PME Stochastics Teaching and Learning Working Group

Letter No 8 - August 1997

Dear Friends,

This Newsletter contains five items.

1. A Report on Stochastics Presentations at Lahti.

2. A General Report on Meetings of the Working Group

3. Plans for the Book Production

4. A Report on Stochastics Presentations at MERGA, New Zealand

5. Next Newsletter

1. Stochastics Presentations at Lahti

Lahti is an extraordinarily relaxed city about 100 km north of Helsinki. Cars drive slowly, pedestrians obey pedestrian lights, and life goes quietly on. Two of the greatest Finnish architects have prominent works in the city. One the church hill is a church by Aalto. From the church the Mariankatu goes down into the valley and up the other side where it is completed by Saarinenís magnificent Town Hall. Sadly the Working Group was meeting when the only tour of the week is run, so I was not able to see all of the interior. There was natural light most of the night and the weather was warm and balmy. In the park by the lake a set of sculptures in stone broods among the trees, rather like the natural granite rocks brooding all over the perpetual Finnish landscape of lakes surrounded by gently rolling hills covered in pine and birch. My only complaint about Finland is that their buildings are built for the winter, and in the summer it is difficult to get enough fresh air inside and to keep enough night light out.

The Conference was held in modern buildings near most of the hotels. Both buildings probably had more attention paid to their exterior than to their interior, and circulation of people was a bit awkward, but the meeting rooms were OK. The programme ran from 0900 to after 1900. Not enough care had been given to the programme and there were clashes of interest and initially little time allowance for moving from room to room. On the last day numbers were much reduced. Since those interested in stochastics were relatively few, partly because of other conferences with a statistical education component this year, this led to some disappointing attendances. The sit-down lunches had been thought about with great care so that we had a wide experience of Finnish cuisine, which was very good. The formal dinner (not seen as formal by all) was a magnificent silver service affair done with great skill and pride. One afternoon was spent on a Lake Cruise, and many people took the saunas as well. The thing which this Australian felt to be missing was the happy hour: there did not seem to be enough time when people were mingling to catch up with everyone.

Of the key-note speakers, the star turn was Shlomo Vinner (Israel). He talked about pseudo-conceptual and pseudo-analytic behaviour and challenged teachers to move beyond these all too human responses by students to seek deeper levels of understanding. All this was illustrated by video clips from Don Giovanni and Some Like it Hot. While it is no longer possible to be a Renaissance Man, Vinner is certainly a candidate for being a Near-Renaissance Man. We need more like him to cross the barriers between academia and society, so that education is more influential than it is at the moment.

A full report on the stochastics papers will be given by Anne Hawkins in the next edition of Teaching Statistics, so I shall merely make some short comments. For a refereed conference the standard of papers was very variable. In my experience people seem to accept this as normal, but we would not tolerate such variation in the medical profession! In general discussions it became clear that ensuring that the current refereeing approach is not ensuring that presentations always take due account of previously published literature, even that published in PME Proceedings. Some issues of the nature of what sort of evidence is appropriate for psychological papers were also raised, and it is clear that thee are diverging views on this matter.

RESEARCH REPORTS

Bueno, Graciela & Cuevas, Carlos A.: A new approach for intelligent tutoring systems: an example for statistical activities. Presented by Carlos Cuevas.

CaÒizares, M. Jes˙s & Batanero, Carmen, Serrano, Luis & Ortiz, J. Jes˙s: Subjective elements in children's comparison of probabilities. Presented by Carmen Batanero.

Fischbein, Efraim & Grossmann, Aline: Tacit mechanism of combinatorial intuitions. Presented by Efraim Fischbein.

Hawkins, Anne & Peter: Are lawyers prey to probability misconceptions irrespective of mathematical education?

Spinillo, Alina Galv„o: Chance estimates by young children: strategies used in an ordering chance task.

Truran Kath & Ritson, Rene: Perceptions of unfamiliar random generators - links between research and teaching

Short Oral Communications

Fern·ndez, Felipe, Monroy, Olga Lucia & RodrÌguez, Liliana: Understanding of the notions of p-value and significance level in the solution of hypothesis tests problems. Presented by Felipe Fern·ndez.

Hartman, Avigail: On the knowledge of high school mathematics teachers for teaching probability

Tarmizi, Rohani Ahmad & Abu Bakar, Kamariah: Correlates of students' performance in statistics

Posters

Batanero, Carmen, Godino, Juan D. & Navas, Fransisco J.: Some misconceptions about averages in prospective primary school teachers

Not everyone who enrolled was able to attend, so the list above is shorted than the one previously circulated. We were particularly pleased that Felipe Fern·ndez from Bogota was able to attend. His English is not strong, but he received a lot of support, and it was good to hear of work being done in Colombia.

2. Stochastics Working Group Meetings

Those who attended all our meetings included

Hazimah Abdul Hamid (Malaysia)

Carmen Batanero (Spain)

Carlos Cuevas (Mexico)

Felipe Fern·ndez (Colombia)

Juan Godino (Spain)

Alan Graham (UK)

Anne Hawkins (UK)

Michel Henry (France)

John Truran(Australia)

Kath Truran (Australia)

Some other people attended only to some of the meetings and other expressing their interest in the topic were not able to attend because of other working group commitments. Three meetings only were scheduled, rather than the four which had been promised. While these meetings were longer than usual, they were rather too long, and unevenly distributed across the week. This made our work just a little more difficult, and led to reduced numbers on the morning after the dinner!!

In the first Meeting Carmen Batanero showed us a copy of the new book The Assessment Challenge in Statistics Education. Kath Truran reviewed the chapter on Data Handling in the new Kluwer International Handbook of Mathematics Education and John Truran reviewed the Chapter on Probability. Felipe Fern·ndez told us a little about work at the private University of the Andes. General information was given about the International Statistical Institute, the IASE (International Association for Statistics Education), the latest Newsletter of the International Study group for Teaching and Learning Statistics and the 1998 ICOTS Conference in Singapore.

Finally, Anne Hawkins reflected on her earlier writings on research in statistics education in the light of today’s situations. She felt that the current issues which needed emphasis were

statistics and probability

more detailed understanding of conceptions and misconceptions

use and interpretation of tables

use of technology

model construction

refining assessment methods

It was felt by some that at the next PME, we should try to find a way of being involved more with the work of younger/newer researchers and that we should encourage more short presentations within our working group.

Juan Godino proposed more extensive use of the WWW in our communications. Although we did not come to any final conclusions on this matter, it is likely that the efforts of individuals will lead us forward in this way during the next couple of years.

The other two meetings were devoted to book planning.

Carmen Batanero also gave a brief presentation on Advanced Stochastic Thinking to the Advanced Mathematical Thinking Working Group. The AMT group has decided to work towards a book which will focus on the teaching of undergraduate mathematics from a psychological persp, which will be edited by David Reid (Canada). It is hoped that the book will be practical, but will not over-simplify. Drafts are required by July 1998. (It is possible, but not yet decided that Carmen & John may contribute a chapter on advanced stochastic thinking to this group) Any other members who are interested in submitting a chapter may obtain full details from <dareid@pop.morgan.ucs.mun.ca>. There is far more to advanced stochastics thinking than can be contained in one chapter.

Attendances at PME oscillate significantly, and this makes it difficult to ensure continuity. It is possible that the meeting in Prague of a European group concerned with mathematics education has led to some conflict of interest. It is also clear that within stochastics education some members are split between their involvement in IASE and their involvement in mathematics education groups. Conferences cost money and time. The latter is sometimes scarcer than the former. Fortunately, e-mail makes communication much easier than ever before.

3. Plans for the Book

There had been substantial airing of ideas on the e-mail before we met together. These were talked through at length and we reached agreement in the following ways.

1. It is important that whatever we do is done in a form which will enable contributors to gain university credit.

2. At this point the proposal to produce a book which is based on a critical analysis of key works in the literature is probably not feasible at least in the short term. At the moment a couple of us are thinking about alternative ways of approaching this issue, and we will present our ideas when they are more clearly formed.

3. It is worth preparing a more general book, which might be prepared in the more traditional form of calling for offers of chapters, and looking to co-ordinate the chapters into a meaningful form. The would be directed at teachers of statistics at all levels, and we would attempt to address pedagogic issues from a research background. This book has to be attractive enough that people will want to read it.

4. The co-ordinators were asked to prepare a draft outline of what the book might look like, together with a general set of guidelines for authors, and to circulate this within the group for initial response. This will be done in time for the next newsletter.

5. Once agreement has been reached on these points, then we might seek a publisher. Several suggestions were put forward, and it was felt that there was sufficient hope of finding support that this approach was worth pursuing.

6. The final working session was spent mainly defining key words and concepts which needed to be addressed. These will be incorporated into the suggestions for a basic book structure.

In 1998 there will be an International Conference on the Teaching of Statistics (ICOTS) in late June in Singapore. PME will be held near Cape Town in middle July with a theme of Diversity and Change in Mathematics Education. It is unlikely that many people will attend both. We have therefore decided that we shall try to arrange working sessions at both meetings to allow people who want to be involved in the book to have an opportunity for personal input on at least one occasion.

In 1999 PME will be held in Israel in mid- July. In 2000, it will be held in Hiroshima from 30 Jul to 6 Aug, ending just two days before ICME starts in Tokyo.

4. A Report on Stochastics Presentations at MERGA, New Zealand, July 1997

There is a strong statistics group in Australian and New Zealand, and we had a particularly good meeting this year, so a summary is provided here. An expanded version will be published later in Teaching Statistics.

Mike Shaughnessy came from the USA to give one of the keynote addresses, entitled Missed Opportunities in Research on the Teaching and Learning of Data and Chance. He argued that we should work more from what children could do, than from what they could not do. He also argued strongly that there was inadequate research into students understanding of variability.

This theme was taken up by Maxine Pfannkuch who has been conducting interviews with practising statisticians to assess how they reason in their work. She also emphasised the importance of understanding variability and thought that it had been neglected in classrooms because of the pure approach usually found there. She argued that the interplay between model and reality plays a great part in the work of real statisticians, and should be more emphasised in classrooms.

Two reports were concerned with work with schoolchildren. Jenni Way summarised the results of asking 48 primary school children to compare proportions in two urns. Jenni is seeking, among other things, to codify the many different categories proposed by a number of other research workers over the last 15 years. If she is successful this will have a number of important consequences for teacher knowledge. Jonathan Moritz and Jane Watson have been looking at the ability of students from Year 6 to Year 11 to interpret a potentially misleading newspaper advertisement. Many students failed to interpret and use the advertisement accurately. These results will contribute to a larger study designed to assess how people respond to visual data.

In tertiary statistics Sue Gordon found that for some students surface learning approaches did tend to produce good marks. Some deep learners obtained poor scores because they disregarded the learning of details which are required in examinations. Anne Williams found that students have trouble with significance tests because they lack adequate statistical language, have implicit procedural knowledge and are more concerned to make a statistical conclusion than to think deeply about the situation. Pam Shaw found that even non-naÔve students showed a significantly greater tendency recognise skewness when distributions are left-skewed rather than right-skewed. John Truran showed how a critical textual analysis of responses to examination questions could provide ways of evaluating questions and refining them in the future. In another paper, he used examples from the introduction of probability into Australian schools to support his argument that curriculum forces within education systems may be constructively interpreted as conforming with the same ecological principles which are to be found in modern zoological thinking.

In teacher education, both Ron Smith and Kath Truran reported on difficulties teachers have with teaching stochastics. Kath found that student teachers lessons tended not to be integrated into an underlying body of knowledge. In particular, they were unable to design a constructive set of questions designed to help children think through the key ideas. Ron argued that teachers needed a different kind of in-service support for stochastics than for other mathematics topics because of their lack of basic knowledge. He also presented hard data that some teachers really do view probability is viewed as a wet Friday afternoon activity.

5. Next Newsletter

This is planned for the middle of October. Please send material for inclusion by 1 Oct 97.

John Truran <jtruran@arts.adelaide.edu.au>

Kath Truran <Kath.Truran@unisa.edu.au>

Carmen Batanero <batanero@goliat.ugr.es>