexts
Risk Initiative Flexibility Confidence
Digital Physical Representational
Tools
Dispositions
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21st century numeracy
Mathematical knowledge
Skills Concepts Estimation Problem solving
Contexts
Risk Initiative Flexibility Confidence
Digital Physical Representational
Tools
Dispositions
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21st century numeracy
Mathematical knowledge
Skills Concepts Estimation Problem solving
Personal andsocial
Contexts
Risk Initiative Flexibility Confidence
Digital Physical Representational
Tools
Dispositions
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21st century numeracy
Mathematical knowledge
Skills Concepts Estimation Problem solving
Personal andsocial
Work
Contexts
Risk Initiative Flexibility Confidence
Digital Physical Representational
Tools
Dispositions
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Workplace numeracy Pilots calculating crosswind
crosswind
45º
Wind velocity20 knots
runway
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Calculating crosswind using a watch face

• Angle is 45º 45 minutes is three quarters
  around the watch face so the crosswind component
  is about three quarters of the 20 knot wind
  speed, namely 15 knots.

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Workplace numeracy Pilots calculating crosswind
Watch face estimate 0.75
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Workplace numeracy Pilots calculating crosswind
Watch face estimate 0.75
Actual value 0.71
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21st century numeracy
Mathematical knowledge
Skills Concepts Estimation Problem solving
Personal andsocial
Work
Contexts
Risk Initiative Flexibility Confidence
Digital Physical Representational
Tools
Citizenship
Dispositions
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Numeracy for critical citizenship
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Numeracy for critical citizenship
YES
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Numeracy for critical citizenship
Are you worried about the rise in crime among
teenagers?
Yes
Do you think there is a lack of discipline and
vigorous training in our Comprehensive Schools?
Yes
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Numeracy for critical citizenship
Do you think young people welcome some structure
and leadership in their lives?
Yes
Do they respond to a challenge?
Yes
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Numeracy for critical citizenship
Might you be in favour of re-introducing National
Service?
Yes!
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Numeracy for critical citizenship
Are you worried about the danger of war?
Yes
Are you unhappy with the growth of armaments?
Yes
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Numeracy for critical citizenship
Do you think theres a danger in giving young
people guns and teaching them how to kill?
Yes
Do you think its wrong to force young people to
take up arms against their will?
Yes
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Numeracy for critical citizenship
Would you oppose the re-introduction of National
Service?
Yes!
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21st century numeracy
Mathematical knowledge
Skills Concepts Estimation Problem solving
Personal andsocial
Work
Contexts
Risk Initiative Flexibility Confidence
Digital Physical Representational
Tools
Citizenship
Dispositions
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Case study Young adults work related numeracy
practices

• Large food manufacturing company
• Supply and purchasing
• Training two young people (aged 22 and 26) to be
  category managers
• Gave them a category to tender plastic film and
  machine tape

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Tendering a category
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How can we develop numeracy practices at school?
Mathematical knowledge
Skills Concepts Estimation Problem solving
Personal andsocial
Work
Contexts
Risk Initiative Flexibility Confidence
Digital Physical Representational
Tools
Citizenship
Dispositions
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How can we develop numeracy practices at school?
Mathematical knowledge
Skills Concepts Estimation Problem solving
Personal andsocial
Work
Contexts
Risk Initiative Flexibility Confidence
Digital Physical Representational
Tools
Citizenship
Dispositions
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Exploiting tools for numeracy

• Claim
• Technology robs learners of the ability to
  think.
• Counter claim
• Technology can change and enhance the way humans
  solve problems.

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Technology as Master
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Technology as Servant
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Technology as Partner

• My calculator has become my best friend. His
  name is Wilbur. Me and Wilbur go on fantastical
  adventures together through Maths land. I dont
  know what Id do without him.

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Technology as Extension of Self

• My calculator is practically a part of myself.
  Its like my third brain. I use it whenever it
  can help me do anything faster.

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Calculators in Primary Mathematics project

• 6 Melbourne schools 1000 children 80 teachers
• Prep-Year 4
• Children given their own arithmetic calculators
• Teachers not provided with activities or program

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Technology as a numeracy tool
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Technology as partner
Underground numbers!
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Exploiting contexts for numeracy

• Connections to real life
• Connections to other school subjects

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Who counts as unemployed?

• Want to work, actively looking for work,
  available to start work immediately
• Want to work, actively looking for work,
  available to start work within 4 weeks
• Want to work, actively looking for work, not
  available to start work within 4 weeks
• Want to work, not actively looking because they
  believe they wouldnt be able to find a job, but
  would be able to start within 4 weeks
• Want to work but not actively looking and not
  available to start within 4 weeks
• Dont want to work
• Permanently unable to work

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Who counts as unemployed?

• Want to work, actively looking for work,
  available to start work immediately
• Want to work, actively looking for work,
  available to start work within 4 weeks
• Want to work, actively looking for work, not
  available to start work within 4 weeks
• Want to work, not actively looking because they
  believe they wouldnt be able to find a job, but
  would be able to start within 4 weeks
• Want to work but not actively looking and not
  available to start within 4 weeks
• Dont want to work
• Permanently unable to work

unemployed
marginally attached
no marginal attachment
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Who counts as unemployed?

• How would the unemployment rate change if we
  redefined the labour force to include people
  who are designated as marginally attached to the
  labour force?
• Go to unemployment spreadsheet

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Cartograms - a different kind of map
Area
Population
www.worldmapper.org
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Cartograms - a different kind of map
Wealth 2002
Undernourishment2000
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Cartograms - a different kind of map
Military spending2002
War deaths 2002
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Cartograms - a different kind of map
Toy exports
Toy imports
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Barbie and beauty

• Is Barbie a realistic representation of human
  proportions?
• What would Barbie look like if scaled up to human
  height?

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Numeracy messages

• Numeracy has no content of its own - it inherits
  its content from the context.
• Workers do use mathematics but not necessarily
  the standard, visible mathematics taught at
  school.
• Technology is ubiquitous in the world outside
  school and should be exploited intelligently to
  develop students numeracy practices.

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New tools, new learners new numeracies?

• Merrilyn Goos
• The University of Queensland
• m.goos_at_uq.edu.au