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Statistics in the NZ Curriculum Stocktake

Statistics in the NZ Curriculum Stocktake. Mike Camden NZ Statistical Association Education Committee Mike: mike.camden@stats.govt.nz NZSA: http://www.stat.auckland.ac.nz/nzsa/ NZSA Newsletter: http://nzsa.rsnz.govt. nz/newsletter58. Health warning: The views in here belong

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Statistics in the NZ Curriculum Stocktake

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  1. Statistics in the NZ Curriculum Stocktake Mike Camden NZ Statistical Association Education Committee Mike: mike.camden@stats.govt.nz NZSA: http://www.stat.auckland.ac.nz/nzsa/ NZSA Newsletter: http://nzsa.rsnz.govt. nz/newsletter58 Health warning: The views in here belong - Either to the Stat Assoc Education Committee - Or to Mike - Or to both. They are not intended as the views of Statistics New Zealand.

  2. Proposed Contents of Session: A Club Sandwich • Stats in Schools: Intros, multchoice test and the big ideas • Workshop 1: Skills for a “Hot Off The Press” • Background, illustrations, opinions and more illustrations • Workshop 2: Stats and your Essential Learning Area • Conclusion: The chocolate investigation; What Now.

  3. Deterministic and Stochastic Thought • Greek: Stokhastikos: Person who aims, targets, forecasts Stokhos: An aim, target • English: Stochastic: involving ‘random’ probability distributions • There’s an ELA called… • MathsMaths and StatsMaths and Stats and Probability • There’s a bunch of mental tools (“Maths”) with two sides: • Deterministic thinking and modellingStochastic thinking and modelling • They’ve both been around since humans stood up, started talking and drawing, and invented Education! • See Paper 8 in http://wwwmaths.anu.edu.au/other/ncms/mathsdocs/Mumford, D (1999). The dawning of the age of Stochasticity.

  4. Some odd things about Stats: • “Maths” has two sides: • Deterministic and Stochastic • Stats (and Probability) is entangled with….Language: English, Te Reo Maori, the othersGraphics and visual communicationContext: all the ELAsMaths • Stats supports active learning in other ELAsvia “investigations” • “Entangled” has two directions …….

  5. The big questions for this session: • Three questions: • 1: How do we build Curriculum so that Stats supports your ELA? • 2: How do we build Curriculum so that your ELA supports Stats? • 3: How can Curriculum trigger students into enjoying and valuing both your ELA and Stats? • JFK’s version (with stochastic input): And so, my fellow educators, ask not what your ELA can do for Stats; ask what Stats can do for your ELA.

  6. A Multichoice Test: Q 1 of 3: for Achievement: • The NZ Stat Assoc Education Committee’s aim is: • A: Stuff Stats into every crack in the Curriculum • B: Chuck half the Maths and replace it with Stats • C: Streamline the Stats and Insert the Interconnectivity among ELAs • (Yes, I did read the Listener!!)

  7. A Multichoice Test: Q 2 of 3: for Merit: • The Essence of Stats is: • A: Weird graphs with kinky names • B: Weird stuff like s2 = S(x – m)2/ n • C: Investigations, contexts, datasets, variability, exploration, conclusions, communication • Which one would look good in the Maths and Stats Essence Statement??

  8. A Multichoice Test: Q 3 of 3: for Excellence: • Life and the tools we make for enjoying it are • A: Mostly deterministic • B: Mostly stochastic • C: Basically stochastic, but deterministic models are often good working approximations. • Hint: Best answer in each Question is C.

  9. Stats in Schools: The big ideas: 1/3 • Stats is quite different from the rest of Maths (our old theme)and so needs very careful treatment • Stats and the rest of Maths stand together (our new theme)giving stochastic and deterministic models of life • Stochastic (ie, variable) aspects of life are becoming moreobvious: technology, environment, social policy … • Some front-end statistical methods are …fun, commonsense, graphical and suddenly accessible to school students • Context is hugely important in statistical thinkingwhich is where you come in! • Stats in the Curriculum must meet the needs of the parties to the Treaty of Waitangi

  10. Stats in Schools: The big ideas: 2/3 • Stats needs careful curriculum links with … the other Maths strandsthe other essential learning areasthe other layers in the Framework: Principles, Future Focused Themes, Skills, Values, AttitudesIs there a literature on this?? • We need a new engine for Stats curriculum, assessment, professional development, resource making • We need a plan to build capability in Stats Pedagogy in NZ • The NZ Stats Community is aware, alert, offering its insights They want NZ to get the Stats right!

  11. Stats in Schools: The big ideas: 3/3 • Graphical data exploration (data visualisation) is profound, powerful, accessible but takes lots of learning (ie, practice with datasets; yours!!).It must not be seen as trivial! • Any Learning Area can link with Stats so that …both are valued as enjoyable and useful • We’re at the forefront …Dammit!!!

  12. A Scalpel for Stats Curriculum Constructors • Any investigation has these stages: • State the purpose, get approval • Design and/or plan all aspects of it • Collect the data into a Unit Record Dataset • Edit/Launder/Clean the datasetwith graphs etc • Explore and/or analyse the datasetwith graphs etcJohn Tukey: “If you haven’t done a graph, then you haven’t done an analysis” • Summarise the findings/information/conclusions • Communicate the Conclusionswith words, numbers and graphs working together(Edwin Tufte: The visual display of quantitative information) • Lets give up writing “Present the Data with Graphs” forever.

  13. Another Scalpel: • Any dataset that is remotely useful or interesting has several related variables: • We stop pretending that variables ever occur alone. • We replace ‘bi-variate data’and ‘multi-variate data’ by‘dataset’. • This thing’s a Dataset • This thing’s a (Frequency) Table

  14. Workshop 1: Skills: what, where, how • See SNZ’s “Hot Off The Press”, NZ Income Survey June 2003 Quarter; 1 Oct 03. • Assume we want all NZers to be able to read, use and critique things like this. • 1 What skills, attitudes and values do they need? • Whereabouts do we put these skills etc in the Curriculum Framework?? • What does NZ need, to ensure effective teaching, learning and assessment of the skills etc??? • Are we in the right Industry????(See Table 10 near the end)

  15. The Middle Bit: • Background, illustrations, opinions, more illustrations …

  16. Some of the Communities of Interest in Maths Ed • NZSA, its Education Com, Maths Teachers and Curric Makers • The intersections are very small.

  17. NZ Statistical Association Education Committee’s conclusions • On Thur 11 Sept 03, the Committee discussed the Stocktake • at length. Main conclusion: it offers to: • Make input into and review the draft Framework document • Be part of research projects that would underpin curriculum and resource writing • Take a leadership role in the writing of the Statistics strand of the Curriculum document • On Thur 9 Oct, it met with MoE people and discussed: • Making input into Stats in the whole curriculum

  18. Health Report for the Statistics Strand in Maths • Bone structure mostly good but • needs a hip replacement • and some physio elsewhere • Soft tissue functioning but • needs several cut-and-tuck operations, • several shots of Botox • and a body-building programme at the gym; • weight-watchers programme not indicated. • Badly needs a hair transplant. • Socialisation: (the main problem for us today) • needs a ”how to win friends and influence people” course.

  19. Biology Part 1: Stats in NCEA Biology Level 3 • Explanatory Note 7: Recording and processing • Data processing would usually involve calcs and graphing (Good!)to establish a relevant pattern or trend. Stat. procedures, where approp., should be used to establish the reliability (??) of the data e.g. mean, standard deviation, confidence intervals, standard error, difference between two means, ANOVA (??), Chi squared test(??). • Sufficient data involves repeats, trials, appropriate range for the independent variable (Exp Design??), appropriate samp size. • Systematically record means data will be presented in a way (eg table, tally chart) that allows it to be interpreted without reference to the method. (??) • See NZSA Newsletter Sept 03: Gwenda Hill; Stats more advanced (more mathematical?) in Biology than in Maths for NCEA L3

  20. Biology Part 2: Views of senior NZ biometricians • Ian Westbrooke; Dept of Conservation; NZSA Conf Jul 03: • Staff’s (university) stats education has been on hypothesis tests and ANOVAs. • What they need isconfidence intervals that can lead to management decisions, and Exploratory Data Analysis (with graphs) • Harold Henderson, Agresearch; NZAMT8; Jul 03:(Bevan Werry speech) • Powerful new methods of data visualisation… produce a new frontier of data analysis. Visualisation tools provide deep insight into the structure of data…. Dynamic statistical graphics are now widely available…. • Using these, the internal components of NCEA (L3) statistics can be presented by students in ways that are relevant, up-to-date and easy to understand.

  21. Biology Part 3: the morals: • What we can and should do in Stats is changing profoundly and fast • How do we assure Statistics (and Maths) their most useful places in all the learning areas? • How can we make the NZ Curriculum Engine produce 21st century objectives?? 2007

  22. The fun of the fair: • Reflections on the Wellington Science Fair: • Impressive statistics from 8 of the 400 Year 7 and 8 people • The essence of statistical quality for statistics judgesdesignreplicationgraphs that show variabilityconclusions • Science, years 7 and 8, seems to do much of the Experimental Design that has been removed from our NCEA L3! • But we don’t provide the commonsense graphic tools needed. • Reflections on the Canterbury and W Coast Science Fair • Winners had their raw data well displayed, and were able to deal with its variability.

  23. The Point of Inflection in Maths Education History • Statistics is very different from the rest of Maths in… • Its rate of change and its age(it is embryonic or possibly adolescent) • The contexts and ways in which it gets used(and therefore the ways it can be valued) • The way in which today’s complex world of technology and social needs depends on it • The ways it can be taught, learned and assessed(the pedagogy…. And the pedagogues!!) • The ways in which it uses computer technology • The ways it can be integrated with other learning areas • Teacher confidence, professional development needs and resource needs, in Maths and other ELAs

  24. Rabid Opinions 1 of 2 • ValuesStats is founded on a Value:information-based decision-making. • Curriculum and Assessment for Stats:We must make sure the engine pulls the carriage, and not the other way round. • A fourth stage in Statistical education??Stage 1: Traditional (what we got, and forgot!)Stage 2: Reformed (Data and EDA-based)Stage 3: Transformed (Value-based)Stage 4: Blossoming!! (Real issues, great data, dynamic software. It really is new.) • Stats and Maths thinking are different; stats can’t be taught as is it were maths

  25. Rabid Opinions 2 of 2 • Hardware and Software: We’ve got to have it:In biology, chemistry, physics, geography, cooking, clothing, PE, …, students use the real tools and materials of the subject.So must Stats!The tools are the computer hardware and software;The materials are the datasets from the other ELAs. • Students enjoy hands-on work with data, owning projects and completing investigations • The Forefront in Stats education:NZ was there, but is now lagging behind.We need to address this, with your help • The Essential Skill Numeracy needs to stay, andto be enhanced with Stat Reasoning, Thinking and Literacy.

  26. Tupaia and James • Oct 1769; the Endeavour sails from Tahiti to NZ. • Tupaia and James are both strong on..HistoryLanguageGraphicsMaths applied to navigation (Tupaia with sun, stars, wind, swells, clouds, birds and stochastic logic) (James with chronometer, sextant, logs and deterministic logic)Stats applied to demography (Tupaia estimated the size of military groups, James extrapolated to estimate the population of Tahiti) • There are two heritages.

  27. A country has 2 Ethnicities, A (the majority) and B. The results of a survey are shown. Is there equity in income? If not, where should interventions be applied?? What subject is this??? (This happens!!) Equity, Ethnicity and Intervention

  28. Quakes and Spins • In the past, earthquakes were seen as stochastic in space and time (and nasty) • Now, we have:large qnd classy datasetssoftware that can let us look into the data’s structurevisualisation skillsand all these are available to schools. • an Excel interlude….

  29. Workshop 2: Stats and your Essential Learning Area • Please team up with people from your ELA or with similar interests. • Think up an “investigation” with a dataset in it. • What Curriculum Level does it belong at? • What statistical skills does it cal on? • How do we get the skills and the links into curriculum documents? • Or.. Go back to Equity, Ethnicity and Intervention;slide 26.

  30. Conclusions: 1/5Into a blossoming future for Maths and Stats Ed • There’s a sea of information on statistical…curriculumpedagogyteacher supportresources (including software)assessment. • We need to take a swim into it! • It includes:ICOTS conferences (next: Brazil 2006)Online and free SERJ and JSEIASE Roundtable (Jul 2005; Sweden). On CurriculumTeaching StatisticsAmerican Statistician, May 03; Special Section on Stat Ed

  31. Conclusions: The Good Stuff 2/5 • Current curriculum has some outstanding strengths:the focus on Investigationsthe progression through investigation types and variable types. • We can’t lose that. • But we can’t rest on our laurels:Statistics has moved a huge distance since the mid 1980’s.The Links have yet to be created;There are conversations that have only just started. • There’s progress in the draftMaths and Stats Essence Statement

  32. Conclusions: The New Stats Strand 3/5 • This time, it won’t be built top-down and in a hurry. • The statistical community must be enabled to take leadership to work on it with all parties: teachers at all levels curriculum experts. • Quality must be designed in;it can’t be patched in at the bottom of the cliff. • This is a great opportunity!

  33. Conclusion: Research, Resources, PD 4/5 • We’re impressed by the care, expertise and work that went into Numeracy. • We’d like an effort modelled on this for Stats:A scan of the sea of recent researchcurriculum analysisresource production, for: stats within maths stats everywhere else; “at large”research into how professional development can be best designedsupport for teachers at every stage. • It’ll need fresh work on how to get Interconnectedness

  34. Conclusions: For Statistics to blossom… 5/5 • We need to build capability in teaching (content and pedagogy) teacher education and support (pre and inservice) resource production curriculum design assessment design research in all the above • We need careful construction of Links. • We need a new engine for leading statistical education! • We all need each other!!!

  35. NZ, with Quakes and 4 Main Centres shown: A C D

  36. Quakes: Depth vs Distance SouthEast of Wgtn

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