Special group 5:

Traditional programming in the Age of CAS

ICTMT 5, Klagenfurt, 6-9 August 2001

(Schedule, tentative as of 8.6.2001)

Chair:Karl Fuchs

Tuesday 10:30 - 11:15 Chair: K. Fuchs, E. Vasarhelyi

Programming in the Age of CAS and the Algorithm as Fundamental idea in mathematics education

Karl Josef Fuchs* (Austria, karl.fuchs@sbg.ac.at), Christian Kraler (Austria, christian.kraler@uibk.ac.at)

Tuesday 16:15 - 17:00 Chair: K. Fuchs

Programming Principles for Mathematics/Engineering Students

Judith Hector (USA, judy.hector@wscc.cc.tn.us)

Tuesday 17:00 - 17:45 Chair: K. Fuchs

The Digraph-CAS-Environment and Misconceptions around Matrixoperations

Wolfgang Lindner (Germany, LindnerW@t-online.de)

Wednesday 10:30 - 11:15 Chair: K. Fuchs

How can we combine the CAS with authoring system tools to create a flexible learning environment

Mihály Klincsik, Hámori Ildikó Perjésiné, Csaba Sárvári*(Hungary, sarvari@witch.pmmf.hu)

Thursday 10:30 - 11:15 Chair: Ch. Kraler

Problem - Analysis - Encoding - Testing = About Program- and Data-Structures

Karl Josef Fuchs, Eva Vasarhelyi *(Austria/Hungary, karl.fuchs@sbg.ac.at, eva.vasarhelyi@sbg.ac.at)

Thursday 16:15 - 17:00 Chair: K. Fuchs

Taylor Series and Finding Zeros with DERIVE and MATHEMATICA

Alfred Dominik (Austria, webmaster@borg-akad.salzburg.at)

Abstracts:

Alfred Dominik, Austria:

Taylor Series and Finding Zeros with DERIVE and MATHEMATICA

The meaningful use of the two Computer - Algebra - Sytems MATHEMATICA and DERIVE in the Calculus Curriculum for 16 to 18 year old students in Austrian Grammar Schools will be demonstrated with the help of Taylor - Polynomials, Bisection- and Newton's method. Specially prepared functions help the students to get better insights into basic ideas of Calculus such as approximation and limit. Additionally the influence of inital values to iteration - processes will be discussed.

Karl Josef Fuchs*, Christian Kraler, Austria:

Programming in the Age of CAS and the Algorithm as Fundamental idea in mathematics education

The authors will concentrate on the basic question of the Special Group by taking How much Programming (knowledge / skills) must a Mathematics - teacher have in the Age of CAS as their theme. Reasons for the motivation and necessity of this question for the process of teaching mathematics with new technology will be given. Different accents in defining the term of Programming will show that fundamental ideas of mathematics such as algorithm, function or modelling are essential parts of these terms. Further discussions will mainly focus on the idea of the algorithm and its importance as a connecting piece between mathematics and computerscience.

Judith Hector, USA:

Programming Principles for Mathematics/Engineering Students

The author has taught computer programming since 1970. She has developed an introductory programming course for mathematics/engineering students. Students develop structured programs on a computer using FORTRAN and the same programs for a TI-92 calculator. Students learn to program certainnumerical techniques such as Newton's method of root finding and Euler'smethods of solving a differential equation. Such techniques are available preprogrammed as black boxes in CAS.

Wolfgang Lindner, Germany:

The Digraph-CAS-Environment and Misconceptions around Matrixoperations

A longtime research at the University Duisburg, Germany, studies the impact of CAS on the belief structur of high school students and on the development of conceptions and skills of Elementary Linear Algebra with special consideration of animated visualisations and algorithmic semiautomations. The design of a Digraph-CAS-Environment (realized in MuPAD) is shown, which represents e.g. airline connections in an informal-visual way. The usual matrixoperations on the quadratic adjacency matrices are introduced and programmed to enhance understanding. Afterwards the extracted concepts and intuitions are transfered to rectangular matrices and the effect of this singular local perturbation of the individual knowlege net is studied. We compare the handling of misconceptions by the students with and without CAS.

Mihály Klincsik, Hámori Ildikó Perjésiné, Csaba Sárvári*, Hungary:

How can we combine the CAS with authoring system tools to create a flexible learning environment

Using Maple CAS as a powerful mathematical tool and the Toolbook Instructor object oriented authoring system we can create new learning environments.We illustrate with case studies the step by step learning methods within an example and from the easier examples towards the complicated ones. With these new methods the user can be focus, concentrate on the local and the global know-ledges together. Our applications particularly applicable via Internet and local network, too.

Karl Josef Fuchs, Eva Vasarhelyi*, Austria/Hungary:

Problem - Analysis - Encoding - Testing = About Program- and Data-Structures

The two authors will show examples for the use of Hand-Held-CAS-Technology in computerscience. From the educational point of view the different problems of interpretation, stepwise refining and modification concentrate on the flexible, effective use of basic comments of an imperative programming tool in many different ways.