We are able to report in this Newsletter that, in spite of some problems, we are on schedule with our planning for next year’s activities, and we now have a very fine improved Web-site. There are several calls for help in this edition: please seriously consider offering your services.

1. PME 24

2. Our Web Site

3. PME Display at ICME-9

4. Statistics Education Research Group (SERG)

5. ICME-9 TSG4: The Teaching and Learning of Statistics

6. Addresses

7. Special Issue of Mathematics Teacher: Focus on Statistics

8. Special Issue of Mathematical Thinking and Learning

9. Next Newsletter

By now you have probably received the first announcement for PME24, which will be at Hiroshima, Japan from 23-27 July, 2000. This will finish just before ICME-9 in Tokyo. Details can be obtained from the website http://www.ipc.hiroshima-u.ac.jp/~pme24. Don’t forget that research reports are due in Hiroshima by 15 Jan 2000.

Our Discussion Group will focus on “The Relationship between Stochastical and Mathematical Thinking, Learning, and Teaching”. Brief presentations will be prepared beforehand to ensure that a rich discussion ensues. We want to approach the issue from a number of perspectives:

We hope that this theme (and approach) will extend through further meetings. The Group will work best if we can have a small number of brief introductions, say, 6 contributions of no more than 10 minutes each.

We are therefore calling for contributions to this discussion. If you have something to say, please contact Dani at dani.ben-zvi@weizmann.ac.il by 15 Jan 2000.

For quite different personal reasons both Dani and Brian have found that they will not be able to attend the Hiroshima meeting, which is a great pity because they have a liveliness and vitality which does wonders for discussions. This means that John will be the only organiser present (provided that his paper is accepted). However, Dani and Brian will still do the co-ordination for the Discussion Group. We would find it useful to know who might be willing to give John a hand during the meetings.

Dani (supported by Dagan - his son) has put a lot of work into revamping our Group’s Newsletter. We have aimed to present it in two main sections: the first is fairly brief and contains information of immediate relevance. The second contains our archival material, and also a vast number of links to other statistical education sites. Dani has put this together as a service to members, and most of us ought to be able to find something there we could use but didn’t know about. There is also a list of members of this group, and some of the members have provided brief biographies of their work. The site is at

Please visit the site, and send you comments to Dani. We should also welcome your own brief biographies to add to our list, and suggestions of any other links, which you think might be of value.

PME is planning to hold a display of its work at the ICME-9 Congress in Tokyo immediately after the PME Conference in Hiroshima. It would be good if our Group could make a contribution to this, giving some indication of our aims and interests, and perhaps one or two examples of typical work done by members of our group.

If there is any one on our list who would like to do this, we should be happy to provide the background to enable them to put a brief display together. What we need first is a name, then we can go to the PME Executive and ask how they want things done. PME would like a name by 31 Dec 1999.

We remind you that from January 2000 the old International Study Group for Research on Learning and Probability and Statistics is being revamped to become the Statistics Education Research Group (SERG), which will be a subset of the International Association for Statistics Education (IASE).

Members are encouraged to join the IASE and to receive announcements of when the new format Newsletter is published electronically. Membership of IASE costs 24 US dollars, and members receive a regular copy of the IASE Review. The last Review contains a membership form, and may be read at http://www.swin.edu.au/maths/iase/review99.doc or you can write to the International Statistical Institute at isi@cbs.nl.

We try not to make our PME Newsletter too long, because this would involve a lot of duplication of material. So members are encouraged to read the SERG Newsletter at http://www.ugr.es/~batanero/iase.html.

There will be 11 speakers at this session from a very wide range of countries. There is one speaker from the Ukraine, and three from South America. An interesting new contribution will come from Li Jun and Lionel Pereira-Mendoza (Singapore) on “Chinese Students’ Probabilistic Thinking” and Linda Gattuso continues her work on averages which she talked about so entertainingly at ICOTS-5. Dani Ben-Zvi continues his work with junior secondary students on constructions of meaning for data representations. Dani’s earlier work in this area was also well received at ICOTS-5. For details please see http://www.swin.edu.au/maths/iase/icme9.html.

We have not been able to contact the following members. If you can help us with their e-mails, please let Dani know.

NCTM’s monthly journal, November 1999, Volume 92, Number 8

ARTICLES

Titanic: A Statistical Exploration, Sandra L. Takis

The Role of Technology in Introductory Statistics Classes, George N. Bratton

Discuss with Your Colleagues: It's All in the Area, J. Todd Lee

Sharing Teaching Ideas: The Double Stuff Dilemma, Marie A. Revak and Jihan G. Williams

What Is Normal, Anyway?, Maria E. Calzada and Stephen M. Scariano

Test Reliability, Kenneth Clark

German Tanks: A Problem in Estimation, David C. Flaspohler and Ann L. Dinkheller

Using Simulation on the Internet to Teach Statistics, Vee Ming Ng and Khoon Yoong Wong

Cooperative Teaching Opportunities for Introductory Statistics Teachers, Deborah J. Rumsey

Data Analysis and Baseball, Gary Talsma

DEPARTMENTS

Activities: Discovering an Optimal Property of the Median, Neil C. Schwertman

Implementing the Assessment Standards for School Mathematics Secondary Students' Performance on Data and Chance in the 1996 NAEP, J. Michael Shaughnessy and Judith S. Zawojewski

Technology Tips: Investigating Distributions of Sample Means on the Graphing Calculator, Gloria B. Barrett

(From Brian Greer)

On the initiative of Lyn English, of Queensland University of Technology, a major new Mathematics Education journal was launched under her editorship by Lawrence Erlbaum Associates at the start of this year. As an Associate Editor, I negotiated for a special issue of the journal on the topic “Statistical Thinking and Learning”, and solicited papers from a small group of leading workers in the field, all of whom agreed to contribute. In the event, the papers required two issues, 1 and 2 of the second volume of the journal, to appear in January and April, 2000.

In planning the contributions, I aimed at a balance of experimental work and overviews of central issues. In Volume 1, there is an introduction by myself, and two reports of research on the developmeof statistical understanding. Inthe introduction, I cite David Moore’s definition of statistics as the mathematical science of gaining information from data, where data are “numbers with a context” (Moore, 1992, p. 1) and suggest that one of the major contributions made by the growing incorporation of statistics into mainstream curricula is the broadening of the boundaries of mathematics to include understanding of the physical and social phenomena modelled through mathematics, and of the nature of the modelling process itself.

The paper by Jane Watson and Jonathan Moritz “The Longitudinal Development of Understanding of Average” is a very detailed study of Australian students’ understanding of concepts relating to averages, based on extensive interviews. A model of the developmental sequence of understanding of concepts relating to averages is presented, and recommendations for teaching are made. The conceptual complexity of interpreting averages in context is particularly well illuminated. Ongoing complementary work is beginning to provide similar in-depth analyses of concepts relating to variation in data (e.g. Shaughnessy, Watson, Moritz, & Reading, 1999).

Richard Lehrer and Leona Schauble, in “Inventing Data Structures for Representational Purposes: Elementary Grade Students’ Classification Models”, report on a study in which children were presented with a very open-ended task requiring them to construct data structures, and which shows how the sophistication of these constructions increases with age. Children were presented with self-portraits done by other children from kindergarten and grades 1, 3 and 5 and the task was to derive and refine models using various attributes that could be used to discriminate the sample of self-portraits on the basis of the age of the artist and to categorise new examples. Whereas the first and second graders evolved systems of attributes in post hoc and unintegrated fashion, the fourth and fifth graders were able to structure their systems of attributes into coherent models, and to consider various kinds of decision rules, such as differentially weighing diagnostic attributes.

The second special issue begins with a paper by Carmen Batanero entitled “Controversies around the Role of Statistical Tests in Experimental Research”. This issue is particularly topical, given the intensive current discussion in many professional bodies, notably the American Psychological Association which has established a Task Force on Statistical Inference that recently published an article (Wilkinson, 1999) to initiate discussion on the topic. Carmen’s paper powerfully makes two points in particular, namely that the importance of understanding statistical thinking and learning extends beyond the school level, and that, in addition to the mathematical and philosophical complexities of the issue (Harlow, Mulaik, & Steiger, 1997), it is essential to understand the thinking of students, and indeed statisticians, better in order to improve the education of the former and the practice of the latter.

The paper by Joan Garfield and Beth Chance, “Assessment in Statistics Education: Issues and Challenges” presents an overview, with numerous examples reflecting new approaches to assessment in relation to differentiated goals of assessment. A conceptualization of doing statistics as a holistic process that stretches from the initial structuring of the data through to interpretation and communication of the results poses challenges of developing appropriate modes of assessment, echoing, in a particularly concentrated fashion, those faced by attempts to enrich assessment within mathematics education in general. In particular, the complexity of conceptual processes, and the prevalence of misconceptions, that characterize statistical thinking, make it imperative to devise methods of assessment that probe understanding.

In the final paper, “Towards Understanding of the Role of Technological Tools in Statistical Learning”, Dani Ben-Zvi offers an analysis illustrated throughout by a classroom example of students interacting with computer software, as well as an overview of available software and Internet resources. Arguably, as with assessment, the teaching/learning of statistics offers a particularly powerful testing-ground for probing fundamental questions. A central point of Dani’s argument is the contention that technological tools do not simply act as cognitive amplifiers, rather they fundamentally transform cognition (Dorfler, 1993); in particular, through experience of direct manipulation of mathematical entities creating “a new mathematical realism” (Balacheff & Kaput, 1996, p. 470).

This is planned for mid-February. Material for publication by 7 Feb 2000, please, to John.

b.greer@qub.ac.uk

jtruran@arts.adelaide.edu.au

Kath.Truran@unisa.edu.au

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