New Strengths in the Curriculum

1
New Strengths in the Curriculums Statistics
Mike Camden Statistics New ZealandNZ
Statistical Association Education Committee
mike.camden_at_stats.govt.nz

• Auckland Maths Assoc PD Day 25 Nov 2008

The views in here are Mikes.
2
Aims

1. To get us feeling even better about the Stats in
   The NZ Curriculums Maths and Stats it
   iscommonsense, do-able, visual, fun, novel,
   useful, vital
2. To help ensure that our students will contribute
   tohealth, 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 activities
2. New Strengths in Curriculums StatisticsTwo 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
   situationsstories about Items 2 to 7
   activities 2 to 12 (some of)
5. Conclusion analysis gt 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,
  endingYou 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.n
  z/dbtw-wpd/virt-exhib/realgold/Science/florence-ni
  ghtingale.html

6
And an ad break

• See NZ Stat Assoc site http//nzsa.rsnz.org/
• and its new teachers page http//nzsa.rsnz.org/te
  achers.shtml
• See StatsNZ site http//www.stats.govt.nz
• and its Schools Corner
• and its brand new Infoshare systemTime 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 Measurem
ent 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
• Theyre different in how they areused, learnt,
  taught, integrated.
• Theyre different in how they usemathematical
  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 Tukeys
  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 havent done a graph,then you havent
  done an analysis.
• He intended this for

Statisticians at work
Please Vote
Students
Teachers
14
Some determinist mathematical logic

• You havent done a graph gt You
  havent done an analysis
• Or in brief
• No Graph gt No Analysis
• Can be seen as

Analysis gt Graph(s)
15
An eg from Tukeys 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 were 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
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 were 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 NZ
Curriculum 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?
Outcome Probability Yes 0.3 No
0.7
These things go from beingOut Ofs to Fractions
to Proportions to Percentages to Probsand
thats hard!
25
Structures in Cheese

• My problemI 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 gt 125 mm
32
(No Transcript)
33
Paua distributions for the judge

• Source I Westbrooke, NZ Dept of Conservation

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 Austs 156 Statistical Local
  Areas

A question How big is the average WA
household?? A look Female vs Male numbers for
the SLAs ( Its easy for kids to do this for
their town,from www.stats.govt.nz )
36
How big is the average WA household??
37
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
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 wont be able
to catch the bus.
The Hurdles Guess what? I got 90 in my
probability test!!!
Well 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
Times are inmin.sec.hundredths

• What do we do now??

41
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??
42
Hurdles vs Marathon bivariate distribution
That blue y x line is for the determinists
and synergists!
y x
Conclusionwords numbers graphs working
together (Edwin Tufte)
Ms Speed
43
4 Cheese Done!

• Data Graphics for Exploration, Communication

44
5 Dolphins

• Hectors 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 midlength RWB
rostrum width at base RL rostrum length ZW
zygomatic width CBL - condylobasal length ML
mandible length Well use Width, Length
46
Are they different sub-species?
47
(No Transcript)
48
(No Transcript)
49
(No Transcript)
50
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 3823 trees.

51
A Possum-browse BACI graphic
52
7 CO2 at Baring Head (Wgtn)
Data Graphics for Exploration, Communication
53
Exploration graphs CO2 Baring Head
What do we see?? What now??
54
More exploration residuals plot
What do we see now?
55
A static but colourful graphic
Median incomes in NZ Territorial
Authorities 2006 Census Well demo an
interactive dynamic graphic
56
Conclusion Exhilarating challenges in Maths
and Stats for
Teachers
Students
Parents, school community, wider community
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 Australia

• ABS site for teacherswww.abs.gov.au/teachers
  and for students www.abs.gov.au/studentsCensus
  at Schoolwww.abs.gov.au/websitedbs/cashome.NSF
• Fuel usehttp//www.greenhouse.gov.au/cgi-bin/tra
  nsport/fuelg
• Fishing in the bayhttp//blogs.mbs.edu/fishing-i
  n-the-bay/
• CO2 data and more, from Austhttp//www.environme
  nt.gov.au/soe/2006/publications
• OZCOTS 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 NIWAftp//ftp.niwa.co.n
  z/tropac/

59
Links 3 NZ contd

• Hectors and Mauis Dolphinshttp//www.rsnz.org/p
  ublish/jrsnz/2002/036.php
• Netballhttp//www.netballnz.co.nz/
• Cheesehttps//www.whitestonecheese.co.nz
• DVD/CD sets with video and data on about 8
  topics 2 sets, small fee from
  jharraway_at_maths.otago.ac.nz
• Florence Nightingale
• http//0-www.aucklandcity.govt.nz.www.elgar.govt.n
  z/dbtw-wpd/virt-exhib/realgold/Science/florence-ni
  ghtingale.html
• See NZSA site http//nzsa.rsnz.org/
• And its new teachers page http//nzsa.rsnz.org/tea
  chers.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 Stochasticitywww.dam.b
  rown.edu/people/mumford
• Data and Story Libraryhttp//lib.stat.cmu.edu/DA
  SL/
• EDA with several free software
  linksen.wikipedia.org/wiki/Exploratory_data_anal
  ysis
• E Tuftehttp//www.edwardtufte.com/tufte/
• The GAISE project, USAhttp//www.amstat.org/educ
  ation/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.or
  g/ R Commander a basic-stats GUI for R
  http//cran.r-project.org/web/packages/Rcmdr/index
  .html
• Statistica, with a free e texthttp//www.statsof
  t.com/

63
Links 7 Data Visualisation etc
Recommended for visualisations http//services.al
phaworks.ibm.com/manyeyes/home http//www.gapminde
r.org/downloads/applications/http//www.dur.ac.uk
/smart.centre/ https//www.geoda.uiuc.edu/
http//www.worldmapper.org/
64
Links 8 UKs Office of National Stats

• Some of the interactive objects on ONS
  sitewww.statistics.gov.uk/economicactivity/index
  2.html
• http//www.statistics.gov.uk/PIC/index.html
• http//www.statistics.gov.uk/populationestimates/s
  vg_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/Usefulwebsites
• 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 users
  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_2935
  64_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 Rosling
• 2006 and 2007 talks
• http//www.ted.com/index.php/talks/view/id/92
• http//www.ted.com/index.php/talks/view/id/140
• Software and data
• http//tools.google.com/gapminder/