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Statistics in the NZ Curriculum Stocktake
Mike Camden
NZ Statistical Association Education Committee
Mike: mike.camden@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.
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
1
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.
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
2
Deterministic and Stochastic Thought
Greek:
Stokhastikos: Person who aims, targets, forecasts
Stokhos:
An aim, target
English: Stochastic: involving ‘random’ probability distributions
There’s an ELA called…
Maths
Maths and Stats
Maths and Stats and Probability
There’s a bunch of mental tools (“Maths”) with two sides:
Deterministic thinking and modelling
Stochastic 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.
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
3
Some odd things about Stats:
“Maths” has two sides:
Deterministic and Stochastic
Stats (and Probability) is entangled with….
Language: English, Te Reo Maori, the others
Graphics and visual communication
Context: all the ELAs
Maths
Stats supports active learning in other ELAs
via “investigations”
“Entangled” has two directions …….
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
4
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.
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
5
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!!)
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
6
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??
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
7
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.
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
8
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 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
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
9
Stats in Schools: The big ideas:
2/3
Stats needs careful curriculum links with …
the other Maths strands
the other essential learning areas
the other layers in the Framework:
Principles, Future Focused Themes,
Skills, Values, Attitudes
Is 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!
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
10
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
We’re at the forefront …
Dammit!!!
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
11
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 etc
John Tukey: “If you haven’t done a graph,
then you haven’t 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.
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
12
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’.
Name
Favourite
Fruit
Gender
Trevor
Mango
Boy
Steve
Apple
Boy
Marion
Apple
Girl
Turiana
Apple
Girl
This thing’s a
Dataset
This thing’s a
(Frequency) Table
Gender
Count
Girl
Boy
Apple
2
1
Mango
0
1
Fruit
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
13
Workshop 1: Skills: what, where, how
See 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)
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
14
The Middle Bit:
Background, illustrations, opinions, more illustrations …
Mussels (Mytius Edulis):
Chaffers Marina:
Shell Vol(ml) vs Shell Length (mm)
Stochastic and deterministic views
ShellVol
Cubic
45
40
35
30
25
20
15
10
5
0
0
20
40
60
80
100
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
15
Some of the Communities of Interest in Maths Ed
NZSA, its Education Com, Maths Teachers and Curric Makers
The intersections are very small.
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
16
NZ Statistical Association Education
Committee’s 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
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
17
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.
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
18
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
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
19
Biology Part 2: Views of senior NZ biometricians
Ian Westbrooke; Dept of Conservation; NZSA Conf Jul 03:
Staff’s (university) stats education has been on hypothesis
tests and ANOVAs.
What they need is
confidence 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, upand easy
to understand.
NZto-date
Statistical Association
Education
Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
20
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??
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
21
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 judges
design
replication
graphs that show variability
conclusions
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 Fair
Winners had their raw data well displayed,
and were able to deal with its variability.
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
22
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 today’s 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
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
23
Rabid Opinions
1 of 2
 Values
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
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
24
Rabid Opinions
2 of 2
 Hardware 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.
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
25
Tupaia and James
Oct 1769; the Endeavour sails from Tahiti to NZ.
Tupaia and James are both strong on..
History
Language
Graphics
Maths 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.
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
26
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!!)
Income ($1000/year)
with Education (Years of Sec+Tert Ed)
for Ethnicities A and B
60
50
40
30
20
10
0
0
5
10
15
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
27
Quakes and Spins
In the past, earthquakes were seen as
stochastic in space and time (and nasty)
Now, we have:
large qnd classy datasets
software that can let us look into the data’s structure
visualisation skills
and all these are available to schools.
an Excel interlude….
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
28
Workshop 2:
Stats and your Essential Learning Area
Please 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.
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
29
Conclusions:
1/5
Into a blossoming future for Maths and Stats Ed
There’s a sea of information on statistical…
curriculum
pedagogy
teacher support
resources (including software)
assessment.
We need to take a swim into it!
It includes:
ICOTS conferences (next: Brazil 2006)
Online and free SERJ and JSE
IASE Roundtable (Jul 2005; Sweden). On Curriculum
Teaching Statistics
American Statistician, May 03; Special Section on Stat Ed
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
30
Conclusions: The Good Stuff
2/5
Current curriculum has some outstanding strengths:
the focus on Investigations
the 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 draft
Maths and Stats Essence Statement
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
31
Conclusions: The New Stats Strand
3/5
This 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!
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
32
Conclusion: Research, Resources, PD
4/5
We’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 research
curriculum analysis
resource production, for:
stats within maths
stats everywhere else; “at large”
research into how professional development can be best
designed
support for teachers at every stage.
It’ll need fresh work on how to get Interconnectedness
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
33
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!!!
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
34
NZ, with Quakes and 4 Main Centres shown:
2
3
4
5
6
7
8
9
11
-800
12
13
14
15
16
17
21
226 800 384
-101
110
142
339
A
209
467
142 400A 339
204
468
C
248
444
-160 D
31
0W
206
498
W
-400
0
117
350
131 C
384
257 -400 462
D95
261
103
297
135
385
248 -800 375
226
-101
142
209
142
204
248
-160
206
400
117
131
257
95
103
135
248
384
110
339
467
339
468
444
31
498
-800
800
350
384
462
261
297
385
375
-3
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
35
Quakes: Depth vs Distance SouthEast of Wgtn
800
400
0
-800
-300
200
700
-400
-800
NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03
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