Download The Future of Statistics in the NZ Curriculum (May 2001)

The Future of Statistics in the NZ Curriculum (May 2001)
Prepared for Ministry of Education Discussion, Thursday 31 May 01.
Adapted for LOGOS#10, Monday 3 Sept 01, Mathematics Education Unit, University of Auckland.
Mike Camden; care of [email protected].
This paper is two years old. However, the issues now are the same, and a bit sharper..
At the back:
Ministry of Education’s Discussion on Mathematics Curriculum
1.
The Education Committee of The New Zealand Statistical Association
The Education Committee of NZSA has taken an active interest in statistics for New Zealand
schools since it began in 1987. An initial purpose was support for teachers on the Bursaries Maths
with Stats Project. It had a major input into the Statistics Strand of MINZC in 1991, into the
Framework Standards later, and has a current interest in NCEA Standards. This paper had the
support of the Education Committee of NZSA
2.
Our Main Recommendation
We support the current structure of the Statistics Strand, but recommend considerable fine-tuning.
This fine-tuning would aim at improving clarity for users of the document, and at making the
progression of learning outcomes stronger and more logical. We would like to see a clearer focus at
each level.
Our reasons for this recommendation are:
 The Curriculum needs more time to become fully embedded. Teachers and resource-writers
have worked successfully at meeting the challenges. A major change now would damage
confidence.
 MINZC can be seen as a “flawed masterpiece”. It set us off strongly in a very sensible
direction, but has a few gaps that have become visible since 1992. The gaps are more evident at
Levels 7 and 8. See Section 11 below.
 The Statistics Strand has a very sound underlying progression.
The progression goes from simple data structures, (single category variables), to the everyday
structures, (case data sets with several category and numerical variables; time series data sets).
The progression then moves from exploration to inference. The Strand has excellent bone
structure, but could do with some cosmetic surgery, (especially at Level 8)!
 The general direction of the Statistics Strand was quite advanced in an international context, and
probably serves the future needs of New Zealand students quite well.
3.
Recommendations about Research
In the interests of both fine-tuning and future reviews, we recommend that research is supported:
 into how the Statistics Strand is operating
 into international developments in curriculum for statistics and probability.
4.
Differences between Mathematics and Statistics
Statistics is mainly embedded in the Mathematics Curriculum, and mainly taught by Mathematics
teachers. (In fact, learning outcomes that are closely aligned to Statistics occur in other learning
areas and in essential skills.)
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However, Statistics is quite different from (the rest of) Mathematics:
 in the way it is applied
 in the ways it can be taught, learned and assessed
 in the ways it can be integrated with other learning areas
 in its history: it is much newer to most of us.
These differences need to be considered in the commissioning of research (as above), and in the
provision of teacher professional development.
5.
Integration
Some assessment in New Zealand schools is focussed on small areas of knowledge within subjects.
It is possible and potentially very useful for Statistics learning to have learning activities and
assessment tasks that go across several subject areas. The Ministry could assist here with
exemplars.
6.
Statistical Literacy or Numeracy
Numeracy (which must include Statistical Numeracy) is in the wider curriculum as one of the eight
essential skills. The Mathematics Curriculum needs to recognise and support this.
7.
The Process Strand
When MINZC was written, there was a lucky coincidence of views: the mathematicians wanted
mathematical processes, and the statisticians wanted investigation processes. The connection needs
to be clarified in the document, and supported in professional development.
8.
The Threads in the Statistics Strand
These threads are;
 Statistical investigations
 Interpreting statistical reports
 Exploring probability
The first thread actually consists of “Statistics in investigations”, and could be relabelled. The
second thread currently seems to include both of the following: reading reports from other people,
and reporting one’s own investigation (which could be better placed in the first. The third thread has
a legacy of traditional mathematics that emerges in places. It could be redirected to be a practical
tool, for a world where people are increasingly aware of “risk” in all parts of life. It also needs to
support the Investigation and Reporting threads. We need to decide whether the statistics and
(especially) probability contents are tools for application, or examples of pure Maths!
9.
Procedures for Improving the Statistics Strand
It would be useful to isolate each “fibre” within the threads and strands: case data, series data,
reporting, probability, inference etc. Each “fibre” could be checked so that it has a strong
progression into new skills at each Level, and has clear consistent wording. In the other dimension,
it is necessary to ensure that each level has a clear focus. The basic aims of the curriculum need to
be continually reassessed. There are changes to the demographics of the groups who proceed
through our curriculum, and changes to the technology, employment opportunities and information
supply that await them. The Addendum (1994) needs to be integrated into the main document;
and/or have its standing clarified. The possibilities for maths and statistics at Level 8, under NCEA,
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need to be thought through.
10.
Support for Teachers
Whether we change the curriculum or not, New Zealand teachers continue to face changes in what
students bring and what the world outside suggests. They continue to deal with the newness of the
whole curriculum, and statistics in particular. They merit ongoing support in terms of professional
development and resources.
Enough of the necessary technology (hardware and software) needs to be made available.
11.
A Reconstruction of "Maths with Stats" at NCEA Level 3.
Notwithstanding the main recommendation above about fine-tuning, we have the opportunity right
now to adapt the statistics and probability objectives at Curriculum and Addendum Level 8 to form
a really useful and attractive set of statistics Standards. Here are some reasons:
 Most of the detailed content needed is already in the Addendum
 Recent work on NCEA Level 3 Standards has already made a movement in this direction
 The NCEA structure will allow schools to construct courses in different and more flexible ways
than are possible with Bursaries
 The international statistics education community (which includes several strong NZ voices) is
quite clear on what such a course would contain
 The NZ community would benefit substantially from having a world-leading course available.
What we would need to do, to achieve this, is:
 Produce 2 or 3 new NCEA Standards, notably in Exploratory Data Analysis and objectives from
the Addendum (They would be expansions of S3.5)
 name it "Stats" rather than the present "Maths with Stats"; and think of it that way (We would
need to train ourselves to think of it in quite a different way)
 ensure access to software, datasets, other resources, support for teachers and professional
development.
Some Reformed, Transformed or Thinking Texts:
Hoerl, R.W., Snee, R.D. (2001). Statistical Thinking: Improving Business Performance. Duxbury.
Griffiths, D., Stirling, W.D. and Weldon, K.L. (1998). Understanding Data. Queensland:
Jacaranda Wiley. (Authors from Queensland, Palmerston North and Ontario)
Moore, D. and McCabe, G. (1999). Introduction to the Practice of Statistics (3rd ed). New York:
W.H.Freeman
Wild, C., Seber, G. (2000). Chance Encounters: A First Course in Data Analysis and Inference.
New York: Wiley. (Both authors from University of Auckland)
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The Ministry of Education’s Discussion on Mathematics Curriculum
The Ministry of Education is running a “Curriculum Stocktake” for the whole NZ School
Curriculum. As part of this, the Ministry called a one-day meeting (31 May), on the Maths
Curriculum. NZSA was invited as a stakeholder.
The day was full of pleasant surprises. These are listed.
1.
Future curriculum documents may look quite different from the present 200-page one.
They are likely to be much shorter (Norway’s document is 1.5 pages), with supporting
documents that are continuously updated. The system may be more dynamic, flexible and
alive.
2.
The process for producing the next maths curriculum is likely to be quite different from
NZ’s past processes. The Ministry seems to be very open to collecting views and acting on
them.
3.
There was a consensus that the real curriculum, (i.e. what actually gets learnt), depends on
several things besides the curriculum document. The foremost of these is teacher
professional development and teacher confidence.
4.
Teachers need time to reflect on their practice, as a key way of maximising their
professional skills in content and pedagogy. (Both content and pedagogy are different from
those for the rest of maths, and evolving). The “Count Me In Too” project is a very
successful professional development project for numeracy in the junior school.
(See: Thomas G, Ward J (2001). An Evaluation of the Count Me In Too Pilot Project.
Ministry of Education, Wellington.)
5.
There is a view that the curriculum is too cluttered, and that numeracy needs to receive most
of the attention in the junior school. We need to ensure that the statistics is not seen as
clutter, but as a great way to enhance numeracy.
6.
Our paper suggested (i) a rewrite to improve clarity and progression without major change,
and (ii) an adjustment of year 13 (Form 7) content to make up a full up-to-date statistics
course. The discussion at the meeting was at a more general or strategic level than this.
These (short-term) issues will need to be addressed later.
7.
For the longer term, we need a very careful (and resourced) think about how we transform
the Statistics curriculum to maintain a world-leading position.
Some Reformed, Transformed or Thinking References
Hoerl, R.W., Snee, R.D. (1995). Redesigning the Introductory Statistics Course. CQPI Report No.
130, University of Wisconsin. (The Transformers)
Moore, D. (1997). New pedagogy and new content: the case of statistics. International Statistical
Review. 65, 2, 123-165. (The Reformer)
Vere-Jones, D. (1995). The coming of age of statistical education. International Statistical Review.
63, 1, 3-25.
Wild, C.J., Pfannkuch, M. (1999). Statistical Thinking in Empirical Enquiry. International
Statistical Review. 67, 3, 223-265. (The Thinkers)
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