Revitalising the curriculum for statistics in NZ schools

1
Revitalising the curriculumfor statistics in NZ
schools
How do we revitalise the curriculum from being
the flawed masterpiece of 1992 to being the
world leader of 2006?How do we support this
world leader curriculum?

• Mike Camden
• NZ Statistical Association Education Committee
• Health warning The views in here belong either
  to Mike or to the NZSA Education Committee (or
  to both). Neither party takes any responsibility
  for them.

2
Contents slides 1 to 15

• Issues behind revitalising stats in the
  curriculum
• Cautionary tales and illustrations
• A recipe for a world-leader statistics curriculum
  strand
• Attached for reference (slide 16 on)
• A multichoice test
• More issues and illustrationsas presented to 3
  Ministry Curriculum Groups in late 2003
• Sources

3
Deterministic and Stochastic Thought

• Greek Stokhastikos Person who aims,
  targets, forecasts Stokhos
  An aim, target
• English Stochastic About variability,
  probability distributions
• Theres an Essential Learning Areaonce called
  Maths, which may becomeMaths and Stats (inc.
  Probability)
• Theres a bunch of mental tools with two parts
• Theyve both been around sincehumans stood up
  and started talking and drawing pictures! Now
  we need a paradigm shift.
• See Mumford, D (1999). The dawning of the age of
  Stochasticity.

Deterministic thinking and modelling
Stochastic thinking and modelling
4
Some of the Communities of Interest

• NZSA, its Education Com, Maths Curric Makers and
  teachers
• The intersections are very small.
• We all need a paradigm shift

5
Towards a great curriculum for statistics
1/4

• Stats is quite different from the rest of Maths
  (our old theme)in many ways, but especially it
  is- newer to teachers (by 2 400 years) - newer
  to teacher educatorsand so needs very careful
  treatmentand we need lots of Statistical
  Pedagogues!
• Stats and the rest of Maths stand together (our
  new theme)giving stochastic and deterministic
  models for life
• Stochastic (ie, variable) aspects of life are
  galloping social policy, health, environment,
  technology,
• Statistical language and structures are
  specialisedso statistical input into curriculum
  and assessment documents is essential

6
Towards a great curriculum for statistics
2/4

• Context is hugely important in statistical
  thinking hence
• 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-solvingthe rest of maths
• Stats supports active learning in other
  subjectsvia investigations and student-driven
  research.Students enjoy doing hands-on work with
  data,owning projects and completing
  investigations
• Any Learning Area can link with Stats so that
  both are valued as enjoyable and useful

7
Towards a great curriculum for statistics
3/4

• We need a new machine for producing stats
  curriculum, assessments, professional
  development and resources for the content and
  the links with the rest of learning
• We need a plan to build capability in Stats
  Pedagogy in NZ for the Maths bit and the links
  with other subjects!
• Statistical and mathematical thinking are
  fundamentally different Stats assumes
  uncertainty, and a need for dataStats cant be
  taught as if it were maths
• Some front-end statistical methods,
  likegraphical data exploration (data
  visualisation) are fun, friendly, powerful,
  commonsense, and suddenly accessible to school
  students

8
Towards a great curriculum for statistics
4/4

• Curriculum structure mustprogress, engage
  attention, deliver the goodsintegrate
  probability with the rest of statistics
• Hardware and Software students use real tools
  and materials in biology, chemistry, physics,
  P.E., cooking, clothingWe need the same for
  Stats!The tools are the computer hardware and
  softwareThe materials are datasets from other
  subjects and contexts
• The parties to the Treaty of Waitangi both use
  statisticswe need to meet the needs of all
• This big challenge needs a partnership, with
  skills fromthe NZ maths education communitythe
  NZ statistical community
• We were at the forefront and will be again by
  revitalising the curriculum like thisDammit!!!

9
The current Auckland-based research project

• The purpose To review the statistics literature
  so as to inform the mathematics curriculum
  project.
• The task  To review and analyse pertinent
  literature on statistics from the perspective of
  curriculum development andto contact
  international researchers working in this field.
  To produce a proposed policy frameworkfor the
  statistics strand of the mathematics curriculum
  project.
• The PeopleAndy Begg, Maxine Pfannkuch, Peter
  Hughes,members of the NZSA Education Committee.
• See also, in press
• Pfannkuch, M. Watson, J. 'Statistics
  education'. In Research in Mathematics Education
  in Australasia 2000-2003

10
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
• needs a how to win friends and influence
  people course

11
Four ways to structure a stats curriculum

• 1 The Chuck Things In methodChuck easy things
  at the start, hard things at end
• 2 The 1992 MiNZC method the practitioner
  method (what we have now)Datasets,
  variables and questions start simple and get more
  varied
• 3 An educational researchers viewLevels of
  abstraction start low and rise higher
• 4 A statistical thinking viewStatistical
  thinking, on variability etc, starts simple and
  gets deep.
• Perhaps we use Methods 3 and 4 to fine-tune
  Method 2.

12
Cautionary Tale 1 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
  subjects- educators and curriculum builders in
  Maths and Stats- the practitioners in the
  statistical community.
• Details

13
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 lead
  to management decisionsExploratory Data Analysis
  (with graphs)
• Harold Henderson, Agresearch NZAMT8 Jul
  03(Bevan Werry speeches 03/04)
• 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, internal components of NCEA (L3)
  statistics can be done by students in ways that
  are relevant, up-to-date and easy to understand.

14
Cautionary Tale 2 of 2 Wgtn Science Fair

• Impressive statistics from 8 of the 400 students
  aged 11,12.
• Science, years 7 and 8 (Level 4), has nice
  Experimental Design which did not make it into
  our NCEA L3 Stats and Modelling!
• The Maths curriculum doesnt provide the
  commonsense graphic tools they could use.

?
15
Recipe a world-leader stats curriculum strand
has

• 1 a new relationship with the rest of mathsa
  new paradigm
• 2 a structure thatprogresses and is gripping
  for students (and teachers)integrates
  probability and the rest of statistics
• 3 strong links with curricula for other subjects
• 4 application of current and new knowledge
  onlearning, statistical methods, technology
• 5 a new machine that calls for the expertise
  ofmaths teachers and statisticians.
• This Curriculum will depend onassessment,
  support for teachers, resources, technology.
• The End but attached arethe test, more issues,
  more illustrations and sources

16
A Multichoice Test Q 1 of 3 for Achievement

• The Maths and Stats Essence Statement should say
  that the Essence of Stats is
• A Weird graphs with kinky names
• B Weirder stuff like s2 S(x m)2/ n
• C Investigations, contexts, datasets,
  variability, exploration, conclusions,
  communication

17
A Multichoice Test Q 2 of 3 for Merit

• The NZ Stat Assoc Education Committees aim is
• A Stuff more Stats into every crack in the
  Curriculum
• B Chuck out half the Maths and replace it with
  Stats
• C Streamline the Stats, slide some bits up and
  down, and insert links with other subjects
• Probability
• Data Graphics

18
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 the longest
  one, C.

19
Towards a great curriculum for statistics
5/4

• Values Stats is founded on a Valueinformation-b
  ased 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
• The Essential Skill Numeracy needs to stay, and
  to be enhanced with Stat Reasoning, Thinking and
  Literacy.

20
Towards a great curriculum for statistics
6/4

• We get real, and use some words used in real life
  statsDatasetVariableDistribution
• Any dataset that is remotely useful or
  interesting has several related variables. SoWe
  stop pretending that variables ever occur
  alone.We replace bi-variate data and
  multi-variate data simply by dataset.

21
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

22
From Maxine Ideas for Stats Curriculum 1/3

• Since 1992, much research in stats education
• Curricula can focus on Statistical Reasoning,
  Thinking and Literacy (inc communication)
  (the soft tissue on the skeleton) probabilistic
  reasoningdata-based empirical inquiry (the bone
  structure)
• Stats and Maths thinking are different stats
  cant be taught as is it were maths
• Big ideasVariation (and the language of),
  uncertainty, reasoning, context, and
  visualisation.sampling reasoning
• SoftwareSuitable and tested stuff exists

23
From Maxine Ideas for Stats Curriculum 2/3

• Professional Development and ResourcesResearch
  shows teachers need teaching and learning
  approaches that develop their own thinking
• ProbabilityThere are ways to rebuild the
  Probability substrand,and link it with the rest.
• DatasetsWas assumed that bi and multivariate
  was for older students. Research shows young
  students can interpret it, eg with
  colour.All interesting questions are about
  relationships.All students can experience
  multivariate datasets.

24
From Maxine Ideas for Stats Curriculum 3/3

• GraphsWas assumed that conventions had to be
  taught first.Research shows students who create
  their own graphs interpret them at a high level
• Stat Literacy and ReportsReports substrand needs
  to be stay and be done better.See International
  Statistical Literacy Project.
• The ForefrontNZ was there, but is now lagging
  behind.We need to address this.

25
From NZSA Ed Com 1/5 Numeracy

• Numeracy has 2 meanings1 the numeracy
  project meaningEg A dishwasher is reduced
  from 995 to 875. The reduction
  is..2 the Stat Reasoning, Thinking and Literacy
  meaning Eg Dishwasher water use varies with
  the Load Sensing Intelligence System.
  The stated 15 litres is a median.
• The latter needs some attention like the former
  has received.
• The two need to support each other.
• Wed like to NOT seemechanical making of
  stem-and-leaf plotsplugging of numbers into
  formulas (glorified substitution)
• We WOULD like to seeperceptive comments on what
  plots showdiscussion on whether the formula is
  sensible in context.

26
From NZSA Ed Com 2/5 Relations between Maths
and Stats

• The methodology behind statistics is
  mathematical
• So we need to link the Stats strand with the
  strands forNumber and Algebra, Measurement,
  Geometryand the process strand
• (Curriculum mapping will be very useful here)
• Example
• The geographers have all the best graphs.
• Theyre ours!! We need to claim them back, and
  take leadership and ownership of Data Graphics.

Mathematicians
Statisticians
27
From NZSA Ed Com 3/5 Research, Resources, PD

• 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.
• The Stats effort may be shorter, but needs to be
  as careful.

28
From NZSA Ed Com 4/5 The New Stats Strand

• 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!

29
From NZSA Ed Com5/5 The Good Stuff

• 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.

30
Jane Watsons Issues in attracting and retaining
students to study statistics at all levels

• Jane is at University of Tasmania and works with
  Years 3 to 9.
• We now know lots about how student understanding
  develops. We need to nurture these ideas.
• We need teacher professional development and
  materials, and methods for working with teachers.
• Students enjoy hands-on work with data,
  ownership, complete investigations and reaching
  conclusions.
• Senior courses need to be lively,
  thought-provoking, with focus on investigations
  and concepts.
• Statistical literacy is a large part of
  quantitative literacy and belongs with the
  essential skills. It motives by usefulness.

31
Illustration Statistical language

• Here are some words from Unit Standard 11122
  STATISTICS
• estimate population parameters from large
  simple random samples
• An editorial tidy-up suggested changing it to
• estimate population parameters of large
  simple random samples
• NZQAs good sense led them to consult us!
• This process highlights the sensitivity of
  language as used in Stats, and the absolute
  necessity for writers to seek statistical input!!

32
Illustration Deterministic and Stochastic Views

• Heres a deterministic
• (algebraic) relation
• ShellVol k ShellLength3
• And a stochastic (statistical) relation of
• ShellVol and ShellLength
• For some Wellington shellfish.
• Which one
• looks nicest??

33
IllustrationTupaia 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.

34
Sources 1/3 References

• Konold C., Higgins T. (2002). Highlights of
  related research Working with data. In S.J.
  Russell, D. Schifter, V. Bastable, Developing
  mathematical ideas. Parsippany, NJ Dale Seymour
  Publications. See Theme 3 (Creating and
  interpreting data displays).
• Konold C, Higgins T. (2003). Reasoning about
  data. In Kilpatrick
• Mumford D (1999). The dawning of the age of
  Stochasticity.
• Mathematics in the NZ Curriculum, 1992, Ministry
  of Education, Wellington.
• Shaughnessy M, Pfannkuch M (2002). How faithful
  is Old Faithful? Mathematics teacher, v 95 n 4
  April 2002.
• Shaughnessy, M. (2003). Research on students'
  understandings of probability. In Kilpatrick.

35
Sources 2/3 Three books in press

• Jones, G. (Ed.). Exploring probability in school
  Challenges for teaching and learning. Dordrecht,
  The Netherlands, Kluwer Academic Publishers (in
  press).
• Ben-Zvi , D., Garfield, J.  (Eds.). The
  challenge of developing statistical literacy,
  reasoning, and thinking. Dordrecht, The
  Netherlands, Kluwer Academic Publishers, (in
  press)
• B.Perry, G. Anthony, C. Diezmann (Eds.), Research
  in Mathematics Education in Australasia
  2000-2003, Sydney, Mathematics Education Research
  Group of Australasia, (in press). Includes
  chapter by Pfannkuch and Watson.
• Also
• Kilpatrick J, W.G. Martin, D. Schifter, (Eds.),
  (2003). A research companion to Principles and
  Standards for School Mathematics. Reston, VA NCTM

36
Sources 3/3 Sites

• http//www.minedu.govt.nz/web/downloadable/dl3526_
  v1/math-nzc.pdf for the Curriculum document.
• http//wwwmaths.anu.edu.au/other/ncms/mathsdocs
  Mumfords paper is No. 8.
• http//www.umass.edu/srri/serg/papers.htmlStats
  Education Research GroupSite for Tinkerplots
  and papers by Cliff Konold et al.
• The IASE Curriculum Roundtable website.
  http//hobbes.lite.msu.edu/IASE_2004_Roundtable/
  See especially Begg A, Statistics curriculum and
  development new ways of working.