PME Discussion Group

for Stochastics Teaching and Learning

<http://www.beeri.org.il/stochastics/>

Letter No 25 - September 2000

Table of Contents

1. PME-24: Discussion Group Meetings in Hiroshima
2. Members Attending
3. PME-25, Utrecht, The Netherlands, 2001
4. Summary of Forthcoming Statistical Education Activities
5. A Comment on Statistical Literacy by Milo Schield
6. ICOTS-6: A Call for Contributions
7. Statistical Education Research Newsletter, 1(3), Sep. 2000
8. Next Newsletter
Group Coordinators

1. PME-24: Discussion Group Meetings in Hiroshima

Numbers at this year's Discussion Group meetings were smaller than in previous years: only 12 participants, but we had several new members, and good discussions on our theme - The Relationship between Stochastical and Mathematical Thinking, Learning and Teaching. The following summary was prepared by Jenni Way and James Nicholson.

John Truran made a general introduction to the Discussion Group, its aims, activities and association with other groups.

Short Presentation by Mario Barra: The Relationship between Probability and Geometry: a Didactic Use

Mario looked at connections between probability, which is very abstract for many students, and geometry, which is practical and concrete and allows students to visualise relationships. He gave a number of very interesting examples of such situations.

There is only space for one example: looking at a cube of 6 x 6 x 6 small cubes and considering how many of the small cubes have at least one extreme position (equivalent to throwing a six on at least one of three dice). Examining the different ways in which the cubes can be counted illuminates different probability forms. The manner in which this method of visualisation can be extended into multiple dimensions, using Cabri-Geometry to model 4, 5 ... dimensions, illustrates well his contention that this is a powerful way for mathematical (geometric) thinking to help with more abstract probability thinking.

Key Points from the Discussion:

• Some of the examples given related to 'equally likely' events, so a 'next step' would perhaps be to examine other types of events.

• The linking of probability to geometry is more than the use of 'metaphor' (a topic of general conversation at PME meetings) because the linking does not just provide a meaning, but in making the connection, provides a way to think.

• A difficulty in the learning and teaching of probability is that it is mostly disconnected from other fields of maths.

• Mario's enthusiasm for his subject was an important reminder to us of the value of enthusiasm as a pedagogic tool.

Short presentation by Jenni Way and Paul Ayres: The Relationship between Pattern and Randomness

A series of studies into various aspects of the probabilistic thinking of Australian primary and secondary students, has revealed a range of decision-making strategies. One particular outcome of note is the insistence of many children to look for patterns in a series of random outcomes. This is perhaps because current teaching of mathematics emphasises the patterns within mathematics. This highlights the conflict between some aspects of probabilistic thinking and other types of mathematical thinking.

Key Points from the Discussion:

• Other strategies that have been identified by other researchers in tasks that involve the listing of outcomes include choosing sequences that appear to be representative of the sample space, that don't appear too random nor too ordered.

• The nature of independence is multi-faceted and children's perceptions of different aspects are hard to distinguish and categorise.

• Children's strategies are not always internally consistent when provided with a range of scenarios, and this poses problems for researchers trying to map out this area.

• The fact that children's intuitions do not seem to develop in this area between ages 11 and 14 is used by curriculum managers as an argument that children are not ready to study such material, where it could be argued that instruction and exploration of the underlying concepts would help provide a frame of reference for the students to use when approaching such situations.

Short presentation by James Nicholson: Perspectives from Students and Teachers on the Differences in Thinking in Mathematics and Statistics (Co-author Gerry Mulhern)

The presentation elaborated on the following key point: In school mathematics, outcomes are almost always unique, though there may be multiple approaches possible which arrive at the same 'solution'. In statistics, students have to do some things which are 'purely mathematical' in the above sense, but there are also situations where the answer in a particular case requires judgement to be exercised, and therefore it is possible to have different answers, each of which has some merit.

Key Points from the Discussion:

• A lot of Statistics courses are taught by mathematicians, therefore the calculations are done well, but not the interpretation. There is a need to start early with the expectation of simple interpretation to provide the basis for more complex interpretations. This links with the concern that there is not enough statistics included in teacher education.

• It is not generally accepted in mathematics that 'answers' are given in words, as is needed in interpreting statistics. This gives added difficulty for students whose native language is different to the language of instruction.

• There is learning value in exploring the relationship between theoretical probability with probability experiments, as one can support the understanding of the other.

• Data sets that support several different arguments and conclusions should be used with students

• A 'consultancy' approach (i.e. students take on a real task for an external agency) can be very useful for emphasising the skills needed in communicating conclusions drawn from statistical analysis to 'non-statistics' people.

• Cultural differences (e.g. superstitions) need to be considered when dealing with uncertain events.

There was general consensus that the theme The Relationship between Stochastical and Mathematical Thinking, Learning, and Teaching was worthy one, and that the use of short presentations to stimulate discussion was a productive strategy. It was observed that all three short presentations, and the resulting discussions, highlighted the fact that stochastical thinking is different from other mathematical thinking and that there was a need to include suitable topics in all levels of curricula.

2. Members Attending

The following is the list of members attending.

Mario Barra

University of Rome, Italy

<barra@mat.unirome1.it>

Max Bunquin

Colegio San Augustin, Philippines

<maxjoke@mailcity.com>

Paul Ayres

University of New South Wales, Australia

<p.ayres@unsw.edu.au>

Carolina Carvalho

University of Lisbon, Portugal

<ccarvalh@fc.ul.pt>

James Nicholson

Queens University, Belfast

<j.r.nicholson@qub.ac.uk>

Steven Nisbet

Griffith University, Australia

<S.Nisbet@mailbox.gu.edu.au>

Chris Reading

University of New England, Australia

<creading@metz.une.edu.au>

Milo Schield

Augsburg College, MN, USA

<schield@augsburg.edu>

Ron Smith

Deakin University, Victoria, Australia

<ronsmith@deakin.edu.au>

John Truran

Private Practice, Australia

<truranjk@camtech.net.au>

Tsuyoshi Sugaoka

Joetsu University of Education, Japan

<sugaoka@juen.ac.jp>

Jenni Way

Cambridge University, UK

<jaw36@cam.ac.uk>

Some of us followed James Nicholson to dinner at a nearby restaurant after the first of our meetings. This proved to be an enjoyable, if somewhat challenging and unpredictable evening, where some members learned quite a lot about Australia's unique food-Vegemite-and the place it occupies in Australian culture.

It was particularly pleasing to have one member from Japan and one from the Philippines. We hope that they will be able to continue to make contributions in the future. Milo Schield had made a special visit to Hiroshima to meet members of the group. Milo's special interests are in Statistical Literacy. Because he was not at the Conference full time, we did not get an opportunity to listen to him talk, so I am printing one short piece of his below as a further contribution to the discussion.

I should also like to thank my co-coordinators, Mario, James and Jenni, for organising, contributing to and reporting on the discussions this year. Their help is much appreciated.

 

3. PME-25, Utrecht, The Netherlands, 2001

After discussion it was agreed that we should apply to the PME International Committee for permission to run the Discussion Group again, and this permission has been given for the meeting in Utrecht from Thursday 12 July to Tuesday 17 July 2001.

PME-25 will be organized by the Freudenthal Institute (FI). The conference will be held at Utrecht University, the Netherlands. The First Announcement will be released in September 2000.

It is always difficult to know who will be present at a meeting twelve months ahead. The only one of the Convenors who was highly likely to be present was Kath Truran, and she was not at Hiroshima. After discussion, it was decided to leave the names of the four convenors unchanged at this stage, but with the understanding that if they were not able to attend, then others would be willing to step in and help as they did this year.

Our discussions will be on the relationship between stochastical and mathematical thinking, learning, and teaching. We consider that there is more on this theme which can usefully be discussed. It is our intention to approach this theme from multiple perspectives, including:

• Philosophical, in terms of the perceived boundaries of the disciplines.

• Historical, in terms of the developments of the disciplines.

• Educational, in terms of the positioning and implementation of the teaching and learning of stochastics within school and tertiary curricula, including such fundamental issues as teacher development, assessment, and technology.

• Psychological, in terms of the specific cognitive and sociocultural processes involved in the teaching and learning of stochastics.

• Research, in terms of cross-fertilization of theoretical frameworks and methodologies.

All members who intend to be at PME25 are invited to make a short presentation (10 minutes) on some aspect of the theme. This would be followed by 20-30 minutes discussion. Please make submissions to Kath at <Kath.Truran@unisa.edu.au>. It would be good if we could have advance notice before the next Newsletter at the end of November.

4. Summary of Forthcoming Statistical Education Activities

SRTL-2

The Second International Research Forum on Statistical Reasoning, Thinking and Literacy, University of New England, Armidale, Australia, August 15 - 20, 2001. See: <http://www.beeri.org.il/srtl/>. Anyone interested in receiving the Second Announcement should write to Dani Ben-Zvi (dani.ben-zvi@weizmann.ac.il).

ISI-53

The 53rd Session of the International Statistical Institute, August 22-29, 2001, Seoul, Korea. See: <http://www.nso.go.kr/isi2001/>.

For the IASE Sessions at ISI-53 see: <http://www.swin.edu.au/maths/iase/isi53.html>.

A pre-conference satellite workshop on statistics literacy is also planned.

ICOTS-6

The IASE Sixth International Conference on Teaching Statistics, July 7-12, 2002, Durban, South Africa. This is the major international conference in Statistics Education that is held every 4 years. A call for contributions is printed below. Details can be found at the ICOTS-6 IPC Website at: <http://www.beeri.org.il/icots6>.

5. A Comment on Statistical Literacy by Milo Schield

For the past five years, I've taught a class in statistical literacy. Students are expected to be able to read any table of national statistics involving a percentage or rate. Specifically, they must be able to decode the part and whole of any part-whole ratio from the headings (the title, the row headings and the column headings) and they must be able to describe a given numerical rate or percentage in words. My students have had considerable difficulty reading certain national tables of rates and percentages. Their problems are often due to certain ambiguities in the use of prepositions within the table.

When a table contains part-whole ratios (rates or percentages), students expect the title to indicate the part and whole. When the preposition "by" is used to indicate relevant variables, they expect "by" to indicate either the part or the whole. They note that "by" is often used to indicate a whole (among those classified BY race and sex). They are sometimes surprised to find that "by" can indicate a part (distributed BY cause of death). They are most confused when "by" is used to indicate both part and whole in the same table (BY gender and reason for taking the job).

I will illustrate this problem using tables of UK national statistics taken from the 1996 edition of "Key Facts": a publication of the Government Statistical Services' Office for National Statistics. (Note: the tables are not published here, but you will be able to deduce the general context without too much trouble.)

In Some Tables of Percentages, "by" Indicates the Part

Consider Table 2.5, "Conceptions: by marital status and outcome". These percentages might be the percentage of conceptions among parents of different marital status. [e.g., conception is the part and marital status is the whole]. But in this table, the presence of the 100% totals by year indicates that conceptions are the whole and these conceptions are distributed BY marital status and outcome (the parts). The use of "by" to indicate the part in a percentage is also found in Table 2.3 "Population: by age and gender", Table 2.4 "Population: by ethnic group and age" and Table 2.10 "Divorce: by duration of marriage." When a table of percentages contains the 100% totals, students have less problem in identifying part and whole.

In Some Tables of Percentages, "by" Indicates the Whole

In some of these tables, the parts shown do sum to 100%. Consider Table 3.3 "Economic Activity status of mother: by age of youngest child." In this table, "by" indicates the whole -- not the part. Mothers are grouped into wholes based on the age of their youngest child. These mothers are then distributed by economic status as the part. When the percentages sum to 100% but the 100% totals are not shown explicitly, students have more difficulty in identifying part and whole.

In some of these tables, the parts shown do not sum to 100%. Consider Graph 3.4 "Women in employment: by occupation" Here, "by occupation" is the whole. Women [who are] in employment is the part. Women [who are] not in employment is not shown, so the parts shown do not sum to 100%. See also Table 3.9, "Proportion of employees receiving job-related training: by gender and age." When the percentages shown do not sum to 100%, students have great difficulty identifying part and whole.

In Some Tables of Percentages, "by" Indicates Both the Part and the Whole

Consider Table 3.8 "Temporary employees: by gender and reason for taking a temporary job." In this table, gender is the whole (as indicated by the total of 100% for each gender) while "reason for taking a temporary job" is part (the percentages for each reason sum to 100% within each gender). Since the 100% totals are indicated explicitly students should have little difficulty, but the use of "by" to indicate both part and whole seems to contribute to their difficulties in identifying part and whole.

Professionals who know the data involved have little difficulty identifying part and whole in these tables using "by". But students-and causal readers of national statistics-have much greater difficulty untangling part and whole.

Editors of national statistics publications might reply as follows. While students may wish that "by" indicate either part or whole, that is not its' function. "By" is not a standard part-whole keyword like "among" or "per" which always indicates the whole in a ratio. "By" merely indicates the following terms are used as indexes in the table or graph. This point was raised in my 1999 talk at the US Bureau of the Census in regard to the US Statistical Abstract. My reply was that this point is sound and well taken. But in failing to use keywords which clearly indicate either part or whole, the table heading fails to communicate -- with precision -- what the table is about.

Recommendations:

1. When "by" is used to indicate the part, and the parts shown are exhaustive, then the ph"distributed by" should be used. Using "by" to indicate the part is generally the exception and should be clearly noted.

2. When "by" is used to indicate the part, and the parts shown are NOT exhaustive, then some other phrasing should be used: "by means of", "because of", etc.

3. If the heading cannot be rewritten to clearly distinguish the part(s) from the whole(s),the table should include a clearly stated expression of at least one of the percentages in the table. In this way, causal readers would be alerted to what is part and what is whole in this particular table. In summary, field test the ability of causal readers to describe any number in the table of interest.

6. ICOTS-6: A Call for Contributions

The International Association for Statistical Education (IASE) and the International Statistical Institute (ISI) are organizing the Sixth International Conference on Teaching Statistics (ICOTS-6) which will be hosted by the South African Statistical Association (SASA) at the International Convention Centre in Durban from July 7 - 12, 2002.

The major aim of ICOTS-6 is to provide the opportunity for people from around the world who are involved in statistics education to exchange ideas and experiences, to discuss the latest development in teaching statistics and to expand their network of statistical educators. The Conference will include keynote speakers, invited speakers, contributed papers, workshops and forums, demonstration lessons, roundtable sessions, poster sessions, book and software displays, hands-on computer sessions and many opportunities for the communication and exchange of experiences and ideas.

As the Conference theme for ICOTS-6 is "Developing a Statistically Literate Society", special sessions on statistics literacy are planned. These will include keynote presentations on statistics literacy and sessions and discussions of the role of statistics in a number of everyday contexts.

ICOTS-6 Topics

Topic 1. Statistics Literacy

Topic 2. Statistics Education at the School Level

Topic 3. Statistics Education at the Post Secondary Level

Topic 4. Statistics Education/Training and the Workplace

Topic 5. Statistics Education and the Wider Society

Topic 6. Research in Statistics Education

Topic 7. Technology in Statistics Education

Topic 8. Other Determinants and Developments in Statistics Education

Topic 9. An International Perspective on Statistics Education

Topic 10. Contributed Papers

The Scientific Program

The scientific program of the Conference has been prepared by the IASE International Program Committee, IPC, for ICOTS-6 on the basis of suggestions received from many members. The IPC is in charge of the overall co-ordination of the scientific program. The IPC has agreed on a list of topics for the invited paper sessions, and identified Topic Convenors who in turn suggested Session Organizers, SO's, for approval of the IPC. The SO's will assume responsibility for the organization of each invited paper session. The topics of invited paper sessions, the SO's names and addresses, and the rules and guidelines for organisers of invited paper sessions are now available on the ICOTS-6 IPC Website at http://www.beeri.org.il/icots6/.

The IPC decided that refereeing procedures will not be implemented in ICOTS-6. If requested, the IASE is normally happy to give permission for authors to submit their papers (or a more comprehensive version) to other journals. If this occurs the author must seek approval of the editor of the ICOTS-6 Proceedings and the IASE President, and the paper is to have an acknowledgement saying "This article was written for, and published in, the ICOTS-6 Proceedings and is reprinted (in revised form, if relevant) here with the permission of the IASE."

Important deadlines

Invited Papers

Expressions of interest for invited sessions are to be received by the relevant Session Organizer, or the IPC Chair by Oct. 15, 2000.

Invitations - Session Organizers will formally invite the speakers by Jan 31, 2001.

Abstracts - each invited speaker has to present a (provisional) title and an abstract (no more than 500 words) of his/her presentation to their Session Organizer by April 1, 2001.

Final manuscript - the authors of invited papers are to submit the final manuscript of their paper to their Session Organizer by December 1, 2001.

Contributed Papers

Expression of interest for contributed paper sessions are to be submitted to Susan Starkings (starkisa@sbu.ac.uk) by December 1, 2001. Papers not accepted for an invited speaker session will also be considered for the contributed paper sessions.

Other Contributions

Abstracts of posters, software demonstration and other special sessions should be submitted to the IPC Executive by February 1, 2002.

Details of the final submission arrangements of papers and other presentations will be announced later.

The Committee is convinced that the ICOTS-6 academic and social program will provide a most rewarding experience. For more information please contact the Conference Chair, Maria-Gabriella Ottaviani (<ottavian@pow2.sta.uniroma1.it>)or the IPC Scientific Secretary, Dani Ben-Zvi (<dani.ben-zvi@weizmann.ac.il>).

7. Statistical Education Research Newsletter, 1(3), Sep. 2000

The third issue of the Statistical Education Research Newsletter (IASE SERN) has been issued electronically. This issue reports on statistical education activities around the world, including conference announcements, dissertations and research report summaries.

The newsletter is edited by: Carmen Batanero, <batanero@goliat.ugr.es>, Joan Garfield, <jbg@tc.umn.edu>, M. Gabriella Ottaviani, <ottavian@pow2.sta.uniroma1.it>, and John Truran, <truranjk@camtech.net.au>.

To download the newsletter visit the IASE Statistical Education Research Group (IASE SERG) Website: <http://www.ugr.es/~batanero/sergroup.htm>.

8. Next Newsletter

This is planned for the end of November. Material for publication by 15 November 2000, please, to John Truran at <truranjk@camtech.net.au>.

Group Coordinators

Dani Ben-Zvi, Weizmann Institute of Science, Israel

<dani.ben-zvi@weizmann.ac.il>

Brian Greer, Queen's University, Belfast, Northern Ireland

<b.greer@qub.ac.uk>

John Truran, University of Adelaide, Australia

<truranjk@camtech.net.au>

Kath Truran, University of South Australia, Australia

<Kath.Truran@unisa.edu.au>

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