ICTMT 5 Klagenfurt - 2001, August 6-9

Posters

Christine Bescherer, Germany:

Internet-Use in Mathematics Education

Virtual activities enrich traditional seminars in Mathematics Education at the University of Education Ludwigsburg (Pädagogische Hochschule) in the German state of Baden-Württemberg. Different types of virtual modules are grouped around 'real lectures' given by different students (nearly) each week. Examples for these modules are communication with teacher and fellow students, co-operation within the seminar group and with the group of another university, HTML-slides for presenting the lectures, work on web-based texts like the NCTM-Standards 2000 (National Council of Teachers of Mathematics, http://standards.nctm.org/). In between the face-to-face meetings the students collaborate in small groups to solve specific virtual tasks. All of these tasks require the use of the Internet either as an resource of information, supply of applications or mean to collaborate via groupware BSCW. (Basic Support for Co-operative Work http://bscw.gmd.de/). The poster shows some examples of the last two year's work.

Manfred Borovcnik, Austria:

Some examples of teaching statistics with EXCEL as a tool

Probability and statistics may be enhanced by the use of simulation. Didactic software for that purpose lacks often in imagination, statistic software is frequently too complex. Easily accessible, also to young students are spreadsheet softwares like EXCEL. With that, a highly flexible tool can thus be integrated in the teaching of probability. This is illustrated by a description of a course and some working results of 13 olds.

Douglas Butler, U.K.:

Why are spreadsheets so unfriendly?

The words MICROSOFT and EDUCATION usually appear together on exhibition stands. So why is it that their spreadsheet excel is so unfriendly to school children? Excel is used in schools extensively throughout the world, and yet its authors appear to give little heed to the needs of the youngsters who are using it. This presentation will list some of the features that give the spreadsheet such a poor feel in the classroom and invite the conference to make appropriate representations to Microsoft.

Jenny Gage, U.K.:

Millennium Mathematics Project

The Millennium Mathematics Project is a long-term initiative, based in Cambridge, UK, which aims to improve the understanding and enjoyment of mathematics among school students and the general public. Projects include:

• NRICH, the international online maths club for children from 5 to 18

• Plus, a complementary international online magazine for older students and the general public

• MOTIVATE, a videoconferencing project for school students in the UK and world-wide

Iavor Hristov, Bulgaria:

Model of deformations of fluid particles due to electric field

A mathematical model of finite deformations of compound drop containing another drop due to electric field are obtained. The fluids are homogenous, incompressible and Newtonian. The cases of concentric and eccentric particles are investigated together.

Dezider Ivanec, Karolina Starin Ton?ka ?pegel-Razbornik, Alenka Cvetkovi?, and Julijana Pal?i?, Slovenia:

Calculating areas (using integrals) with TI-92

Use of technology can improve the understanding of some elementary problems in mathematics. Our poster presents how to find the area of the region using TI 92. We researched how using technology improves the visualisation of the students and therefor the understanding the connection between the area of the region and the definite integral. The poster also contains several practical examples.

Yasuto Kajiwara, Japan:

Serving hints for the students at the on-line exercise

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In the WWW-based on-line exercise system for learning the relation between the symbolic expressions and the graphs of quadratic functions, we are developing an automatic hint service for the students. To study the optimum timing for the hint, we attach the monitor function to the system for the teacher or the TA to observe the students condition. By monitoring the progress of the students, the teacher is able to decide if a hint should be given to the student or not. If the teacher selects a hint among the hint-list and sends one of them to the student, it appears on her page at the next action. The teacher is allowed also to select the method how the hint is displayed on the student's display; a new hint-window automatically appears or a hint button for the hint window is added to the page. The timing is recorded to a file on the server, and will be used to set the timing of automatic hint service.

Hermann Kautschitsch and Gert Kadunz, Austria:

THALES - a DGS in classroom use for finding conjectures and strategies to prove elementary geometric theorems

The DGS THALES was used in a classroom experiment with 15 years olds, especially to see whether students may independently of teaching find conjectures about elementary geometric theorems. Results are quite promising and support the thesis of advantages of experimental learning. Students could find invariants in the posed problems and were quite successful to find or invent strategies to prove the underlying theorems.

Liisa Leinonen, Finland:

About Probability Concept and Pupils' Understanding of Probability

To interpret the probability there are several views: axiomatic, classical, statistical and subjective. We can say that the probability forms the theoretical base of statistics. Conclusions from sample data about populations, must necessarily be subject to some uncertainty. We can think of probability as a measure of uncertainty. This is one of the main reasons why probability is so important in teaching and learning mathematics and statistics. In Finland we have none or just a little, and very incomplete, research of the probability concept. Any systematic research has not been done in our schools. In many (foreign) studies pupils' misunderstandings and inconsistencies about probability and difficulties to apply the probability in the problematical situations have been discovered. In my poster I describe my ongoing research about the probability concept and its empirical realisation in the secondary school level in Northern Finland. In the design of my research I have used previous

Brigitte Leneke, Germany:

Graphics calculators for younger pupils

There are different positions about learning mathematics by using graphics calculators in math lessons of younger pupils (aged 10 -12 years). The poster wants to show some ideas about the support of this calculators in math lessons. So they can help in solving problems by using proportional relations, in working with data and in the geometry to draw, change and move of figures. To use graphic s calculators for this problems means at the same time to work with co-ordinates, to use the different possibilities in representation of relations (equation, table, graph) and to work heuristic experimentally.

Marie Thérèse Loeman, Belgium:

How to learn from and make history in mathematics ?

After three years of participation in the EEP Comenius action 1 "The history of some aspects of mathematics like..." a design was composed, taking pictures out of the total project website :

http://mathsforeurope.digibel.org
It reflects different aspects of history of mathematics which drew the attention of all involved teachers and students.
The renaissance-looking picture of the Flemish mathematician Simon Stevin appears next to the drawing illustrating a man wondering why the apples are falling down. Indeed the latter is referring to the inspiration the great mathematician Isaac Newton got out of this common experience. In the centre one can see the man inside a circle and a square, based on the rules of proportion explained by Vitruvius, and designed by Leonardo Da Vinci. The magic square and the dies are inserted because of the intrigating "story of numbers" which is to be found in all times and in all civilisations. In figure in the left bottom corner demonstrates the 'geometrical' approach of the irrational numbers given by Socrates and explained in Plato's Dialogues "Menon". The spiral in the triangle wants to draw the attention to the golden ratio, not only known and applied in many ancient constructions but also to be ever found in art and nature. The fractals, 'discovered' and 'more explored with the help of IT" during the past century show that this is one of the many fields wherein a lot of interesting mathematical properties are waiting to be revealed by the next generations of inspired mathematicians. This composition, made out of several works of our project, also wants to point out to what is useful to become a good mathematician : learning from the thinking patters of mathematicians from the past, using all possible and available means and tools, looking around for (to be open for) mathematical properties in numbers, games, constructions, nature ...

Erich Neuwirth, Austria:

Visualising recursion dependency diagrams and algebraic notation

Recursion usually is perceived as rather complex and theoretical. On the other hand, Pascal's triangle and Galton's board are visual tools illustrating recursive concepts in a very accessible way. Building on these ideas we will show that visual representations can be important conceptual tools for gaining insight into properties of recursive structures.

Günther Ossimitz, Austria:

Systems Thinking, System Dynamics and Math Teaching

Can the use of system dynamics modelling and simulation technology in math classes trigger systems thinking abilities of the students? Empirical investigations by Günther Ossimitz, University of Klagenfurt, indicate "YES". The poster will give an overview about the fascinating possibilities of studying practical systems and thus achieving systemic thinking abilities by technology-oriented math teaching.

Harry Silfverberg, Finland:

Using Voronoi diagrams produced by DGS as a tool in an educational study

The Voronoi diagram of a collection of points is a partition of space into cells, each of which consists of the points closer to one particular point than to any others. According to the prototype theoretical explanation students at the lowest van Hiele levels tend to classify geometrical figures on the basis of extent of the similarity of the figure and the visual prototypes. The poster will graphically show how well Voronoi diagrams and partitions based on the different selection of prototypes fit to the empirical data gathered in Silfverberg's research (1999) about the ways how students at the lowest van Hiele levels classified a given collection of triangles into acute, right, obtuse, equilateral and isosceles triangles.

Elena Varbanova, Bulgaria:

Tradition and Innovation in Teaching and Learning Double Integrals

The sense of novelty tells the teachers not to hold back from using technology in the Teaching-Learning-Assessing (TLA) process. Their sense of responsibility tells them that it is a matter of great concern not to damage and replace a traditionally successful methodology by a pseudo-methodology. This paper represents a DERIVE-supported approach to teaching and learning double integrals. It shows a way in which tradition can go on through technology. The focus is on finding an appropriate combination of tradition and innovation, i.e. of traditional TLA process and the process of doing and learning mathematics in a CAS environment. The leading motto is: "Knowledge is Power, Technology is a powerful Tool".