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New tools, new learners … new numeracies?. Merrilyn Goos The University of Queensland. 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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New tools new learners new numeracies

New tools, new learners … new numeracies?

Merrilyn Goos

The University of Queensland


Some questions

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?


What is numeracy

What is numeracy?

  • Numeracy involves …

  • A numerate person can …

  • A numerate person knows …

  • A numerate person is …


What is numeracy1

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


Early definitions of numeracy

Early definitions of numeracy

  • The mirror image of literacy, but involving quantitative thinking.

    Crowther Report, 1959 (UK)


Early definitions of numeracy1

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)


Elements of quantitative literacy

Elements of quantitative literacy

culturalappreciation

numbersense

symbolsense

confidence withmathematics

logicalthinking

practicalskills

quantitativeliteracy

makingdecisions

mathematicsin context

prerequisiteknowledge

interpretingdata


Mathematical literacy

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 individual’s current and future private life, occupational life, social life with peers and relatives, and life as a constructive, concerned and reflective citizen.

PISA, 2001


Distinguishing numeracy from mathematics

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


20th century numeracy

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)


21st century numeracy

21st century numeracy

Mathematical knowledge

Contexts

Tools

Dispositions


21st century numeracy1

21st century numeracy

Mathematical knowledge

Skills

Concepts

Estimation

Problem solving

Contexts

Tools

Dispositions


21st century numeracy2

21st century numeracy

Mathematical knowledge

Skills

Concepts

Estimation

Problem solving

Contexts

Risk

Initiative

Flexibility

Confidence

Tools

Dispositions


21st century numeracy3

21st century numeracy

Mathematical knowledge

Skills

Concepts

Estimation

Problem solving

Contexts

Risk

Initiative

Flexibility

Confidence

Digital

Physical

Representational

Tools

Dispositions


21st century numeracy4

21st century numeracy

Mathematical knowledge

Skills

Concepts

Estimation

Problem solving

Contexts

Risk

Initiative

Flexibility

Confidence

Digital

Physical

Representational

Tools

Dispositions


21st century numeracy5

21st century numeracy

Mathematical knowledge

Skills

Concepts

Estimation

Problem solving

Personal andsocial

Contexts

Risk

Initiative

Flexibility

Confidence

Digital

Physical

Representational

Tools

Dispositions


21st century numeracy6

21st century numeracy

Mathematical knowledge

Skills

Concepts

Estimation

Problem solving

Personal andsocial

Work

Contexts

Risk

Initiative

Flexibility

Confidence

Digital

Physical

Representational

Tools

Dispositions


Workplace numeracy pilots calculating crosswind

Workplace numeracy: Pilots calculating crosswind

crosswind

45º

Wind velocity20 knots

runway


Calculating crosswind using a watch face

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.”


Workplace numeracy pilots calculating crosswind1

Workplace numeracy: Pilots calculating crosswind

Watch face estimate 0.75


Workplace numeracy pilots calculating crosswind2

Workplace numeracy: Pilots calculating crosswind

Watch face estimate 0.75

Actual value 0.71


21st century numeracy7

21st century numeracy

Mathematical knowledge

Skills

Concepts

Estimation

Problem solving

Personal andsocial

Work

Contexts

Risk

Initiative

Flexibility

Confidence

Digital

Physical

Representational

Tools

Citizenship

Dispositions


Numeracy for critical citizenship

Numeracy for critical citizenship


Numeracy for critical citizenship1

Numeracy for critical citizenship

YES


Numeracy for critical citizenship2

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


Numeracy for critical citizenship3

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


Numeracy for critical citizenship4

Numeracy for critical citizenship

Might you be in favour of re-introducing National Service?

Yes!


Numeracy for critical citizenship5

Numeracy for critical citizenship

Are you worried about the danger of war?

Yes

Are you unhappy with the growth of armaments?

Yes


Numeracy for critical citizenship6

Numeracy for critical citizenship

Do you think there’s a danger in giving young people guns and teaching them how to kill?

Yes

Do you think it’s wrong to force young people to take up arms against their will?

Yes


Numeracy for critical citizenship7

Numeracy for critical citizenship

Would you oppose the re-introduction of National Service?

Yes!


21st century numeracy8

21st century numeracy

Mathematical knowledge

Skills

Concepts

Estimation

Problem solving

Personal andsocial

Work

Contexts

Risk

Initiative

Flexibility

Confidence

Digital

Physical

Representational

Tools

Citizenship

Dispositions


Case study young adults work related numeracy practices

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


Tendering a category

Tendering a category


How can we develop numeracy practices at school

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


How can we develop numeracy practices at school1

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


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.

Exploiting tools for numeracy


Technology as master

I often don’t know if I’ve used it correctly and as a consequence I can’t be sure if my answer is correct or not.

Technology as Master


Technology as servant

I regularly use technology for familiar tasks purely as a time saver and to verify and check my answers.

Technology as Servant


Technology as partner

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 don’t know what I’d do without him.”


Technology as extension of self

Technology as Extension of Self

“My calculator is practically a part of myself. It’s like my third brain. I use it whenever it can help me do anything faster.”


Technology as a numeracy tool

Technology as a numeracy tool


Exploiting contexts for numeracy

Exploiting contexts for numeracy

  • Connections to real life

  • Connections to other school subjects


Who counts as unemployed

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 wouldn’t 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

  • Don’t want to work

  • Permanently unable to work


Who counts as unemployed1

Who counts as “unemployed”?

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 wouldn’t 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

  • Don’t want to work

  • Permanently unable to work

marginally attached

no marginal attachment


Who counts as unemployed2

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


Cartograms a different kind of map

Cartograms - a different kind of map

Area

Population

www.worldmapper.org


Cartograms a different kind of map1

Cartograms - a different kind of map

Wealth 2002

Undernourishment2000


Cartograms a different kind of map2

Cartograms - a different kind of map

Military spending2002

War deaths 2002


Cartograms a different kind of map3

Cartograms - a different kind of map

Toy exports

Toy imports


Barbie and beauty

Barbie and beauty

  • Is Barbie a realistic representation of human proportions?

  • What would Barbie look like if scaled up to human height?


Numeracy messages

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.


New tools new learners new numeracies1

New tools, new learners … new numeracies?

Merrilyn Goos

The University of Queensland

[email protected]


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