PME Working Group for Stochastics Teaching and Learning
<http://www.ugr.es/~batanero/pmegroup>
<http://www.ugr.es/local/batanero/pmegroup.htm>
Letter No 15 - September 1998
Dear Friends,
Please note that Newsletter No 16 is being sent at the same time, containing some conference announcements.
This Newsletter contains 10 items
1. “Teaching and Learning Statistics: Implications for Research”—Call for Contributions”
2. A Call for Help—Commentators Needed for a Brief Job.
3. PME in General
4. Working Group at PME 22, Stellenbosch
5. Other Stochastics Activities at the Conference
6. Proposal for an Electronic Data Base.
7. Next PME
8 Dave Pratt’s Thesis on the Internet
9. The Late Efraim Fischbein
10. Next Newsletter
1. TEACHING AND LEARNING STATISTICS: IMPLICATIONS FROM RESEARCH
You will recall reading in recent Newsletters about the proposal to produce a publication that addresses the above theme.
At both the ICOTS conference in Singapore and the PME conference in Stellenbosch we put details of the proposal before members for discussion and consideration. It has taken a great deal of time and thought on the part of many people and the following is the structure which eventually came from members at both conferences.
It was agreed that trying to address issues of both Probability and Statistics in one publication was too much and it was finally decided to limit this publication to Statistics and to produce a further publication in the same mode that addresses issues relating to Probability.
Intended audiences are new and current researchers in statistical education in different areas such as Mathematics Education, Psychology and Education. It would also be directed to statisticians interested in the problems of statistical education, as well as to university lecturers and teacher educators.
The chapters are intended to establish a broad background regarding statistical education and its implication in educational practice. Each chapter should address a relevant part of statistical education and will include a critical survey of the main previous research, its methodology, findings and limitations, especially those concerned with psychology and mathematics education. Its main section will be a practical case study to amplify the theory and raise important issues, and to ensure that strong links are made between research and practice.
Chapter length will be limited to a maximum of 10 000 words. Language should encourage effective use by the target readers. The use of schemes, diagrams, examples of assessment tasks and students’ responses will be encouraged to facilitate understanding.
In the first section of each chapter the authors will introduce the key questions which the chapter aims to address. The final section will suggest some teaching implications, including a summary of known cognitive and pedagogical difficulties. Potential areas for future research will also be included.
The following are the proposed chapter headings:
0 Introduction
1 Historical/Philosophical/Epistemological and Theoretical Issues, including Statistical Thinking
2 Collection and Organisation of Data
3 Graphs
4 Averages and Dispersion
5 Assessment
6 Model Fitting
7 Sampling/Estimation
8 Hypothesis Testing
9 Computers
10 Summary of the Book
11 Forward Looking
It is clear that the publication must be synthesised and that chapters need to be written by the right people, quite possibly more than one author for each chapter. Threading, or the making of clear links between chapters, is also important in a publication of this type and to ensure that it takes place the following are suggested
— Authors to suggest possible threads,
— Authors would see all abstracts before writing so that they can the big picture as a basis for their own writing, and
— Authors of similar abstracts might collaborate to produce one chapter.
The editorial panel is in the process of being arranged, and we hope to have it in place by December. Publishers would need to see 2 or 3 complete chapters and some abstracts to convince them of the worth of the project. Finding a publisher will probably take some time. With this in mind I would be grateful for expressions of interest by 7th December, 1998.
Expressions of interest should provide a title and a brief abstract (from the proposed chapter headings) of the intended chapter (300-350 words). The abstract will focus on the topic of the chapter while keeping in mind the issues of audience and intent summarised above in paragraphs 4 & 5.
Abstracts to arrive no later than 7th December, 1998, can be e-mailed to <Kath.Truran@unisa.edu.au>
or a hard copy sent to: Kath Truran, School of Education, Magill Campus, University of South Australia Magill, South Australia 5072
2. A Call for Help—Commentators Needed for a Brief Job.
Our group has been trying to co-operate with the Advanced Mathematical Teaching and Thinking Working Group, who are planning to produce a book on Advanced Mathematical Thinking. Two chapter offers have been received on Advanced Stochastic Thinking. David Reid distributed these at Stellenbosch, but no-one felt competent to comment on the one by Carmen & John. He would like two people from this group to read the abstracts (2 pages) and comment on how they would fit into the book. If you write to <jtruran@arts.adelaide.edu.au> I will send you a copy of the abstracts and the specifications, and you can send your replies direct to David Reid. This needs to be done as quickly as possible, and no later than the end of September.
Volunteers please!!
3. PME in General
PME this year was held at the University of Stellenbosch, about 50 km north-east of Cape Town. It is the oldest Afrikaans university in the country and presented some interesting contrasts to other universities and other parts of South Africa.
Stellenbosch was founded soon after Cape Town in the eighteenth century, to provide a market garden for the colony, and has now developed into a large wine-growing region. It has retained a lot of old houses, and many of us were taken on an excellent guided tour of the city, which was a great help in interpreting its history.
The campus was amazingly neat, tidy, and well organised. The only real problem was the lack of wide open spaces for circulation in the building where most sessions were held. And the campus was far safer at night and out of term time than my own campus in Adelaide. The whole atmosphere was far more relaxed than we had expected to find in South Africa, which did a lot for producing a pleasant conference. In some ways the place was old-fashioned, but this had a charm of its own, and certainly the old-fashioned personalised hospitality we received at our small guest-house (Roland’s Uitspan—highly recommended) would encourage us to go back there in the future.
The South Africans went out of their way to make us welcome and to create a favourable impression. The Conference started with some modern Black African dancing in Wellington Boots (a comment on industrial conditions from the workers’ side) after which we all processed behind a “Deep South” Jazz band through the streets to the Town Hall for an abundant reception (+ a direct link to the World Cup Final). The Conference Dinner later in the week was a classic example of South African catering—good food, but enormous portions, with both chicken and lamb for the main course. Apparently, they think that this is the way to breed good rugby players. Unfortunately, poor weather meant that some of the organised tours had to be re-arranged, but it did not spoil our trip to Cape Point (near the Cape of Good Hope). The final night of the Conference saw a display of more traditional Black African Dancing and Christian Revival Music.
For the South Africans this was an important conference because it gave them an opportunity to be accepted back fully into the academia fold. And of course all of us needed to come to terms with a country with such a chequered history. Things will not be easy for the Rainbow Nation—the New South Africa. White South Africans are leaving the country in droves, and many are disaffected with a policy of posidiscrimination towards black South Africans. Many white South Africans see the ANC Party as leading the country into anarchy. For them the huge primitive shanty towns on the outskirts of Cape Town are political manoeuvres by the ANC which will make the black people worse off than they would have been under the old regime. Equal opportunity for all will be a long time coming. At Stellenbosch wine industry workers were on strike when some of the Conference went to visit the wineries. This prompted some members to donate money to the strike fund. At the same time the comfort enjoyed in all our hotels could not have been achieved at a price we could have afforded if the employees were paid Australian-standard wages. It is impossible to become an “instant expert”. I merely report so that others may be aware of some of the issues which we encountered.
4. Working Group at PME 22, Stellenbosch
About a dozen people attended the three very constructive meetings of the Working Group. The first session was largely a business meeting where we got to know each other better, and ensured that members were kept up to date on other activities of interest.
We had one talk, from Andrew Ahlgren, who outlined the scheme of the American Association for the Advancement of Science to construct knowledge maps as part of a Numeracy 2061 Project. The aim of the project is to develop literacy in natural and social sciences, mathematics & technology. Andy would be happy to send copies of this to members. Contact him at <aahlgren@aaas.org>
At the other meetings we discussed the proposals for the book project. These were very good meetings with a free exchange of views, which eventually achieved a high degree of consensus. We eventually decided that the book should focus on the teaching of statistics, and that it should have a structure reasonably similar to the structure by which statistics is taught in most tertiary and secondary institutions. There was a minority view that a more radical approach focussing more on process approach and less on a content approach would be preferable. It was agreed that only one of the two approaches could be used, and the more conservative view was taken, mainly because it was more likely to be marketable. Full details of the book proposal have been given in paragraph 1 above.
These discussions took up most of our time, so other issues like the planned data basis were put on hold for the time being.
5. Other Stochastics Activities at the Conference
A Key-Note Address was given by Paul Cobb, Vanderbilt University, USA, on “Analysing the Mathematical Learning of the Classroom Community: The Case of Analysis” This paper looked at Year 7 children's interpretation of two data sets which had been specially had been specially designed to raise interesting issues. His purpose was a broad theoretical one of trying to develop the idea of collective mathematical development. As a Constructivist, Cobb prefers not to talk about mathematical content but rather to see it as something which emerges from the collective practices of the classroom community. The data sets themselves were very interesting, and provoked some good discussion from the children.
A Research Forum on the theme “Learning and Teaching Data Handling” was held over three sessions under the leadership of Paul Laridon, University of Witwatersrand, Johannesberg.
In the first session Carmen Batanero, University of Granada, Spain, on behalf of Juan Godino, Granada, & Antonio Estapa, University of Jaen, Spain, talked on “Building the Meaning of Statistical Association through Data Analysis Activities” She presented the results of two teaching experiments designed to examined tertiary students' understanding of association and to see how their learning might become more effective. The data was interpreted within a three-level model of extensional, instrumental, and intensional elements of meaning. In his reaction, Michael Glencross, University of Transkei, South Africa, commented on the importance of developing good teaching as a result of such research, and made some observations on whether statistics really was mathematics or not.
In the second session, Janet Ainley, University of Warwick, UK, on behalf of Elena Nardi & Dave Pratt, also from Warwick, talked on “Graphing as a Computer-mediated Tool”. This presented results of children's work at interpreting data with the assistance of computing facilities. Some of the data was deterministic, some stochastic. The results were presented within an activity model of Experiment-Data-Graph.
The reaction was made by Ricardo Nemirovsky, TERC (details not given), Cambridge MA, USA, who emphasised the importance of symbol-use as a powerful tool for expression and the need to encourage students to reflect on the relationship between empirical observation and logical necessity.
The third session was a general discussion which tended to focus on the Warwick work and its potential. Carmen had earlier pointed out some links between the two theoretical models being used, but this issue was not really addressed.
The following Research Reports were also presented
Jan Bezuidenhout, Piet Human & Alwyn Olivier—”Some Misconceptions Underlying First-year Students' Understanding of 'Average Rate' and of ‘Average Value’” University of Stellenbosch
These three researchers presented some test items which showed that students presented a wide range of responses when asked to make calculations of average rate when presented with some discrete sets of data, and concluded that the students had some conceptual deficiencies.
Hari Prasad Koirala—“Pre-service Teachers' Conceptions of Probability in Relation to its History”, Eastern Connecticut State University.
Hari presented some questions to mathematically trained pre-service teachers and tried to establish whether they held classical, frequentist or subjective views of probability, and found a variety of responses, which depended to some extent on the questions asked. He proposed that each student’s approach could be represented by a point on the inside of a triangle whose three sides represented a scale of preference for each of the three approaches.
Dave Pratt & Richard Noss, London University, —“The Co-ordination of Meanings for Randomness” some electronic games”
Dave talked about building a computational environment for ex-ploring stochastic systems in order to observe the ways in which children make meaning about ideas like fairness, ran-dom-ness and chance. He gave examples from the thinking of two children.
John Truran—“Using Research into Children's Understanding of the Symmetry of Dice in Order to Develop a Model of How They Perceive the Concept of a Random Generator”
John analysed a number of reports into children’s under-standing of dice. Taken together the reports suggested that the received wisdom that children see dice as biased against “6” could not be sustained. He presented a summary of current knowledge in a structure which would be suitable for a handbook on probability education and research.
There were also two Short Oral Communications
Michael Glencross—“Developing a Statistics Anxiety Scale” Michael has modified a mathematics anxiety scale to look at students’ views of statistics, and has done preliminary testing.
Sandra Magina, & Maria Cristina Maranhão PUC-SP—“Using Databases to Explore Students' Conceptions of Mean and Cartesian Axes” They used Tabletop software to provide concrete experience of cartesian axes & means. Data collection phase was seen as an important preliminary to the interpretation phase.
There were also four Poster Presentations. I was unable to attend the official Poster Session, and unfortunately the posters were removed straight afterwards, so I had no chance to look at them later. This was a great pity.
Andrew Ahlgren, AAAS, Washington DC—“K-12 Connections in Understanding Prob-ab-ility and Statistics” This reported on an AAAS (American Association for the Advancement of Science) Project 20061 literacy in natural and social science, maths & technology. It presented a draft “growth of understanding map” for the idea of Uncertainty.
Ilouize du Plessis & Claire Roux, University of Pretoria —“Teaching an Introductory Statistics Course to Social Science Students: a Case Study Approach”. This course aimed to illustrate concepts and logical thinking, rather than expecting students to master complex formulae.
Pablo Flores, Juan Godino & Carmen Batanero—“Contextualising Didactical Knowledge about Stochastics in Mathematics Teachers’ Training” This related epistemological reflection on stochastics and didactical knowledge”
Tatjana Hodnik, University of Ljubljana—“Teaching Statistics in Primary School in Slovenia” Research project on the introduction of statistics in 10 primary schools over 10 years.
6. Proposal for an Electronic Data Base.
As mentioned above, this project was deferred because of lack of time.
7. Next PME
This will be held in Haifa, Israel, from 25-30 July, 1999. The first announcement will be available by 30 September 99 at <http://edu.technion.ac.il/conference/pme23/>. The home page is already in place, but it is only rudimentary at this stage.
We have had some concerns over the last two years about the reviewing process of stochastics papers at PME. Papers do not seem to have always been refereed by those who are familiar with the field. So we encourage stochastics researchers attending the Israel Conference and who fulfil the eligibility criteria for refereeing (currently one paper accepted for presentation at a previous PME conference) to offer their services for refereeing. It is important that the judgements made on papers should be of as high a quality as possible.
Our suggestion that a Research Forum on the teaching of probability be held at Haifa was not accepted. The fora proposed have all been rather more general than research in a specific field. Immediately after the conference we applied to continue the Stochastics Working Group for 1999 on the grounds that our book project was likely to need further work. At this stage we have still received no reply as to whether the proposal has been accepted or not. We are currently looking at a way of running the Mini-forum on Data Handling which we wanted to hold. Changes in the structure of Working Groups and Discussion Groups have meant that this will be harder to run than we had anticipated. Dani will be acting as the local organiser for the group.
8. Dave Pratt’s Thesis on the Internet
Dave Pratt’s PhD Thesis—”The Construction of Meanings In and For a Stochastic Domain of Abstraction”—has recently been completed. Well done, Dave. It uses a computer-based domain to investigate children’s evolving meanings for randomness, and tries to asses their understanding from an holistic point of view rather than by looking for misconceptions, as many earlier researchers have done. The thesis may be down-loaded from
<http://fcis1.wie.warwick.ac.uk-/~Dave_Pratt>.
It runs to 468 pages, plus various appendices, so allow plenty of time to print it. You also get a free photo of Dave as an added bonus.
9. The Late Efraim Fischbein
Professor Fischbein died recently, after an illness of some months. He was an honorary life member of PME and was still presenting his research at its meetings as recently as 1997. As a mark of respect Carmen & I have prepared a summary of his work in stochastics research including a full bibliography. This will be published in the next International Study Group Newsletter.
10. Next Newsletter
A second Newsletter (No 16) is being sent at this time containing announcements of two conferences in the near future, as well as the call for contributions to our proposd book. It is being sent as a second document, so that it may be passed on to anyone you know who might be interested.
The next regular Newsletter is planned for November and will contain a report of our success to date with our call for contributors to the book. Please send material for inclusion by 1 Nov.
John Truran <jtruran@arts.adelaide.edu.au>
Kath Truran <Kath.Truran@unisa.edu.au>
Dani Ben-Zvi <ntdben@wiccmail.weizmann.ac.il>
Carmen Batanero <batanero@goliat.ugr.es>
Web Page <http://www.ugr.es/local/batanero/–pmegroup.htm>