PME Discussion Group

for Stochastics Teaching and Learning

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

Letter No 22 - March 2000

To download this letter in MS Word fomat click here

 

This is a brief letter to keep you informed of our planning for the Hiroshima meeting.

Table of Contents

1. PME 24

2. Abstracts of Discussion Group Papers

3. IASE Statistical Education Research Group (IASE SERG)

4. PME’s Research Interests of Members Data Base

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

6. Next Newsletter

1. PME 24

<http://home.hiroshima-u.ac.jp/pme24/index.html>

Refereeing is now in hand, but results will not be available until near the end of April.

Thank you to those who have agreed to offer a brief introduction to our Discussion Group’s meetings, and to James Nicholson (Belfast) and Jenni Way (Cambridge/Sydney) for offering to help with the leadership of the group in Hiroshima. If you would still like to contribute to the Discussion Group’s meetings, please write and let us know.

Our Discussion Group will focus this time on “The Relationship between Stochastical and Mathematical Thinking, Learning, and Teaching”. Brief contributions will be presented to ensure that a rich discussion ensues (see abstracts in item 2 below). We want to approach the issue from a number of perspectives:

  1. Philosophical, in terms of the perceived boundaries of the disciplines.
  2. Historical, in terms of the developments of the disciplines.
  3. 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.
  4. Psychological, in terms of the specific cognitive and sociocultural processes involved in the teaching and learning of stochastics.
  5. Research, in terms of cross-fertilization of theoretical frameworks and methodologies.

2. Abstracts of Discussion Group Papers

Please feel free to comment on these abstracts. It would be good if we could have some preliminary debate for the next Newsletter.

(A) Perspectives from Students and Teachers on the Differences in Thinking in Mathematics and Statistics.

James Nicholson, School of Psychology, Queen's University of Belfast, Northern Ireland.

My current research is looking at conceptual challenges facing students taking Statistics as part of an A-level in Mathematics. One of the themes emerging from the interviews conducted so far relates to the differences in the type of thinking required. There seem to be some distinct areas in which differences are experienced, for example:

1) Outcomes in Mathematics are anticipated to be predictable, where outcomes in Statistics are a mixture of predictable and variable.

2) Value judgements are required in a variety of contexts, but they do not form a part of school mathematics, for example, when should you use an approximation, what significance level is appropriate, etc.

3) Interpretation in context is required, for example 'formal statements' of the results of an hypothesis test can be learnt by rote, but if the outcome has to be expressed in terms of the original context much more is required.

I will discuss examples of these, and others, and try to assess their impact in the classroom.

(B) Relations between probability and others languages of science, particularly referred to the pitagorean "aritmo-geometry" carried on d-dimensions and in the continuum and discrete spaces, closely connected: a didactic use.

Mario Barra, Dipartimento di Matematica, Università "La Sapienza", Roma, Italia.

Starting from:

1) some experiments with students, 10-24 years, and teachers,

2) some suggestions growing from the answers of students and teachers to many questionnaires,

3) an analysis of the peculiarity of probability and its teaching,

4) a little analysis of the new exigencies of our society, and

5) some Bruno de Finetti's suggests.

I put forward for consideration to create a close understanding between probability and, particularly, geometry, but also with combinatorial calculus, physics, analytic calculus, numerical analysis, and theory of numbers.

My purposes are:

a) a better understanding and memorising of probability, "seeing the probabilistic measures" and their proprieties in geometry and in some languages of sciences,

b) a better consideration of different cognitive styles, and

c) a growth, in the students, of a positive correlation between inductive and deductive thinking, developing the abilities to visualise and to generalise, using particularly the pitagorean "aritmo-geometry", carried in d-dimensions, in a continuum and discrete spaces in close connection.

References

Tall, D. O. (Ed.) (1991). Advanced Mathematical Thinking. Kluwer: Holland.

Barra, M. (1995). Random images on mental images. In R. Sutherland & J. Mason (Eds.) Exploiting Mental Imagery with Computers in Mathematics Education, (pp.263-277). Springer.

(C) The Relation between Pattern and Randomness

Jenni Way, NRICH Online Maths Project, University of Cambridge, UK.

Our research into various aspects of the probabilistic thinking of primary and secondary students in Australia, has revealed a range of decision-making strategies. One particular outcome that has captured the attention of Paul Ayres (University of NSW, Australia) and me is the insistence of many of the children to look for patterns in a series of random outcomes. We feel this is because current teaching of mathematics emphasizes the patterns within mathematics. We would like to discuss this conflict between probabilistic thinking and other mathematical thinking in the discussion group at Japan.

3. IASE Statistical Education Research Group (IASE SERG)

<http://www.ugr.es/~batanero/sergroup.htm>

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 IASE Statistical Education Research Group (IASE SERG), which will be a subset of the International Association for Statistics Education (IASE). The next edition IASE Statistical Education Research Newsletter (IASE SERN) will be published on about 1 May 2000.

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/newsletters.html>, or you can write to the International Statistical Institute at <isi@cbs.nl>.

The aim of the IASE SERN Newsletter Editors is to make it a very comprehensive document of up to day news in stochastics education research. This PME Newsletter is deliberately kept brief, and should be seen as a supplement to IASE SERN. Please consider subscribing to IASE, and read the Newsletter at <http://www.ugr.es/~batanero/sergroup.htm>.

4. PME’s Research Interests of Members Data Base

<http://igpme.tripod.com/>

You may not be aware that PME has a list of members’ research interests on its Web Site. This is possibly not terribly up to date, and the “Data Handling” list is very short. Nevertheless the list may be of some value, and it would benefit from having other names added. Think about it!

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

<http://www.swin.edu.au/maths/iase/icme9.html>

Speakers from 11 countries are presenting papers on statistical education from age 11–18, students in higher education, and adults that fall into the following categories.

(i) research that has been carried out on students learning statistics and how this can help the statistical educators of tomorrow,

(ii) new innovations used and/or proposed to be used in the statistics teaching environment,

(iii) practical examples of statistical work carried out in developing countries and the way forward for these countries,

(iv) work related statistical education and its relationship to the classroom,

(v) how future statistical education can be enhanced, and

(vi) global statistical education for the future.

If you would like any further information then please feel free to contact Susan Starkings, Head of Mathematics Support, SouBank University, Borough Road, London SE1 OAA, UK, e-mail: <starkisa@sbu.ac.uk>.

6. Next Newsletter

This is planned for mid-May. Material for publication by 7 May 2000, please, to John Truran, at his new address: <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> (note new address)

Kath Truran, University of South Australia, Australia

<Kath.Truran@unisa.edu.au>

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