Statistics in the NZ Curriculum Stocktake

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Statistics in the NZ Curriculum Stocktake

• 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

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.
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Proposed Contents of Session A Club Sandwich

• Stats in Schools Intros, multchoice test and the
  big ideas
• Workshop 1 Skills for a Hot Off The Press
• Background, illustrations, opinions and more
  illustrations
• Workshop 2 Stats and your Essential Learning
  Area
• Conclusion The chocolate investigation What Now.

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Deterministic and Stochastic Thought

• Greek Stokhastikos Person who aims,
  targets, forecasts Stokhos
  An aim, target
• English Stochastic involving random
  probability distributions
• Theres an ELA 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
  Education!
• 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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Some odd things about Stats

• Maths has two sides
• Deterministic and Stochastic
• Stats (and Probability) is entangled
  with.Language English, Te Reo Maori, the
  othersGraphics and visual communicationContext
  all the ELAsMaths
• Stats supports active learning in other ELAsvia
  investigations
• Entangled has two directions .

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The big questions for this session

• Three questions
• 1 How do we build Curriculum so that Stats
  supports your ELA?
• 2 How do we build Curriculum so that 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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A Multichoice Test Q 1 of 3 for Achievement

• The NZ Stat Assoc Education Committees aim is
• A Stuff 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 ELAs
• (Yes, I did read the Listener!!)

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A Multichoice Test Q 2 of 3 for Merit

• 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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A Multichoice Test Q 3 of 3 for Excellence

• Life and the tools we make for enjoying it are
• A Mostly deterministic
• B Mostly stochastic
• C Basically stochastic, but deterministic models
  are often good working approximations.
• Hint Best answer in each Question is C.

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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
  becoming moreobvious technology, environment,
  social policy
• Some front-end statistical methods are fun,
  commonsense, graphical and suddenly accessible
  to school students
• 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

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Stats in Schools The big ideas 2/3

• Stats needs careful curriculum links with the
  other Maths strandsthe other essential learning
  areasthe other layers in the Framework
  Principles, Future Focused Themes, Skills,
  Values, AttitudesIs there a literature on this??
  
• We need a new engine for Stats curriculum,
  assessment, professional development, resource
  making
• We need a plan to build capability in Stats
  Pedagogy in NZ
• The NZ Stats Community is aware, alert, offering
  its insights They want NZ to get the Stats right!

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Stats in Schools The big ideas 3/3

• 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!
• 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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A Scalpel for Stats Curriculum Constructors

• 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

• 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 Dataset
• This things a (Frequency) Table

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Workshop 1 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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The Middle Bit

• Background, illustrations, opinions, more
  illustrations

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Some of the Communities of Interest in Maths Ed

• NZSA, its Education Com, Maths Teachers and
  Curric Makers
• The intersections are very small.

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NZ Statistical Association Education Committees
conclusions

• On Thur 11 Sept 03, the Committee discussed the
  Stocktake
• at length. Main conclusion it offers to
• Make input into and review the draft Framework
  document
• Be part of research projects that would underpin
  curriculum and resource writing
• Take a leadership role in the writing of the
  Statistics strand of the Curriculum document
• On Thur 9 Oct, it met with MoE people and
  discussed
• Making input into Stats in the whole curriculum

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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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Biology Part 1 Stats in NCEA Biology Level 3

• Explanatory Note 7 Recording and processing
• Data processing would usually involve calcs and
  graphing (Good!) to establish a relevant pattern
  or trend. Stat. procedures, where approp.,
  should be used to establish the reliability (??)
  of the data e.g. mean, standard deviation,
  confidence intervals, standard error, difference
  between two means, ANOVA (??), Chi squared
  test(??).
• Sufficient data involves repeats, trials,
  appropriate range for the independent variable
  (Exp Design??), appropriate samp size.
• Systematically record means data will be
  presented in a way (eg table, tally chart) that
  allows it to be interpreted without reference to
  the method. (??)
• See NZSA Newsletter Sept 03 Gwenda Hill Stats
  more advanced (more mathematical?) in Biology
  than in Maths for NCEA L3

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Biology Part 2 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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Biology Part 3 the morals

• What we can and should do in Stats is changing
  profoundly and fast
• How do we assure Statistics (and Maths) their
  most useful places in all the learning areas?
• How can we make the NZ Curriculum Engine produce
  21st century objectives??

2007
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The fun of the fair

• Reflections on the Wellington Science Fair
• Impressive statistics from 8 of the 400 Year 7
  and 8 people
• The essence of statistical quality for statistics
  judgesdesignreplicationgraphs that show
  variabilityconclusions
• Science, years 7 and 8, seems to do much of the
  Experimental Design that has been removed from
  our NCEA L3!
• But we dont provide the commonsense graphic
  tools needed.
• Reflections on the Canterbury and W Coast Science
  Fair
• Winners had their raw data well displayed, and
  were able to deal with its variability.

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The Point of Inflection in Maths Education History

• 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

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Rabid Opinions 1 of 2

• ValuesStats is founded on a Valueinformation-ba
  sed decision-making.
• Curriculum and Assessment for StatsWe must make
  sure the engine pulls the carriage, and not the
  other way round.
• A fourth stage in Statistical education??Stage
  1 Traditional (what we got, and forgot!)Stage
  2 Reformed (Data and EDA-based)Stage 3
  Transformed (Value-based)Stage 4 Blossoming!!
  (Real issues, great data, dynamic
  software. It really is
  new.)
• Stats and Maths thinking are different stats
  cant be taught as is it were maths

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Rabid Opinions 2 of 2

• Hardware and Software Weve got to have itIn
  biology, chemistry, physics, geography, cooking,
  clothing, PE, , students use the real tools and
  materials of the subject.So must Stats!The
  tools are the computer hardware and softwareThe
  materials are the datasets from the other ELAs.
• Students enjoy hands-on work with data, owning
  projects and completing investigations
• The Forefront in Stats educationNZ was there,
  but is now lagging behind.We need to address
  this, with your help
• The Essential Skill Numeracy needs to stay, andto
  be enhanced with Stat Reasoning, Thinking and
  Literacy.

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Tupaia and James

• Oct 1769 the Endeavour sails from Tahiti to NZ.
• Tupaia and James are both strong
  on..HistoryLanguageGraphicsMaths 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.

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Equity, Ethnicity and Intervention

• A country has 2 Ethnicities,
• A (the majority) and B.
• The results of a survey are shown.
• Is there equity in income?
• If not, where should interventions be applied??
• What subject is this???
• (This happens!!)

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Quakes and Spins

• In the past, earthquakes were seen as stochastic
  in space and time (and nasty)
• Now, we havelarge qnd 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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Workshop 2 Stats and your Essential Learning
Area

• Please team up with people from your ELA or with
  similar interests.
• Think up an investigation with a dataset in it.
• What Curriculum Level does it belong at?
• What statistical skills does it cal on?
• How do we get the skills and the links into
  curriculum documents?
• Or.. Go back to Equity, Ethnicity and
  Interventionslide 26.

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Conclusions 1/5Into a blossoming future
for Maths and Stats Ed

• Theres a sea of information on
  statisticalcurriculumpedagogyteacher
  supportresources (including software)assessment
  .
• We need to take a swim into it!
• It includesICOTS conferences (next Brazil
  2006)Online and free SERJ and JSEIASE
  Roundtable (Jul 2005 Sweden). On
  CurriculumTeaching StatisticsAmerican
  Statistician, May 03 Special Section on Stat Ed

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Conclusions The Good Stuff 2/5

• Current curriculum has some outstanding
  strengthsthe focus on Investigationsthe
  progression through investigation types and
  variable types.
• We cant lose that.
• But we cant rest on our laurelsStatistics has
  moved a huge distance since the mid 1980s.The
  Links have yet to be createdThere are
  conversations that have only just started.
• Theres progress in the draftMaths and Stats
  Essence Statement

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Conclusions The New Stats Strand 3/5

• This time, it wont be built top-down and in a
  hurry.
• The statistical community must be enabled to
  take leadership to work on it with all parties
  teachers at all levels curriculum experts.
• Quality must be designed init cant be patched
  in at the bottom of the cliff.
• This is a great opportunity!

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Conclusion Research, Resources, PD
4/5

• Were impressed by the care, expertise and work
  that went into Numeracy.
• Wed like an effort modelled on this for StatsA
  scan of the sea of recent researchcurriculum
  analysisresource production, for stats
  within maths stats everywhere else at
  largeresearch into how professional development
  can be best designedsupport for teachers at
  every stage.
• Itll need fresh work on how to get
  Interconnectedness

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Conclusions For Statistics to blossom 5/5

• We need to build capability in teaching
  (content and pedagogy) teacher education and
  support (pre and inservice) resource
  production curriculum design assessment
  design research in all the above
• We need careful construction of Links.
• We need a new engine for leading statistical
  education!
• We all need each other!!!

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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