Mike Camden NZ Statistical Association Education Committee Mike: mikemden@statst.nz

1. Statistics in the Social Sciences Curriculum StocktakeAn Aid to Revitalising the CurriculumFor Geography, History, Economics and Social Studies. 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

2. 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. • However, the presentation includes: • a “Hot Off The Press” information release and • some Time Series data from Statistics New Zealand. For specific data, contact Lesley.Hooper@stats.govt.nz

3. Proposed Contents of Session: A Sandwich • Stats in Schools: the big ideas, a report on its current health, three scalpels and a multichoice test • Workshop: Income, Age and Ethnicity • Illustrations: Inflation, Migration, Cautionary Tales, Tupaia and James, Quakes, the chocolate investigation and Conclusions. • At the end: a present: a “Hot Off The Press” from SNZ.

4. Deterministic and Stochastic Thought • Greek: Stokhastikos: Person who aims, targets, forecasts Stokhos: An aim, target • English: Stochastic: involving variability, probability distributions • There’s an Essential Learning Area 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 the Social Sciences! • See Paper 8 in http://wwwmaths.anu.edu.au/other/ncms/mathsdocs/Mumford, D (1999). The dawning of the age of Stochasticity.

5. The big questions for this session: • Three questions: • 1: How do we build Curriculum so Stats supports your ELA? • 2: How do we build Curriculum so 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. 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 galloping: social policy, health, environment, technology, … • 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 • Values: Stats is founded on a Value:information-based decision-making

7. Stats in Schools: The big ideas: 2/3 • Stats needs careful curriculum links with … the social and other scienceslanguage and graphics: verbal and visual communicationthe other layers in the Framework: Principles, Future Focused Themes, Skills, Values, Attitudes; Problem-solvingIs there a literature on this?? • Stats supports active learning in other ELAsvia “investigations” and student-driven research;students enjoy hands-on work with data, owning projects and completing investigations • We need a new engine for Stats curriculum, assessment, professional development, resource making:for the content and the links with the rest of learning

8. Stats in Schools: The big ideas: 3/3 • We need a plan to build capability in Stats Pedagogy in NZ:for the Maths bit and the links with other ELAs • The NZ Stats Community is aware, alert and offering insights They want NZ to get the Stats right! • 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! • Some front-end statistical methods are …fun, commonsense, graphical and suddenly accessible to school students • Any Learning Area can link with Stats so that …both are valued as enjoyable and useful • We’re at the forefront …Dammit!!!

9. 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.

10. A Scalpel for Stats Curriculum Constructors 1/3 • 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.

11. Another Scalpel: Real-life Datasets 2/3 • 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 (Case) Dataset • This thing’s a (Frequency) Table

12. Last Scalpel: Case and Series Datasets 3/3 • A case dataset: • A time-series dataset: • Which subject owns them??

13. A Multichoice Test: Q 1 of 2: for Merit:(Assume that being here gets you Achievement) • The NZ Stat Assoc Education Committee’s aim is: • A: Stuff more 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 Essential Learning Areas • (Yes, I did read the Listener!!)

14. A Multichoice Test: Q 2 of 2: for Excellence: • 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??

15. Workshop: Income, Education and Ethnicity • A country wants to find out whether there is Equity between its two main Ethnic Groups. • It does a sample survey of its people, and asks questions about Income, Education and Ethnicity. • If it is not achieving Equity, it wants to design Interventions, to assure that it does achieve Equity. • Q1: Whose subject is this? • Please find a colleague or two, and attack the sheet of paper. • Next: Illustrations and Conclusions

16. NZ’s Consumer Price Index; All Groups In WW2, our boys in Cairo had $2 to spend a week. What’s that today??

17. Migration: Long term Arrivals and Departures

18. Cautionary Tale 1 of 2: Wgtn Science Fair • Impressive statistics from 8 of the 400 Year 7 and 8 people. • Science, years 7 and 8, does nice Experimental Design which not make it into our NCEA L3 Stats and Modelling! • The Maths curriculum doesn’t provide the commonsense graphic tools they could use.

19. Cautionary Tale 2 of 2: Biology in Curriculum Level 8 and in Practice • School:NCEA L3 Biology inherits stuff from Bursary Biology(eg: Chi Square tests, ANOVA) • Practice (Dept of Conservation, AgResearch):Biologists need graphical and commonsense analysisfor decision-making. • The Moral:NZ needs conversations that involve …- educators and curriculum builders in all ELAs- educators and curriculum builders in Maths and Stats- the practitioners in the statistical community. • Details …

20. Biology Contd: 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. Tupaia and James (with thanks to Anne Salmond) • Oct 1769; the Endeavour sails from Tahiti to NZ. • Tupaia and James are both strong on...Geography, History (both knew NZ was there), Economics, Social Studies, Language and GraphicsMathematical Processes 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 down here.

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

23. Conclusion: Revitalising the Curriculum • NZ has an exhilarating opportunity or in fact necessity:for statistics in the whole NZ curriculum. • We need:a really good stats strandreally good links with social and other sciencesnew conversationsmachinery for activating the statistical communityaccess to international research and best practiceMinistry resourcing of these new actionsa plan to build NZ’s capability in statistical education. • This will be:lots of fun! • The End, but there are a 7 more slides with extra information …

24. Another Workshop: 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)

25. Equity, Ethnicity and Intervention • A country has 2 Ethnicities, • A (the majority) and B. • The results of a survey are: • Is there equity in income? • If not, where should interventions be applied?? • What subject is this??? • (This happens!!) • An answer: Education explains differences in Income, but the big difference in Education needs to be targetted.

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

27. Quakes: Depth vs Distance SouthEast of Wgtn

28. Example: The two parts of “Maths and Stats”: • Here’s a deterministic • (algebraic) function: • ShellVol = k ShellLength3 • And a stochastic (statistical) scatterplot of • ShellVol and ShellLength • For some Wellington shellfish.

29. Net Migration (Long term Arrivals – Departures)with Trend; in Persons per Month. Source: SNZ.

30. 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