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:

1. To get us feeling even better about the Stats in The NZ Curriculum’s Maths and Stats: it is:commonsense, do-able, visual, fun, novel, useful, vital

2. To help ensure that our students will contribute to:health, sustainability, climate, justice …(from West Aust Mathematics Curriculum Framework)

3. To give bright ideas for next week,next year!

3

Contents:1. The handout: a range of activities2. New Strengths in Curriculum’s Statistics:

Two big ideas: one woolly, one sharpStructures in the Statistics strandStructures in Cheese

3. An investigation with Paua (Item 1)the storyactivity 1

4. More investigations: multivariate situations:stories about Items 2 to 7 activities 2 to 12 (some of)

5. Conclusion: analysis => graphs

4

But first: two historical items:

William Gosset discovers

the Student t distribution

in the Guinness Brewery, Dublin

1: from 1908:

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 Nightingalehttp://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 new Infoshare system:Time Series galore!

Mean and Median Earnings: Auckland and NZ: Quarterly: 1999 Q2 to 2007 Q2

5,000

10,000

15,000

00 01 02 03 04 05 06 07

Mean Earnings - AkMedian Earnings - AkMean Earnings - NZMedian Earnings - NZ

7

And a pic of the Waitakere City gender balance:

Females vs Males for Area Units of Waitakere Cit

2006 Census

0

1000

2000

3000

0 1000 2000 3000

Y+X line

Herald

8

And a pic of the Kapiti gender balance:F06 (Nr. Females 2006) (up)

vs M06 (Nr. Males 2006) (across) for the 18 Area Units

of Kapiti Coast District

0

1000

2000

3000

4000

5000

0 1000 2000 3000 4000 5000

the y = x line

Otaki

Waikanae West

Paraparumu Central

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:

They have: big similarities … big differences …

Deterministic mathematics:NumberAlgebraMeasurement SpaceWA: ‘in context …investigate, generalise, reason, concludeabout patterns in number... space ….

Stochastic mathematics: Chance and Data (probability and statistics) WA: ‘locate, interpret, analyse, conclude from data … … with chance’

… and data’

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:

Please VoteStudents Teachers

Statisticians at work

14

Some determinist mathematical logic:

‘You haven’t done a graph => You haven’t done an analysis’

Or in brief:No Graph => No AnalysisCan 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 strandThe Statistics strand is:A Haphazard Heap A Subtle Set of Structures

Please Vote

average

modeS

tem and leaf

The t

test

median

spread

The Pie

line graph

Box and whisker thingy

Som

ething normal

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

3: Variables: Categorical, Numerical

2: Datasets: case, series

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:

3: Variables: Categorical, Numerical

2: Datasets: case, series

A cross-sectional or case datasetCapsicum prices ($/kg) at several shops:and one date: 16 Aug 2008Shop Type Green Orange RedA Greengrocer 6.50 6.75 7.50B Supermarket 7.00 7.50 8.00C Supermarket 6.00 6.50 7.00A time-series datasetand one shop: Bunbury PeppersCapsicum prices ($/kg) at several dates:Date Weather Green Orange RedJun Fine 6.50 6.75 7.50Jul Wet 7.00 7.50 8.00Aug Wet 6.00 6.50 7.00

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 ……...

Graphics make all this accessible.

The Pauas: item 1

The others: items 2 to 7

22

Structures in Stats Investigs bit: contd5: The group we’re investigating:

A population

A sample …… from a population

In Curriculum from Level 6

23

Structures in Stats Investigs bit: concld

Problem → Plan → Data → Analysis → Conclusion

Graphs for Exploration, Analysis, Discovery:

Graphs for Communication of findings:

The Mathematics and Statistics in The NZ Curriculum progresses through all these structures

6: Graphs: two roles

7: Variation … Variation … Variation … Variation … Variation

Underlying everything in life and work (and Stats):

24

Structures in the Probability strand: brief:

Question or Experiment → Outcomes → Probabilities → Probability distribution → Decisions

Has the coffee arrived yet? Outcome Probability 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??

Name Energy FatTot FatSat Sodium ProteinBrie 1508 30.0 21.0 629 23.4Mt Domet Brie 1689 36.5 25.0 629 19.9Camembert 1496 32.0 22.0 629 18.4Chef's Brie 1496 32.0 22.0 629 18.4Caterer's Brie Log 1598 32.0 22.0 629 24.4Farmhouse 1672 32.9 23.0 707 26.8Airedale 1672 32.9 23.0 707 26.8Livingstone Gold 1672 32.9 23.0 707 26.8Totara Tasty 1753 35.8 23.8 750 24.4Creamy Havarti 1751 38.0 25.2 750 20.3Windsor Blue 1883 43.5 30.5 1140 16.1Moeraki Blue Bay 1838 41.0 28.7 825 18.9Highland Blue 1500 30.0 19.5 1140 23.1Monte Cristo 1637 31.1 21.2 707 28.6Island Stream 1786 33.9 23.0 707 31.3Stoney Hill Feta 1368 26.0 17.7 629 23.9Mt Dasher Feta 1368 26.0 17.7 629 23.9Fuschia Creek Feta 1363 27.0 18.9 629 21.4Manuka Feta 1363 27.0 18.9 629 21.4

28

Graphs of 2 ‘univariate’ distributions:Frequency Distribution: Saturated Fat (%):

0

1

2

3

4

18 19 20 21 22 23 24 25 26 27 28 29 30 31

Fetas

Frequency Distribution: Sodium (g/100g)

012

34567

89

10

630 730 830 930 1030 1130

What do we do now??

29

Graph of a ‘bivariate’ distribution:Whitestone Cheeses:

Sodium (mg/100g) vs Saturated Fat (%) (both jittered) Source: Whitestone Brochure 2008

0

500

1000

0 10 20 30

Bries

Goldens

Blues

Fetas

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

Some Paua dataOrigin PauaSize

A 136A 132A 131A 126A 130A 128A 125A 130A 126A 129B 138B 135B 130B 136B 130B 138B 130B 135B 127B 130

32

The Paua data:Here's a mini version of the data, for a short tactile activity. That's not enough to make sensible decisions, but it's a taste. You need to chop this card up.A: underlined, green: 10 values here: B: Blue, italics: 5 vals:

121 125 126123 126 130124 129 130125 129 135125 136 138

33

Paua distributions for the judge:

Source: I Westbrooke, NZ Dept of Conservation

CabbagePatch

Disputed

120 125 130 135

Paua size (mm)

120 125 130 135 140

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Paua size (mm)

Re

lativ

e fr

eq

ue

ncy

CabbagePatchDisputed

34

More investigations: multivariate situations:

Stories about Items 2, 3, 5, 6, 7

Activities on these

35

2: Census data from the neighbours:

Data on Westn Aust’s 156 ‘Statistical Local Areas’:ABS_MAWA_CensusData.xls A local sample of the 156 SLAsSLA Name Male01 Fem01 Total01 Male06 Fem06 Total06AvHhSize01AvHhSize06Mandurah (C) 20,935 22,302 43,237 24,918 26,719 51,637 2.5 2.4Murray (S) 4,881 4,773 9,654 5,478 5,444 10,922 2.5 2.5Bunbury (C) 13,359 13,848 27,207 13,681 14,144 27,825 2.5 2.4Capel (S) - Pt A 1,299 1,305 2,604 2,818 2,893 5,711 3.1 3.2Dardanup (S) - Pt A2,864 2,961 5,825 3,601 3,669 7,270 2.9 2.7Harvey (S) - Pt A4,666 4,680 9,346 5,439 5,397 10,836 3.0 2.9

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 )

36

How big is the average WA household??

Freq Dist: Household Size 06: WA SLAs

0

10

20

30

1.5 1.7 1.9 2.1 2.3 2.5 2.7 2.9 3.1 3.3 3.5 3.7 3.9

37

Nr.Females vs Nr.Males:WA SLAs

with y = x line

0

20,000

40,000

0 20,000 40,000

Difference: Females - Males vs Nr.Males:WA SLAs

-2,000

0

2,000

4,000

0 20,000 40,000

Major citesInner regionalOuter regionalRemoteVery remote

Bunbury

BunburyBunburyBunbury Melville

Female vs Male numbers for the 156 WA SLAs:

withRegression,

Residuals, and Remoteness

38

3: Txt Olympics: www.learnngmedia.co.nz An activity from a new Media/Stats book:

The SprintCall 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!!!

Motutapu College is holding a Texting Olympics to find out who has the fastest thumb in the school! Events include:

We’ll use this to do some ‘Statistical Thinking’ …

39

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 …

40

The Txt data:

Name Sprint Marathon HurdlesRachel 0.05.44 0.49.67 0.42.40John 0.12.91 3.42.78 1.47.06Francine 0.18.75 2.55.59 1.46.65Michelle 0.05.00 1.00.00 0.49.56Jennifer C. 0.06.00 1.03.00 0.53.44Abigail 0.05.00 1.15.00 0.46.74Jessica 0.04.66 1.01.00 0.40.96Georgina 0.08.65 1.19.85 0.55.13Nathan 0.11.10 1.44.75 1.06.62Glenn 0.12.19 1.20.43 1.21.75Ryan 0.12.16 1.45.94 1.07.35Emma A. 0.04.06 0.46.07 0.43.13Jake 0.06.69 1.12.08 0.43.47Nirvana 0.08.22 0.51.31 0.28.41Devon 0.05.97 1.11.53 1.53.12Matthew 0.05.47 1.48.82 1.14.84Ryan 0.07.09 1.28.75 1.07.83Ashley 0.04.29 1.48.50 1.28.69Joanna 0.05.50 1.30.00 0.41.72Winston 0.08.12 0.43.31 0.39.56Anthony 0.07.30 1.54.94 0.54.90Stephanie 0.04.00 0.55.88 0.30.50Anna 0.07.88 1.39.94 1.00.72Jennifer D. 0.04.97 1.01.38 0.45.03Sian 0.10.43 1.20.25 1.13.66Aditya 0.16.94 3.57.22 2.53.34Alana 0.06.69 0.37.88 0.25.13Louis 0.07.38 1.28.50 0.40.44Emma B. 0.04.81 1.10.00 0.53.72Owen 0.05.46 1.03.59 0.51.59

What do we do now??

Times are inmin.sec.hundredths

41

Sprints: the univariate distribution:Frequency of Times for Sprint

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Time (seconds; rounded)

Frequency

StephanieEmmaAshleyJessicaEmmaJennifer

Add variables by re-using data-ink:Draw graph as blocks; write names in blocks;Colour-code: girls and boys

What now??

42

Hurdles vs Marathon: bivariate distributionHurdles vs Marathon by Gender

with linear regressions

0

50

100

150

200

0 50 100 150 200 250Time: Marathon (seconds)

Time: Hurdles

(seconds)

Girls

Boys

Ms Speed

That blue y = x line is for the determinists and synergists!

y = x

Conclusion:words numbers graphs

working together

(Edwin Tufte)

43

4: Cheese: Done!

Data Graphics for Exploration, Communication:

44

5: Dolphins: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??

possums

45

Dataset comes from 59 skeletons in 3 museums.

Selected measurements: simplified definitions:RWM - rostrum width at midlengthRWB – rostrum width at baseRL – rostrum lengthZW – zygomatic widthCBL - condylobasal lengthML – mandible length

We’ll use Width, Length

46

Are they different sub-species?

Dolphin Head Measurements:Width vs Length by Island

40

50

60

70

250 260 270 280 290 300 310 320Length (mm)

Width (mm)

Nth

Sth

47

48

49

50

6: Possum Browse:Australian brush-tailed possum Trichosurus vulpeculaIntroduced 1837 and 450 times No natural predatorsDamages foliage, fruit, birds A BACI project: Before/After Control/InterventionTwo ‘lines’ chosen ‘Control’ not treated ‘Intervention’: 1080 poison by airPercentage foliage cover estimated Before/After at 38+23 trees.

51

A Possum-browse BACI graphic:Foliage cover 99 (%) vs Foliage cover 98 (%)

y = 0.8121x + 20.031

R2 = 0.3653

y = 0.7378x + 11.95

R2 = 0.6299

0

20

40

60

80

100

0 20 40 60 80 100

Control

Treated

Linear(Treated)

Linear(Control)

52

7: CO2 at Baring Head (Wgtn)

CO2 data (ppm) from Australia; Cape GrimmYear Month CO2 Conc 1977 1 330.791977 2 330.781977 3 331.021977 4 330.911977 5 330.951977 6 331.491977 7 331.801977 8 332.311977 9 332.901977 10 332.981977 11 332.751977 12 332.35

etc etc etc

CO2 data (ppm) :from NZ: Baring Head:

Yr Mth Day Hour CO21973 1 6 8 326.371973 1 9 11 326.401973 1 12 17 326.541973 1 13 10 325.471973 1 16 20 326.291973 1 17 9 325.871973 2 5 22 327.671973 2 8 3 325.881973 2 11 2 326.391973 2 12 13 325.961973 2 12 20 326.261973 2 13 3 325.68etc etc

Data Graphics for Exploration, Communication:

53

Exploration graphs: CO2: Baring HeadCO2 at Baring Head (Wellington)

Model fitted by linear regression:y = 1.4749x - 2584.7

R2 = 0.9956

320

330

340

350

360

370

380

1973 1978 1983 1988 1993 1998 2003

What do we see?? What now??

54

More exploration: residuals plot

Residuals: CO2 - Fit (ppm)

-3

-2

-1

0

1

2

3

4

5

1973 1978 1983 1988 1993 1998 2003

What do we see now?

This data comes from:ftp://ftp.niwa.co.nz/tropac/which is provided byNational Institute of Water and Atmospheric Research

55

A static but colourful graphic:

Median incomes in NZ Territorial Authorities;

2006 Census

We’ll demo an interactive dynamic graphic

56

Conclusion: Exhilarating challenges in Maths and Stats for:

Teachers

Parents, school community, wider community

Students

Researchers and teacher educators

Resource designers

Assessment designers even!

Statistical workers

‘Discovery statistics: (Chris Wild; Auckland)

the daily experience of statistical practitioners’

57

Links 1: AustraliaABS site: for teacherswww.abs.gov.au/teachers and for students www.abs.gov.au/studentsCensus at School:www.abs.gov.au/websitedbs/cashome.NSFFuel use:http://www.greenhouse.gov.au/cgi-bin/transport/fuelgFishing in the bay:http://blogs.mbs.edu/fishing-in-the-bay/CO2 data and more, from Aust:http://www.environment.gov.au/soe/2006/publicationsOZCOTS 2008:http://silmaril.math.sci.qut.edu.au/ozcots2008/

58

Links 2: NZ

Curriculum and some resources:

http://nzcurriculum.tki.org.nz/

http://www.nzmaths.co.nz/

http://www.nzamt.org.nz/

http://www.censusatschool.org.nz/

www.stats.govt.nz

http://www.learningmedia.co.nz/

Computer assisted statistics teaching:

http://cast.massey.ac.nz/

CO2 data, and more, from NIWA:ftp://ftp.niwa.co.nz/tropac/

59

Links 3: NZ contd:Hector’s and Maui’s Dolphinshttp://www.rsnz.org/publish/jrsnz/2002/036.php

Netball:http://www.netballnz.co.nz/

Cheese:https://www.whitestonecheese.co.nz

DVD/CD sets with video and data on about 8 topics; 2 sets, small fee; from jharraway@maths.otago.ac.nz

Florence Nightingale: http://0-www.aucklandcity.govt.nz.www.elgar.govt.nz/dbtw-wpd/virt-exhib/realgold/Science/florence-nightingale.html

See NZSA site: http://nzsa.rsnz.org/And its new teachers page http://nzsa.rsnz.org/teachers.shtml

60

Links 4: Internat Assoc for Stat Education

http://www.stat.auckland.ac.nz/~iase/

ICME 11, Monterrey, Mexico. July 2008

ICOTS 8, Ljubljana, Slovenia July 2010

Statistics Education Research Journal (SERJ)International Statistical Literacy Project (ISLP)

ICMI/IASE Study: Statistics Education in School

61

Links 5: Elsewhere:

David Mumford: The Age of Stochasticity:www.dam.brown.edu/people/mumford

Data and Story Library:http://lib.stat.cmu.edu/DASL/

EDA: with several free software links:en.wikipedia.org/wiki/Exploratory_data_analysis

E Tufte:http://www.edwardtufte.com/tufte/

The GAISE project, USA:http://www.amstat.org/education/gaise/

62

Links 6: Elsewhere contd:Gallery of Data Visualization The Best and Worst of Statistical Graphics http://www.math.yorku.ca/SCS/Gallery/ R: a language and environment for statistical computing and graphics. http://www.r-project.org/ R Commander: a basic-stats GUI for R: http://cran.r-project.org/web/packages/Rcmdr/index.html

Statistica, with a free e text:http://www.statsoft.com/

63

Links 7: Data Visualisation etc:

Recommended for visualisations:http://services.alphaworks.ibm.com/manyeyes/homehttp://www.gapminder.org/downloads/applications/http://www.dur.ac.uk/smart.centre/ https://www.geoda.uiuc.edu/ http://www.worldmapper.org/

64

Links 8: UK’s Office of National Stats:

Some of the interactive objects on ONS site:www.statistics.gov.uk/economicactivity/index2.html

http://www.statistics.gov.uk/PIC/index.html

http://www.statistics.gov.uk/populationestimates/svg_pyramid/default.htm

You need to install the SVG software, whichis available in the last link.

65

Links 9: Links of Links from Pip:

For links from conferences

http://aucksecmaths.wikispaces.com/MexicoFor a few others

http://nzstatsedn.wikispaces.com/Useful+websites

Information for Auckland Secondary Maths Teachers

http://aucksecmaths.wikispaces.com/

http://www.nzqa.govt.nz/ncea/resources/maths/index.html

/

66

Links 10: OECD eXplorer : New platform: visualising & analysing stats

OECD has launched a powerful, interactive tool for visualising and analysing regional statistics. OECD eXplorer combines maps and other graphics via the Internet, to increase the user’s understanding of regional differences and structures across and within OECD countries. To try out the regional maps and statistics using OECD eXplorer, go to: http://www.oecd.org/document/50/0,3343,en_2649_33735_41564530_1_1_1_1,00.html .

This development is part of the overall strategy to improve the accessibility and usability of OECD statistics (see also the visualisation of data contained in the OECD Factbook using dynamic graphics http://www.oecd.org/document/1/0,3343,en_2825_293564_40680833_1_1_1_1,00.html).

The development of OECD eXplorer is the result of a fruitful cooperation between OECD and the National Centre for Visual Analytics (NCVA, http://ncva.itn.liu.se/) at Linköping University, Sweden. In the seminar on generating knowledge from statistics, organised by Statistics Sweden and OECD in Stockholm in May, Professor Mikael Jern from NCVA presented a first version with some OECD statistics. Since then, the development team at NCVA has worked intensively on improving the tool and adapting it to all the needs expressed by OECD.

67

Links 11: Hans Rosling

www.ted.com search Rosling2006 and 2007 talks:http://www.ted.com/index.php/talks/view/id/92http://www.ted.com/index.php/talks/view/id/140

Software and datahttp://tools.google.com/gapminder/