NZSA Education Committee

We’re looking forward to an eventful year. The Maths and Stats learning area in the school Curriculum (http://nzcurriculum.tki.org.nz/) has three offshoots that we intend to keep an eye on. They are:

• The Glossary. The draft, double-sided, weighed in at 300 grams (it came without page numbers!). It will be electronically accessible from the Curriculum, and will be a magnificent aid for teachers of statistics, Year 1 to Year 13. It will both make sense in school Curriculum terms, and be statistically accurate. That’s not easy to achieve.

• The “tier two exemplars”. These will give teachers a lively view of how statistics can be presented actively.

• The NCEA Achievement Standards and Unit Standards for assessment in the last three years of school. These are being created by a NZ Association of Maths Teachers team. Many teachers are very keen for NZQA to have a broad set of statistics standards that can provide credit for their wide range of students.

We’re also hoping to support conference organisers (NZSA, NZAMT, MERGA) in arranging for statistical education content.

The (Australian) National Forum on Building Networks in Statistics Education took place on 9 and 10 February, at Queensland University of Technology. Prof Helen MacGillivray hosted this as part of her Australian Learning and Teaching Council senior fellowship. She very kindly allocated three places to NZSA reps. These were filled by Lindsay Smith (Epsom Girls’ Grammar), John Harraway, and Mike Camden (all Education Committee members). Also representing NZ and NZSA were Jennifer Brown, Sharleen Forbes, Irene David, and Murray Black. Our hosts tolerated us taking up quite a lot of the discussion time.

The primary focus was on the tertiary sector. Issues discussed included:

• A network of Australia and NZ Statistics educators. This will shortly exist in some electronic form, and may meet again at the NOZCOTS or similar event. Watch this space.

• Resource sharing

• Interactions with industry and employers

• Postgraduate support

• Service courses

• Engaging students in interdisciplinary research and study

• The SSAI review

• History and roles of IASE

• R (courtesy of John Maindonald)

• School Curriculum and support for teachers.

The Australian National Curriculum Board in December 2008 released the National Mathematics Curriculum Framing paper. The Forum produced a submission on this (see below). NZ reps have sent in an NZSA Submission on this. (See further below).

Forum members were in agreement about the issues facing statistical education. We could summarise them like this. In both tertiary and school statistics, all these skills are necessary:

Mathematical thinking  

Mathematical methods

Statistical thinking       

Statistical methods

They’re all quite different in pedagogy. We agreed that the future for all of them is vibrant with exciting possibilities and applications to 21st  century problems

Education committee members made contact at last with our SSAI equivalents: the Statistical Education Interest Group. We look forward to closer statistical education relations.

 Mike Camden

General principles for Statistics within National School Curriculum

The principles expressed here were formulated from discussion at the National Forum on Building Networks in Statistics Education, held on 9th, 10th February, 2009, as part of Professor Helen MacGillivray’s ALTC (Australian Learning and Teaching Council) Senior Fellowship. More than 50 delegates from 17 Australian and 3 New Zealand universities, together with representatives from the Australian Bureau of Statistics and Statistics New Zealand, contributed to the formulation of these principles.

Statistics and probability should be included within the mathematics curriculum throughout all years of schooling.

1. The Subject should be called Mathematics and Statistics.

2. Mathematics and Statistics are needed throughout all years of schooling to develop:

   •  numerical and statistical literacy for all

   •  mathematical and statistical thinking

   •  concepts and skills

   • foundations for future learning across all capabilities

3. The emphasis in Mathematics and Statistics across all levels should be on developing student capabilities, concepts, skills, thinking and problem-solving.

4. Mathematics and Statistics should be developed as core learning. This core learning underpins, and is applied in, many other disciplines.

5. Mathematical and Statistical thinking and problem-solving are complementary, and together they provide full quantitative thinking and problem-solving. Mathematical and statistical knowledge, skills and thinking are needed in all disciplines, albeit to different extents.

6. Hierarchies of Mathematics and Statistics curricula at senior school level (and possibly middle school level) should avoid forcing early choices on students. In particular, there should be no separation or semi-separation of Mathematics and Statistics at senior school level as this can cause significant choice problems for students and the future majors at universities.

7. Relevant and appropriate expertise and experience should be involved to produce sound, developmental Statistics in conjunction with Mathematics. It is essential to have a special task force for the Statistics part of the Mathematics and statistics curriculum. The amount of content of Statistics within the curriculum at any level may vary, but statistical education expertise is essential in the framing of content and skills development across the curriculum levels.

8. Training of primary and middle school teachers must include training to teach Mathematics and Statistics at those levels. As well, the training of senior school teachers needs to include tertiary content in Statistics.

9. Teachers should not be required to teach Mathematics and Statistics without adequate training and support. This applies as much in middle school as in senior school. Statistics in curricula must be well-supported with resources and professional development.

10. Statistics and probability at the senior level can complement mathematical development for mutual benefit, particularly with calculus and introductory linear algebra.

11. The Statistics components should include emphasis on data investigations.

12. The development of modern and up to date skills and thinking in Mathematics and statistics need support by relevant Information Technology. This should be acknowledged in any curriculum document.

Professor Helen MacGillivray

Australian Learning and
Teaching Council (formerly Carrick) Senior Fellow

Response from NZSA and NZSA Education Committee

The National Mathematics Curriculum Framing paper of November 2008 invites ‘feedback and advice’ from ‘all those interested’. We’re very interested in Australia building a contemporary statistics component into its mathematics curriculum. We have been active in developments here, and would like to share some insights from our experiences. We’re sure that much of what we say will be familiar to you already.

We are very impressed by your intention to create a ‘futures-oriented curriculum’, and by your high-level description of this. Everything that you have stated in there applies very strongly to statistics, such as the need for ‘real-life connections’.

However, there are some ways in which the ‘stochastic’ side of mathematics differs from the more familiar ‘deterministic’ side. It is important that these differences are planned for in the design, writing and implementation of the curriculum. These are listed below

1. Newness
   The stochastic side is much less familiar to teachers (and parents and the whole community) than the deterministic side. Hence there is a need for very careful curriculum design, and for teacher support and resourcing.

2. Expertise
   Design and writing of the statistics and probability needs to involve people with expertise in maths pedagogy, statistics pedagogy, and current professional practice in statistics.  There are not many people with all these skills. Hence the team members need to be well chosen and well supported by their professional associations.

3. Expertise in Australia
   Australia (and NZ too) contains a considerable number of people with expertise in statistical pedagogy. Many of these take leading roles in the International Association for Statistical Education, and the rest of the world community in statistical education. It makes sense to make use of this expertise.

4. International developments in statistical pedagogy
   Statistical pedagogy has been through major transformations in the last two decades, and has been the subject of much fresh research (with plenty of this in Australia). The curriculum can build on these developments.

5. Newly accessible parts of professional practice in statistics
   Professional practice in statistics is advancing in many directions. In some of these, the intuitive and visual sides of statistical investigation have been liberated by digital technology. One of these is ‘data visualisation’, and the dynamic and interactive sides to it. Another is the important area of ‘resampling and randomisation’ (which we gather originated in Tasmania!). The curriculum can take the bold step of including these, and being open to others.
   
   As you say, ‘digital technology can make previously inaccessible maths accessible’. This is very true throughout statistics and probability for school.

6. Differences summarised
   The stochastic side differs from the deterministic side in how it is used (by students and public), what can and needs to be learnt, how this is taught and learnt, how it is assessed, how teachers are supported, how it interacts with other subjects, and how it achieves intellectual rigor. Getting the curriculum to reflect all this is a challenge.

In conclusion, we agree with you that both mathematical (deterministic) thinking skills and statistical (stochastic) thinking skills are utterly essential for tomorrow’s citizens and workers. To build the best curriculum for both these will involve the people and professional groups that can access the latest in research into the pedagogy, and the latest in professional practice.

We wish you a successful curriculum-building process.

Mike Camden
for NZ Statistical Association Education Committee

 Jennifer Brown
President, NZ Statistical Association