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New Strengths in the Curriculum’s Statistics

New Strengths in the Curriculum’s Statistics. Auckland Maths Assoc: PD Day: 25 Nov 2008. Mike Camden: Statistics New Zealand NZ Statistical Association: Education Committee mike.camden@stats.govt.nz. The views in here are Mike’s. Aims:.

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New Strengths in the Curriculum’s Statistics

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  1. New Strengths in the Curriculum’s Statistics Auckland Maths Assoc: PD Day: 25 Nov 2008 Mike Camden: Statistics New ZealandNZ Statistical Association: Education Committee mike.camden@stats.govt.nz The views in here are Mike’s.

  2. Aims: • To get us feeling even better about the Stats in The NZ Curriculum’sMaths and Stats: it is:commonsense, do-able, visual, fun, novel, useful, vital • To help ensure that our students will contribute to:health, sustainability, climate, justice …(from West Aust Mathematics Curriculum Framework) • To give bright ideas for next week,next year!

  3. Contents: • The handout: a range of activities • New Strengths in Curriculum’s Statistics:Two big ideas: one woolly, one sharpStructures in the Statistics strandStructures in Cheese • An investigation with Paua (Item 1)the storyactivity 1 • More investigations: multivariate situations:stories about Items 2 to 7 activities 2 to 12 (some of) • Conclusion: analysis => graphs

  4. But first: two historical items: 1: from 1908: • William Gosset discovers • the Student t distribution • in the Guinness Brewery, Dublin 2: from 1863: …

  5. 2: Florence to George: 1863 • “Real Gold: Treasures of Auckland City Library” Letter to Sir George Gray, 28 Jul 1863, ending:You will do a noble work in New Zealand. • But pray think of your statistics. • I need not say, think of your Schools. • But people often despise statistics • as not leading to immediate good. • Believe meYours ever SincerelyFlorence Nightingale • http://0-www.aucklandcity.govt.nz.www.elgar.govt.nz/dbtw-wpd/virt-exhib/realgold/Science/florence-nightingale.html

  6. And an ad break … • See NZ Stat Assoc site: http://nzsa.rsnz.org/ • and its new teachers page: http://nzsa.rsnz.org/teachers.shtml • See StatsNZ site: http://www.stats.govt.nz • and its Schools Corner • and its brand newInfoshare system:Time Series galore!

  7. And a pic of the Waitakere City gender balance:

  8. And a pic of the Kapiti gender balance:

  9. Two big ideas: one woolly, one sharp • The woolly big idea: two sides of maths • The sharp big idea: the highly technical bit

  10. The woolly big idea: two sides of maths: Deterministic mathematics: Number Algebra Measurement Space WA: ‘in context … investigate, generalise, reason, conclude about patterns in number... space …. Stochastic mathematics: Chance and Data (probability and statistics) WA: ‘locate, interpret, analyse, conclude from data … … with chance’ … and data’ • They have: • big similarities … • big differences … Writers of resources, texts, activities, assessmentscould aim for this patch: a fresh challenge

  11. The 2 sides: similarities and differences • Similarities: The Western Australia version: • ‘People who are mathematically able [in both bits] can contribute greatly towards many difficult issues facing the world today: health, environmental sustainability, climate change, social injustice.’ • Differences: • They’re different in how they are:used, learnt, taught, integrated. • They’re different in how they use:mathematical thinking and rigor.

  12. The sharp big idea: the highly technical bit • John Tukey • 1915-2000 • Stats prof at Princeton • Inventer of Fast Fourier Transform Tukey’s test for means… etc etc etc etc etc etc etc EDA (1977) Stem-and-leaf Box-and-whisker etc etc

  13. The sharp big technical idea from Tukey: • ‘If you haven’t done a graph,then you haven’t done an analysis.’ • He intended this for: Statisticians at work Students Please Vote Teachers

  14. Some determinist mathematical logic: • ‘You haven’t done a graph => You haven’t done an analysis’ • Or in brief: • No Graph => No Analysis • Can be seen as: Analysis => Graph(s)

  15. An eg from Tukey’s EDA book: Nitrogen: • Rayley (1894) wanted density of Nitrogen: • Gets N from 15 sources: 7 from air 8 from other sources He discovered …. (Hint: starts with A)

  16. Structures in the Statistics strand • The Statistics strand is: • A Haphazard Heap A Subtle Set of Structures Please Vote The Pie Box and whisker thingy line graph The t test mode Something normal Stem and leaf average median spread

  17. Most of MAWA votes for Structure …

  18. The Waikato teachers vote: Photo: Harold Henderson

  19. Structures in Stat Investigations: in brief: 1: The Statistical Enquiry Cycle: Problem → Plan → Data → Analysis → Conclusion 2: Datasets: case, series 3: Variables: Categorical, Numerical 4: Exploration, Analysis 5: The group we’re investigating: 6: Graphs: two roles 7: Variation … Variation …Variation …Variation …Variation

  20. Structures in Stats Investigs bit: contd: 2: Datasets: case, series 3: Variables: Categorical, Numerical

  21. Structures in Stats Investigs bit: contd 4: Exploration, Analysis 1 variable: Categorical Numerical2 variables: x and y: Categorical / Categorical Categorical / Numerical Numerical / Categorical Numerical / Numerical 3 variables: hmmmmmmmm4 and more variables ……... The Pauas: item 1 The others: items 2 to 7 Graphics make all this accessible.

  22. Structures in Stats Investigs bit: contd 5: The group we’re investigating: A population … from a population A sample … In Curriculum from Level 6

  23. Structures in Stats Investigs bit: concld 6: Graphs: two roles Problem → Plan → Data → Analysis → Conclusion Graphs for Exploration, Analysis, Discovery: Graphs for Communication of findings: Underlying everything in life and work (and Stats): 7: Variation … Variation …Variation …Variation …Variation The Mathematics and Statistics in The NZCurriculum progresses through all these structures

  24. Structures in the Probability strand: brief: Question or Experiment → Outcomes → Probabilities → Probability distribution → Decisions Has the coffee arrived yet? OutcomeProbability Yes 0.3 No 0.7 These things go from beingOut Ofs to Fractions to Proportions to Percentages to Probs;and that’s hard!

  25. Structures in Cheese • My problem:I like eating cheeseI avoid saturated fat and salt • What do I do?

  26. Cheese continued: Whitestone, Oamaru, makes: cheese datasets Map from www.geographx.co.nz

  27. Cheese: the data: • What do we do now??

  28. Graphs of 2 ‘univariate’ distributions: Fetas What do we do now??

  29. Graph of a ‘bivariate’ distribution: How many variables? What sorts? What do I eat?? Other conclusions??

  30. An investigation with Paua (Item 1) • The story • The activity • And a mini-version: …

  31. 1: Shellfish in Court: a Paua story • Pauas (A) are taken from a bay, legally. Pauas (B) may have come from a marine reserve. • What might 2 the distributions look like? • How would your students graph them? • What would a judge think? • What actually happened??? Legal minimum: length > = 125 mm

  32. Paua distributions for the judge: • Source: I Westbrooke, NZ Dept of Conservation

  33. More investigations: multivariate situations: • Stories about Items 2, 3, 5, 6, 7 • Activities on these

  34. 2: Census data from the neighbours: • Data on Westn Aust’s 156 ‘Statistical Local Areas’: A question: How big is the average WA household?? A look: Female vs Male numbers for the SLAs: ( It’s easy for kids to do this for their town,from www.stats.govt.nz )

  35. How big is the average WA household??

  36. Female vs Male numbers for the 156 WA SLAs: withRegression, Residuals, and Remoteness

  37. 3: Txt Olympics: www.learnngmedia.co.nzAn activity from a new Media/Stats book: Motutapu College is holding a Texting Olympics to find out who has the fastest thumb in the school! Events include: The Sprint Call me The Marathon Can you pick me up after school today. I have football practice and won’t be able to catch the bus. The Hurdles Guess what? I got 90% in my probability test!!! We’ll use this to do some ‘Statistical Thinking’ …

  38. Texting Olympic: Activity 1 (of 5) • ‘You need to select five students for the finals of “The fastest thumb in school”. • They need to be the five students who can best represent the class in all three events. • Discuss with a classmate your ideas on how to select these students. • Justify your decision with reference to the data’ A Year 9 class at Newlands College (Wellington) borrowed stopwatches …

  39. The Txt data: • What do we do now?? Times are inmin.sec.hundredths

  40. Sprints: the univariate distribution: Add variables by re-using data-ink: Draw graph as blocks; write names in blocks; Colour-code: girls and boys What now??

  41. Hurdles vs Marathon: bivariate distribution That blue y = x line is for the determinists and synergists! y = x Conclusion:words numbers graphs working together (Edwin Tufte) Ms Speed

  42. 4: Cheese: Done! • Data Graphics for Exploration, Communication:

  43. 5: Dolphins: possums • Hector’s Dolphin: North Island South Island populations • Are they different sub-species? • Dataset contains head length head width etc • for 59 individuals • What do we do??

  44. Dataset comes from 59 skeletons in 3 museums. Selected measurements: simplified definitions: RWM - rostrum width at midlength RWB – rostrum width at base RL – rostrum length ZW – zygomatic width CBL - condylobasal length ML – mandible length We’ll use Width, Length

  45. Are they different sub-species?

  46. 6: Possum Browse: • Australian brush-tailed possum Trichosurus vulpecula • Introduced 1837 and 450 times • No natural predators • Damages foliage, fruit, birds • A BACI project: Before/After Control/Intervention • Two ‘lines’ chosen ‘Control’ not treated ‘Intervention’: 1080 poison by air • Percentage foliage cover estimated Before/After at 38+23 trees.

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