1 NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03 Statistics in the NZ Curriculum Stocktake Mike Camden NZ Statistical Association Education Committee Mike: [email protected]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.
Statistics in the NZ Curriculum Stocktake. Mike Camden NZ Statistical Association Education Committee Mike: [email protected] NZSA: http://www.stat.auckland.ac.nz/nzsa/ NZSA Newsletter: http://nzsa.rsnz.govt. nz/newsletter58. Health warning: The views in here belong - PowerPoint PPT Presentation
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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
Statistics in the NZ Curriculum Stocktake
Mike Camden
NZ Statistical Association Education CommitteeMike: [email protected]
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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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
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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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
Deterministic and Stochastic ThoughtGreek: Stokhastikos: Person who aims, targets, forecasts
Stokhos: An aim, target
English: Stochastic: involving ‘random’ probability distributions
There’s an ELA called…
MathsMaths and StatsMaths and Stats and Probability
There’s a bunch of mental tools (“Maths”) with two sides:
Deterministic thinking and modellingStochastic thinking and modelling
They’ve both been around since humans stood up, started talking and drawing, and invented Education!
See Paper 8 in http://wwwmaths.anu.edu.au/other/ncms/mathsdocs/Mumford, D (1999). The dawning of the age of Stochasticity.
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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
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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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
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?
JFK’s 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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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
A Multichoice Test: Q 1 of 3: for Achievement:The NZ Stat Assoc Education Committee’s 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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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
A Multichoice Test: Q 2 of 3: for Merit:The Essence of Stats is:
A: Weird graphs with kinky names
B: Weird stuff like 2 = (x – )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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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
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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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
Stats in Schools: The big ideas: 1/3Stats is quite different from the rest of Maths (our old theme)
and so needs very careful treatmentStats and the rest of Maths stand together (our new theme)
giving stochastic and deterministic models of lifeStochastic (ie, variable) aspects of life are becoming more
obvious: 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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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
Stats in Schools: The big ideas: 2/3Stats 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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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
Stats in Schools: The big ideas: 3/3Graphical 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
We’re at the forefront …Dammit!!!
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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
A Scalpel for Stats Curriculum ConstructorsAny investigation has these stages:State the purpose, get approvalDesign and/or plan all aspects of itCollect the data into a Unit Record DatasetEdit/Launder/Clean the dataset with graphs etcExplore and/or analyse the dataset with graphs etc
John Tukey: “If you haven’t done a graph, then you haven’t done an analysis”
Summarise the findings/information/conclusionsCommunicate 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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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
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 data’and ‘multi-variate data’ by‘dataset’.
This thing’s a DatasetThis thing’s a (Frequency) Table
Name Favourite Fruit
Gender
Trevor Mango Boy
Steve Apple Boy
Marion Apple Girl
Turiana Apple Girl
Count
Gender Girl Boy
Fruit
Apple 2 1
Mango 0 1
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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
Workshop 1: Skills: what, where, howSee SNZ’s “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?
2 Whereabouts do we put these skills etc in the Curriculum Framework??
3 What does NZ need, to ensure effective teaching, learning and assessment of the skills etc???
4 Are we in the right Industry????(See Table 10 near the end)
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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
The Middle Bit:Background, illustrations, opinions, more illustrations …
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
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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
Some of the Communities of Interest in Maths EdNZSA, its Education Com, Maths Teachers and Curric Makers
The intersections are very small.
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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
NZ Statistical Association Education Committee’s conclusionsOn Thur 11 Sept 03, the Committee discussed the Stocktake
at length. Main conclusion: it offers to:Make input into and review the draft Framework documentBe part of research projects that would underpin
curriculum and resource writingTake 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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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
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 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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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
Biology Part 1: Stats in NCEA Biology Level 3Explanatory 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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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
Biology Part 2: 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 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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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
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??
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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
The fun of the fair: Reflections on the Wellington Science Fair:Impressive statistics from 8 of the 400 Year 7 and 8 peopleThe essence of statistical quality for statistics judges
designreplicationgraphs 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 don’t provide the commonsense graphic tools needed.Reflections on the Canterbury and W Coast Science FairWinners had their raw data well displayed,
and were able to deal with its variability.
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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
The Point of Inflection in Maths Education HistoryStatistics 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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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
Rabid Opinions 1 of 2Values
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.)
Stats and Maths thinking are different; stats can’t be taught as is it were maths
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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
Rabid Opinions 2 of 2Hardware and Software: We’ve got to have it:
In 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 software;The materials are the datasets from the other ELAs.
Students enjoy hands-on work with data, owning projects and completing investigations
The Forefront in Stats education:NZ 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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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
Tupaia and JamesOct 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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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
Equity, Ethnicity and InterventionA 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!!)
Income ($1000/year) with Education (Years of Sec+Tert Ed)
for Ethnicities A and B
0
10
20
30
40
50
60
0 5 10 15
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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
Quakes and SpinsIn the past, earthquakes were seen as
stochastic in space and time (and nasty)
Now, we have:large qnd classy datasetssoftware that can let us look into the data’s structurevisualisation skills
and all these are available to schools.
an Excel interlude….
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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
Workshop 2: Stats and your Essential Learning AreaPlease team up with people from your ELA or with similar
interests.
1 Think up an “investigation” with a dataset in it.
2 What Curriculum Level does it belong at?
3 What statistical skills does it cal on?
4 How do we get the skills and the links into curriculum documents?
5 Or.. Go back to Equity, Ethnicity and Intervention;slide 26.
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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
Conclusions: 1/5Into a blossoming future for Maths and Stats EdThere’s a sea of information on statistical…curriculumpedagogyteacher supportresources (including software)assessment.
We need to take a swim into it!It includes:ICOTS 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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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
Conclusions: The Good Stuff 2/5Current 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.The Links have yet to be created;There are conversations that have only just started.
There’s progress in the draftMaths and Stats Essence Statement
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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
Conclusions: The New Stats Strand 3/5This 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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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
Conclusion: Research, Resources, PD 4/5We’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.
It’ll need fresh work on how to get Interconnectedness
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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
Conclusions: For Statistics to blossom… 5/5We 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 aboveWe need careful construction of Links.We need a new engine for leading statistical education!We all need each other!!!
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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03