revitalising the stats curriculum; nzsa conference: july 2004 1 revitalising the curriculum for...

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Revitalising the Stats curriculum; NZSA Conference: July 2004

Revitalising the curriculumfor statistics in NZ schools

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.

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?

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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 testMore issues and illustrations

as presented to 3 Ministry Curriculum Groups in late 2003Sources

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Deterministic and Stochastic ThoughtGreek: Stokhastikos: Person who aims, targets, forecasts Stokhos: An aim, target

English: Stochastic: About variability, probability distributions

There’s an Essential Learning Areaonce called Maths, which may becomeMaths and Stats (inc. Probability)

There’s a bunch of mental tools with two parts:

They’ve 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 thinkingand modelling

Stochastic thinking and modelling

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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

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Towards a great curriculum for statistics: 1/4Stats 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

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Towards a great curriculum for statistics: 2/4Context 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

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Towards a great curriculum for statistics: 3/4We 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 can’t 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

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Towards a great curriculum for statistics: 4/4Curriculum structure must

progress, 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 statistics;we need to meet the needs of all

This big challenge needs a partnership, with skills from:the NZ maths education communitythe NZ statistical community

We were at the forefront; and will be again by revitalising the curriculum like thisDammit!!!

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The current Auckland-based research projectThe 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 People:Andy 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

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Health Report for the Statistics Strand in MathsBone structure mostly good but needs a hip replacement and some physio elsewhereSoft 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 indicatedBadly needs a hair transplantSocialisation: needs a ”how to win friends and influence people” course

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Four ways to structure a stats curriculum:1: The Chuck Things In method:

Chuck 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 researcher’s view:Levels of abstraction start low and rise higher

4: A statistical thinking view:Statistical thinking, on variability etc, starts simple and gets deep.

Perhaps we use Methods 3 and 4 to fine-tune Method 2.

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Cautionary Tale 1 of 2: Biology in Curriculum Level 8 and in PracticeSchool:

NCEA 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 Moral:NZ 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 …

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Biology Contd: Views of senior NZ biometriciansIan Westbrooke; Dept of Conservation; NZSA Conf Jul 03:

Staff’s (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.

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Cautionary Tale 2 of 2: Wgtn Science FairImpressive 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 doesn’t provide the commonsense graphic tools they could use.

Sciences Maths Soc ScisLevel 1 Level 1 Level 1Level 2 Level 2 Level 2Level 3 Level 3 Level 3Level 4 Level 4 Level 4Level 5 Level 5 Level 5Level 6 Level 6 Level 6Level 7 Level 7 Level 7Level 8 Level 8 Level 8

?

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Recipe: a world-leader stats curriculum strand has1: a new relationship with the rest of maths

a new paradigm2: a structure that:

progresses and is gripping for students (and teachers)integrates probability and the rest of statistics

3: strong links with curricula for other subjects4: application of current and new knowledge on:

learning, statistical methods, technology5: a new machine that calls for the expertise of:

maths teachers and statisticians.This Curriculum will depend on:

assessment, support for teachers, resources, technology.The End … but attached are

the test, more issues, more illustrations and sources

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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 2 = (x – )2/ n

C: Investigations, contexts, datasets, variability, exploration, conclusions, communication

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A Multichoice Test: Q 2 of 3: for Merit:The NZ Stat Assoc Education Committee’s 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

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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 the longest one, C.

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Towards a great curriculum for statistics: 5/4Values: Stats is founded on a Value:

information-based decision-making

Curriculum and Assessment for Stats:We 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.

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Towards a great curriculum for statistics: 6/4We get real, and use some words used in real life stats:

DatasetVariableDistribution

Any dataset that is remotely useful or interesting has several related variables. So:We stop pretending that variables ever occur alone.We replace ‘bi-variate data’ and ‘multi-variate data’ simply by ‘dataset’.

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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 today’s complex world of technology

and social needs depends on itThe ways it can be taught, learned and assessed

(the pedagogy…. And the pedagogues!!)The ways in which it uses computer technologyThe ways it can be integrated with other learning areasTeacher confidence, professional development needs and

resource needs, in Maths and other ELAs

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From Maxine: Ideas for Stats Curriculum 1/3Since 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 can’t be taught as is it were maths

Big ideas:Variation (and the language of), uncertainty, reasoning, context, and visualisation.sampling reasoning

Software:Suitable and tested stuff exists

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From Maxine: Ideas for Stats Curriculum 2/3Professional Development and Resources:

Research shows: teachers need teaching and learning approaches that develop their own thinking

Probability:There are ways to rebuild the Probability substrand,and link it with the rest.

Datasets:Was 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.

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From Maxine: Ideas for Stats Curriculum 3/3Graphs:

Was 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 Forefront:NZ was there, but is now lagging behind.We need to address this.

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From NZSA Ed Com: 1/5: Numeracy‘Numeracy’ has 2 meanings:

1 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.

We’d like to NOT see:mechanical making of stem-and-leaf plotsplugging of numbers into formulas (glorified substitution)

We WOULD like to see:perceptive comments on what plots showdiscussion on whether the formula is sensible in context.

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From NZSA Ed Com: 2/5: Relations between Maths and StatsThe 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.”

They’re ours!! We need to claim them back, and take leadership and ownership of Data Graphics.

MathematiciansStatisticians

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From NZSA Ed Com: 3/5: Research, Resources, PDWe’re impressed by the care, expertise and work that went

into Numeracy.

We’d like an effort modelled on this for Stats:A scan of the sea of recent researchcurriculum analysisresource production, for: stats within maths stats everywhere else; “at large”research 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.

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From NZSA Ed Com: 4/5: : The New Stats StrandThis time, it won’t 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 in;it can’t be patched in at the bottom of the cliff.

This is a great opportunity!

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From NZSA Ed Com:5/5: The Good StuffCurrent curriculum has some outstanding strengths:

the focus on Investigationsthe progression through investigation types and variable types.

We can’t lose that;

But we can’t rest on our laurels:Statistics has moved a huge distance since the mid 1980’s.

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Jane Watson’s 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.

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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”

NZQA’s 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!!

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Here’s a deterministic

(algebraic) relation:

ShellVol = k ShellLength3

And a stochastic (statistical) relation of

ShellVol and ShellLength

For some Wellington shellfish.

Which one

looks nicest??

Mussels (Mytius Edulis): Chaffers Marina:

Shell Vol(ml) vs Shell Length (mm)Stochastic and deterministic views

051015202530354045

0 20 40 60 80 100

ShellVol

Cubic

Illustration: Deterministic and Stochastic Views

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Illustration: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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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 KilpatrickMumford 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.

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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

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Sources: 3/3: Siteshttp://www.minedu.govt.nz/web/downloadable/dl3526_v1/math-nzc.pdf

for the Curriculum document.

http://wwwmaths.anu.edu.au/other/ncms/mathsdocs; Mumford’s paper is No. 8.

http://www.umass.edu/srri/serg/papers.htmlStats Education Research Group:Site 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.

revitalising the stats curriculum; nzsa conference: july 2004 1 revitalising the curriculum for...

Documents

revitalising stats

great curriculum

rest of maths stats

world leader curriculum

careful curriculum links

curriculum cautionary

ministry curriculum

essential slide