Secretary and Editor: Carmen Batanero

Departamento de Didáctica de las Matemáticas

Facultad de Ciencias de la Educación, Universidad de Granada

e-mail: e-mail: batanero@goliat.ugr.es, http://www.ugr.es/local/batanero/

Associate Editor: John Truran

Mathematics Education

Graduate School of Education,University of Adelaide

e-mail: jtruran@arts.adelaide.edu.au

This issue contains a detailed report of the work carried out at the III Iberoamerican Conference of Mathematics Education (III Cibem, Caracas, July, 1998). A stochastics working group has been set up at this conference, with an initial number of 24 researchers from different Iberoamerican countries, where there is an increasing potential for statistical education to develop. We invite you to send us reports about statistical education research in other geographical areas to be included in the next issues.

The recent loss of Efraim Fischbein is a sad new for both the scientific and human point of view. He was not just a scientist and a humanist, but a kind and caring person who was able to provide inspiration and encouragement for the work of many of us. In particular he was one of the founders of both the PME Group (Psychology of Mathematics Education) and this Study Group, in which he has been actively involved until very recently. We are including a note on his work, as a modest homage to his memory; however, the best honor we can do is trying to follow his example and developing his ideas in our future works.

Please, remember that the newsletters are available from our web page at the University of Granada (http://www.ugr.es/local/batanero/).

Rasimah Aripin

Faculty of Information Technology and Quantitative Sciences

MARA Institute of Technology

40450 Shah Alam, Selangor, Malaysia

drasimah@psmb.itm.edu.my

Rasimah is an associate professor in statistics at MARA Institute of Technology. Currently, she is teaching statistical theory, regression analysis and time series analysis, besides supervising research students. She is particularly interested in the development of classroom and other real-life activities to enhance the teaching of mathematical and statistical concepts. Her current projects include the study on the understanding of basic calculus concepts among first year statistics students and the use of technologies in the teaching of statistics.

Mariana Baquero

Universidad de Palermo.

Luis M. Campos 735 4to 14(1426) Capital Federal. Argentina

mbaque@mail.palermo.edu.ar

Mariana gained her Degree in Applied Mathematics at the University of Buenos Aires in 1981 and since then has taught mathematics at secondary level and algebra and analysis to engineers. She is currently continuing her training with a grant to complete a Bachelor in Marketing. Since 1991, she has been part-time lecturer at the University of Palermo, where she teaches statistics and decision theory, using all kind of resources to teach statistics to students from Pedagogy, Marketing and Management.

Roberto Behar

Departamento de Producción e Investigación de Operaciones

Facultad de Ingeniería Universidad del Valle

Apartado Aéreo 25360, Cali, Colombia

rbehar@pino.univalle.edu.co, rbehar@eio.upc.es (Spain)

Roberto is currently working on the use of interactive multimedia in the teaching of statistics. He is reviewing the related bibliography to build a base framework for his project, and building some applications relating to some concepts which are suitable for being introduced by using this tool. Even though this is a recent project, his interest in statistics has developed since he first started teaching the topics at the School of Engineering, Universidad del Valle. Cali, Colombia in 1979. He is on Sabbatical at the Departamento de Estadistica e Investigación de Operaciones, Escuela de Ingenieros, Universidad Politécnica de Catalunya, Barcelona, Spain.

Carlos Bouza

Departamento de Matemática Aplicada,

Universidad de La Habana, Cuba

bouza@matcom.uh.cu

Carlos got his PhD in 1978 at the University of Belgrade. His main interests are: Sampling, nonparametric and robust procedures, and stochastic programming. He has published more than 50 papers in journals of Cuba, Brazil, Mexico, Spain, France, Germany, etc. He is chair of statistics, and secretary of operational research at the Facultad de Matemática y Computación; reviewer for _Zentralblatt fur Mathematik_, and contributing editor of _Current Index to Statistics_. His main interests are the teaching of statistics to non-mathematicians and using non-presential methods for graduate courses. Carlos will be very glad of discussing the results of the following developed work:

1. Teaching statistics at masters level without lecturing. Written guides were prepared and consultations were periodically given. A combination of homework, theoretical exercises and use of computers was used to assess progress. There was a good result with mathematicians but not with social science specialists. The paper was discussed in an international congress on distance teaching. A joint research was developed with the department of sociology, Universidad Nacional de Educación a Distancia [UNED-Madrid] up to 1994. A comparison of this teaching method with classical teaching methods is in progress.

2. Comparing the "logic based" and "mathematical model based" approaches for teaching statistics to non-mathematicians. The use of mathematical reasoning is being compared with the use of common logic for introducing concepts and using models. Carlo's thesis is that philosophy is the real kernel of statistics and it should be used for teaching to students. They should develop and understanding of what is statistically feasible and be able to manage the logic of a model. In this way non-parametric and normal based inference can be learned without conflict. These ideas have been discussed in a conference last March.

Dr. Henrik Dahl

Agder College, Tordenskioldsgt 65

Postuttak, 4604 Kristiansand, Norway

Henrik.Dahl@hia.no

Henrik is now advising a master degee in the didactics of mathematics having the title: "From probability theory around 1700 to Norwegian schools in the year 2000". The students name is Hege Therese Syvertsen and she will finish in June 1999. He is also presenting a paper on the Statistical Tests Controversy at theISI 52 Session in Finland.

Carl Lee

Department of Mathematics Central Michigan University,

Mt. Pleasant MI 48859, USA

Carl.M.Lee@cmich.edu, www.cmich.edu/~3ldzoah/

Carl has been involved in developing a teaching strategy that integrates projects, in-class hands-on activities, and co-operative learning using computer technology. Two articles have been published:

a) Promoting active learning in introductory statistics course using the PACE strategy. PACE stands for Projects, Activities, Co-operative learning using computers, and Exercises. This work appeared in the Proceedings, The 5th International Symposium on Mathematics Education at Mexico City, pp. 199-206, 1997. The entire paper is posted on his web page at www.cst.cmich.edu/users/LeeC

b) An assessment of the PACE model for introductory statistics. Appeared in the Proceedings, ICOTS 5 held at Singapore, 1998. The entire article is also on Carl's web page. This was an interview study on how students learn introductory statistics. An interview of students from traditional lecture/note taking class and from a class taught by using the PACE model was conducted to investigate the understanding and problem solving skills of these students after three months of completing the course. A similar interview study was also conducted at another university recently. A presentation will be given at the 3rd International Conference on the Research in Undergraduate Mathematics Education, 1998.

Maria Meletiou

610 W. 30th St., #220

Austin, TX 78705, USA

meletiou@fireant.ma.utexas.edu

Maria is a doctoral student in mathematics education at the University of Texas at Austin. She comes from Cyprus, where she graduated in 1990 from the Pedagogical Academy of Cyprus and worked for a year as an Elementary school teacher. In 1991, she came to the United States as a Fulbright Scholar to study Mathematics. She got her B.A. in Mathematics in May of 1993, and M.Sc. in Statistics in August of 1994. She has since then been in the Ph.D. program in Mathematics Education, while at the same time being enrolled in the M.Sc. program in Operations Research and Industrial Engineering, from which she has just graduated. Right now, she is at the stage of starting to work on her dissertation. Her advisor is Dr. Jere Confrey and this fall she will be working with her, trying to design a Math Modelling course for high school teachers. Her focus will be on trying to understand students' (as well as their teachers') understanding of the concept of sampling. She has already done some research on undergraduates' understanding of sampling, but would like to get even more insights into the topic by looking at younger students who have not been a exposed to formal statistics courses.

Dr. Parimal Mukhopadhyay,

Indian Statistical Institute, 203 B.T.Road, Calcutta 700 035

International Statistical Education Center, Calcutta,

203 B.T.Road, Calcutta 35, India

parimal@isical.ac.in

Associate Professor at the Indian Statistical Institute and Member-Secretary, Board of Directors at the International Statistical Education Centre in Calcutta. His field of interest are survey sampling, linear models, and population mathematics. He has published more than fifty papers in _Survey Sampling_, _Jounal of. Applied Statistical Sciences_, _Communications in Statistics_, _Journal of Statistical. Planning and Information_, _Metrika_, _Metron_, Statistics, _Journal of Statistical.Reseacher_, _Pakistan Journal of Statistics_, _Sankhya_, _Journal of the Indian Statistical Association_, _Calcutta Statistical Association Bulletin_, _Australian Journal of Statistics_. He has published the following books:

1. _Theory of probability_ (1991). Calcutta: New Central Book.
1. _Inferential problems in survey sampling_ (1996). New York: Wiley Eastern Limited
1. _Mathematical statistics_ (1996). Calcutta: New Central Book.
1. _Small area estimation in survey sampling_ (1998). New Delhi: Narosa Publishers
1. Theory and methods of survey sampling (1998). New Delhi: Prentice Hall of India
1. Applied statistics (1998). Calcutta: New Central Book.

His current interests include small area estimation in survey sampling, analysis of complex surveys, and robustness studies. He has conducted and guided several statistical survey projects and is currently conducting a several survey project on small area population estimation. He completed a survey project on intergeneration occupational mobility at Calcutta. He has been visiting Professor at the University of Ife, Nigeria, Moi University, Kenya, University of Stockholm, Sweden, as well as the Insdian Statistical Institute, Calcutta, and visited several Universities at Canada, Netherlands, and Australia.

Note: Throughout the Newsletter, members names are highlighted in capital letters.

John TRURAN, University of Adelaide

Few would disagree that three of the giants of mathematics education in this half-century have been Piaget, Freudenthal and Fischbein. With the recent death of Efraim Fischbein, their direct contribution to mathematics has now come to an end, but in their printed works we still have three sets of shoulders on which to stand as we seek to look further into how mathematics is learned.

Two aspects common to these three men seem particularly relevant to those of us working in the field of stochastic teaching and learning. The first is that all three were expert in far more than stochastic education: Piaget in genetic epistemology, Freudenthal in mathematics, and Fischbein in psychology. In my view, their broader vision helped to sharpen their contribution to mathematics education. The second is that all of them made a significant contribution to stochastic teaching and learning. For all three, from their different perspectives, this special problem was seen as an important part of their wider enterprise. Recently, there has been some discussion about the question "is stochastics a part of mathematics?". Perhaps these giants would suggest that a better question is "what does an understanding of stochastics and its learning have to offer to knowledge in general?"

The bibliography published below gives a good idea of the range of Fischbein's interests within mathematics education. His primary interests were in mental models and forms of reasoning. He was concerned with both young children and adolescents, and, like Freudenthal but unlike Piaget, he was also concerned with the relevance of his work to the teaching of mathematics.

Fischbein's major stochastic work The Intuitive Sources of Probabilistic Thinking in Children was published in 1975, the same year that the 1951 work of Piaget & Inhelder The Origin of the Idea of Chance in Children was translated into English. I do not know if this was a coincidence or not (one of the translators was Harold D. Fischbein) but it did mean that at about the stage when the serious study of probability started to develop, there were two conflicting points of view available as starting points. Piaget & Inhelder had argued for a stage-related development, which required the understanding of combinatorial operations as a pre-requisite for full understanding. Fischbein had argued for a much earlier understanding of the idea based on a more holistic approach, which he saw as one manifestation of intuitive thinking. The probability research community was lucky to have such a broad set of opinions on which to base its research; sadly, it does not seem to have made as much use of the opportunity as it might have.

His stochastics research work was based on small, very carefully defined problems whose responses were subjected to classical classification analysis. This has meant that his work is relatively easy to replicate, although few have taken up the challenge so far. While he was prepared to make strong claims for his data, he was also careful to emphasise that his results about responses could only suggest inferences about the thinking processes employed by his respondents. Personally, I have found his work with Nello and Marino on children's responses to tossing three dice in different ways to be particularly illuminating, and of great value for classroom practice.

Although I heard Fischbein lecture, I did not know him as a person, but others have told me of his kindness to them, and his encouragement of their work. Fischbein was an honorary life member of PME, and was still attending its meetings and presenting new research until the last 12 months of his life. The last paper he presented, with Grossmann, was on children's intuitive understanding of factorial numbers. So in 1997 he was still following up ideas which he had first addressed at least as early as 1970. His breadth of interests, profundity of thought, and continued enthusiasm for research into the last years of his life have been an inspiration for us all.

Note by Marie Paule LECOUTRE

I was very sad to learn that Professor Ephraim Fischbein died last July. His death is really a very great loss for the scientific community, and I keep many memories from him more as a friend than as a colleague. I am sending you the abstract of a paper that I prepared with his collaboration, and that is to be published in "Recherches en Didactique des MathÈmatiques". It is probably one of the last publications of the Professor.

LECOUTRE M. P. & FISCHBEIN E. (1998). Evolution avec l'age de "misconceptions" dans les intuitions probabilistes en France et en Israel. (Evolution with age of misconceptions within probabilistic intuitions in France and Israel) _Recherches en Didactique des MathÈmatiques_,18 (1), in press.

This research aims to investigate the evolution, with age, of probabilistic intuitively based misconceptions. The main purpose of this "exploratory" experiment is to analyse the different cognitive models, which were activated in the various uncertainty situations considered here. A

secondary object is to compare the findings obtained in France and in Israel. The results obtained from 687 subjects in France and 98 subjects in Israel in grades 5,7,9 11 and from students are very complex : Some misconceptions grow weaker with age (it's the case in particular for the recency effects and the representativeness bias), whereas others grow stronger (especially for the "Falk phenomenon" related to conditional probabilities). A discussion and interpretation of these results, with the help of the notion of cognitive models spontaneously developed by the subjects, are presented.

The references have been compiled by Carmen and arranged in date order to make it easier to see the development of Fischbein's work.

FISCHBEIN. E., Pampu, E., & Minzat, I. (1967). L'intuition probabiliste chez l'enfant. [The child's intuition of probability]. _Enfance_ 2, 193-208.

FISCHBEIN. E., Pampu, E., & Minzat, I. (1969). Initiation aux probabilitÈs · l'Ècole ÈlÈmentaire. [Introduction to probability in the secondary school]. _Educational Studies in Mathematics_ 2, 16-31.

FISCHBEIN, E., Pampu, E., & Minzat, I. (1970). Comparison of ratios and the chance concept in children. _Child Development_ 41, 365-376.

FISCHBEIN, E., Pampu, E., & Minzat, I. (1970). Effects of age and instruction on combinatorial ability in children. _British Journal of Educational Psychology_ 40, 261-270.

FISCHBEIN, E., Barbat, I., & Minzat, J. (1971). Intuitions primaires et intuitions secondaires dans l'initiation aux probabilitÈs. [Primary and secondary intuitions in the introduction of probability]. _Educational Studies in Mathematics_ 4, 264-280.

FISCHBEIN, E., Barbat, I., & Minzat, J. (1974). L'acquisition des stratÈgies expÈrimentales par les adolescents. [The acquisition of experimental strategies among adolescents]. _Revue Roumaine des Sciences Sociales, SÈrie de Psychologie_ 2, 131-148.

FISCHBEIN, E. (1975). _The intuitive sources of probability thinking in children_. Dordrecht: Reidel.

FISCHBEIN, E., Barbat, I., & Minzat, J. (1975). Syllogistic reasoning in children and adolescents. _Revue Roumaine des Sciences Sociales, SÈrie de Psychologie_ 19 (1), 21-23.

FISCHBEIN, E. (1977). Image and concept in learning mathematics. _Educational Studies in Mathematics_ 8, 153-165.

FISCHBEIN, E., Slovic, P., & Lichtenstein, S. (1977). Knowing with certainty: The appropriateness of extreme confidence. _Journal of Experimental Psychology: Human Perception and Performance_ 3, 52-564.

FISCHBEIN, E., Tirosh, D., & Hess, P. (1979). The intuition of infinity. _Educational Studies in Mathematics_ 10, 30-40.

FISCHBEIN, E., Tirosh, D., & Melamed, U. (1981). Is it possible to measure the intuitive acceptance of a mathematical statement? _Educational Studies in Mathematics_ 12, 491-512.

FISCHBEIN, E. (1982). Intuition and proof. _For the Learning of Mathematics_ 3 (2), 8-24.

FISCHBEIN, E. (1983) Intuition and analytical thinking in mathematics education. _Zentralbaltt f¸r Didaktik der Mathematik_ 2, 68-74.

FISCHBEIN, E. (1983). Intuition and axiomatics in mathematical education. In M. Zweng, T. Green, J. Kilpatrick, H. Pollack, & M. Suydam (Eds.), _Proceedings of the Fourth International Congress on Mathematical Education_ (pp. 599-602). Boston: Birkhauser.

FISCHBEIN, E., & Gazit, A. (1984). Does the teaching of probability improve probabilistic intuitions? _Educational Studies in Mathematics_ 15, 1-24.

FISCHBEIN, E., Deri, M., Nello, M. S., & Marino, M. S. (1985). The role of implicit models in solving verbal problems in multiplication and division. _Journal for Research in Mathematics Education_ 16 (1), 3-17.

FISCHBEIN, E. (1987). _Intuition in science and mathematics_. Dordrecht: Reidel.

FISCHBEIN, E., & Gazit, A. (1988). The combinatorial solving capacity in children and adolescents. _Zentralblatt f¸r Didaktik der Mathematik_ 5, 193-198.

FISCHBEIN, E. (1989). Tacit models and mathematical reasoning. _For the Learning of Mathematics_ 5 (2), 9-14.

FISCHBEIN, E., Tirosh, D., Stavy, R., & Oster, A. (1990). The autonomy of mental models. _For the Learning of Mathematics_ 10(1), 23-30.

FISCHBEIN, E., Nello, M. S., & Marino, M. S. (1991). Factors affecting probabilistic judgements in children and adolescents. _Educational Studies in Mathematics_ 22, 523-549.

FISCHBEIN, E., & Schnarch, D. (1996). Intuitions and schemata in probabilistic thinking. In L. Puig, & A. GutiÈrrez (Eds.), _Proceedings of the XX Conference on the Psychology of Mathematics Education_ (v.2, pp. 353-360). University of Valencia.

FISCHBEIN, E., & Grossman, A. (1997). Schemata and intuitions in combinatorial reasoning. _Educational Studies in Mathematics_ 34, 27-47.

FISCHBEIN, E., & Grossmann, A. (1997). Tacit mechanism of combinatorial intuitions. In E. Pehkonen (Ed.), _Proceedings of the 21st Conference of the International Group for the Psychology of Mathematics Education_ (v.2, pp. 265-272). Lahti, Finland: Lahti Research and Training Centre

FISCHBEIN, E., & Schnarch, D. (1997). The evolution with age of probabilistic, intuitively based misconceptions. _Journal for Research in Mathematics Education_ 28(1), 96-105.

4. STOCHASTICS WORKING GROUP AT THE III CIBEM, IBEROAMERICAN CONFERENCE ON MATHEMATICS EDUCATION

Organisers: Audy SALCEDO, Universidad Central de Venezuela / Universidad Nacional Abierta, audysalc@reacciun.ve, and Carmen BATANERO, Universidad de Granada, batanero@goliat.ugr.es.

4.1. Panel: Statistical Education in Iberoamerica. Pedro NEL PACHECO, presented the curent state of teaching statistics in Colombia, as well as some personal experiences. Nelly LEON, Venezuela, discussed the training needs for primary and secondary statistics teachers who are responsible to introduce the students in this topic, and very often lack adequate training. Dione LUCCHESI DE CARVALHO, Brasil presented a restrocpective account of the teaching of statistics in her country as well as plans for future. Claude GAULIN, presented an international perspective of statistical education, and in particular a summeary about the PME stochastics working group work at Stellembosch, this year and future plans. At the end of the conference it was decided to start up an Iberaomerican statistical education research network.

Elena FERNANDEZ de Carrera, Stella M. Vaira, & Liliana E. Contini, Universidad Nacional del Litoral. Santa Fe, Argentina: Reassessing the empirical definition of probability in high school. Relationship with computers and the role of simulation.

Understanding the correct reasoning of probabilities is not just a current need in scientific world, but also in the ordinary citizen's work activities for understanding everyday facts. Going back in history, we can see that the fact that Pascal and Fermat were interested in probabilities made other mathematicians also interested in them. In 1812 Laplace wrote: Theorie Analytique des Probabilites, a book which was the basis for the development of this theory throughout the 19th and 20th centuries. These contributions have influenced almost all branches of Science, and the empirical definition or frequentist approach -some authors also call it a-posteriori probability- makes the student come close to an understanding of the role that probability and randomness play in the real world. These ideas help to show how to apply statistics in a variety of disciplines. Difficult concepts such as bias, approximation, estimation and verisimilitude are simpler when working with this definition. It is also easier to understand simulation, that is, it is natural to deduct its meaning.

Although simulation has reached the media, do we know if newspaper' readers really understand its meaning? Statistics curricula in secondary school are generally based on poor descriptive statistics, with lengthy calculations by hand and boring tables, without discovering the potential of calculators or computers. Time is spent in meaningless calculus, where students are able neither to understand correctly the rich concepts underlying a graph or statistics summary, nor to reach all the information provided by them. When probability is part of the secondary school curricula, it is based on the classic definition and thus the lessons turn into a new way of teaching combinatorics. In word of Dr. Santalo: "in reality they are just combinatorial problems, where the idea of probability only serves to give them an attractive context".

If taught in this way statistics is neither understood nor used, mainly because everybody retains the underlying false idea that statistics problems have a unique solution. These problems are solved with certain grade of reasonableness that could not be reached without probability. Combinatorial reasoning is highly important. Learning to count and built tree diagrams organises thought; moreover it is a basic tool in mathematics, and in probability and statistics in particular. But uncertainty is fundamental, to define their boundaries and know its magnitude.

The importance of the definition of probabilities through relative frequency is also due to other relevant underlying ideas, such as population to be studied, working with samples to infer population characteristics, the possibility of committing errors when we take a measure, and the importance of checking these errors. Inferential statistical methods are based on probability, mainly in the idea of relative frequency. In particular, we use the probability concept to approach a simple stochastic experiment, which are needed, increasing its complexity in accordance with the student's age. This is why we apply the experimental teaching of probability to simple problems. Computing of the number of fishes in a lake, the number of persons in an event, inhabitants per square metre, the probable growth of a particular plant species, just to mention some examples, make probability full of possibilities to be included in secondary education. After this, simulation, through its application to simple examples, starting with random numbers table and following with computers. Moreover, students should develop a real comprehension of the power and limitations of simulations and experimentation only by comparing experimental results to mathematically derived probabilities, which frequently require combinatorial reasoning. (Batanero et al. 1998)

An example of analysis situation and its simulation: Two children A and B throw darts to a square paper of side 1. After a while, B tells A that if they draw a diagonal of the square, the number of darts falling above or below that diagonal is about the same. As A is not convinced, the children ask his teachers to help them to solve the problem. He suggest to do the following experiments:

Take 50 numbers from a random number table, with the following criterion: Counting the number of even and odd numbers that come up. The even numbers represent the darts falling above the diagonal and the odd numbers the darts felling below the diagonal. A table is built with these numbers. When a greater number of repetitions is needed, a computer with a spreadsheet is used to generate random numbers. This is the Monte Carlo method to solve probability problems. This situation is just an example of what can be done to make students understand that probability is not simply a mathematical game, but also a powerful tool to know the world we are living in.

References:

Santalo, L. (1982). _Probabilidad y estadística_. Monografía OEA

Chung, K. L. (1983). _Teoría elemental de la probabilidad y de los procesos estocásticos_Reverté.

GAL, I., & GARFIELD, J. (1998). Curricular goals and assessment challenges in statistics education. In I. Gal, & J. B. Garfield (Eds.), _The assessment challenge in statistics education_. IASE.

BATANERO C., GODINO, J. D., & Navarro-Pelayo, V. (1998). Combinatorial reasoning and its assessment. In I. GAL; & J. B. GARFIELD (Eds.), _The assesment challenge in statistics education_. IASE.

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Estela KAUFMAN Fainguerlent, & Janete Bolite Frant, Universidade Santa Ursula, IEM-USU, Brazil: Representations of probabilistic thinking.

This paper reports results from a large cross-cultural research that is being conducted by mathematics educators from the Universidade Santa Ursula, Brazil and Rutgers University, USA. The purpose of this study is to understand better how students develop awareness of mathematization while reflecting upon their strategies and/or convincing each other that their strategy works. In particular we examine fourth grade students' discussions about dice problems, their hypotheses and how they justify their probabilistic reasoning. This investigation was supported by a grant from the National Science Foundation (MDR9053597) to Rutgers, the State University of New Jersey, and has been supervised by the late Robert B. Davis and Carolyn A. MAHER.Introduction: The emergence of statistical teaching for K-8 students in Brazil is very recent. The introduction of statistics as a mathematical topic at initial teaching levels has being experimented with in a non-systematic way for five years. In 1997, the Ministerio da Educacao e Cultura MEC published the Parametros Curriculares Nacionais, a document where introductory statistics became a required part of the national curriculum. This was due to the social demand to emphasise the importance of statistics in society. The aim is to develop the students' abilities in data collection and organisation, in construction, interpretation, and use of tables, graphs, and other kinds of representations, and in communication of results. There are now some text books developing these statistical ideas. In 1996, the Universidade Santa Ursula in its graduate course in mathematics education (masters degree) developed an agreement for scientific co-operation with Rutgers University. The goal of the agreement was to develop research in mathematics education. In 1997, we developed some statistical activities as a component of our cross-cultural research program.

Method: In Brazil, these activities were experimented with in a private urban school in Rio de Janeiro. We worked with eight students: two fourth graders, two fifth graders, two sixth graders, and two seventh graders. The students worked in pairs. We used the same two activities with each pair of students. At the beginning the students made conjectures about the tasks and discussed their ideas. Data for this study were collected using videotapes and audiotapes of interactions during pair engagement working. We also used a collection of students' written work and researchers' notes.

Results and Discussions: The data analysis reported here concerns the work by two fourth graders: Carolina and Rodrigo, for which we analysed videotapes, their transcriptions and written work. We believe that the result of this study can contribute to better understanding of students' probabilistic/ statistical thinking.

Research task given to the students: A game is played by two players and involves rolling two dice. Player A gets a point if the sum of the two number on the dice is 2, 3, 4, 10, 11, or 12. Player B gets a point if the sum is 5, 6, 7, 8, or 9. The first player to get 10 points is the winner. Is the game fair? Why? Or Why not?

The children were asked to play the game with a partner. (They could play several games if they wished.) Afterwards the children were asked whether the results of playing the game supported their answer to the question above and to explain their response. They were also asked whether they thought that the game was unfair, and how could they change the game to be fair. Carolina and Rodrigo played the game using two imaginary players Antonio (A) and Pedro (B). Rodrigo and Carolina said immediately that Antonio will win because he had more numbers and, more importantly, the highest ones. Additional results of this study include: a) Different representations of game scores; b) Discussion of the game's fairness; c) Beliefs: A trick can affect the dice rolls; d) Use of an old experience to justify a new one.

References:

MAHER, C. A. (1998). Is this game fair? The emergence of statistical reasoning in young children. In L. PEREIRA-MENDOZA et al. (Eds.), _Proceedings of the Fifth International Conference on Teaching of Statistics_. Voorburg: IASE.

MAHER, C. A. (1995). Children's development of ideas in probability and statistics: Studies from classroom research. _Bulletin of the International Statistical Institute_, 2.

Secretaria de Educacao Fundamental (1997). Parametros Curriculares Nacionais. Brasilia, Brazil. MEC/SEF

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Roberto MEYER, Nancy Colomba, Nerina Gimenez, & Lucia Colla, Facultad de Formación Docente en Ciencias (UNL) - Escuela de Enseñanza Media 340, Santa Fe, Argentina: Preliminary experiences and conclusions from a research on probability and statistics methodology within the context of Argentinean curricular reform.

Educational reform: A reform of the educational system including the training of 5-17 year-old students is taking place in Argentina. With respect to mathematics teaching, the need for students to acquire knowledge which allows them to enlarge their everyday experience and to integrate specific thinking processes directed to solving real problems is emphasised. As regards the teaching of probability and statistics, the students are expected to know how to collect, organise, process and interpret statistical information, and understand, estimate and use probabilities for decision making.

The research team and their activities: Within this context we started working on the following points to develop teaching strategies: a) Diagnosing the mathematics teachers' knowledge about probability, statistics, and computer management; b) Designing a strategy for teaching probability and statistics at E.G.B. (Basic General Teaching) 2 and 3 and Polymodal levels. C) Including personal computers (software methodology) in the teaching of this area. D) Experimental evaluation of the statistics teaching design with a 13-year-old group (E.G.B. Level 3)

Main characteristics of the evaluated design: The teaching strategy has been based on acquiring concepts through data analysis, in an inductive strategy consistent with "Scientific Method". In this approach, the mathematical content of any statistical concept is not the only relevant aspect (therefore teaching is not just transmission of information) and the meaningfulness for the student plays a decisive role in learning. The classroom turns into a experimental classroom, and personal computers serve to create situations that facilitate the generation of skills to formulate, interpret, relate and solve problems.

The process starts by stating transdisciplinary research projects. Through this strategy, the students and their teachers define a problem which can be experimentally investigated, and through applying Scientific Method steps; reach the exploratory data analysis stage. Here the teacher acquires a leading role starting to develop statistical concepts up to the extent that the students need for analysing the data gathered. In this way, the different statistical measures are not just defined, estimated and graphed, but strategies and results are discussed and conclusions are set up. As a result, the statistics learning starts to be meaningful (through reception or discovery) and the student starts to acquire a capacity for turning data into information.

The case and its design: Intermediate level teachers joined the research team. They specifically agreed to work with students between 12 and 14 years old (E.G.B. 3). Two pre-existing groups (experimental - control), with a similar school performance were chosen and were guided by the same teacher. The control group was guided by a traditional teaching manual. The experimental group was guided by following the approach strategy elaborated by the research team and with the help of a personal computer in the classroom, which was only used by the teacher. Our hypothesis stated that the magnitude of the incentive has a different effect according to whether it refers to a simple or complex discriminative learning. This will handle two types of (2 or more level) variables: the kind of incentive and the type of task. We applied a questionnaire to both groups to evaluate the main effects and possible interactions. Results showed differences of at least 2 points (on a 0 to 10 scale) in favour of the experimental group. In the paper we discuss the results, their implications, institutional difficulties (institutional variables) and other aspects which can serve to validate or improve the experience.

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Ignacio MENDEZ, IIMAS, UNAM, Mexico: Statistics and scientific method.

It is well known that the teaching of statistics is often very difficult. In this work we suggest that this difficulty arises mainly because statistics is not presented as a part of scientific method, and because of ignorance about the epistemology and role of statistics in scientific research. A course of statistical methods for professionals in agronomy, medicine, psychology, etc., should include a substantive content of philosophy and methodology. The course should begin with an evaluation of philosophic aspects such as objectivity, empiricism, concepts & variables, indeterminism, theory & practice, causality, etc. Methodological concepts such as samples and populations, control of alternative explanations, confusion factors, would also be needed. It is also important to assess the crucial role and links between research problem, hypothesis, design and analysis. The role and limitations of mathematical models must also be considered, especially the fact that a model represents reality only to an approximate extent, and that this representation is always mediated by the design. All models are false, though some of them are very useful. As a very brief but valid diagnosis, I asked my students whether they consider the following statements to be true or false:

1. Statures of human beings follow a normal distribution.
1. In order to do science we have to be totally objective.
1. Finding no significant differences in a research project constitutes a failure.
1. Finding significant differences in a research project constitutes a success.
1. An experimental group of 100 people carried out a very intensive exercise program for a year; another control group of 100 people, did not engage in the intensive program. After the year, the amount of High Density Lipoproteins (HDL) was determined for each person. The average content was 12.3 for the experimental group and 18.2 for the control group. A t-test was performed, and a very significant result was found (P<0.0001). Can we deduce that the intensive exercise program reduces the HDL level?

With a moderate to high frequency, the students consider all statements -or at least 1, 4 and 5- to be true, though all of them are false. This can be deduced using ideas from experimental design, confounding factors, power of a test, etc. The main reason is that the so-called scientific method is neither infallible, nor unique. Scientific attitude implies a great effort to eliminate or minimise the possible errors in each aspect of research. Even when is not possible to be purely objective, the use of statistics in research can reduce the degree of subjectivity.

Very frequently the theory postulates that a factor X is a (probabilistic) cause of an effect Y. We study all the relevant factors A1, A2, A3, ...Ak that may influence this causal relationships. With the help of design and analysis, we test whether the association of X with Y still remains if we treat A1, A2, A3, ...Ak as conditional variables. If such conditional association does not disappear, we obtain support for the causality hypothesis. The conditioning may be done by design (blocking, randomisation, homogeneity) or by using statistical models (linear, logarithmic , logistic, simultaneous linear structural equations, etc.) to evaluate the association between Y and X, adjusted or corrected by the As. A very good example is the causality studied by statistical models between smoking and pulmonary cancer.

In this context is important to point out that a statistically significant result only eliminates the explanation of the random occurrence of the result (with a possible Type I error). But there may be many alternative explanations. In question 5 above, the significance means that this result is difficult to obtain if the population's averages for the program and control groups are equal. But this does not imply that the difference is due to de effect of the program. Alternative explanations for the difference in HDL between groups are: age, diet, measurement errors, etc.

There is a basic reasoning required in order to test a scientific hypothesis usually expressed as a causal relationship. The term "test" is not clear, since the procedure contrasts or compares the implications of the theory and expected data with the empirical findings and observed data. That is, statistical tests compare the model assumed by the hypothesis, with a set of observed data. The logical reasoning is H, D, AA implies P, where H is the hypothesis to be tested, D is the research design, that is, all the empirical procedures realised to obtain the data, AA are the Additional Assumptions needed in the design modelling and deduction; and finally P is a prediction. The reasoning is: If H is true, then with design D, and under the Additional Assumptions AA, the observations P should follow. It is very important to have several other explanations which also imply P, with the same Design D when H is not true. These alternative explanations must be considered during the design and analysis, to produce a design and an analysis that makes impossible, or at least very improbable, the occurrence of these alternative explanations. One of these alternative explanations is usually the random occurrence of P, when H is not true. This is the so-called null hypothesis

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Jorge Luis ROMEU. SUNY-Cortland, NY/USA: Experiences in Iberoamerican international collaboration.

Introduction and Motivation: It is quite evident that, at the closing of the 20th century, there exists a move to integrate across traditional national boundaries. Such new trend is already present in regional economic activities: MERCOSUR in South America; NAFTA in North America; EU in Europe. This new trend is also observed in the formation of international business organisations (trans-nationals), and in political (social democratic and Christian democratic internationals) and labour movements (OIT).

In a similar way and for similar reasons it is necessary to become integrated in other areas of human activity such as higher education. The main objective of the present paper is to highlight and discuss the need for the internationalisation of higher education in Iberoamerica, and some of the required procedures to achieve this, and to propose starting a project to undertake it in one area. In addition to the above-mentioned needs, several economic and technological conditions make it possible to undertake such internationalisation at this time. The appearance, in the last twenty years, of advances such as the Internet and personal computers, of relatively inexpensive transmissions of radio and TV programming via satellite and cable, of portable cellular phones, faxes and copying machines, in conjunction with an increase in the quantity and quality of the traditional infrastructure (roads, railways, electricity, etc.) make the internationalisation of education a real possibility.

In this paper we will discuss our past and ongoing experiences in international education, and in international collaboration between institutions of higher learning and research. With this background, we propose to initiate a project for professional and educational integration, within Iberoamerica, in the areas of applied mathematics and statistics. We propose the utilisation of the new technology cited above to accomplish this objective in a reasonable time, within cost and quality. The project's ultimate objective would be to form professionals, within the entire Iberoamerican region, who have (i) similar educational levels; (ii) similar core curriculum in the technical areas; (iii) similar or compatible technical vocabulary; a good knowledge of, and an easy access to (iv) professional and (v) higher education institutions within the Iberoamerican region; (vi) easy contact with similar professionals in other countries within the region and (vii) links to establish working relations and partnerships between individuals and groups of professionals within the region.

Summarising, the objective of this paper is to provide, via our international experiences in education and research, a framework through which the above-described international collaboration may be achieved within the Iberoamerican region. We all have similar political, demographic, socio-economic and ecological problems that transcend our own borders. But we also have similar historic, cultural and linguistic backgrounds that allow us to work together to help resolve them.

Problems and Solutions: This author has a first hand knowledge of some of the problems that arise when undertaking these types of international projects, for we have been closely associated with them for the past few years. For example, we have developed and directed the SUNY-Mexico exchange project since its inception in 1994. We have also worked and/or co-ordinated faculty development projects in Spain (Galicia and the Basque Country) and Venezuela (Orinoco plains). We have also helped to develop curriculum in operations research for an Argentinean university. And we have submitted proposals to NSF and FIPSE for moving researchers and students among US, Mexican and Canadian institutions in the areas of system simulation and the ecology. Our projects have specialised, primarily but not exclusively, in working with provincial universities and research institutions.

The Mexican project is the oldest, most ambitious and most successful of them all. It started as a faculty and student exchange project, with the intention of moving people between the SUNY system (350,000 students in 64 campuses, that constitute the State University of New York) and several Mexican institutions and university systems (Romeu, 1997). It includes the following options: (i) long stages such as sabbaticals, Fulbrights and other year-long leaves for teaching or research; (ii) short stages such as attendance at seminars, intensive courses, professional meetings, training sessions and internships for from one to four weeks; (iii) intermediate stages, usually summer or inter-session vacations, for short or intensive courses; (iv) scholarships, fellowships and teaching assistantships for faculty seeking graduate degrees, research or post graduate experiences in American universities; (v) exchange of books, journals, software, research material, data, etc.; (vi) donation of educational materials; (vii) exchange of students for a complete semester or school year, accepting all the courses taken in the host institution for full accreditation in the home institution; (vii) exchange of faculty with exchange of teaching loads and possibly also of houses, cars, etc. but not of salary.

The above mentioned Mexican project has, in four years and through grants obtained from different sources, but not surpassing US$3500, brought eleven Mexican faculty to SUNY's yearly, one-week Conference on Instructional Technology (CIT). Mostly from provincial universities, they come with full scholarships that cover registration, room, board and conference materials including workshops. On several occasions USIS has provided air fares. Also several boxes of mathematics and science textbooks have been collected and donated to Mexican universities. In return, a SUNY wide administrator last year attended a UNAM international conference in Mexico City.

We have also taught, via an ingenious co-operative program arranged with several universities in Northern Spain, several short, intensive courses on the use of discrete event simulation in teaching statistics (Romeu, 1997a). This course was originally developed and taught in several Mexican institutions while we were Fulbright scholars there in the Spring of 1994. We have also taught courses on the use of technology in science education in Venezuela. And we have implemented a need assessment study for a faculty development project between this Venezuelan institution and our own, using distance learning and other methods (Romeu 1998). Then, one Venezuelan faculty spent a month in our SUNY Campus, in an internship, visiting my classes and learning the software and technology that I use in teaching mathematics and statistics. Finally, and through the Internet, a group of five faculty (four of us in American universities and one in Argentina) developed all the courses for a Masters degree in O.R. for a provincial university in Patagonia, Argentina.

All the above experiences show how, with very few or no resources other than our enthusiasm and creative thinking, most of the problems that arise in developing international education projects can be successfully resolved. In our presentation we will share some of these experiences, the problems that appeared and the solutions implemented to overcome them. Through these examples, we hope to contribute to, and provide starting impetus for, the implementation of the project for internationalisation of higher education in applied mathematics and statistics, discussed above.

References:

ROMEU, J. L. (1997). Technology and international education. _Proceedings of the SUNY Conference for Instructional Technologies (CIT97)_ (pp. 98-100). SUNY-Brockport.

ROMEU, J. L. (1997). _On simulation and statistical education. American Journal of Mathematics in Management Sciences_, 17(3-4), 397-420.

ROMEU, J. L. (1998). The Internet in education across borders. _Proceedings of the SUNY Conference for Instructional Technologies (CIT98)_ (pp. 111-113). SUNY-Cortland.

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Audy SALCEDO, Universidad Central de Venezuela / Universidad Nacional Abierta, Venezuela: International academic organizations in the area of educational statistics.

During decades, mathematics at the initial school levels was an exclusive domain of deterministic thought. Probability and statistics were only studied at the college level. However, this situation has been changing in the last years. The work carried out by the psychologists investigating children's probabilistic thought, the recognition and acceptance of mathematics education as a field of production of knowledge, the high volume of information produced by society in general and computers development are some of the conditions that have allowed the elementary concepts of probability and statistics to be included at primary school; moreover they contributed to the conformation of a new field of research: Statistics education. There are, moreover, organisations that for many years have being concerned about the teaching and learning of statistics. Organisations like the International Statistical Institute (ISI) and the American Statistical Association (ASA) have promoted since their foundation the training of professionals in the area and have pointed out the need for a statistical education for all citizens.

The ISI was founded in 1885, as a centre of interest to develop and improve statistical methods, as well as their applications. This Institute has showed its concern for statistical education, first through the Education Committee and currently through the International Association for Statistical Education (IASE). Jointly with UNESCO, ISI worked in training specialist in statistic in different parts of the world. Also, it organises, through the IASE, the International Conferences on Teaching Statistics (ICOTS) and the Round Table Conferences, which coincide with the International Congress of Mathematics Education (ICME). Both type of conferences are devoted to the discussion of issues related to the teaching and learning of statistics.

The ASA initial objective is to favour the excellence in the use of statistics in the natural and social sciences. The interest of the ASA for statistical education has leaded it to associate with the NCTM to organise the Combined Committee of Curriculum of Statistics and Probability. This committee has undertaken several projects, such as the Statistics Teacher Network highlights (STN). The STN is a publication whose objective is to strengthen the teaching of the probability and the statistics for the kindergarten, elementary and high school levels. The STN is published three times a year in both hard copy and a the ASA Web page and it contains revisions of books and of software for teaching statistic, as well as activities for teaching statistic and probability carried out successfully in classrooms. Oher statistical, educational or computing societies that have organised sections or specific divisions for the Statistics Education, such as the Royal Statistical Society, the Centre for Statistical Education of the University of Nottingham, the American Educational Research Association (AERA), the Statistical Society Japanese, the Spanish Society of Investigation in Mathematical Education, the Computers in Teaching Initiative (CTI), the Centre for Statistics and the International Association for Statistical Computing (IASC). Moreover, there are other organisations whose central interest is the statistical education:

1. The International Study Group for Research on Learning Probability and Statistics. This Group is an informal net of people who share a common interest for inquiring on the teaching and learning of probability and statistics in all the educational levels.

2. Working Group for the Teaching and Learning of Stochastic of the PME. This group meets at the annual congresses of the PME and carries out diverse activities, the most important is the one of diffusion of research studies in the area.

The statistical education community is at a stage of expansion. We consider that there are several factors that have contributed to its development, but without a doubt an important one has been the work carried out for international academic organisations. IberoamÈrican scholars are aware of this expansion. However, in our case certainly exist inconveniences that are necessary to confront. For example, among teachers, teacher educators, administrators and politicians the prevalence of deterministic thought still persists; elementary school teachers are responsible of teaching notions of elementary of probability and statistics to children without necessary formation; and the existence of a limited number of research studies in didactics of the statistic. We consider that a form of collaborating to solve this problem could be the constitution of an Ibero-American Group of Education Statistics. This organisation would be open to all persons interested in improving the statistical education in IberoamÈrica. Among the possible objectives of this group could be: (a) to allow the association and communication among people whose major concern is the statistical education; (b) to promote reasearch in this field; (c) to generate a movement that contributes to recognise the importance of the probability and statistics in the world current; to help to improve the formation of educational of the levels of primary and secondary in the didactics of statistics. The problems faced by scholars in the field of statistical education are extremely wide and complex. Therefore, it is necessary to unite efforts to consolidate the field and to improve our knowledge about the teaching and learning of statistics.

Adela Abad, University of Panam·, Panam·: Difficulties in learning joint probability distributions.

In the course on probability at the second year of a Statistics major, students face the difficulty of working with join probability distributions. We have carried out research with a sample of 12 students taken from those taking the course in the academic year 1996-97. The following variables were considered: Average scores in Mathematics at university level, number of times that the student has taken statistics, and his evaluations. The purpose was to determine the more frequent difficulties and deficiencies when working with these concepts. The methodology included: Presentations with debate, developing examples, discussing practical problems and applying tests. Our results show difficulties to compute join discrete probabilities, to verify the variables independence and to find E(XY). For continuous variables difficulties are related to the distribution function and its notation, to computing joint probabilities, and to obtaining marginal density functions. More emphasis on both the conceptual and computational components of join distributions is suggested.

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Flor ARGENTI de Monagas, Venezuela: How to select a statistic method in research. A new approach for teaching of the statistics

At university level, both at undergraduate and graduate level, the teaching of statistics is limited to teaching pre-determined concepts and procedures which do not fulfil students' expectations of using this discipline for data analysis, which is a necessary step in the research process. We suggest here a new focus in the teaching of statistics at graduate level, where the information given the student on the different statistical methods is complemented with guiding their selection according to the research purpose (descriptive or inferential), the type of variables and measurement scale, the number, size and relationship among the samples, and the dimensions of the contingency table. As well, some relationships are shown among the different methods to promote the students' relational learning.

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Celi Aparecida Espasandin Lopes & Anna Regina Lanner of Moura, PRAPEM/FE/ UNICAMP, Brazil: Statistics and probability at compulsory education: A curricular analysis.

This study aims to analyse the way in which statistics and probability is presented in the curricular proposals for compulsory level mathematics in some Brazilian regions. An analysis will be developed which considers as reference points criteria like the conceptions about statistics and probability underlying these proposals, the probabilistic and statistical concepts selected, and the aims of teaching these notions to the students. We consider the wide contribution of the study of statistics to the students' formation. We verify the goal of giving the students autonomy and critical capacity to develop as citizens. We do not mean that only this study is sufficient to provide them with this evolution, as a pedagogical practice coherent with this proposal is also needed. We think these topics are as important as the study of geometry, algebra or arithmetic, whose meaningful work also contributes to this formation. Understanding percentages, indexes of population growth, rate of inflation, etc. is not enough. What is also needed is a critical analysis of data, including the assessment of its veracity. In the same way the ability to organise and represent a data set and interpret it to make decisions is needed. All of this implies rethinking the role of teacher in the learning process, as well as making teachers aware of their political action trough their pedagogical practice.

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Felipe FERNANDEZ, Olga L Monroy, & Liliana RodrÌguez. Una empresa docente, Colombia: Methodology used to manage students' errors in a course on statistics.

This article reports on the use of some methodologies in a statistics course that were intended to help students cope with their daily mistakes. These methodologies emerged within the design, development/implementation and assessment of a series of problematic situations conceived to be used as exercises to be solved by students majoring in social sciences. Each situation was designed to be used along two one-hour long lesson: During the first hour each student worked alone; the second hour was dedicated to working in teams. Collective analysis was applied to the documents produced by the individual students, to determine his/her mistakes and provided the guidelines for the design of the group working session. This was spent with the students discussing their mistakes and trying to solve them. We found that students could not identify all the problems underlying their mistakes. However, our methodology enabled questioning and discussion about the likely causes of their mistakes, thus favouring the development of conceptual comprehension around the notions related to hypotheses testing. In addition, this activity provided both students and instructors with a valuable assessment tool.

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Gonzalez, Patricia, BAQUERO, Mariana, & Latorre Adriana. University of Palermo. Buenos Aires. Argentina: Teaching statistics in a Business School.

Courses in statistics are not usually the favourites in a School of Marketing. The students' question is: Why should we study mathematics in a Business School? Mathematics educators' problem is to achieve motivation by making the relevance of statistics explicit. The apathy or rejection has two explanations: Students have a poor training in their secondary studies, and even those with a strong mathematics formation, do not realise what the contribution of statistics can be to their training as administration professionals. Our proposal is intended to show: a) The abilities required in this field; b) The potentials and dangers of using of technology to teach statistics; c) An important source of motivation. The distinction between good information and that producing biases and fallacies, as sometimes presented in the media. We believe that a content revision is necessary to help students adapt to the technological needs of our society.

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Nelly A. LeÛn GÛmez, University PedagÛgica Experimental Liberator, Instituto PedagÛgico de MaturÌn, Venezuela. Applying combinatorial analysis to solving probability problems at upper levels.

Finding out the size and form of sample spaces is really difficult for IPM students of the course on probability and statistics in the speciality of mathematics, and this difficulty is increased when they need to apply counting methods, characteristics of combinatorics. This fact has led to research to establish students' knowledge of concepts like permutations, arrangements and combinations and the way in which they apply these concepts to solve probability problems. This research was carried out with seven volunteer students after revising combinatorial notions and studying the basic concept definitions and properties of probability. A questionnaire, adapted from Navarro- Pelayo, Batanero and Godino was given to the students to assess their combinatorial reasoning. The questions were modified to introduce probability calculus. Our results show the students' limitations to describe the sample space and events and to determine the combinatorial model (selection, distribution, partition) and combinatorial operation (combinations, permutations, arrangement) to count their elements.

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Nelly A León Gómez, Universidad Pedagógica Experimental Libertador InstitutoPedagógico de Maturín Venezuela Exploring basic concepts of probability at upper levels.

In recent years basic probability and statistics concepts have been introduced at Primary levels. Different studies recommend the exploration of situations where the ideas of chance, frequency, certainty, impossibility, possibility and probability are present. Students' interpretations of these ideas, which have been acquired from different sources such as games, should be taken into account. Our experience shows that even mathematics teacher, with statistics and probabilistic training have been unable to introduce these concepts adequately. This concern has led the author to explore the conceptions about these ideas which are held by students of Mathematics at IPM at the beginning of a course on Probability and Statistics. The aim was to clarify their misconceptions and provide them with strategies useful to their future professional work. We have analysed the conceptual categories derived from the answers to an exploratory questionnaire and have suggested some conclusions.

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Dione Lucchesi de Carvalho, UNICAMP - Sao Paulo Brazil: Teaching statistics to young and adults immigrants.

Due to the inefficiencies of Brazilian employment politics, many rural workers immigrate to big cities looking for a job. Some of these people, or their sons, sometimes lack school preparation, and attend courses directed to the training of youths and adults. At secondary and upper primary levels these immigrant students share the classroom with urban workers who have also being excluded from school for different socio-economic reasons. Interaction between these two students groups is full of preconceptions socially developed in the big cities. With the aims of improving this interaction, discussing these preconceptions, and establishing good classroom relationships, the mathematics teacher, with the help of the history, geography and Portuguese teachers, has developed a statistics project for the 3rd level of secondary education. This project involves all the school and at the end of the year a document on each student's profile and reflections is produced. The activities involved in developing the project have been videotaped.

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Zuly Millan Boadas, Universidad Experimental Pedagógica Liberador-Instituto Pedagógico de Caracas: Research: A methodological strategy for teaching statistics at upper levels.

There is a generally high percentage of failures in statistics courses at university level. This problem throughout their educational careers because of students' poor mathematical background, lack of application of contents to real contexts which do no encourage significant learning, and instructors' lack of pedagogic training. Within the subject of educational statistics, a methodological strategy is being implemented, which is based on critical application of statistical tools to diverse real educational research processes. This has led to students' deeper understanding of statistical tools, transfer of statistical knowledge to other scenarios, and learning linked to reality, which is reflected in better student statistical levels. In the paper we present the work, methodology, advantages and limitations of the experience to serve as a reference for statistical training at university levels

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Mercedes Puga Las Casas, Universidade Guarulhos, Universidade Paulista, Brazil: Teaching statistics at primary levels.

The aim of this research was to assess the teaching of statistics and primary level student's performance. We also try to find alternative paths to create adequate conditions in mathematics classrooms to develop students' productive thinking by means of the teaching of statistics. Subjects were at the seventh level of first and second grades in a public school at the area of Macedo, in Guarulhos, São Paulo, which have got the mathematical knowledge required for a basic program. Action research served to take an active role about the observed data, produce knowledge, gain experience and answer some proposed questions. As a result a proposal for teaching statistics was suggested to teachers, where students' creativity could be developed within a meaningful mathematical practice. We thus hope to more effectively contribute to increase students' interest in studying mathematics, improve their understanding about the world they live in, and develop their mathematical and logical thinking

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Maria do Carmo VILA, Students' conceptions in a random situation of simulation with the use of concrete random generators.

After different pilot trials with a significant number of students, two main objectives were formulated in this research: a) Studying the Brazilian students' conceptions when carrying out the simulation of a simple random situation; b) comparing the student's conceptions with their respective "Green’s levels". To reach these aims a test taken from David Green was given to 518 students from three different schools and three different school levels. Clinical interviews were given to 11 students from those at the first Green's level, 11 from the second level, and 11 from the third level, selected among the 518 students. Data analysis served to identify 5 main conceptions concerning the simulation model, and 7 conceptions concerning the validation of this model. We realised that an elaborated conceptions about random situations is necessary but not sufficient for constructing a successful model of that random situation. As regard the second objective, it appeared that the conceptions are generally better elaborated as the Green's level is higher.

5. A BIBLIOGRAPHY ON BAYESIAN STATISTICS

Collected by Bruno LECOUTRE, C.N.R.S. et Université de Rouen, France, bruno.lecoutre@univ-rouen.fr, http://epeire.univ-rouen.fr/labos/eris

The references hereafter more specifically concern the teaching of Bayesian methods for experimental data analysis, in the framework of the current debates about significance tests. They include some teaching experiences, methodological discussions, and basic textbooks and articles that can serve as references, especially in my fields of interest: psychology and clinical trials. A more complete bibliography on the uses and misuses of statistical inference can be get in the web site above.

Albert, J. (1995). Teaching inference about proportions using bayes and discrete models. _Journal of Statistics of Education_ [on line], 3(3). Available e-mail: archive@jse.stat.ncsu.edu, Message: send jse/v3n3/albert.

Albert, J. (1997). Teaching Bayes' rule: A data-oriented approach. _The American Statistician_, 51, 247-253.

American Psychological Association, Board of Scientific Affairs (1996). Task force on statistical inference initial report (draft). Available on the internet at address: http://www.apa.org/science /tfsi.html.

Berry, D. A. (1993). A case for Bayesianism in clinical trials. _Statistics in Medicine_, 12, 1377-1393.

Berry, D. A., & Stangl, D. (Eds.) (1995). _Bayesian biostatistics_. New York: Marcel Dekker.

Berry, D.A. (1997). Teaching elementary Bayesian statistics with real applications in science. _The American Statistician_, 51, 241-246.

Freeman, P. R. (1993). The role of p-values in analysing trial results. _Statistics in Medicine_, 12, 1443-1452.

Gelman, A., Carlin, J. B., Stern, H. S., Rubin, D. B. (1995). Statistical methods: A Bayesian approach. New York: Chapman and Hall.

Goodman, S. N., & Berlin, J. A. (1994). The use of predicted confidence intervals when planning experiments and the misuse of power when interpreting results. _Annals of Internal Medicine_, 121, 200-206.

Hively, W. (1996). The mathematics of making up your mind. _Discover_, May, 90-97.

Iversen, G. (1998). Student perceptions of Bayesian statistics. Proceedings of the Fifth International Conference on Teaching Statistics (pp, 231-237). Singapore. IASE.

Kadane, J.B. (1995). Prime time for Bayes. _Controlled Clinical trials_, 16, 313-318.

LECOUTRE, B. (1996). Traitement statistique des données expérimentales: Des pratiques traditionnelles aux pratiques bayésiennes (Statistical analysis of experimental data: From traditional practices to Bayesian practices)- Avec programmes Windows(r) par B. LECOUTRE et J. POITEVINEAU (Windows programs available on the Internet at address: http://epeire.univ-rouen.fr/labos/eris/pac.html). Saint-Mandé (France): C.I.S.I.A. [http://www.cisia.com].

LECOUTRE, B. (1998). Teaching Bayesian methods for experimental data analysis. Proceedings of the Fifth International Conference on Teaching Statistics (pp. 239-244). Singapore: IASE.

LECOUTRE, B. (1998). Teaching analysis of variance and procedures for assessing the magnitude of effects: The specific analysis approach. Submitted for publication.

LECOUTRE, B., & POITEVINEAU, J. (1992). PAC (Programme d'Analyse des Comparaisons): Guide d'utilisation et manuel de rÈfÈrence (Program for the Analysis of Comparisons: Windows limited version available on the Internet at address: http://epeire.univ-rouen.fr/labos/eris/pac.html). Saint-Mandé (France): C.I.S.I.A. [http://www.cisia.com/logiciels/pac.htm]

LECOUTRE, B., & POITEVINEAU, J. (1998). More than 300 references about the practice of significance tests in the analysis of experimental data (especially in psychology, also in clinical trials): uses, misuses and abuses, criticisms, alternative solutions and examples of applications. Available on the Internet at address: http://epeire.univ-rouen.fr/labos/eris/pac.html.

Lee, P. (1989). Bayesian statistics: An introduction. Oxford: Oxford University Press.

Lewis, C. (1993). Bayesian methods for the analysis of variance. In G. Keren & C. Lewis (Eds.), A handbook for data analysis in the behavioral sciences. Statistical issues (v. 2, pp. 233-256). Hillsdale, NJ: Erlbaum.

MOORE, D. S. (1997). Bayes for beginners? Some reasons to hesitate. _The American Statistician_, 51, 254-261.

Novick, M. R., & Jackson, P. H. (1974). Statistical methods for educational and psychological pesearch. NewYork: McGraw-Hill.

O'Hagan T. (1996). First Bayes: A [Windows] program intended to help with teaching and learning elementary Bayesian statistics. Available on the internet at address: http:\\www.maths.nott.ac.uk\personal\aoh\.

Phillips, L. D. (1973). Bayesian statistics for social scientists. London: Nelson.

Racine, A., Grieve, A. P., Flihler, H., & Smith, A. F .M. (1986). Bayesian methods in practice: Experiences in the pharmaceutical industry. _Applied Statistics_, 35, 93-150.

Rouanet, H. (1996). Bayesian methods for assessing importance of effects. _Psychological Bulletin_, 119, 149-158.

Rouanet, H., & LECOUTRE, B. (1983). Specific inference in ANOVA: From significance tests to Bayesian procedures. _British Journal of Mathematical and Statistical Psychology_, 36, 252-268.

Rouanet, H., LECOUTRE, M. P., Bert, M. C., LECOUTRE, B., Bernard, J. M., & Le Roux, B. (1997). Statistical inference in the strategy of the researcher (first edition in french entitled L'Inférence statistique dans la démarche du chercheur, 1991). Berne: Peter Lang, in press.

Schield, M. (1998). Using Bayesian strength of belief to teach classical statistics. Proceedings of the Fifth International Conference on Teaching Statistics (pp. 245-251). Singapore: IASE.

Schmidt, F. L. (1996). Statistical significance testing and cumulative knowledge in psychology: Implications for training of researchers. _Psychological Methods_, 1, 115-129.

Spiegelhalter, D. J., Freedman, L. S., & Parmar, M. K. B. (1994). Bayesian approaches to randomized trials (with discussion). _Journal of the Royal Statistical Society A_, 157, 357-416.

Stangl, D. (1998). Classical versus Bayesian paradgim: Can we teach both? Proceedings of the Fifth International Conference on Teaching Statistics (pp. 253-259). Singapore: IASE.

_Statistics in Medicine_ (1993). Vol. 12, special issue on Bayesian inference.

_The Statistician_ (1993). Vol. 42, special issue: Conference on Practical Bayesian Statistics (1992).

At both the ICOTS conference in Singapore and the PME conference in Stellenbosch members of the PME Stochastics working group put details of this project 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. It may include 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:

1. Introduction
1. Historical, philosophical, epistemological and theoretical issues, including statistical thinking
1. Collection and organisation of data
1. Graphs
1. Averages and dispersion
1. Association
1. Model fitting
1. Sampling/ estimation
1. Hypothesis testing
1. Computers
1. Summary of the book
1. 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 it is hopes 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 expressions of interest should be sent 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

The CWS has maintained a site on the world wide web for well over a year. The site http://sun.cwru.edu/isi/ has undergone a few revisions and now contains several sections, including: (i) The committeeís terms of reference; (ii) information about each of the 8 committee members and their e-mail addresses; (iii) reports on the committeeís recent and current activities; and (iv) a collection of "Brief Reports" on relevant publications, meetings, individual and group initiatives, and other professional news items. The site was last updated in June 1998.

A current project, launched following its approval at the open meeting of the CWS in Istanbul (during the ISIís 51ST Session) last August, is a worldwide pilot study on the "relative characterizations of women statisticians". Characterizations will be based on information obtained on four categorical variables: Field of Study, Sector of Statistical Activity, Level of Responsibility, and Income Scale. The project was spearheaded, and is being coordinated, by committee member Lelia Boeri de Cervetto and her two principal collaborators in Buenos Aires. Currently, local teams in about 30 different countries are involved in this project and are at various levels of progress in it. A report on the findings will be presented during the ISIís 52nd Session in Helsinki in August 1999.

The CWS is organizing a sessions at the 52nd Session of the ISI (10-18 August, 1999, in Helsinki, Finland), the CWS will participate in the scientific program with an Invited Papers meeting on "The Role of Women in Statistics in the New Millenium", organized by committee member Denise Lievesley (denise@essex.ac.uk). More information available from Mary Regier, mhr@po.cwru.edu

Laurie Snell has put the Proceedings of the 1996 IASE Round Table Conference " The impact of new technologies on Research" on the Chance web site http://www.dartmouth.edu/~chance) under "Teaching Aids." The direct address is:

http://www.dartmouth.edu/~chance/teaching_aids/IASE/cover.html

To view the book, you will need to have Adobe Reader 3.0 on your computer. If you don't have this, instructions on how to get it are on the cover page of the book.

The Proceeedings of the Conference can be obtained from: CTMA Ltd, 425 Race Course Road, Singapore 218671, Tel: (65) 299 8992, FAX: (65) 299 8983, Email: ctmapl@singnet.com.sg

Brian PHIILIPS <bphillips@swin.edu.au> has started to set up a post conference web site that gives names and emails of those registered as full participants, the Networking Groups which were formed at the conference, some interesting sites, including the site specially constructed for the conference by New Zealand Group, and links to future events such as ISI in Helsinki next year.

Below we include the list of contributed papers and posters at the conference, to complete the program that was included in the previous newsletters.

Session 9. Contributed papers. Convener Shir Ming Shen, hrntssm@hkucc.hku.hk

Session 9.1. Organiser Michael GLENCROSS, glencross@getafix.utr.ac.za

Pierce, R. & Roberts, L. Introductory statistics: Critical evaluation and clear communication.

McLean, A. The forecasting voice: A unified approach to teaching statistics.

Carr, R. Statistics in a day.

Gandhi, B. V. C. A continued education program in statistics and research methodology for science teachers in Puerto Rico.

Miller, T. K. The random variable concept in introductory statistics.

LEE, C. An assessment of the PACE strategy for introductory statistics course.

CALLAERT, H. Stumbling blocks on the road towards statistical literacy.

Smith, P. J. Softwaring insight.

Rayner, J. C. W. & Carolan, A. Assessing robustness of the one-sample t-test.

Maier, H. How to teach solution of problem of linear regression and correlation without calculus of differentiation, a direct approach.

Jin'e, L. From conditional probalility to Bayes' formula.

Fernandez, G. C. J. Partial plots in regression analysis.

Ulmer, M. B. Regression as a foundation for a quantitative elements course for the liberal arts.

CAPILLA, C., & Montesinos, A. A case study of teaching statistics in environmental science studies.

Svensson, E. Teaching the measurement process in biostatistics.

Gastardo, M. T. Teaching applied statistics for the behavioral sciences at the American College of Greece.

Champely, S. & Lemoine, Y. Teaching tabular display: A two-hour lecture for re-presenting some statistical principles

Godden, G. Addressing the nurse's need for personalised tuition in a distance offering of introductory service statistics.

Kwong, K. S. Strategy of playing a board game called RISK.

Guffey, J. Are the extremes the only approaches to statistical education?

Ganesalingam, S., Ganesh, & S, Kumar, K. A statistical look at family welfare data - application of some multivariate techniques.

Bajaj, V. H. On warranty policies of two wheeler vehicles in India.

Perelli D'Argenzio, M. P., Rigatti-Luchini, S., & Moncecchi, G. Some psychopedagogical aspects of introducing basic concepts of statistics at the primary school.

César, M. & Esgalhado, A. Challenging you - Statistics learning in peer interaction.

Naumov, A. New approach to course design of experiments.

Session 9.2. Organiser Susan STARKINGs, starkisa@vax.sbu.ac.uk

Les, J., Maillardet, R., & Cumming, G. Online explanations for learners: The 'play it again SAM' facility.

Jones, A., & Crowe, S. M. IMS - Interactive Multimedia Statistics.

Makhloof, M. A., & Alawar, M. Integrating technology in teaching statistics in higher education in United Arab Emirates.

Ng, A. M., & Nobar, P. M. Use of commercial computer software in higher education instituitions with special reference to statistical software.

McKenzie, J. Jr & Rybolt, W. H. The Cons and pros of using spreadsheet software in an applied statistics course.

Ho, S. Y., Nobar, P. M. & Ng, A. M. Exploitation of possible types of computer software to enhance the learning and teaching qualities.

Selvanathan, E. A., & Selvanathan, S. Teaching statistics to business students: Making it a success.

Chacko, I. Teaching basic statistics to student teachers in a developing country: The story of frustration for teacher and learners.

BEGG, A. Changing school statistics.

Malvicini, S., & Severino, L. Satistics: A grande career in Argentina.

Jili, W., & Yi, L. Statistical in-service training of China under transition of economic system.

Porter, A. Curriculum, pedagogy and reflective practice: Toward a model for improving statistical education.

Chandra, S. Some aspects of teaching methods in India, with special reference to statistics.

LAMPRECHT, T. Utilising technology to develop thinking skills in an introductory statistics course at tertiary level.

Ryan, S. Problem-based learning in introductory statistics.

Blejec, A.Teaching statistics with simulated data.

Jihong, L., & Delin, L. Difficulties and measurements in statistical continuing education in China.

WANG, A. L. Teaching introductory random walk.

Hilton, S. Improving statistical education using a randomized experiment.

Trimarco, K. A. The effect of a graduate learning experience on anxiety, achievement, and expectations in research and statistics.

Ayres, P. & WAY, J. The effectiveness of using a video-recording to reproduce randomly generated sequences in probability research.

Reading, C. Reactions to data: Students' understanding of data interpretation.

Zhang, J., Bertness, C. & Pan, K. Two ways to teach an elementary statistics course: the workshop approach vs. the traditional approach. Which one is the winner?

Wasik, J. L. Factors related to success in a college statistics literacy course.

10 Poster sessions. Convener Peng Yee Lee Singapore, leepy@am.nie.ac.sg. Organiser: Tang Wee Kee tangwk@am.nie.ac.sg

Arora, M. S. & Rogerson, A. Mathematics education into the 21st century.

Voit, K. Comparing the use of graphing calculators and compupers on student achievement in an introductory statistics course.

Yuang-Tswong, L. Statistical curriculum development and evaluation.

Chacko, I. Teaching basic statistics to student teachers in a developing country.

Svensson, E. Teaching biostatistics to clinical research groups.

Svensson, E. Teaching the measurement process in biostatistics.

LAMPRECHT, T. Using CAE in teaching introductory probability to disadvantaged students.

CAPILLA, C., & Montesinos, A. a case study of teaching statistics in environmental science studies.

CAÑIZARES, M. J., & BATANERO, C. A study on the stability of equiprobability bias in 10- 14 year-old children.

MacGillivray, H. Real statistical education for real people

Fitzgerald, S. Instructional methods and statistics achievement at the university level: A meta-analysis.

Cheung, P. H. Statistics in the school curriculum in Hong Kong.

Carvalho, C. & César, M. Peer interaction in an unusual statistical task.

Chaubey, Y. P. Hypothesis testing by examples: A power function approach.

Melgaard, H., Christensen, N., Iwersen, J., & Voss Skotner, L. Use of statistical thinking to improve business processes.

Motoryn, G. R. Teaching economic statistics. The Ukrainian experience.

Pérez Ocón, R. The training of researchers and technicians in the statistical sciences in Spain.

VALLECILLOS, A. Experimental study of the learning of the significance level concept.

8.2. MERGA, XXI Annual Conference of the Mathematics Education Research Group of Australasia, 5–8 July, 1998, Gold Coast, Australia

The following papers were presented at the conference and have been published into: C. Kanes, M. Goos, & E. Warren (Eds.) (1998) _Teaching Mathematics in New Times, Proceedings of the Twenty First Annual Conference of the Mathematics Education Research Group of Australasia Incorporated_. No place of publication: MERGA Inc.

Ayres, P., & WAY, J. Factors influencing predictions about randomly generated sequences (pp. 74–81).

The detailed analysis of four probability experiments conducted with Grade 5 and 6 students revealed trends and patterns in both the group and individual data. These results suggested that certain variables in the experiments, such as particular sequences of outcomes and the confirmation/refutation of student predictions, influenced the students' decisions making strategies. The use of video recordings of deliberately controlled probability experiments offers the potential to systematically explore these influential factors with large sample of students.

Chick, H. L., & WATSON, J. M. Showing and telling: Primary students’ outcomes in data representation and interpretation (pp. 153–160).

Students, in triads in a near-classroom environment were videotaped while they worked in interpreting and representing supplied data. Their reponses were categorised using the SOLO taxonomy. Representation skills varied from copying out some of the data to relating two variables graphically; interpretation skills varied similarly. Moreover, there appeared to be connections of the collaboration, which took place within groups.

MORITZ, J. B. Long odds: Longitudinal development of student understanding of odds (pp. 373–380).

Students' understanding of odds is explored by analysis of response data collected in 1992, 1995 and 1997. Students were asked to interpret a newspaper headline, "North at 7-2". Responses included interpreting the numbers as the score, and in three contexts of expression involving chance, frequency of wins, and betting. Levels of responses were assigned according to the SOLO developmental model, Longitudinal development for individuals was observed, and females tended to interpret the numbers at the score, while males were more likely to respond in the context of chance or betting. Levels of response from Grade 6 and 9 students in 1995 and 1997 were lower than in 1993.

WATSON, J. M. Numeracy benchmarks for years 3 and 5: What about chance and data? (pp. 669– 676).

Since January 1997 there has been much debate within Australia on the type of numeracy benchmarks which should apply to children in Year 4 and 5. As well as debate on the breadth and depth of understanding, there has been difficulty in some area: establishing what children actually do know and can do. Although the data included in this report were not collected to answer questions related to numeracy benchmarking, they may help inform the debate about what children in Years 3 and 5 know and can do in the area of chance and data.

WAY, J. This is a funny game. You can’t say who’s going to win!: Three case studies of children’s probabilistic thinking ( pp. 677–684).

Three case studies of children are used to illustrate the variety of strategies employed by children when asked to make probability judgements in several game contexts. The children's responses ranged from idiosyncratic and intuitive reactions to the deliberate application of proportional reasoning. It was found that certain combinations of variables in the task design stimulated different mathematical thinking.

8.3. PME 22, Stellembosch, July, 1998 (Reported by John TRURAN)

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.

Cobb, P. Analysing the mathematical learning of the classroom community: The case of statistical data analysis.

This paper looked at Year 7 children's interpretation of two data sets which 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.

8.3.3. Research Forum: Learning and teaching data handling, organised by Paul Laridon. Two papers with reactions were presented.

BATANERO, C., GODINO, J. D., & ESTEPA, A. Building the meaning of statistical association through data analysis activities.

Carmen 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.

Ainley, J., Nardi, E., & PRATT, D. 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.

Bezuidenhout, J., Human, P., & Olivier, A. Some misconceptions underlying first-year students' understanding of 'average rate' and of average value.

They 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.

KOIRALA, H. P. Pre-service teachers' conceptions of probability in relation to its history.

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 students' 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.

PRATT, D., & Noss, R. The co-ordination of meanings for randomness some electronic games.

We are aiming to build a computational environmen for exploring stichastic systems, with which we can observe children's meaning-making for ideas such as fairness, randomness and chance, and how these meanings evolve during interaction with the tools in that domain. We discuss the work of two children in order to illustrate how the tools re-shaped their sense of randomness and chance.

TRURAN, J. 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 understanding 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

GLENCROSS, M. Developing a statistics anxiety scale. Michael has modified a mathematics anxiety scale to look at students' views of statistics, and has done preliminary testing.

Magina, S. & Cristina Maranhao, M. C. 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.

AHLGREN, A. Connections in understanding probability 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.

du Plessis, I., & Roux, C. 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.

Flores, P., GODINO, J. D., & BATANERO, C. Contextualising didactical knowledge about stochastics in mathematics teachers training. This related epistemological reflection on stochastics and didactical knowledge.

Hodnik, T. Teaching statistics in primary school in Slovenia. Research project on the introduction of statistics in 10 primary schools over 10 years.

8.4.Section on Statistical Education at the ASA Joint Statistical Meetings in Dallas, Texas, August 9-13, 1998 (Information sent by Joan GARFIELD)

Holcomb, J., & Ruffer, R. Using a term-long project sequence to teach introductory
data analysis.

The authors propose a series of projects for introductory data analysis classes. These assignments combine four current trends in statistics education: Computers, real data, collaborative learning, and writing. Students use statistical and word processing software to complete the analysis and present their results in report form as a team. Concepts are linked by using the same multivariate data set throughout the sequence of assignments.

Weinstein, J., Goldman, R., McKenzie, J. Jr., Sharpe, N., & Sevin, A. The BCASA conference on technology in statistics education.

In March of 1998 the authors organized a conference on technology in statistics education. Participants attended sessions in which expert users showed how the software (or graphing calculator) he or she was demonstrating could be used to solve the same preassigned problem. Demonstrations included computational and conceptual software, graphing calculators, and general statistical software packages. In this paper the authors will present a summary and their impressions of this conference.

Shoultz, G. Lab experiments, Writing data analysis reports, and journal article excerpts: Three quarters of experiences in teaching an elementary statistics class.

Hands-on experiments, writing data analysis reports, and the use of excerpts from journal articles were all introduced over three quarters in an elementary statistics class. This presentation discusses experiences with implementing each of the above methodologies. Laboratory experiments created by the presenter, from the Elementary Statistics Laboratory Workshop (University of South Carolina, 1997), and from Spurrier's "Activity-based statistics" (1996) are presented. Experiences with the use of Zealure Holcomb's "Interpreting basic statistics: A Guide and based on excerpts from journal articles" are discussed.

Rumsey, D. A cooperative teaching approach to introductory statistics.

Many of today's university undergraduate curricula include two seemingly conflicting themes: 1) Increase the quality of teaching to include emphasis on pedagogical elementssuch as active learning, in the undergraduate statistics classroom; and 2) Cope with a decrease in teaching resources. In this paper, a means by which a department of mathematics or statistics can maintain and increase their standards teaching excellence inintroductory statistics while coping with ever-increasing budgetary pressures is proposed. This process involves promoting what we call cooperative teaching, applying the concepts of cooperative learning to a group of instructors.

Buchanan, P. Impact of a "Learning Support System" on performance in an elementary statistics course.

A study was conducted to determine to what extent, if any, student performance in an elementary statistics class could be improved by providing them with a student learning support system': guidance on studying statistics. Two different instructors each taught a large class with about 240 students in each class. Each class met three times per week with the instructor and twice weekly with a TA. There were three TA's per class, two recitation sections per TA, and about 40 students per recitation section. For each TA, one section served as a treatment' group: students who were given the learning support system', and the other section was a control' group, so that there were six sections in each group. TA's were instructed to go over the learning support system with students in the treatment group and to remind (urge) them to follow the suggestions contained in it. Pre-and- Post Surveys were given in the 1st and 12th weeks of the semester to ascertain attitudes and usage of the system. Performance was assessed using a common test in the two classes. The results of the study will be discussed.

Peck, R., & Daly, J. A Studio environment for introductory statistics.

A studio classroom is one designed to support complete integration of the lecture and laboratory components of a course. After experimenting with studio classrooms in chemistry and physics, and with NSF support, Cal Poly designed and built a studio classroom for statistics instruction. This classroom is equiped with computers and work areas for group and individual activities, and has "fancy" audio-visual equipment and computer projection capabilities. This room has enabled instructors to experiment with technology-assisted, and activity based pedagogies that are made possible by this type of non-traditional teaching space. In this paper, we describe the studio environment for statistics instruction at Cal Poly and its impact on how we teach introductory statistics.

Pierce, R. Using the RAQ method in an introductory statistics course.

This talk will describe the author's experience using the RAQ method in an introductory statistics course and a mathematics appreciation course. Based on the classroom practice of Dr. Bansenauer, the RAQ method integrates and extends the ideas of the 4MAT Learning Styles and the Reading to Answer Questions technique. The approach not only improved students' experience in the statistics class, but also made the professor's experience more satisfying.

Collings, P. B., & Allen, R. Effectiveness of practical application. Graphics and frequency distribution graphics in multimedia lectures.

In an ongoing effort to enhance instruction of introductory statistics at Brigham Young University, multimedia resources are being produced for instructors. A study of the instructional benefits comparing two different types of visual examples (including a control) was conducted. Working within the constraints of an existing course of introductory statistics, we administered the four treatments of the 2 x 2 factorial to approximately 900 students in 47 lab sections. eaching assistants were trained to deliver the multimedia based reatments to their lab sections. Student's understanding of the concepts presented was measured by targeted questions on the their mid-term exam that was administered the week following the treatments. This paper will present the results of the experiment and problems encountered in conducting the experiment.

Masters, B. Predicting success in an undergraduate statistics course.

Can successs in an undergraduate statistics course be predicted? A set of demographic variables have been used to attempt to predict success of the students in an undergraduate statistics course. The predictive power of standardized tests, like the ACT and SAT, are investigated in a data set containing information on seven-thousand students. Various other demographic variables are studied in an effort to complete a multivariate model to predict student success.

The South African Statistical Association holds its annual conference in the first week of November every year. See the website:http://www.directories.co.za/sasa

This conference will take plac in Victoria Falls, Zimbabwe (3 hours flight from Cape Town). More information is avilable from http://www.biostat.ucsf.edu/IBC98.

This is a meeting of the International Biometric Society. Cape Town is one of the most beautiful cities in the world. Further information from Tyna LAMPRECHT <ajl4@icon.co.za>

The Symposium 1999 will focus on new trends in theory, applications and software of applied stochastic models and data analysis. Provisional topics are: Human resources; environment; management and administration; production; inventory and logistics; marketing; finance; insurance; planning and control; quality, reliability and safety; information systems and official statistics; sample surveys; research and development; and travel and tourism. Particular attention will be paid to the application of new technologies in business and industry such as data mining, data warehousing, symbolic learning, neural networks, genetic and fuzzy algorithms, computer graphics, knowledge-based systems, and decision support systems

Chairs: Professor Jacques Janssen, CADEPS-ULB (Solvay Business School), Av. F. Roosevelt, 50, BP 194/7,B-1050 Brussels, Belgium, ,janssen@ulb.ac.be; Professor Helena Bacelar-NicolauProfessor Fernando Costa Nicolau, Lab. EstatÌstica e An·lise de Dados Faculdade de Psicologia e C. Educa_ao Faculdade de Ciencias e Tecnologia, Lisbon, Portugal, hbacelar@fc.ul.pt

web page: www.di.fct.unl.pt/asmda99

The International Study Group for Research on Learning Probability and Statistics is offering the first in a series of International Research Forums, to be held in Israel in July 1999. Sponsored by the Weizmann

Institute of Science and the University of Minnesota, this forum offers an opportunity for a small number of researchers from around the world to meet for a few days to share their work, discuss important issues, and initiate collaborative projects. The topic of the first forum will be Statistical Reasoning, Thinking and Literacy. One outcome of the forum will be the publication of monograph summarizing the work presented, discussions conducted, and issues emerging from this gathering.

Background: Research into statistical education has been growing and receiving increased attention in the past twenty years, which is illustrated by the large number of the papers presented at international conferences, articles published in statistics and educational journals, and even entire books devoted to a particular aspect of statistical education.

The five International Conferences on Teaching Statistics (ICOTS), held every four years, beginning in 1982, helped to progressively link an informal research network of people interested in carrying out research on the teaching and learning statistics at all age levels. It was at ICOTS I in 1982 that the International Study Group for Research on Learning Probability and Statistics was formed.

The goal of the new study group was to encourage research in statistical education; promote the exchange of information between members; develop instruments by which concepts about probability and statistics could be assessed; and in general, improve the teaching and interpretation of probability and statistics by dissemination of research findings.

Currently, the chair of the study group (Carmen Batanero, University of Granada, Spain) produces an electronic newsletter every three months to serve as a link between members and to provide information useful to research. It contains summaries of research papers written by members, information about members, summaries of recent dissertations, and other publications of interest, information concerning recent and forthcoming conferences, and Internet resources of interest. There are currently over 250 members representing to 42 different countries.

The only times members have been able to meet and share their work has been at the ICOTS conferences, every four years. However, in 1996, the IASE decided to focus a roundtable conference on research, continuing the previous tradition by the ISI Education Commitee, and 24 members of the international research community had an opportunity to meet, share and discuss their work, and focus on the important topic of research on the role of technology in teaching and learning statistics.

This meeting formed new collaborations, produced a high-quality, edited volume of papers (which is now on the web), and helped identify important issues and needed areas of research. This kind of productivity is only possible when small numbers of people meet together for several days to discuss research details in depth. Unfortunately, the ICOTS meetings do not allow this type of intense and in-depth discussion, allowing only for formal presentations of papers followed by general audience discussion.

At the most recent meeting of ICOTS, held in June 1998 in Singapore, several papers focused on the related topics of Statistical Reasoning, Statistical Thinking, and Statistical Literacy. There seemed to be an overlap among the topics, yet important distinctions between them, none of which have as yet been addressed. It became apparent that when statistics educators or researchers talk about or assess statistical reasoning, thinking, or literacy, they may all be using different definitions and understandings of these cognitive processes. The similarities and differences among these processes are important to consider when formulating learning goals for students, designing instructional activities, and evaluating learning by using appropriate assessment instruments. In addition, in recent years, we have seen an increasing research emphasis on the socially and culturally situated nature of mathematical (statistical) activity. It suggests the importance of participation in the statistical practices established by the classroom community, in scaffolding the statistical reasoning processes of the individual student. A small, focused conference consisting of researchers interested in these topics appears to be an important next step in clarifying the issues, connecting researchers and their studies, and generating some common definitions, goals, and assessment procedures. Some of the questions to be discussed in the forum are:

What constitutes Statistical Reasoning, Thinking and Literacy (SRTL)?

What are the different definitions and understandings of SRTL?

How are these three types of processing statistical information similar and different from each other?

What are the contributions of research on SRTL?

What models have been suggested and explored?

What are the developmental aspects of SRTL?

What do we know about the development of SRTL in different age/grade levels?

What do we know about SRTL of professional statisticians

Can we use this information for educational purposes?

What methodologies are appropriate for assessing SRTL?

What types of research studies are needed to help us better understand these ways of processing information and to help promote them in educational settings?

What are the implications of research into SRTL on learning goals, curriculum design, and assessment?

What do we still need to know?

Organization

Dani BEN-ZVI (Weizmann Institute of Science, Israel) and Joan GARFIELD (University of Minnesota, USA) are co-chairs of the International Research Forum, assisted by Carmen BATANERO (University of Granada, Spain; Chair of the International Study Group for Research on Learning Probability and Statistics) and an advisory committee, they will organize the program, invite participants, and edit the research monograph.

The format of the Research Forum is for 12-15 participants to meet together for three two-hour sessions each day for three days, where most of the sessions will focus on the viewing and discussing of videotapes of students, illustrating statistical reasoning or thinking processes. Background papers by participants and others will be collected and distributed prior to the forum, including current theories of

statistical thinking, reasoning and literacy; details on recent research on these topics, and descriptive information on the context of the videos to be viewed.

All sessions will be held at Kibbutz Be'eri, which is in the southern part of Israel. Participants will arrive on Sunday, July 18. On that day there will be an orientation to the Kibbutz and a welcome reception.

Meetings will take place on Monday, Tuesday and Wednesday. On Thursday, there will be a visit and tour of the Weizmann Institute of Science in Rehovot, followed by a reception there. On Friday, participants may leave the Kibbutz to tour or travel to PME. Participants will need to pay for their own travel to the Research Forum as well as their housing and meals at Kibbutz Be'eri. The estimated cost to participants for housing and meals at the Kibbutz will be about US$60 per day.

The Research Forum organizers invite anyone interested in participating in this forum to contact them as soon as possible. Initial expressions of interest are invited as well as brief descriptions of relevant work to be shared at the forum.

Please contact:

Dani BEN-ZVI, at ntdben@wiccmail.weizmann.ac.il

Joan GARFIELD, at jbg@tc.umn.edu

In addition to attending the PME Stochastics Project Group, and discussion group on Data Handling, researchers are invited to submit proposals to present a personal presentation at the conference, according to the following tentative deadlines:

Proposals of research forum presentations must be in the hands of the Conference Chair by 15 November 1998.

Proposals of research report presentations must be in the hands of the Conference Chair by 15 January 1999.

Proposals for short oral communications, posters, working groups and discussion group presentations must be in the hands of the Conference Chair by 1 March 1999.

More information from http://edu.technion.ac.il/conference/pme23

The 9th International Conference on the Teaching of Mathematical Modelling and Applications, ICTMA 9, will be held in Lisbon, Portugal, 30 July - 3 August 1999. The aim of this conference is to provide a forum for the presenttion and exchange of information, experiences, opinions and ideas relating to the teaching, learning and assessment of mathematical modelling, mathematical models and applications of mathematics. People engaged in research or practice in these topics at secondary and higher levels of education are invited to participate, present papers or conduct workshops.

For further information, please consult the Chair of the Programme Committee, Professor João Filipe Matos, Departamento de Educao, Faculdade de Ciencias, Universidade de Lisboa, Portugal (joao.matos@fc.ul.pt),

Any person actually participating in the Session may present one contributed paper in the Session. Contributed Paper Meetings will be arranged by the Local Programme Committee. To assist in this, authors are requested to classify their papers according to the indicative list of topics below.

1. Teaching basic statistics
1. Educating statistical majors
1. Statistical education
1. Teaching statistics for non-statisticians
1. Statistical literacy

Application for the Submission of a Contributed Paper is to be returned to CONGREX, the official congress office of the 52nd ISI Session, by January 10, 1999. Detailed instructions on how to prepare a manuscript will then be sent to each author. Instructions to authors will also be published on the homepage of the Session at http://www.stat.fi/isi99, in December, 1998.

The Ninth International Congress on Mathematical Education, ICME-9, is going to be held 31 July - 7 August 2000, at the Chiba Convention Centre, Makuhari, at the Tokyo Bay, near Narita Airport. Further information will be available in forthcoming issues of this Bulletin. Whole Japanese community of Mathematics education are looking forward to meeting you in Japan in the year 2000 at the ICME 9. Besides research and scientific activities we are planning social and cultural activities which will give you a better understanding of Japan.

Chairman International Program Commitee: Prof. Hiroshi Fujita

President National Organising Commitee: Prof. Hiroshi Fujita

Chairman: Prof. Yoshishige Sugiyama

Secretary: Prof. Toshio Sawada

http://www.ma.kagu.sut.ac.jp/˜ICME-9/index.html

Scientific Committee: Carmen BATANERO, Spain, Chair; Theodore CHADJIPADELIS, Greece; Joan B GARFIELD, USA; Anne HAWKINS, UK; Yuki Miura, Japan; David Ospina, Colombia; Brian PHILLIPS, Australia

Local Organising Committee: Yuki Miura, Surugadai University, Chair; Kensey Araya, Fukushima University; Masakatsu Murakami, The Institute of Statistical Mathematics. Toshiro Shimada, Professor Emeritus, Meiji University; Mikio Eda, Meiji University, Secretary

Since 1968, a number of Round Table Conferences have been organised on topics in statistics education. These round table conferences were initially organized by the Education Committee of the International Statistical Institute and, since 1988, by IASE (the International Association for Statistical Education). It has been usual for these conferences to be held as satellite meetings to each meeting of ICME (International Congress on Mathematics Education), which is held every four years. 2000 will be the year of the IASE Round Table in Japan on the topic: Training Researchers in the Use of Statistics. This meeting will be held at the Meiji University which is located in the central area of Tokyo, before or after (ICME 9) which will held in Japan.

The goal of the Round Table Conferences is to bring together a small number of experts, representing as many different countries as possible, to provide opportunities for developing better mutual understanding of common problems, and for making recommendations concerning the topic area under discussion. A main outcome is the publication of a book containing conference papers and summaries of discussions. The following are possible topics and issues to be discussed at the IASE 2000 Round Table Conference: