There are several hot issues current in the statistical education community. Steve Haslett questions Trevor Mallard about the contribution of NZSA to the NCEA statistics achievement standards. Gwenda Hill documents problems relating to Statistics in NCEA Biology.  Mike Camden describes the questions and Maxine Pfannkuch drafts some of the answers concerning the Secondary School Statistics curriculum, to be considered by the NZSA Education sub-committee on Thursday 11 September.  Two members of the Ministry of Education's Curriculum team contributed to the NZSA Education sub-committee on 9 October.  This page will be regularly updated.  Your input is invited.

A reply has been received from the Minister's office dated 12 September.  Details to follow.

Dear Sir

Stats More 'Mathematical' in Biology than in Maths for NCEA

NCEA Level 3 assessment replaces the Bursary examination in 2004. Assessment is in the form of Achievement Standards, some of which are internally assessed and some which will be assessed during the year.

This note is intended to get us (the NZSA membership) focussed on the current Maths Curriculum Stocktake, and the opportunities for Statistics in it.

Recent History

The Ministry of Education launched the New Zealand (School) Curriculum Stocktake in 2000.  There is a Curriculum Stocktake Reference Group that meets occasionally.  The Curriculum Stocktake Report was published by Ministry of Education in September 2002.

This year the Ministry set up a group to work on the Mathematics part of this, which is called the Mathematics Curriculum Stocktake.  It has about 18 members, who are mostly Mathematics Educators, and has met twice, for one-day meetings.  We need to find a process that will represent the views of NZSA and the interests of Statistics for it.

NZ has a foundation curriculum document called The New Zealand Curriculum Framework (Ministry of Education, 1993). It has Principles, seven “Essential Learning Areas”, Essential Skills and Attitudes and Values.  The Maths group’s first job is to revise the Maths part of the Framework. We have an urgent task, in the next month or so, of making sure that Statistics is clearly and correctly valued throughout the new Framework document.  In particular, there is a one-page ‘essence statement’ for Maths.  We need to have statistics mentioned in there and in essence statements for other Essential Learning Areas.

Statistics is not mentioned as such in the 1993 Framework. It does contain this: “Students  … will learn to collect, organise and interpret data”, which seems to be an inadequate description of what Statistics in school could be. We hope the new one treats Statistics better! We need to make sure that it doesn’t get inadvertently swallowed by Maths.

The Ministry has commissioned and received reviews of New Zealand’s curriculum documents from the Australian Council for Educational Research and the Foundation for Educational Research (UK).  These two reports, and other documents, are available via www.tki.org.nz under Community and Curriculum Stocktake; and via www.minedu.govt.nz.
See http://www.tki.org.nz/r/nzcurriculum/about_e.php.

The Current Situation

It seems that the current situation has these components:

• The timescale for curriculum development is not 14 days (as it was in 1992!), but from now to 2006.  The new curriculum documents may be in action from 2007.

• The replacement for Maths in the New Zealand Curriculum (1992) is likely to be a much slimmer book, with the ‘suggested learning experiences” etc. in more flexible supporting documents.

• It would be good for us to be represented on the Mathematics Curriculum Stocktake Group. The person would be expected (by the Ministry) to liaise with the statistical community.  There would be 3 or 4 one-day meetings a year.

• This is a stocktake rather than a revolution.  The new curriculum is likely to build on or fix the old.

• The wider stocktake (i.e. not just the maths part) gives a chance for Statistics to take its role as underpinning several (or all?) other areas. NZSA input is needed here too. 

• The current curriculum has its roots in the mid-1980s.  Thinking and research on the pedagogy of some (or all) Maths strands has moved a lot since then. What has happened in Stats in this time?

• We may be able to use the new curriculum to enhance our arguments for resource development in statistics.

• It is possible that there will be research projects, eg for people to filter the vast Statistical Education literature for aspects of best practice that we can use here.  There’s an NZSA role in support, planning and quality assurance.

• The Ministry and the Maths education community have, very appropriately, invested an impressive amount of expertise in The Numeracy Development Project. It ‘assists teachers in developing the characteristics of effective teaching of mathematics’. It draws on:
  - the number framework (which is a carefully thought-out progression of skills in numeracy);
  - research on children’s strategies for thinking and learning in numeracy;
  - research on professional development strategies for teachers of maths.
  This is a model that could be converted for Statistics. See below!

• There is a ‘stats framework’ hidden within the Stats strand of the Curriculum now. It is a progression in variable type and data structure, from simple to more complex.

Issues for NZSA to deal with now

Here are a few issues :

• We need to clarify that statistics (as done or as could be done throughout the schools) is quite different from maths (in purpose, use, history, integration, pedagogy, assessment, structure…).

• We need to answer this question:
  The process skills at the heart of Maths are problem-solving, logical thinking and communication.
  The process skills at the heart of stats are ……???

• We need a process for ensuring that NZSA (or whatever subset of it is interested) either has a well-founded view, or agrees with the Education Committee, or both!

• The Stats strand in the curriculum has very good bone structure, but could do with :
  -            a hip transplant (the Probability bit needs to be attached better);
  -            a few shots of Botox (there’s plenty of cosmetic improvement desirable);
  -            a body-building programme at the gym (rather than a weight-watchers’ programme -  it could do with some more muscle);
  -      some relationship therapy (to integrate it more with other subjects).
  We need to agree what the strengths and weaknesses (and fixes) are.

• We need to assist the Ministry in resourcing and setting up research projects, in issues like searching the Stat Ed literature, reconstructing the curriculum, creating resources etc..

• There are a few simple shifts in thinking for teachers, maths educators and ourselves, that could unleash statistical education into a useful and enjoyable future.

• We need to deal with the fact that the science curriculum documents require more statistical thinking than the statistics strand of the maths curriculum does.

• Perhaps the time is right for a Statistical Literacy Development Project. Here are some words converted from the Numeracy Project, with the ‘Numeracy’ replaced by ‘Statistics”. Does this sound like a useful possibility?:
  ’The Statistical Literacy Development Project assists teachers in developing the characteristics of effective teaching of statistics. It draws on:
  - the statistics and probability framework (we’d need to ensure we have a good one);
  - research on children’s strategies for thinking and learning in Statistical Literacy;
  - research on professional development strategies for teachers of statistics.’

Since the last curriculum review in 1991 there has been a great deal of new research in statistics education internationally and in Australasia. The current research suggests that the curriculum should be focussed on developing students’ statistical reasoning, thinking, and literacy as well as developing students’ probabilistic  reasoning. There should be an awareness that statistical thinking and mathematical thinking are different and that statistics cannot be taught as though it was mathematics.  The statistics that is of greatest value to the greatest numbers is data-based  empirical enquiry, rather than the simple application of standard mathematics emphasised in the past.

The big ideas of statistics are variation, reasoning  and decision-making under uncertainty, integrating the statistical with the contextual, etc., and these should be prominent in the curriculum.

There are many areas of concern with the current curriculum. Below are some ideas, based on international research, that the NZ curriculum  review should seek to address.

Technology

Technology now precludes the use of statistical tables and the curriculum should be written to reflect this. Students should obtain results preferably from computer software. Suggest that curriculum state that Tinkerplots (for junior students) and Fathom (for senior students) should be the technology used. Tinkerplots and Fathom are written and tested software specifically designed to help students learn to reason statistically, especially with statistical graphics, and to make the desired mental connections. Research suggests that these two software packages meet the criteria for learning statistics. Graphics calculators may be an interim option but this curriculum is for 2006.

Professional Development for Teachers and Resources

The teacher work force is under-educated in modern approaches to data analysis and will not be able to move forward without serious attention to professional development and appropriate resource development. Research is clearly showing that teachers need teaching and learning approaches that will develop their own statistical thinking.

Probability

Students need more exposure to asymmetric probability problems, to problems in a variety of contexts,  to strong connections being made between marbles-in-urn classical situations to social situations, to social context problems, to problems expressed in frequencies rather than probabilities, and students should experience the nature of randomness versus experiencing patterns and determining relationships in mathematics (deterministic thinking). An intuitive, frequentist,  theoretical  teaching approach should be encouraged.

Variation reasoning

Variation is at the heart of statistical thinking.  More experiences of variation in many different contexts are required for students to gain an appreciation of variation.  For example, more emphasis needs to be put on discussing the shape of the data, different kinds of variation, and the language of variation.

Sampling  reasoning

Fundamental to statistical inference is recognising that sample data can be used to make predictions and decisions about the underlying population. The curriculum needs to thoroughly address this issue and start early on building conceptual understanding of how to select a sample and how to draw conclusions from sample data. Recent research is calling for better instructional methods to be found to improve students’ conceptual understanding of sampling in relation to statistical inference.

Data representation and interpretation

All interesting questions are about comparisons and relationships. There has been an assumption in the curriculum that bivariate /multivariate data sets can only be handled by older students – a lot of research is now showing that young students can handle such data and are able to interpret data in ways that they have not been conceived before (e.g. with colour). There has been too much “univariatitis” and this needs to replaced by all students experiencing multivariate data sets.

Another assumption of the curriculum is that the experience of drawing graphs and knowing the conventions are necessary prerequisites for being able to interpret graphs effectively. Studies are challenging this conventional view of graphing and assumptions about the types of graphs that are appropriate for age levels. For example, (1) students who create their own graphical representations (by hand) interpret them at a much higher level than the representation would indicate, (2) by allowing the development of interpretation skills before explicit teaching of the conventions and technicalities of graphing the computer may allow re-evaluation of the progression traditionally applied to the teaching and learning of graphing skills.

Statistical literacy

The interpretation and critical evaluation of statistically-based reports is a feature of the current curriculum but has not been addressed adequately in teaching or assessment.  There is an international movement to address this situation with the recent setting up of the International Statistical Literacy Project. The curriculum should continue to feature this sub-strand, incorporating recent research and conceptual frameworks  and provide more guidance on teaching and learning approaches.

Improving teaching and the curriculum

More research attention should be focussed on working with teachers in the classroom to develop students’ reasoning, thinking and literacy.

The above ideas are only a sample of the number of considerations that a curriculum review of the statistics strand should debate, discuss, and research thoroughly. Statistics education in NZ was originally  at the forefront of international curriculum development but it is now lagging behind. This situation needs to be addressed urgently.

From my son's 7th Form Maths with Stats book:
"An insurance company is like an automobile going down the road at high speed. The Managing Director has his hands on the wheel, the Marketing Director has her foot on the accelerator, the Finance Director is heaving with all his might on the hand-brake, and the Statistician is in the back seat screaming directions from a map she has just made by looking out the back window."

These have been sent by the Ministry of Education to NZQA for registration. [Follow this link to see these documents - Ed.] These standards will be reviewed after their first year of use, and interested people (like NZSA and its education committee) will have the opportunity to contribute to this review.

Comment - Richard Penny

I sometimes feel that the stuff we feel is important in early teaching of statistics (e.g. graphs, tables, data collection) is assumed

• trivial compared to real maths

• common sense

and thus why go to any trouble teaching it?

This is similar to the attitude that says questionnaire design is trivial and doesn't have to be taught Thus one can safely ignore the vast amount of work done on cognitive analysis in the last 15 years. Judging by many of the very bad questionnaires I've been subjected to recently this appears to be the case.

I wonder whether the NZSA needs to support something like the quantitative literacy programme of the American Statistical Association. It's not like we'd have to start from scratch, but could use many of their resources.

Richard Penny