Working group 4:
Probability simulators and data analysis programmes

ICTMT 5, Klagenfurt, 6-9 August 2001

(Schedule, tentative as of 28/06/2001)

Chair: Manfred Borovcnik

Tuesday 10:30 - 11:15 Chair: Manfred Borovcnik

A sample of ideas in teaching statistics

Piet van Blokland (Netherlands, pjvanblokland@chello.nl)

Tuesday 16:15 - 17:00 Chair: Manfred Borovcnik

Simulation and Modelling with Lisp-Stat: A Flexible Software for Teaching Statistics

Joachim Engel*, Marcus Otto (Germany, Engel_Joachim@ph-ludwigsburg.de)

Tuesday 17:00 - 17:45 Chair: Manfred Borovcnik

Design and Use of a Computer Language for Teaching Mathematics - Some Examples from Statistics

Marcus Otto*, Joachim Engel (Germany, Otto_Marcus@ph-ludwigsburg.de)

Wednesday 10:30 - 11:15 Chair: Manfred Borovcnik

Let the spreadsheet throw the dice - Spreadsheets as Monte Carlo simulation engines

Erich Neuwirth (Austria, erich.neuwirth@univie.ac.at)

Thursday 9:30 - 10:15 Chair: Manfred Borovcnik

Improving statistical reasoning: a computer program for high-school students

Peter Sedlmeier (Germany, peter.sedlmeier@phil.tu-chemnitz.de)

Thursday 10:30 - 11:15 Chair: Manfred Borovcnik

Classical and Bayes-statistics in the school supported by computer

Oedoen Vancso (Hungary, vancso@ludens.elte.hu)

Thursday 16:15 - 17:00 Chair: Manfred Borovcnik

Virtual Experiments and Probability

Giora Mann*, Nurit Zehavi (Israel, giorama@macam.ac.il)

Abstracts:

Joachim Engel*, Marcus Otto, Germany:

Simulation and Modelling with Lisp-Stat: A Flexible Software for Teaching Statistics

We illustrate how a simulation based use of computers supports conceptual learning in statistics. We focus on three areas of application: 1. simulation via bootstrap 2. modelling functional relationships between two variables that are corrupted by noise 3. demonstration of the central limit theorem. The basis is the programming environment Lisp-Stat.

Giora Mann*, Nurit Zehavi, Israel:

Virtual Experiments and Probability

A good model in probability must agree with observations. It is not practical to perform the real experiment many times. In a CAS environment we can perform a virtual experiment many times with relative ease. This changes modelling in probability to be twofold - programming a virtual experiment which controls the traditional modelling.

Erich Neuwirth, Austria:

Let the spreadsheet throw the dice - Spreadsheets as Monte Carlo simulation engines

Monte Carlo simulation (using computer generated pseudo random numbers) is an extremely helpful tool for illustrating concepts in probability and statistics. It is surprisingly easy (and surprisingly unknown) that this kind of simulation can easily be done with spreadsheet programs. We will show some simple examples from probability and some moderately advanced examples from inductive statistics (testing and estimation) to demonstrate how simulation can help "getting the feeling" for randomness convergence of frequencies to probabilities.

Marcus Otto*, Joachim Engel, Germany:

Design and Use of a Computer Language for Teaching Mathematics - Some Examples from Statistics

During the last years, we designed a computer language and used it in mathematics education. Our aim was to establish a tool for learning and doing mathematics. The language can be shaped to meet the needs of a course. Besides using such a language for algorithmic purposes, one can create its own mathematical structures based on their features, relations and operations. Students can use this to investigate the concepts presented in a course. Taking concepts from probability and statistics as examples, we illustrate how to incorporate our language into mathematical teaching.

Peter Sedlmeier, Germany:

Improving statistical reasoning: a computer program for high-school students

New results in research on judgment under uncertainty show a way of how to improve the teaching of statistical reasoning (Sedlmeier, 1999). The implications of this research are that (i) successful learning needs doing, and (ii) that the format in which information is represented plays a decisive role. Statistical problems are, for instance, solved much better if the relevant pieces of information are presented as frequencies rather than probabilities. It also helps a lot if random processes can be observed rather than only read about. A computer program is presented that incorporates these implications from psychological research (Sedlmeier & Köhlers, 2001). The software accompanies an elementary text book on probability theory to be used in high school.

Piet van Blokland, Netherlands:

A sample of ideas in teaching statistics

Probability and statistics in secondary school should be presented in such a way that it demonstrates the importance of this subjects in society. Some realistic simulations will be shown. Polls are an often used tool in modern society to investigate opinions. In this lecture a huge dataset of 50000 students will be presented The effect of sampling will be shown. In order for the students to grasp the idea of central limit theorem, technology will help. Pictures which can be manipulated by students will help students to understand better the ideas behind hypothesis testing.

Ödön Vancso, Hungary:

Classical and Bayes-statistics in the school supported by computer

In this presentation I would like to show such software which help to understand by visualisation, representation or counting some main ideas of the classical statistics for example: normal distribution and Laplace-condition, confidence-interval, testing hypothesis. On the other side I talk about working (following one idea of Dieter Wickmann) on a program which also can be used in the school and give a possibility to teach Bayes-statistics earlier than the Universities and Highschools. This software have been developed by mathematics and informatics students of Eötvös Lóránd University of Budapest leading by Éva Vásárhelyi, László Szabadi and me.