Statistics in the Social Sciences Curriculum Stocktake An Aid to Revitalising the Curriculum For Geo

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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_at_stats.govt.nz
• 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 data
• from Statistics New Zealand.
• For specific data, contact Lesley.Hooper_at_stats.gov
  t.nz

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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 Thought

• Greek Stokhastikos Person who aims,
  targets, forecasts Stokhos
  An aim, target
• English Stochastic involving variability,
  probability distributions
• Theres an Essential Learning Area called
• MathsMaths and StatsMaths and Stats and
  Probability
• Theres a bunch of mental tools (Maths) with
  two sides
• Deterministic thinking and modellingStochastic
  thinking and modelling
• Theyve 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/nc
  ms/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?
• JFKs 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 1/3

• 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
  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 Valueinformation-b
  ased decision-making

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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
  researchstudents enjoy hands-on work with data,
  owning projects and completing investigations
• We need a new engine for Stats curriculum,
  assessment, professional development, resource
  makingfor the content and the links with the
  rest of learning

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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
• Were at the forefront Dammit!!!

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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.

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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 dataset with graphs etc
• Explore and/or analyse the dataset with graphs
  etcJohn Tukey If you havent done a graph,
  then you havent done an
  analysis
• Summarise the findings/information/conclusions
• Communicate 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
2/3

• Any dataset that is remotely useful or
  interesting has several related variables
• We stop pretending that variables ever occur
  alone.
• We replace bi-variate dataand multi-variate
  data bydataset.
• This things a (Case) Dataset
• This things a (Frequency) Table

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Last Scalpel Case and Series Datasets
3/3

• A case dataset
• A time-series dataset
• Which subject owns them??

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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 Committees 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 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??

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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

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NZs Consumer Price Index All Groups
In WW2, our boys in Cairo had 2 to spend a week.
Whats that today??
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Migration Long term Arrivals and Departures
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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 doesnt provide the
  commonsense graphic tools they could use.

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Cautionary Tale 2 of 2 Biology in Curriculum
Level 8 and in Practice

• SchoolNCEA 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 MoralNZ 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 biometricians

• Ian Westbrooke Dept of Conservation NZSA Conf
  Jul 03
• Staffs (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 Spins

• In the past, earthquakes were seen as stochastic
  in space and time (and nasty)
• Now, we havelarge and classy datasetssoftware
  that can let us look into the datas
  structurevisualisation skillsand all these are
  available to schools.
• 
  an Excel interlude.

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Conclusion Revitalising the Curriculum

• NZ has an exhilarating opportunity or in fact
  necessityfor statistics in the whole NZ
  curriculum.
• We needa 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 NZs capability
  in statistical education.
• This will belots of fun!
• The End, but there are a 7 more slides with
  extra information

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Another Workshop Skills what, where, how

• See SNZs 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)

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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.

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NZ, with Quakes and 4 Main Centres shown
A
C
D
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Quakes Depth vs Distance SouthEast of Wgtn
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Example The two parts of Maths and Stats

• Heres a deterministic
• (algebraic) function
• ShellVol k ShellLength3
• And a stochastic (statistical) scatterplot of
• ShellVol and ShellLength
• For some Wellington shellfish.

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