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New tools, new learners … new numeracies?

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?

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

  2. 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?

  3. What is numeracy? • Numeracy involves … • A numerate person can … • A numerate person knows … • A numerate person is …

  4. 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

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

  6. 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)

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

  8. 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

  9. 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

  10. 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)

  11. 21st century numeracy Mathematical knowledge Contexts Tools Dispositions

  12. 21st century numeracy Mathematical knowledge Skills Concepts Estimation Problem solving Contexts Tools Dispositions

  13. 21st century numeracy Mathematical knowledge Skills Concepts Estimation Problem solving Contexts Risk Initiative Flexibility Confidence Tools Dispositions

  14. 21st century numeracy Mathematical knowledge Skills Concepts Estimation Problem solving Contexts Risk Initiative Flexibility Confidence Digital Physical Representational Tools Dispositions

  15. 21st century numeracy Mathematical knowledge Skills Concepts Estimation Problem solving Contexts Risk Initiative Flexibility Confidence Digital Physical Representational Tools Dispositions

  16. 21st century numeracy Mathematical knowledge Skills Concepts Estimation Problem solving Personal andsocial Contexts Risk Initiative Flexibility Confidence Digital Physical Representational Tools Dispositions

  17. 21st century numeracy Mathematical knowledge Skills Concepts Estimation Problem solving Personal andsocial Work Contexts Risk Initiative Flexibility Confidence Digital Physical Representational Tools Dispositions

  18. Workplace numeracy: Pilots calculating crosswind crosswind 45º Wind velocity20 knots runway

  19. 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.”

  20. Workplace numeracy: Pilots calculating crosswind Watch face estimate 0.75

  21. Workplace numeracy: Pilots calculating crosswind Watch face estimate 0.75 Actual value 0.71

  22. 21st century numeracy Mathematical knowledge Skills Concepts Estimation Problem solving Personal andsocial Work Contexts Risk Initiative Flexibility Confidence Digital Physical Representational Tools Citizenship Dispositions

  23. Numeracy for critical citizenship

  24. Numeracy for critical citizenship YES

  25. 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

  26. 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

  27. Numeracy for critical citizenship Might you be in favour of re-introducing National Service? Yes!

  28. Numeracy for critical citizenship Are you worried about the danger of war? Yes Are you unhappy with the growth of armaments? Yes

  29. 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

  30. Numeracy for critical citizenship Would you oppose the re-introduction of National Service? Yes!

  31. 21st century numeracy Mathematical knowledge Skills Concepts Estimation Problem solving Personal andsocial Work Contexts Risk Initiative Flexibility Confidence Digital Physical Representational Tools Citizenship Dispositions

  32. 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

  33. Tendering a category

  34. 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

  35. 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

  36. 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

  37. 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

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

  39. 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.”

  40. 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.”

  41. Technology as a numeracy tool

  42. Exploiting contexts for numeracy • Connections to real life • Connections to other school subjects

  43. 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

  44. 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

  45. 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

  46. Cartograms - a different kind of map Area Population www.worldmapper.org

  47. Cartograms - a different kind of map Wealth 2002 Undernourishment2000

  48. Cartograms - a different kind of map Military spending2002 War deaths 2002

  49. Cartograms - a different kind of map Toy exports Toy imports

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