mike camden nz statistical association education committee mike: [email protected]

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NZ Statistical Association Education Committee: For Soc Sci Curriculum Stocktake Group; 14 Nov 03

Statistics in the Social Sciences Curriculum Stocktake

An Aid to Revitalising the CurriculumFor Geography, History, Economics and

Social Studies.

Mike Camden

NZ Statistical Association Education CommitteeMike: [email protected]

NZSA: http://www.stat.auckland.ac.nz/nzsa/

NZSA Newsletter: http://nzsa.rsnz.govt. nz/newsletter58

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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 datafrom Statistics New Zealand.For specific data, contact [email protected]

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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.

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Deterministic and Stochastic ThoughtGreek: 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.

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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.

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Stats in Schools: The big ideas: 1/3Stats 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 thinking which 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

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Stats in Schools: The big ideas: 2/3Stats 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

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Stats in Schools: The big ideas: 3/3We 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!!!

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Health Report for the Statistics Strand in MathsBone structure mostly good but needs a hip replacement and some physio elsewhereSoft 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.

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A Scalpel for Stats Curriculum Constructors 1/3Any investigation has these stages:State the purpose, get approvalDesign and/or plan all aspects of itCollect the data into a Unit Record DatasetEdit/Launder/Clean the dataset with graphs etcExplore and/or analyse the dataset with graphs etc

John Tukey: “If you haven’t done a graph, then you haven’t done an analysis”

Summarise the findings/information/conclusionsCommunicate the Conclusions

with words, numbers and graphs working together(Edwin Tufte: The visual display of quantitative information)

Lets give up writing “Present the Data with Graphs” forever.

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Another Scalpel: Real-life Datasets 2/3Any 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) DatasetThis thing’s a (Frequency) Table

Name Favourite Fruit

Gender

Trevor Mango Boy

Steve Apple Boy

Marion Apple Girl

Turiana Apple Girl

Count

Gender Girl Boy

Fruit

Apple 2 1

Mango 0 1

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Last Scalpel: Case and Series Datasets 3/3A case dataset:

A time-series dataset:

Which subject owns them??

Arrivals and Departures;long term. From SNZ.

Month Arr DepDec-01 8725 5321Jan-02 11348 6638Feb-02 9056 4874Mar-02 7210 5469Apr-02 7048 5306May-02 5920 5276Jun-02 6854 4925Jul-02 8517 5062

Aug-02 7217 4119Sep-02 8106 3687Oct-02 7496 3370Nov-02 8574 3839

Some Earthquakes of January 2000.Easting Northing Depth Felt? Magn2673781 6227293 -218 N 4.2892884960 6379810 -65 Y 4.4542558485 6106030 -196 N 4.0352801415 6334897 -158 N 4.4792868211 6462464 -212 N 4.0492800798 6334719 -165 N 4.566

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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!!)

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A Multichoice Test: Q 2 of 2: for Excellence:The Essence of Stats is:

A: Weird graphs with kinky names

B: Weird stuff like 2 = (x – )2/ n

C: Investigations, contexts, datasets, variability, exploration, conclusions, communication

Which one would look good in the Maths and Stats Essence Statement??

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Workshop: Income, Education and EthnicityA 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

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NZ’s Consumer Price Index; All GroupsQuarter CPIJun-14 19Sep-14Dec-14Mar-15Jun-15Sep-15 21Dec-15Mar-16

etc etcMar-99 998Jun-99 1000Sep-99 1004Dec-99 1006Mar-00 1013Jun-00 1020Sep-00 1034Dec-00 1046Mar-01 1044Jun-01 1053Sep-01 1059Dec-01 1065Mar-02 1071Jun-02 1082Sep-02 1087Dec-02 1094

SNZ's Consumer Price Index; All Groups; Base 1000 in Jun 99

0

1000Jun-14

Jun-19

Jun-24

Jun-29

Jun-34

Jun-39

Jun-44

Jun-49

Jun-54

Jun-59

Jun-64

Jun-69

Jun-74

Jun-79

Jun-84

Jun-89

Jun-94

Jun-99

In WW2, our boys in Cairo had $2 to spend a week. What’s that today??

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Migration: Long term Arrivals and DeparturesMonth Arrs DepsJan-50 2104 476Feb-50 1729 606Mar-50 1511 639Apr-50 929 630May-50 2317 619Jun-50 1515 643Jul-50 1286 629

Aug-50 1025 1000Sep-50 1807 464Oct-50 2014 708Nov-50 1511 510Dec-50 1030 855Jan-51 2205 662Feb-51 888 597Mar-51 1707 471Apr-51 1585 364May-51 2166 686Jun-51 2058 485Jul-51 745 789





Aug-55 1722 860Sep-55 1464 676Oct-55 1654 855Nov-55 2640 790Dec-55 1777 688Jan-56 1695 1052

NZ Arrivals and Departures: Monthly from 1950

0

2000

4000

6000

8000

10000

12000

Jan-50

Jan-53

Jan-56

Jan-59

Jan-62

Jan-65

Jan-68

Jan-71

Jan-74

Jan-77

Jan-80

Jan-83

Jan-86

Jan-89

Jan-92

Jan-95

Jan-98

Jan-01

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Cautionary Tale 1 of 2: Wgtn Science FairImpressive 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.

Sciences Maths Soc ScisLevel 1 Level 1 Level 1Level 2 Level 2 Level 2Level 3 Level 3 Level 3Level 4 Level 4 Level 4Level 5 Level 5 Level 5Level 6 Level 6 Level 6Level 7 Level 7 Level 7Level 8 Level 8 Level 8

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Cautionary Tale 2 of 2: Biology in Curriculum Level 8 and in PracticeSchool:

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 …

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Biology Contd: Views of senior NZ biometriciansIan 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.

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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.

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Quakes and SpinsIn 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 skills

and all these are available to schools.

an Excel interlude….

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Conclusion: Revitalising the CurriculumNZ 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 …

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Another Workshop: Skills: what, where, howSee 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?

2 Whereabouts do we put these skills etc in the Curriculum Framework??

3 What does NZ need, to ensure effective teaching, learning and assessment of the skills etc???

4 Are we in the right Industry????(See Table 10 near the end)

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Equity, Ethnicity and InterventionA 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.

Income with Education, by Ethnicity:

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10

20

30

40

50

60

0 2 4 6 8 10 12 14

Education (years)

Income

(k$)

A

B

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NZ, with Quakes and 4 Main Centres shown:

A

C

D

2 226 384 226 3843 -101 110 -101 1104 142 339 142 3395 209 467 209 4676 142 339 142 3397 204 468 204 4688 248 444 248 4449 -160 31 -160 31

11 206 498 206 49812 117 350 117 35013 131 384 131 38414 257 462 257 46215 95 261 95 26116 103 297 103 29717 135 385 135 38521 248 375 248 375-800

-400

0

400

800

-800 -400 0 400 800

-800

-400

0

400

800

-800 -300 200 700

A

WW

C

D

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Quakes: Depth vs Distance SouthEast of Wgtn

-800

-400

0

400

800

-800 -300 200 700

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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 ShellLengthFor some Wellington shellfish.

Mussels (Mytius Edulis): Chaffers Marina:

Shell Vol(ml) vs Shell Length (mm)Stochastic and deterministic views

051015202530354045

0 20 40 60 80 100

ShellVol

Cubic

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

-8000

-4000

0

4000

8000Jan-50

Jan-53

Jan-56

Jan-59

Jan-62

Jan-65

Jan-68

Jan-71

Jan-74

Jan-77

Jan-80

Jan-83

Jan-86

Jan-89

Jan-92

Jan-95

Jan-98

Jan-01

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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 itThe ways it can be taught, learned and assessed

(the pedagogy…. And the pedagogues!!)The ways in which it uses computer technologyThe ways it can be integrated with other learning areasTeacher confidence, professional development needs and

resource needs, in Maths and other ELAs

mike camden nz statistical association education committee mike: [email protected]

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