erstellt von *** nuss ***, 5. 1. 2002 - dont edit! ============================================================= Protokollierung startete am 8. 1. 2002, 23:30 Uhr ============================================================== Peter Nussbaumer , / Test und Rückmeldung Vortrag Lieber Herr Kutzler, wieder melde ich mich über unser Submission Form, um zu testen, wie es funktioniert - diesmal mit dem IE 5.5. Ich habe alle von Ihnen im heutigen mail vorgeschlagenen Änderungen durchgeführt, mit Ausnahme der Verschiebung des Menüpunktes \"Social Program\". Diese Änderung ist mit besonders viel Arbeit verbunden, und das würde ich gerne erst beim letzten Schliff unserer Homepage mitmachen. Was uns noch fehlt, ist die Anmeldung zur Konferenz. Bis Ende der Woche erhalte ich vom Verkehrsbüro alle relevanten Daten und URLs. Es ist geplant, dass wir am Montag mit der Schülergruppe das Anmeldeformular und die Anmeldeformalitäten ins Netz stellen, sodass dann bis etwa Mittwoch nächster Woche alle Fehler bereinigt sein könnten. Wenn in der englischen Version alles OK ist, dann würde ich am Donnerstag die deutsche Version ins Netz stellen. Liebe Grüße, Peter Nussbaumer ====>> Tuesday 08th of January 2002 11:34:58 PM <<==== --------------------------------------------------------------------------- Peter Nussbaumer , / Netscape / deutsches Eingabeformular, Test Vortrag Hallo Herr Kutzler, nur so zum Testen. (;^) Liebe Grüße, Peter Nussbaumer ====>> Tuesday 08. January 2002 11:37:01 PM <<==== --------------------------------------------------------------------------- Peter Nussbaumer , / peter.nussbaumer@pgv.at Testmail Testmail Testmail Testmail Testmail Testmail !!! Vortrag acdca Lieber Herr Kutzler, habe die Ergänzung des Submisson Form durchgeführt Liebe Grüße, Peter Nussbaumer ====>> Thursday 10th of January 2002 12:18:01 AM <<==== --------------------------------------------------------------------------- Mr Terence Etchells Liverpool John Moores University Byrom Street, L3 3AF Liverpool / UK t.a.etchells@livjm.ac.uk Z transforms, Derive 5 and High Order Linear Recurrence (Difference) Equations Vortrag derive With the advent of the new programming constructs in Derive 5, this lecture describes an example of how Derive’s mathematical capabilities can be significantly extended using these constructs. In particular we show how the string function in Derive 5.04+ can be used to determine the structure of mathematical expressions entered into user defined functions. The Z transform and its inverse are not internal functions in Derive, but we describe Derive 5 functions that will produce both Z and inverse Z transforms for certain classes of functions. We define and program known results for calculating Z transforms and apply complex analysis to automate the calculation of the inverse Z transform. We conclude by applying the Z and inverse Z transform functions to the solution of high order linear recurrence (difference) equations, significantly extending Derive’s current ability to solve only first and second linear difference equations. We conclude by highlighting a few improvements that would greatly help the Derive programmer construct, edit and debug their programmes. ====>> Thursday 10th of January 2002 10:33:20 AM <<==== --------------------------------------------------------------------------- Peter Nussbaumer , / deutsche Version im Netz, englische Version korrigiert Vortrag acdca Lieber Herr Kutzler, ich habe heute die deutsche Version unserer Homepage ins Netz gestellt und dabei Fehler in der englischen Version ausgebessert. Morgen sollte ich die Daten vom Verkehrsbüro erhalten, sodass bis nächsten Montag der letzte Punkt, registration form, erstellt werden könnte. Liebe Grüße, Peter Nussbaumer ====>> Thursday 10. January 2002 09:23:29 PM <<==== --------------------------------------------------------------------------- Peter Nussbaumer BG und BRG Tulln Donaulände 72, 3430 Tulln / Österreich peter.nussbaumer@pgv.at Testmeldung sonstiges derive beide Bitte Herr Kutzler, kontrollieren Sie, ob alle Datenfelder für Sie in der eMail vorkommen Danke, Peter Nussbaumer ====>> Thursday 10. January 2002 10:33:55 PM <<==== --------------------------------------------------------------------------- Peter Nussbaumer Gym Tulln Donaulände 72, 3430 Tulln / Austria peter.nussbaumer@pgv.at Testmeldung - englischsprachiges Formular Vortrag acdca Habe alle vorgeschlagenen Änderungen durchgeführt. Danke für die Fehlerkorrektur! Liebe Grüße, Peter Nussbaumer ====>> Thursday 10th of January 2002 10:35:22 PM <<==== --------------------------------------------------------------------------- Jindal ASHA JINDAL Reader, DCETA, NCERT Sri Aurobindo Marg, New Delhi / India asha_jindal@hotmail.com Using IT Tools For Interactive Exploratory Learning Vortrag acdca Abstract An application computer program can be used by a subject teacher for creating need based interactive learning environment in the classroom. Various concepts can be explained in graphical mode in addition to numerical mode. Variables can be changed just by click of mouse and in turn cause effect relationship can be investigated on computer monitor. The paper illustrates how a school teacher, having no knowledge of high level programming language can simulate situations related to curricular subject in a classroom with a spreadsheet program which will make learning richer, flexible, interactive, exploratory and hence more meaningful. The illustrations are exemplar and will serve the purpose of follow up activities/ exercises what a student has already learnt in traditional classroom. ====>> Friday 11th of January 2002 10:08:30 AM <<==== --------------------------------------------------------------------------- Dr. ASHA JINDAL Reader, DCETA, NCERT Sri Aurobindo Marg, New Delhi / India asha_jindal@hotmail.com Using IT Tools For Interactive Exploratory Learning Vortrag acdca Abstract: An application computer program can be used by a subject teacher for creating need based interactive learning environment in the classroom. Various concepts can be explained in graphical mode in addition to numerical mode. Variables can be changed just by click of mouse and in turn cause effect relationship can be investigated on computer monitor. The paper illustrates how a school teacher, having no knowledge of high level programming language can simulate situations related to curricular subject in a classroom with a spreadsheet program which will make learning richer, flexible, interactive, exploratory and hence more meaningful. The illustrations are exemplar and will serve the purpose of follow up activities/ exercises what a student has already learnt in traditional classroom. ====>> Friday 11th of January 2002 10:09:24 AM <<==== --------------------------------------------------------------------------- , / Vortrag acdca deutsch ====>> Friday 11. January 2002 02:36:12 PM <<==== --------------------------------------------------------------------------- , / Vortrag acdca deutsch ====>> Friday 11. January 2002 02:36:27 PM <<==== --------------------------------------------------------------------------- , / Vortrag acdca deutsch ====>> Friday 11. January 2002 02:36:32 PM <<==== --------------------------------------------------------------------------- Hans-Jürgen Elschenbroich Studienseminar S II Neuss Mainstr. 95, D-41469 Neuss / Deutschland elschenbroich@t-online.de Discovering Functions in a dynamic way Vortrag acdca beide Functions are an important theme in secondary school math teaching. They are tought as a part of Algebra, new technology is used by plotting their graphs. In this way students often get only a static view of functions and their parameters. With Dynamic Geometry Software (like Cabri II, Geometers Sketchpad, Euklid-Dynageo) it is possible to obtain a dynamic approach. Students can change the independent variable x and study what happens with y and how the graph develops as a locus of P(x/y). They can change the parameters a, b, c and study what happens with the graph of the function. It is easy to change the variables with slices and immediately one can see the result. This offers a new way to detect properties of functions. This will be demonstrated on the basis of quadratic functions/ parabolas. ====>> Friday 11. January 2002 09:55:37 PM <<==== --------------------------------------------------------------------------- Hans-Jürgen Elschenbroich Studienseminar S II Neuss Mainstr. 95, D-41469 Neuss / Deutschland elschenbroich@t-online.de Dem Höhenschnittpunkt auf der Spur Vortrag acdca deutsch Mit Hilfe Dynamischer Geometrie-Software (Cabri II) kann nicht nur zu einem einzelnen Dreieck der Höhenschnittpunkt konstruiert werden, sondern es kann seine Spur untersucht werden, wenn die Gestalt des Dreiecks verändert wird. Wird die Ecke C auf einer Parallelen zu AB bewegt, ergibt sich eine Parabel. Der Nachweis, dass diese Spur tatsächlich eine Parabel ist, erfolgt über klassische Abstandsüberlegungen. Anschließend werden diese Ergebnisse auf quadratische Funktionen in der S I-üblichen Funktionsschreibweise angewandt. So werden ausgehend von einem elementaren Problem Querverbindungen von Algebra und Geometrie mit Hilfe von DGS (wieder) aufgebaut, Aspekte, die über Jahrzehnte aus unserem Mathematikunterricht verschwunden sind. ====>> Friday 11. January 2002 09:57:01 PM <<==== --------------------------------------------------------------------------- Professor Bunpot Suwannaprasert Naresuan University Phitsanulok-Nakornsawan, 65000 Phitsanulok / Thailand bunpots@nu.ac.th Web-Base Instruction on Mathematics Vortrag acdca This study investigated the feasibility of utilizing existing technology as a mean for developing a prototype Thai Web-Base Instruction (TWBI) for teaching mathematics on the Internet. Results of this study indicated that it is possible to develop a TWBI by using every program concerned to produce the web sites for teaching mathematics. The results could also be applied to different instructional subjects. ====>> Sunday 13th of January 2002 10:49:30 PM <<==== --------------------------------------------------------------------------- Studiendirektor Eberhard Lehmann Rückert-Oberschule Berlin, CAS-Projekt im SINUS-Modellversuch Geitnerweg 20c, 12209 Berlin / Deutschland mirza@snafu.de Mathematikunterricht mit Parametern - schon in der Sekundarstufe 1 Vortrag acdca deutsch Mathematikunterricht mit Parametern - schon in der Sekundarstufe 1 Eberhard Lehmann, Berlin Abstract Computeralgebrasysteme eröffnen zahlreiche neue Möglichkeiten für einen neuartigen Mathematikunterricht. Dazu gehört auch die Fähigkeit von CAS, Module (Bausteine) mit Parametern zu verarbeiten, beispielsweise für magische Quadrate: (hier folgt ein Bild, siehe E-Mail an Bernhard Kutzler) Diese Module führen zu einigen neuartigen Arbeitsmöglichkeiten, die Parameter schon frühzeitig in das Blickfeld rücken. Aufgrund der zahlreichen Formeln im Unterricht schon der Sekundarstufe 1 eignet sich dieser Ansatz sogar als eine Leitlinie für den Unterricht beider Sekundarstufen. In dem Vortrag werden die Aussagen mit konkreten Unterrichtsbeispielen verdeutlicht. Dabei werden u. a. auch \"Tipps und Tricks zum Forschen und Entdecken an Bausteinen\" gegeben. Berlin, d. 14.1.2002 Eberhard Lehmann, Geitnerweg 20c, D 12209 Berlin mirza@snafu.de PS: Einordnung in die Vortragsschienen kann ich schlecht vornehmen. ====>> Monday 14. January 2002 11:24:48 AM <<==== --------------------------------------------------------------------------- Dr. Mary Ann Connors Westfield State College 19 Sterling Drive, 01027 Easthampton / USA connorseds@charter.net A Predator-Prey Model With a Computer Algebra System Vortrag derive The purpose of this paper is to present a predator-prey model using a hand-held computer algebra system (TI-89/TI-92 Plus) to enrich and enhance the learning of ordinary differential equations and linear algebra. The example provides the opportunity for student active learning. This practical application of a second-order model will be examined from graphical, numerical and analytical points of view. Students can represent differential equations and their solutions in various geometric ways. For example, students can readily use time graphs or solution curves graphed as a time series plot and/or a phase portrait to better understand long term behavior. Tables also provide information. Matrices, eigenvalues and eigenvectors are also easily handled on the TI-89 to determine the exact solutions to systems of ordinary differential equations.In this presentation we will demonstrate how students use the technology to analyze the predator prey model from biology. We will investigate time and phase portrait plots related to the model. ====>> Tuesday 15th of January 2002 05:44:16 PM <<==== --------------------------------------------------------------------------- Mr. Andy Ventress Rich Central High School 3600 W. 203rd, 60467 Olympia Fields, IL / USA rc124@hotmail.com The Digital Camera and Mathematics - What\'s the Connection ? Workshop derive I will supply digital cameras for hands on workshop experiences. Activities will be shared with particpants showing how the digital camera can be use to author problems dealing with curve fitting and other concepts. Geometer\'s Sketchpad and TI Interactive along with graphing calculators will be used during the workshop. I anticipate a 90 minute workshop. The cameras will be supplied by Casio, Inc. I am a presenter for Casio, Inc and also a math teacher at the secondary level for the past 34 years. ====>> Wednesday 16th of January 2002 05:22:22 PM <<==== --------------------------------------------------------------------------- Homero Flores Colegio de Ciencias y Humanidades-UNAM Cataratas y Llanura s/N, Mexico, City / Mexico ahfs@servidor.unam.mx GEOMETRIC PROOF IN UPPER MIDDLE SCHOOL: Workshop derive Regardless its complexity, it is relevant to teach Mathematical proof in Upper Middle Level (UML, grades 10-12), because it can foster the development of a critical and reflexive reasoning in our students. In this workshop I present a teaching proposal of geometric proof in UML based on Brousseau’s Didactical Situations theory, with the aid of TI-92 calculators and Sketchpad. The goal of the workshop is to reflect on the use of a-didactical situations in a CAS environment and the development of a reflexive thinking in the student, while attendants involve themselves in hands-on proof activities. Proposed duration: One session of two hours, or two sessions of 90 minutes, depending on the TI-92 and Sketchpad skills of the attendants. ====>> Wednesday 16th of January 2002 07:12:12 PM <<==== --------------------------------------------------------------------------- Homero Flores Colegio de Ciencias y Humanidades-UNAM Cataratas y Llanura s/N, Mexico, City / Mexico ahfs@servidor.unam.mx GEOMETRIC PROOF IN UPPER MIDDLE SCHOOL: Workshop derive Regardless its complexity, it is relevant to teach Mathematical proof in Upper Middle Level (UML, grades 10-12), because it can foster the development of a critical and reflexive reasoning in our students. In this workshop I present a teaching proposal of geometric proof in UML based on Brousseau’s Didactical Situations theory, with the aid of TI-92 calculators and Sketchpad. The goal of the workshop is to reflect on the use of a-didactical situations in a CAS environment and the development of a reflexive thinking in the student, while attendants involve themselves in hands-on proof activities. Proposed duration: One session of two hours, or two sessions of 90 minutes, depending on the TI-92 and Sketchpad skills of the attendants. ====>> Wednesday 16th of January 2002 07:12:41 PM <<==== --------------------------------------------------------------------------- Mag. Dr. Thomas Himmelbauer Gymnasium Neulandschule 1190 Wien Alfred-Wegener-Gasse 10-12 Klitschgasse 40, 1130 Wien / Austria j.himmelbauer@chello.at Aufgaben aus der Bewegungslehre mit dem TI-92 Plus Vortrag acdca deutsch An Hand mehreren Beispielen soll demonstriert werden, wie mit Hilfe der Parameterdarstellung von Funktionen des TI-92 Plus Bewegungslehre veranschaulicht und in den Mathematikunterricht als Anwendung integriert werden kann. Die Behandlung des freie Falles, des schiefen Wurfs, von Brems- und Überholvorgänge von Kraftfahrzeugen, des Wendekreises von Fahrzeugen, der Zentripetalbechleunigung von Fahrzeugen in Kurven und von Verfolgungsprobleme benötigt Vektorrechnung, genauso wie Trigonometrie oder Analysis. Dabei hilft der TI-92 bei der Veranschaulichnung, entlastet bei der Berechung und ermöglicht so die Bearbeitung für den Schüler schwierigerer, aber auch interessanter Aufgaben. ====>> Thursday 17. January 2002 06:36:49 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Peter Nussbaumer BG und BRG Tulln Donaulände 72, 3430 Tulln / Österreich peter.nussbaumer@pgv.at Mitvortragende: erster Name zweiter Name dritter Name Vortrag: Testmeldung zur Überprüfung Vortrag acdca Sehr geehrter Herr Kutzler, ich habe die Änderungen im Anmeldeformular für Beiträge auf der englischen und der deutschen Site durchgeführt. Bitte kontrollieren Sie, ob die Mail bei Ihnen \"vernünftig\" ankommt und schicken Sie mir bitte ein Mail. Danke und liege Grüße, Peter Nussbaumer ====>> Saturday 19th of January 2002 01:39:56 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Nelson Urrego Universidad Javeriana cr99B 73-54, none Bogotà / Colombia nurrego@javeriana.edu.co Mitvortragende: Vortrag: Recursive procedures and recursive functions using DERIVE Vortrag derive In the formation of mathematicians and computer engineers, the study of recursive functions and recursive predicates constitute a very important subject because it allows to students to understand the reaches and limits of the mechanical procedures in a rigorous and abstract way. In order to make more effective this study and to motivate the students, the design and implementation of algorithms for solving problems related with Recursion Theory are proposed as pedagogical tools. For this purpose, such algorithms are represented with the help of DERIVE. This Mathematical Assistant allows to program recursive algorithms for the representation of interesting functions and procedures such as the generation of prime numbers and the implementation of 1-1 Primitive Recursive correspondence between Nn and N, among others. Some examples of these algorithms and the advantages of the use of DERIVE for its implementation are presented in this lecture. ====>> Monday 21st of January 2002 05:37:08 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Nelson Urrego Universidad Javeriana cr99B 73-57, none Bogotà / Colombia nurrego@javeriana.edu.co Mitvortragende: Vortrag: Recursive procedures and recursive functions using DERIVE Vortrag derive In the formation of mathematicians and computer engineers, the study of recursive functions and recursive predicates constitute a very important subject because it allows to students to understand the reaches and limits of the mechanical procedures in a rigorous and abstract way. In order to make more effective this study and to motivate the students, the design and implementation of algorithms for solving problems related with Recursion Theory are proposed as pedagogical tools. For this purpose, such algorithms are represented with the help of DERIVE. This Mathematical Assistant allows to program recursive algorithms for the representation of interesting functions and procedures such as the generation of prime numbers and the implementation of 1-1 Primitive Recursive correspondence between Nn and N, among others. Some examples of these algorithms and the advantages of the use of DERIVE for its implementation are presented in this lecture. ====>> Monday 21st of January 2002 05:37:42 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Nelson Urrego Universidad Javeriana cr99B 73-57, Bogotà / Colombia nurrego@javeriana.edu.co Mitvortragende: Vortrag: Recursive procedures and recursive functions using DERIVE Vortrag derive In the formation of mathematicians and computer engineers, the study of recursive functions and recursive predicates constitute a very important subject because it allows to students to understand the reaches and limits of the mechanical procedures in a rigorous and abstract way. In order to make more effective this study and to motivate the students, the design and implementation of algorithms for solving problems related with Recursion Theory are proposed as pedagogical tools. For this purpose, such algorithms are represented with the help of DERIVE. This Mathematical Assistant allows to program recursive algorithms for the representation of interesting functions and procedures such as the generation of prime numbers and the implementation of 1-1 Primitive Recursive correspondence between Nn and N, among others. Some examples of these algorithms and the advantages of the use of DERIVE for its implementation are presented in this lecture. ====>> Monday 21st of January 2002 05:38:37 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Fernando Hitt Universite de Quebec a Montreal (Departement de Mathematiques) Case Postale 8888, Succursale Centre Ville, H3C 3P8 Montreal, Quebec / Canada fhitta@data.net.mx, msantos@purdue.edu Mitvortragende: Fernando Hitt Manuel Santos Vortrag: Searching for Advantages of the Technological Dimension in Mathematical Problem Solving Vortrag derive Departamento de Matemática Educativa del Cinvestav-IPN, México Summary Teachers’ reluctance to use technology in mathematics classes might be related to the types of problems they use. In general, those problems are exercises and often are not seen as a means to develop students’ problem solving abilities. What kind of problems do teachers need to select in order to use technology efficiently? Current curriculum reforms recognize that the use of technology plays an important role in students’ learning of mathematics. Technology is used as a generic term that includes the use of various types of software, hand calculators (symbolic and graphic), and other devices. In this paper, we reflect on basic principles that promote a new culture based on visual understanding and problem solving using technology. Current curriculum reforms recognize that the use of technology plays an important role in students’ learning of mathematics. Technology is used as a generic term that includes the use of various types of software, hand calculators (symbolic and graphic), and other devices. Each type of technology might offer particular advantages for students to develop special features of mathematical thinking. Thus, there is interest in exploring ways in which the use of technology becomes relevant in dealing with mathematical tasks. ====>> Thursday 24th of January 2002 10:56:40 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Fernando Hitt Universite de Quebec a Montreal (Departement de Mathematiques) Case Postale 8888, Succursale Centre Ville, H3C 3P8 Montreal, Quebec / Canada fhitta@data.net.mx, msantos@purdue.edu Mitvortragende: Fernando Hitt Manuel Santos Vortrag: Searching for Advantages of the Technological Dimension in Mathematical Problem Solving Vortrag derive Summary Teachers’ reluctance to use technology in mathematics classes might be related to the types of problems they use. In general, those problems are exercises and often are not seen as a means to develop students’ problem solving abilities. What kind of problems do teachers need to select in order to use technology efficiently? Current curriculum reforms recognize that the use of technology plays an important role in students’ learning of mathematics. Technology is used as a generic term that includes the use of various types of software, hand calculators (symbolic and graphic), and other devices. In this paper, we reflect on basic principles that promote a new culture based on visual understanding and problem solving using technology. Current curriculum reforms recognize that the use of technology plays an important role in students’ learning of mathematics. Technology is used as a generic term that includes the use of various types of software, hand calculators (symbolic and graphic), and other devices. Each type of technology might offer particular advantages for students to develop special features of mathematical thinking. Thus, there is interest in exploring ways in which the use of technology becomes relevant in dealing with mathematical tasks. ====>> Thursday 24th of January 2002 10:57:38 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Fernando Hitt Universite de Quebec a Montreal (Departement de Mathematiques) Case Postale 8888, Succursale Centre Ville, H3C 3P8 Montreal, Quebec / Canada fhitta@data.net.mx, msantos@purdue.edu Mitvortragende: Fernando Hitt Manuel Santos Vortrag: Searching for Advantages of the Technological Dimension in Mathematical Problem Solving Vortrag derive Summary: Teachers’ reluctance to use technology in mathematics classes might be related to the types of problems they use. In general, those problems are exercises and often are not seen as a means to develop students’ problem solving abilities. What kind of problems do teachers need to select in order to use technology efficiently? Current curriculum reforms recognize that the use of technology plays an important role in students’ learning of mathematics. Technology is used as a generic term that includes the use of various types of software, hand calculators (symbolic and graphic), and other devices. In this paper, we reflect on basic principles that promote a new culture based on visual understanding and problem solving using technology. Current curriculum reforms recognize that the use of technology plays an important role in students’ learning of mathematics. Technology is used as a generic term that includes the use of various types of software, hand calculators (symbolic and graphic), and other devices. Each type of technology might offer particular advantages for students to develop special features of mathematical thinking. Thus, there is interest in exploring ways in which the use of technology becomes relevant in dealing with mathematical tasks. ====>> Thursday 24th of January 2002 10:57:58 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Eva Dimitrova Department of Mathematics, Higher Institute of Food and Flavour Industries 26 Maritsa Blvd.., 4002 Plovdiv / Bulgatia eva_di@hotmail.com Mitvortragende: Penka Georgieva Vortrag: Research on the influence of some factors on the teaching of Mathematics in The Higher Institute of Food and Flavour Industries Vortrag acdca We investigated the influence of the following factors: type of secondary school the students have come from, the entry test type and the major. Our research covers several student groups formed on the basis of the factors chosen. There is a clearly formed tendency for the students from secondary technical schools to show a better ability to cope with the mathematical courses in our Institute and to have higher ratings than those from high schools. There are also differences in adaptation and in ratings between students in Technical and Technological Faculties. Our study and the conclusions we have drawn enable us to analyze the situation and to prepare more precise and detailed approach to the different groups in developing innovative methods in teaching Mathematics using educational software such as the mathematical assistant CAS DERIVE. ====>> Saturday 26th of January 2002 06:45:42 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Eva Dimitrova Department of Mathematics, Higher Institute of Food and Flavour Industries 26 Maritsa Blvd., 4002 Plovdiv / Bulgaria eva_di@hotmail.com Mitvortragende: Penka Georgieva Vortrag: Research on the influence of some factors on the teaching of Mathematics in The Higher Institute of Food and Flavour Industries Vortrag acdca We investigated the influence of the following factors: type of secondary school the students have come from, the entry test type and the major. Our research covers several student groups formed on the basis of the factors chosen. There is a clearly formed tendency for the students from secondary technical schools to show a better ability to cope with the mathematical courses in our Institute and to have higher ratings than those from high schools. There are also differences in adaptation and in ratings between students in Technical and Technological Faculties. Our study and the conclusions we have drawn enable us to analyze the situation and to prepare more precise and detailed approach to the different groups in developing innovative methods in teaching Mathematics using educational software such as the mathematical assistant CAS DERIVE. ====>> Saturday 26th of January 2002 06:59:17 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Eva Dimitrova Department of Mathematics, Higher Institute of Food and Flavour Industries 26 Maritsa Blvd., 4002 Plovdiv / Bulgaria eva_di@hotmail.com Mitvortragende: Penka Georgieva Vortrag: Research on the influence of some factors on the teaching of Mathematics in The Higher Institute of Food and Flavour Industries sonstiges derive We investigated the influence of the following factors: type of secondary school the students have come from, the entry test type and the major. Our research covers several student groups formed on the basis of the factors chosen. There is a clearly formed tendency for the students from secondary technical schools to show a better ability to cope with the mathematical courses in our Institute and to have higher ratings than those from high schools. There are also differences in adaptation and in ratings between students in Technical and Technological Faculties. Our study and the conclusions we have drawn enable us to analyze the situation and to prepare more precise and detailed approach to the different groups in developing innovative methods in teaching Mathematics using educational software such as the mathematical assistant CAS DERIVE. ====>> Saturday 26th of January 2002 07:01:46 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Bengt Ahlander Ostrabo gymnasiet, Uddevalla Kaempegatan 36, 45181 Uddevalla / Sweden ba@ostrabo.uddevalla.se Mitvortragende: Vortrag: Let the students explore algebra with CAS, TI89 Vortrag derive These symbolic calculating tools, CAS, Computer Algebra System, will change the way to teach mathematics more than the start of using graphing calculators did. With these tools we will get more time over to discuss the concepts of mathematics, more time to let the students explore algebra themselves and more time to increase the understanding of mathematics. The question is not if, but when and how, we should use CAS in our math classes. In my presentation I will show some examples how to work with TI89 and simultaneously reinforce the concepts of mathematics. All students in my class use TI89 and the age of the students are 17-19 years old. ====>> Sunday 27th of January 2002 12:56:13 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Walther Neuper IST TU Graz, HTL Salzburg Itzlinger Hauptstr. 30, 5020 Salzburg / Aut neuper@ist.tugraz.at Mitvortragende: Vortrag: Re-engieering Algebra Systems for Education Vortrag acdca englisch Currently available algebra systems (CAS) tend to sabotage the \'white-box\' phase of teaching mathematics --- teachers must forbid students to shortcut studying the concepts by \'pushing a button\'. The \\isac-project is dedicated to the development of educational software which supports a major part of learning math: modeling, specifying and solving problems in steps which the user can input interactively (checked by the system) {\\em and} which can be suggested by the system interchangeably. These goals involve re-engineering functionalities of CAS. The talk presents \\isac\'s design decisions on the kind of steps and their realization by concepts of symbolic computation (matching and rewriting), discusses the advantages and limitations of the design decision, and demonstrates the features implemented by \\isac so far. ====>> Monday 28. January 2002 11:12:17 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Walther Neuper IST TU Graz, HTL Salzburg Itzlinger Hauptstr. 30, 5020 Salzburg / Aut neuper@ist.tugraz.at Mitvortragende: Andreas Griesmayer Alan Krempler Stefan Karnel Vortrag: Re-engieering Algebra Systems for Education Vortrag acdca englisch Currently available algebra systems (CAS) tend to sabotage the \'white-box\' phase of teaching mathematics --- teachers must forbid students to shortcut studying the concepts by \'pushing a button\'. The \\isac-project is dedicated to the development of educational software which supports a major part of learning math: modeling, specifying and solving problems in steps which the user can input interactively (checked by the system) {\\em and} which can be suggested by the system interchangeably. These goals involve re-engineering functionalities of CAS. The talk presents \\isac\'s design decisions on the kind of steps and their realization by concepts of symbolic computation (matching and rewriting), discusses the advantages and limitations of the design decision, and demonstrates the features implemented by \\isac so far. ====>> Monday 28. January 2002 11:15:42 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: , / Mitvortragende: Vortrag: Vortrag acdca deutsch ====>> Tuesday 29. January 2002 01:39:47 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Temple Fay Technikon Pretoria, Pretoria, South Africa and Univ. of So. Miss. Box 5045, 39406 Hattiesburg, Mississippi / USA thfay@hotmail.com Mitvortragende: Lawrence Mead Vortrag: A Radiative Reaction Model Vortrag acdca We investigate a nonrelativistic model for the classical electrodynamic equations of motion for a radiating particle. This model is suitable for discussion in a beginning differential equations course and beginning physics course on particle dynamics. It is of interest as it is linear of third order and the third derivative acts as a damping term. Boundedness of the solution becomes of critical importance and we determine conditions for bounded solutions in the unforced and simple sinusoidal forcing cases. We also iscuss the sensitivity of numerical solutions. Our discussion suggests further investigations suitable for undergraduate research projects or small group investigations. ====>> Tuesday 29th of January 2002 01:58:43 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Stephan V. Joubert Technikon Pretoria Church Street Arcadia, 0001 Pretoria / Republic of South Africa joubertsv@techpta.ac.za Mitvortragende: Temple H. Fay Vortrag: Dimensional Analysis and DERIVE Vortrag derive We promote Dimension Analysis as a technique that promotes better understanding of the role of units and dimensions in mathematical modeling problems. Our student base consists of undergraduate students from the Science and Engineering Faculties who generally have one or two semesters of calculus and some linear algebra as part of their curriculum. Because of \"In Service Training\" which is an integral part of their education, they have a reasonable understanding of the link between theory and practice in their particular industry, but manipulating mathematical formulae is not necessarily a strong point. Dimensional Analysis involves both dimensionless products and linear algebra and, because of the latter, this branch of mathematical modelling was, until recently, beyond the reach of most of our undergraduates. However, we have found that we can blend the skills of a good technologist with the use of computer algebra systems to successfully teach Dimensional Analysis to these undergraduates. ====>> Tuesday 29th of January 2002 03:15:41 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Stephan V. Joubert Technikon Pretoria Church Street Arcadia, 0001 Pretoria / Republic of South Africa joubertsv@techpta.ac.za Mitvortragende: Temple H. Fay Vortrag: Dimensional Analysis and DERIVE Vortrag derive We promote Dimension Analysis as a technique that promotes better understanding of the role of units and dimensions in mathematical modeling problems. Our student base consists of undergraduate students from the Science and Engineering Faculties who generally have one or two semesters of calculus and some linear algebra as part of their curriculum. Because of \"In Service Training\" which is an integral part of their education, they have a reasonable understanding of the link between theory and practice in their particular industry, but manipulating mathematical formulae is not necessarily a strong point. Dimensional Analysis involves both dimensionless products and linear algebra and, because of the latter, this branch of mathematical modelling was, until recently, beyond the reach of most of our undergraduates. However, we have found that we can blend the skills of a good technologist with the use of computer algebra systems to successfully teach Dimensional Analysis to these undergraduates. ====>> Tuesday 29th of January 2002 03:16:24 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Stephan V. Joubert Technikon Pretoria Church Street Arcadia, 0001 Pretoria / Republic of South Africa joubertsv@techpta.ac.za Mitvortragende: Temple H. Fay Vortrag: Dimensional Analysis and DERIVE Vortrag derive We promote Dimension Analysis as a technique that promotes better understanding of the role of units and dimensions in mathematical modeling problems. Our student base consists of undergraduate students from the Science and Engineering Faculties who generally have one or two semesters of calculus and some linear algebra as part of their curriculum. Because of \"In Service Training\" which is an integral part of their education, they have a reasonable understanding of the link between theory and practice in their particular industry, but manipulating mathematical formulae is not necessarily a strong point. Dimensional Analysis involves both dimensionless products and linear algebra and, because of the latter, this branch of mathematical modelling was, until recently, beyond the reach of most of our undergraduates. However, we have found that we can blend the skills of a good technologist with the use of computer algebra systems to successfully teach Dimensional Analysis to these undergraduates. ====>> Tuesday 29th of January 2002 03:17:17 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Test Kutzler ACDCA , / b.kutzler@eunet.at Mitvortragende: Vortrag: Vortrag acdca ====>> Tuesday 29th of January 2002 08:47:38 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Test Kutzler ACDCA , / b.kutzler@eunet.at Mitvortragende: Vortrag: Vortrag acdca ====>> Tuesday 29th of January 2002 08:48:06 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: , / Mitvortragende: Vortrag: Vortrag acdca ====>> Tuesday 29th of January 2002 08:50:26 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Allen Klinger UCLA 405 Hilgard Ave., 3531-H Boelter Hall, 90095-1596 Los Angeles / USA klinger@cs.ucla.edu Mitvortragende: Vortrag: Internet Exposition, Visualization, and Assessment Vortrag acdca Computer algebra systems relate to applied science in diverse ways. Yet mathematical structures reveal underlying truths, not the physical systems they model. Historic choices of notation constrain large populations to relative ignorance. This paper presents ways to overcome mathematical anxiety, indeed, instead stimulate active learning. The method is technology-based, depending on software (markup languages) and hardware (computer networks). The paper presents a many year set of experiences in preparing material and applying them in classes, individual directed studies, and for interaction with professionals (presentations, informal discussions). The conclusion concerns both quantitative and anecdotal evaluation of learning accomplished. The paper makes a case for the applicability of novel assessment strategies in technology-based delivery of mathematical knowledge (e.g., via distance learning forms of programmed instruction). ====>> Wednesday 30th of January 2002 02:23:33 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Eduardo Ramon Bravo de las Casas Universitary Professor Ave 74 Edif 50-A Nro 6794 puebl Griffo, 55500 Cienfuegos / Cuba ebc2047@hotmail.com Mitvortragende: Vortrag: orally or posters sesion Vortrag acdca Postgraduate Mathematics and Computing Science for specialist of different profiles. Abstracts The explosion of the volume of information scientist-technique, marks to an accelerated reduction of the terms of life of the ideas scientist-techniques, on the other hand it is possible to indicate that we are in the beguinimg of the XXI century and we have a great difference between a very reduced group of countries highly developed and a great majority of underdeveloped countries, in which talks about to its technological and scientific development, because in the developed countries there is impetuous a technological unfolding, very difficult to be followed by the countries of little development, which more and more makes the tasks complex to solve by the professionals of the different specialties. From these initial reflections we restlessness arises to think about how to complete formation of professionals left our classrooms in order that they are more efficient and more plenary sessions in development of his different activities, because it must consider that the Superior Education of any country is the one in charge to form the professionals for the economy, science, the technique and the culture of the nation, that is the reason that we thought that it is of great importance and utility the improvement of the Mathematical one and the Computation of postdegree that distributes itself, as a result of the previous thing the necessity considers to elevate the quality and the assimilation of Computation that is distributed, based on cultural an historical approach and of the activity, as well as to obtain that the same one constitutes a system based on the theory of the activity and the formation by stages of the mental actions, that allows to elevate the assimilation of this postdegree. In the present work the experiences take shelter of the author in the teaching Postdegree to Engineers, Economists and Scientists whose terminal profile are not the Mathematics and Computer science, become conclusions of the work developed in the application of a didactic system based on the cultural and the historical approach and of the activity, that entails to elevate the quality of the assimilation of the mathematical knowledge and computation, having in account these hypotheses of work set out the structures of different courses from postdegree for the personnel graduated as Scientistics, Economists, Engineers and other sciences in order to obtain different intentions, as they are from elevating his level in mathematics and Computation in order that they use them like daily tools to turn professionals of these branches into professionals who exert the Mathematics and Computation like profession, besides to transform them into professors of these specialties, in addition this education to postdegree has like a very positive result the fact that it has been managed to adapt it so that also serves as overcoming and improvement to the specialists in Mathematics and Computation, in the work also the experiences are exposed to take that education postgraduated to the graduated ones as Mathematicians and Computation like a safe channel of overcoming as such, that will allow them to be more effective in its development in the different spheres from work, all this structure based on cultural an historical approach and from the activity it has been very effective in obtaining Mathematicians and Computation of the professionals to whom it has been distributed, the propose structure of postdegree has been conceived being based on the existing structures of Postdegree in the System of Superior Education of the Republic of Cuba but it is considered applicable to the structure of postdegree of any country interested in implanting it for the improvement of his professionals. ====>> Wednesday 30th of January 2002 05:04:07 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Eduardo Ramon Bravo de las Casas Universitary Professor Ave 74 Edif 50-A Nro 6794 puebl Griffo, 55500 Cienfuegos / Cuba ebc2047@hotmail.com Mitvortragende: Vortrag: orally or posters sesion Vortrag acdca Significant Teaching and Creativity in undergraduate Mathematics at the Universities Abstracts In the work different questions are approached as they are Mathematical Education and its Significant Education and Creativity. A necessary introduction referring to the history of the Mathematics. Critic to different tendencies in Mathematical Education and characteristics of the Mathematics social importance of the different approaches from curriculum in the education of the Mathematics. The bourbakismo in Cuba and other countries of Latin America. The Mathematics and their Significant and Creative Education related to the basic concepts of the Mathematics. The use of the problem methods in the education of the Mathematics in the undergraduate Education necessary introduction to the subject. The problem structuring of the education of the Mathematics. It is sustained in theoretical bases processed from some of the main currents and programs of the educational development. ====>> Wednesday 30th of January 2002 05:05:48 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Eduardo Ramon Bravo de las Casas Universitary Professor Ave 74 Edif 50-A Nro 6794 puebl Griffo, 55500 Cienfuegos / Cuba ebc2047@hotmail.com Mitvortragende: Vortrag: orally or posters sesion Vortrag acdca Significant Teaching in Engineering Why not? Abstracts In the work different questions are approached as they are Mathematical Education and its Significant Education. A necessary introduction referring to the History of the Mathematics is made. Critic to different tendencies in Mathematical education and the social characteristics of the currículum in Mathematics and its social importance in the different approaches of the Education in Mathematics. The bourbakism in Cuba and other countries of Latin America, its role and forms. The Mathematics and their Significant Education related to the basic concepts of the Mathematics. The use of the problem methods in the Mathematical Education in engineering.A necessary introduction to the subject. The probllem structuring of the Mathematical education in engineering. ====>> Wednesday 30th of January 2002 05:07:30 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Bernhard Kutzler ACDCA Hasnerstr. 9, 4020 Linz / Austria b.kutzler@eunet.at Mitvortragende: Vortrag: blabla Vortrag acdca blabla ====>> Wednesday 30th of January 2002 06:09:24 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Gay L. Nixon Retired from Edmonds School District, Lynnwood, WA but actively tutor math daily. 1609 175th Street SW, 98037 Lynnwood, Washington / USA gaynixon@juno.com Mitvortragende: Vortrag: Absolute Value: Geometrically, Algebraically and Technologically Workshop acdca We will work for useful and enduring understanding of absolute value by: 1) geometrically by analyzing the equations on number lines; (We will make sense of the symbolism of absolute value by use of words and graphs.) 2) algebraically by solving the equations in a logical manner; (We will solve the absolute value equations algebraically using some easily remembered formulas.) 3) technologically by verifying results on the TI-83+ calculator. (We will graph the equations on the calculator, sketch them on the worksheet in provided grids and analyze them.) This is not part of my abstract, but an explanation of why I chose workshop over lecture. Participants will receive a packet will all worksheets and explanations. We will work through all of the materials together. This could be considered a lecture or a workshop, but I expect the participants to work through the packet with me seated at tables, which is much preferable to a lecture format. ====>> Wednesday 30th of January 2002 10:48:53 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Gay L. Nixon Retired from Edmonds School District, Lynnwood, WA but actively tutor math daily. 1609 175th Street SW, 98037 Lynnwood, Washington / USA gaynixon@juno.com Mitvortragende: Vortrag: Absolute Value: Geometrically, Algebraically and Technologically Workshop acdca We will work for useful and enduring understanding of absolute value by: 1) geometrically by analyzing the equations on number lines; (We will make sense of the symbolism of absolute value by use of words and graphs.) 2) algebraically by solving the equations in a logical manner; (We will solve the absolute value equations algebraically using some easily remembered formulas.) 3) technologically by verifying results on the TI-83+ calculator. (We will graph the equations on the calculator, sketch them on the worksheet in provided grids and analyze them.) End of Abstract:This is not part of my abstract, but an explanation of why I chose workshop over lecture. Participants will receive a packet will all worksheets and explanations. We will work through all of the materials together. This could be considered a lecture or a workshop, but I expect the participants to work through the packet with me seated at tables, which is much preferable to a lecture format. ====>> Wednesday 30th of January 2002 10:50:17 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: David Pountney Liverpool John Moores University, School of Computing & Mathematics Byrom St., Liverpool, L3 3AF / U.K. d.c.pountney@livjm.ac.uk Mitvortragende: Vortrag: Assessing Engineering & Science Mathematics in the presence of a CAS Vortrag acdca Since at least the early 1990s, academics have advocated that the presence of a CAS will dramatically affect the way we teach and assess mathematics for Engineering and Science students at University. However in many cases, the change has not been as dramatic as forecast and indeed a CAS often gets the blame for mathematical ills of students . This paper looks at reasons for this and reconsiders the future for CAS use for such students, based on a consideration of the mathematical skills (as perhaps opposed to subject knowledge) that we wish such students to acquire. Specific examples are used to illustrate the ideas. It is conjectured that assessment issues remain a significant stumbling block to progress and that this pertains not only to Universities but to pre-University 16-19 year old mathematics education also. Again illustrative examples are described to show how an approach based on assessment of mathematical skills rather than techniques could lead to changes in teaching and learning where the use of a CAS is a natural consequence for students. ====>> Friday 01st of February 2002 03:11:57 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Pedro Rodríguez Department of Applied Mathematic. University of Málaga Campus Teatinos. Complejo Tecnológico, 29071 Málaga / Spain prodriguez@uma.es Mitvortragende: Jose Luis Galán Mª Ángeles Galán Yolanda Padilla Vortrag: COMPLEX.MTH: SOLVING PROBLEMS OF FUNCTIONS OF A COMPLEX VARIABLE FOR ENGINEERING USING DERIVE Vortrag derive In this paper we present the file COMPLEX.MTH, created for being used in subjects that deal with complex variable, aimed at Engineering students. Such file contains a series of macros which permit to solve some typical problems related to complex variable. The macros contained in the file can be grouped within the following blocks: - Complex numbers (different forms of a complex number, arithmetic of complex numbers, loci in the complex plane). - Functions of a complex variable (real and imaginary parts of a complex function, standard functions). - Differentiation of complex functions (Cauchy-Riemann conditions, analytic and harmonic functions). - Complex integrals (line integral of a complex function, analytic function integration, Cauchy’s integral formula, the residue theorem). - Conformal mapping (basic conformal mapping, fundamental theorem). We also show in the paper some examples of applications that have been carried out with our students of Telecommunication Engineering. Finally, we include the conclusions obtained after using this file. ====>> Friday 01st of February 2002 06:32:28 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Pedro Rodríguez Department of Applied Mathematic. University of Málaga Campus Teatinos. Complejo Tecnológico, 29071 Málaga / Spain prodriguez@uma.es Mitvortragende: Jose Luis Galán Mª Ángeles Galán Yolanda Padilla Vortrag: ANALVEC.MTH: INTEGRATION AND VECTOR FIELD PROBLEMS FOR ENGINEERING USING DERIVE Vortrag derive In this paper we present the file ANALVEC.MTH, created for being used in subjects that deal with integration and vector field theory, aimed at Engineering students. Such file contains a series of macros which permit to solve some typical problems related to vector fields. The macros contained in the file can be grouped within the following blocks: - Scalar and vector fields (gamma and beta functions, gradient, divergence, curl and laplacian). - Line integrals (exact differentials, potential function, line integral of non-exact differentials). - Double and triple integrals (double integration in cartesian and polar coordinates, triple integration in cartesian, cylindrical and spherical coordinates). - Surface integrals. Gauss’ theorem (surface area, unit normal vectors, flux of a vector field, Gauss’ theorem). We also show in the paper some examples of applications that have been carried out with our students of Telecommunication Engineering. Finally, we include the conclusions obtained after using this file. ====>> Friday 01st of February 2002 06:33:37 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Shin Watanabe Tokai University 3-20-1 Orito, 424-8610 Simizu / Japan watanabe@scc.u-tokai.ac.jp Mitvortragende: Vortrag: The mathematical laboratory with TI-89 and CBL Vortrag derive We want to make the room of mathematical laboratory with TI-89 and CBL in every school.@@In mathematics lessons teaching mathematical knowledge is given to student. So we make the system of teaching which is making mathematics by student.@@One example, we connect the two subjects, math and physics using TI-89 and CBL.@We teach mathematics with enjoy at mathematical lesson. ====>> Saturday 02nd of February 2002 04:44:19 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Shin Watanabe Tokai University 3-20-1 Orito , 424-8610 Shimizu / Japan watanabe@scc.u-tokai.ac.jp Mitvortragende: Vortrag: Problem solving with graphic calculator Vortrag acdca In my mathematical lessons, I want to teach math with problem-solving stile.@ ====>> Saturday 02nd of February 2002 05:33:26 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Hongguang FU PO. Box 237, 610041 Chengdu / P.R. China Fu_hongguang@hotmail.com Mitvortragende: Zhenbing ZENG Vortrag: A New Dynamic Geometry Software with a Prover and a Solver Vortrag acdca As we know, dynamic geometry technology has been used in mathematics education widely, and many dynamic geometry software such as GSP and Cinderella etc has been developed. But, all these software do not have the function to solve problem by computer automatically. In order to do it, we must introduce a automated reasoning engine (prover) and a symbolic computation platform (solver). Moreover, for the goal of education, the prover and solver should produce a readable process similar to it given by hand. In recent years, we are researching and developing such a new dynamic software with a prover and a solver. By the end of last year, the project almost finished. So in this paper we will illustrate our software and show some interesting examples. We believe that the new dynamic geometry software will very helpful for students and teachers. ====>> Monday 04th of February 2002 07:00:05 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Csaba Sárvári Pécsi Tudományegyetem Boszorkány ut 2, 7624 Pécs / Ungarn sarvari@witch.pmmf.hu Mitvortragende: Vortrag: CAS-basierte Lehrplan - Lehrplan-basierte Modularisierung mit CAS Vortrag acdca deutsch Anwendung CAS verändert, ergänzt den Inhalt der Lehrpläne und auch die benutzten Methoden. In dieser Hinsicht können wir sagen: CAS beeinflusst die Lehrplangestaltung. Grundsetzlich ist aber die andere Richtung: alle unsere Verfahren sollen vom Lehrplan, von den Lernzielen determiniert, reguliert werden. Modularisierung ist ein wichtiges und effizientes Strukturierungs- und Organisationsprinzip des kognitiven Wissens. Prozess der Modularisierung mit CAS ist ein dynamisches Verfahren, in dem Mass der Auslagerung soll immer von Zielen des Lehrplanes bestimmt werden. Im Vortrag wird Themenkreis der Modularisierung aus dieser Hinsicht behandelt und mit Beispielen aus der Hochschulunterricht demonstriert werden. ====>> Monday 04. February 2002 08:38:10 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Al Maturo Leysin American School CH-1854 LEYSIN, / Switzerland AMATURO@las.ch Mitvortragende: Vortrag: TI-83 Plus Calculator Workshop Workshop acdca TI-83 Plus Calculator Workshop. This workshop is designed to teach one how to use the Texas Instruments TI-83 & TI-83 Plus Calculators with hands on exercises. Al Maturo of the Leysin American School will demonstrate the capability of the TI calculators as well as offer exercises to allow the user, you, a chance to learn \'hands on\' how to use this classroom tool. Al Maturo is a teacher of IB and AP Mathematics and uses the TI calculators when appropriate in the classroom. The workshop is designed for the new user, or for those with little experience with the TI Calculators. Although we will use the TI 83 Plus, this workshop is compatible with TI-82 and TI-83 Calculators. Calculators will be provided for those without one, but feel free to bring your own. ====>> Monday 04th of February 2002 12:21:03 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Mihaly Klincsik Pécsi Tudományegyetem Boszorkány ut. 2., 7624 Pécs / Hungary klincsik@witch.pmmf.hu Mitvortragende: Csaba Sárvári Vortrag: How can we combine the CAS with authoring system tools to create a learning environment containing flexible feedback opportunities Vortrag acdca Using CAS as a powerful mathematical tool and the Toolbook Instructor object oriented authoring system we can create efficient learning environment. We are using two different types of learning-feedback modules: - interactive feedback moduls are assisting in acquirement of the learning topics; - exam modules. The two different modules are forming a connected, coherent unit. The first form allows for the students to modify their answers and gives interactiv opportunity to get more information by communication with CAS worksheets. In order the teacher could be able to modify the learning process there are used log-file. This containes information about navigations and activities of the user. All the tests are available on the network. The second form is made for exam-environment, thus allows only one opportunity to give answer. In our presentation we perform the results about measuring made at our highschool-course, too. ====>> Monday 04th of February 2002 01:06:01 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Michel Beaudin École de technologie supérieure 1100, Notre-Dame West, H3C1K3 Montréal / Canada mbeaudin@seg.etsmtl.ca Mitvortragende: Vortrag: Using both: Derive 5 and the TI-92 Plus Vortrag derive The talk will give examples of how Derive 5 AND the TI-92 Plus can be used by the teacher and/or engineering students. It will compare some answers given by the two systems for various problems. Some of the examples will show that both systems can be used in partnership and this helps the students for a better understanding of basic concepts. This is what we have done for the last two years: using the TI-92 Plus with the students and switching to Derive when we think that it can do a better job. Because there is so many similarities between the 2 systems, using both systems is not too difficult for the students. Finally, based on our teaching experience, we will give some suggestions for future versions of Derive and the symbolic TI. ====>> Monday 04th of February 2002 03:56:40 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Vladimir Dyakonov October Revolution 13, 72, / Russia dyak@keytown.com Mitvortragende: Vortrag: To: Dyakonov Vladimir Pavlovich sonstiges derive In the report is made review of application of system of computer algebra Derive and microcalculators TI-89/92 in Russia and in the countries of fotmer USSR. The popularity of Derive is marked. In Russia are issued 3 books on this system, 2 of then are written by the author of this report. Now author of this report prepare the book \"World of Dreive. An educational course \" and another book \" Handbook about new foreign microcalculators \". Calculators TI-89/92 are applyed very few in Russia. I hope the corporation Texas Instrument will take part in the development of the market of Russia in near feature. ====>> Monday 04th of February 2002 05:04:03 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Vladimir Dyakonov October Revolution 13, 72, 214004 Smolensk / Russia dyak@keytown.com Mitvortragende: Vortrag: To: Dyakonov Vladimir Pavlovich sonstiges derive In the report is made review of application of system of computer algebra Derive and microcalculators TI-89/92 in Russia and in the countries of fotmer USSR. The popularity of Derive is marked. In Russia are issued 3 books on this system, 2 of then are written by the author of this report. Now author of this report prepare the book \"World of Dreive. An educational course \" and another book \" Handbook about new foreign microcalculators \". Calculators TI-89/92 are applyed very few in Russia. I hope the corporation Texas Instrument will take part in the development of the market of Russia in near feature. ====>> Monday 04th of February 2002 05:05:46 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Eugenio Roanes-Lozano Dept. Algebra, Fac. de Educación, Univ. Complutense de Madrid c/ Rector Royo Villanova s/n, 28040 Madrid / Spain eroanes@fi.upm.es Mitvortragende: Eugenio Roanes-Macías Matilde Villar-Mena Vortrag: Linking The Geometer\'s Sketchpad 3 with DERIVE 5 Vortrag derive Both Computer Algebra Systems (CASs) and Dynamic Geometry Systems (DGSs) have reached a high level of development. Powerful Euclidean Geometry packages exist in some CASs, but CASs have incorporated neither mouse drawing capabilities nor dynamic capabilities. Mean- while, the well-known DGSs do not provide algebraic facilities. After analysing theoretically the situation and after approaching the problem from Maple, we have now developed a new DERIVE Euclidean Geometry package (denoted ParamGeo) plus an external translator (both freely available from the authors). They make it possible to draw a geometric configuration with the mouse (using The Geometer\'s Sketchpad 3) and to obtain the equations of the drawn configuration in DERIVE-acceptable syntax. To obtain complicated formulae or to perform automatic theorem proving from sketches are direct applications. ====>> Monday 04th of February 2002 07:01:15 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Gary Harris Department of Mathematics and Statistics Texas Tech University, 79409 Lubbock, TX / USA harris@math.ttu.edu Mitvortragende: Vortrag: Distance Delivery of a Graduate Level Mathematics Course for High School Teachers Vortrag acdca Here we report on the development and implementation of a graduate level mathematics course taught via the internet for in-service high school mathematics teachers. The course uses WebCT, MAPLE, and MWS Logo. We discuss the philosophy and rationale for the development of the course, the goals of the course, and the logistics involved with the distance delivery of the course. Also we provide examples of the course materials. We include profiles of the students and instructor involved with the course, and conclude with the assessment of the course’s success from the point of view of both the students and the instructor. ====>> Monday 04th of February 2002 10:13:39 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Alan McRae Washington and Lee University Robinson Hall, 24450 Lexington, VA / USA mcraea@wlu.edu Mitvortragende: Vortrag: A New Perspective on Geometry: A web-based series of independent study courses Vortrag acdca The purpose of these courses, a portion of which is near completion, is to make publicly available a comprehensive series of web sites for discovery-based, interactive courses on geometry. They will be offered at Washington and Lee University as part of our independent study program in modern geometry, allowing the student to choose those branches of geometry of greatest interest to her. The courses are developed with the help of student research scholars during the summer months. Ideas and definitions at each step in the learning process will be both motivated and illustrated, sometimes via interactive and dynamic geometric tools such as Cinderella. The theory will then proceed to develop through problems, reading assignments, and projects. Some of these problems will take the form of missing steps in interactive exercises written in Java. The students will then add their own contributions to the web course as appropriate (a beautiful new solution, an interesting find in an old journal, a surprising application, etc.). I will illustrate this program by looking at the first completed course, which is on finite geometries. Work will begin soon on a course for geometric probability. ====>> Monday 04th of February 2002 11:47:57 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Hajime Yamashita Professor, Waseda University 1-6-1 Nishiwaseda, Shinjyuku, 169 Tokyo / Japan yamashit@mn.waseda.ac.jp Mitvortragende: Vortrag: Ducational Evaluation Applying Fuzzy Theory Vortrag acdca I would like to present the educational evaluation applying fuzzy theory. I wiould explain the evaluation method and its practical effectiveness by the case study. ====>> Tuesday 05th of February 2002 10:02:55 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Hajime Yamashita Professor, Waseda University 1-6-1 Nishiwaseda, Shinjyuku, 169 Tokyo / Japan yamashit@mn.waseda.ac.jp Mitvortragende: Vortrag: Eucational Evaluation Applying Fuzzy Theory Vortrag acdca I would like to present the educational evaluation applying fuzzy theory. I wiould explain the evaluation method and its practical effectiveness by the case study. ====>> Tuesday 05th of February 2002 10:04:15 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Hans-Joachim Brenner Albert-Schweitzer-Gymnasium mit Spezialschulteil math./nat.-w. Richtung Erfurt Am Buchenberg 2, 99097 Erfurt / Deutschland Hans-Joachim.Brenner@t-online.de Mitvortragende: Vortrag: Diskussion der Ziele des Mathematikunterrichtes anhand von Unterrichtsbeispielen Vortrag acdca deutsch Seit drei Jahren wird der TI-89 im Mathematikunterricht der Klassen 10 bis 12 unseres Gymnasiums genutzt. Erstmals ist in diesem Jahr ein CAS bei den Abiturprüfungen in Thüringen zugelassen (8 beteiligte Schulen). Im Vortrag möchte ich Unterrichtsbeispiele vorstellen und Vorschläge unterbreiten, wie auf der Grundlage bisher gültiger Lehrpläne der Unterricht gestaltet werden kann, wie ein Lehrplan den neuen Gegebenheiten angepasst werden sollte und welche Schwerpunktsetzung bei den Zielen des Mathematikunterrichtes aus meiner Sicht sinnvoll ist. (Die Bewältigung des Alltages muss stärker in den Mittelpunkt der Diskussion gestellt werden. Und dafür ist es notwendig, dass man sich auf grundlegende Ziele einigt.) Im Einzelnen habe ich folgende Beispiele vorgesehen: a) Abstandsbestimmungen im Raum, b) Bilder rationaler Funktionen, c) Untersuchung rekursiver Zahlenfolgen. Dabei werde ich Möglichkeiten aufzeigen, wie im Unterricht die einzelnen Teilgebiete der Mathematik stärker als oft üblich miteinander verknüpft werden können und wie in Leistungskontrollen auch „einfache Punkte“ für den Schüler erreichbar sind. ====>> Tuesday 05. February 2002 12:13:37 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: CHIKUNJI CHITENG\'A JOHN University of Zambia, Dept. of Mathematics and Statistics, Box 32379 Great East Road, Lusaka / Zambia jchikunji@natsci.unza.zm Mitvortragende: Vortrag: Classification of Finite Local Rings Using Computer Programmes in MATLAB Vortrag derive Computer technology has been a source of interest over the years and is providing new tools for doing and organising mathematical research in terms of computations, experimentation, modelling and problem solving. The purpose of this paper is to make use of elements from MATLAB (MATrix LABoratory) to device computer programmes that determine the structure and classification, up to isomorphism, of a naturally arising class of finite associative local rings. We demonstrate this in the case where the finite local ring has a finite residue field K of prime characteristic p, although our results apply in fact over any field K. ====>> Tuesday 05th of February 2002 01:20:37 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Victor Lysytsya Acad.Lyapunov,9, fl.60, 61166 Kharkov / Ukraine lisitsa@univer.kharkov.ua Mitvortragende: Vortrag: An idea of electronic textbook for subject \"Analytical geometry\" Vortrag acdca Contemporary education, especially mathematical education, actively uses computer technologies. It is connected with wide possibilities of computers: high speed of processing of information, possibility to store much information, possibility to use mathematical packets and so on. All these possibilities one can use for making computer courses in different subjects. As an exampl we may propose an idea of making computer manual for the subject \"Analytical geometry\", which is taught at the faculty of machanics and mathematics in Kharkov National University. ====>> Tuesday 05th of February 2002 01:33:43 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: PETER SCHOFIELD TRINITY & ALL SAINTS COLLEGE Brownberrie Lane, Horsforth, LS18 5HD LEEDS / UK p_schofield@tasc.ac.uk Mitvortragende: Vortrag: Some General-Purpose Tools for 2D- and 3D-Linear Transformation Geometry with DERIVE 5 Workshop derive The concept of a General-Purpose Tool for plotting in DERIVE 5 is that of an instruction that will generate expressions for plotting in both the 2D-Plot Window and 3D-Plot Window (depending upon the information in its argument places). In addition, the tool can be applied to (almost) all of the types of objects that can be plotted. It can also process either a single object or a list of such objects. The tools are contained in a DERIVE Users File 2D-&3D-Transformations.dfw. The workshop activities will based around the following general-purpose tools: PARA – plots objects with respect to user-selected intervals (when required); TRAN– linearly transforms objects using a 2x2 or 3x3 matrix; DIS – displaces objects using a row or column displacement vector; INV – inverts objects with respect to the 2D- or 3D-axes; STR – stretches objects in the directions of the 2D- or 3D-axes; ROT – rotates objects about the origin (2D) or about an axis through the origin (3D); REF – reflects objects in an line through the origin (2D) or a plane containing the origin (3D). The file 2D-&3D-Transformations.dfw also contains instructions for drawing a selection of 2D- and 3D- laminas and objects, including: unit squares, triangles, regular polygons and circles; three point triangles and parallelograms; stretched polygons and ellipses; unit cubes, tetrahedrons, spheres, cones and double cones; four point tetrahedrons and parallelepipeds; cuboids, spheroids, etc. ====>> Tuesday 05th of February 2002 04:54:03 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: PETER SCHOFIELD TRINITY & ALL SAINTS COLLEGE Brownberrie Lane, Horsforth, LS18 5HD LEEDS / UK p_schofield@tasc.ac.uk Mitvortragende: Vortrag: Folding, Cutting and Joining DERIVE 5 Style Vortrag derive This lecture describes how DERIVE 5 can be used to establish direct links between transformation geometry activities at Key Stages 1 and 2 of the UK National Curriculum for Mathematics (approx 5-11 yrs) and related topics in a Mathematics Subject Studies Module for Primary Education Degree Students. The first form of KS 1\\2 activity involves folding and cutting sheets and strips of paper to form attractive symmetry group (cut-out) patterns. Using a DERIVE 5 Users File 2D-&3D-Transformations.dfw (containing general-purpose tools for transformation geometry) these activities will be simulated in DERIVE’s 2D-Plot Window. The second form of KS 1\\2 activity involves constructing regular polyhedrons by joining together networks of their faces. Using 2D-&3D-Transformations.dfw the networks, transformations and polyhedrons will be constructed in a similar manner in DERIVE’s 3D-plot Window. In particular, the cube and dodecahedron will be highlighted. The presenter will also explain how these can form challenging activities for the above degree course students. ====>> Tuesday 05th of February 2002 05:01:43 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Tabitha Mingus Western Michigan University 1903 W. Michigan Avenue, 49008 Kalamazoo / USA tabitha.mingus@wmich.edu Mitvortragende: Vortrag: Technology as a Pedagogical Amplifier in Developing Students\' Geometric Intuition of Eigephenomena in Linear Algebra Workshop acdca The concepts of linear transformations and their associated eigenphenomena are critical concepts with which students struggle in linear algebra. These topics, however, can be grounded in their understanding of linear transformations as functions and linked to a geometric perspective of these functions\' effect on vectors in the cartesian plane and in 3-space. This workshop will take participants through a series of classroom and laboratory activities that develop first a geometric sense of the different classes of linear transfor- mations and then progressively and constructively build the concepts of eigenvectors and eigenvalues using a mix of technologies, namely calculators with matrix capabilities, an electronic compass such as Geometer\'s Sketchpad and a home-grown program designed to depict the effect of a linear transformation on 2-space when applied iteratively. Examples of student work and the results comparative assessments of their understanding to a control group will also be discussed. ====>> Tuesday 05th of February 2002 05:11:58 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Andreas Griesmayer TU Graz - Institut fuer Softwaretechnologie Inffeldgasse 16b, 8010 Graz / Austria agriesma@ist.tu-graz.ac.at Mitvortragende: Vortrag: Tools for Interactive Specification of Problems Vortrag acdca deutsch Since the introduction of algebra systems (CAS) to math education, the emphasis on the phase of specification in problem solving has increased. CAS provide for calculational power, but they don\'t support specification: selecting a function (e.g. solve) and eventually setting a switch appropriately has to be done after specification. The isac-project aims at an educational CAS which supports all phases, modeling, specifying and solving problems. For the purpose of interactive specification isac holds the math knowledge in a 3-dimensional universe along the axes \'domains\', \'problem types\' and \'methods\'. The talk discusses the issue not to get lost on such a huge and complicated knowledge base and possibilities for respective tools, presents the already implemented tools for browsing the hierarchy along the axis of problem types and for specifying interactively, and demonstrates the new features of isac for specifying and solving problems by breaking them down to subproblems. ====>> Tuesday 05. February 2002 06:10:36 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Sandy Scaffetta Johnson University of Oklahoma 820 Van Vleet Oval, 73019 Norman / USA johnson@ou.edu Mitvortragende: Vortrag: Using the Internet in a Graduate History of Mathematics Course Vortrag acdca This presentation with demonstrate the possibilities of using the Internet for supplemental research and dissemination of information gathered and displayed by graduate students enrolled in a History of Mathematics course. The presentation will include links, examples of research, examples of projects, methods of disseminating information, historical electronic timelines, and more. The research data is a combination of traditionally and electronically gathered information, formulated for display and access over the Internet. ====>> Tuesday 05th of February 2002 06:53:47 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Pedro Rodríguez Department of Applied Mathematic. University of Málaga Campus Teatinos. Complejo Tecnológico, 29071 Málaga / Spain prodriguez@uma.es Mitvortragende: José Luis Galán Yolanda Padilla Mª Ángeles Galán Vortrag: TEACHING MATHEMATICS IN ENGINEERING WITH DERIVE. AN EXPERIENCE IN THE UNIVERSITY OF MÁLAGA Vortrag derive In this paper we present an experience carried out in courses for undergraduate students in Technical Telecommunication Engineering. The normal use given to practicals with computers generally consists of solving specific problems using the primitive functions of the software chosen. The experience we present consists of teaching Mathematics with DERIVE using some kind of innovative practicals in order to use the computer as a tool for mathematical creativity. The main innovative aspect of these practicals is that the students have an active role in the sense they should elaborate themselves utility files to solve the typical problems for the different subjects. This fact implies that the students need to deal with programming in DERIVE, understand the subject and know how to solve typical problems. We will explain the reasons for choosing DERIVE and the details of developing these practicals. We will focus on a specific practical. We will end with the obtained conclusions and with the corresponding references. ====>> Tuesday 05th of February 2002 11:53:32 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Meira Hockman School of Mathematics, University of Witwatersrand, Johannesburg, South Africa P O Wits, 2050 Johannesburg / South Africa 036mhh@cosmos.wits.ac.za Mitvortragende: Vortrag: Dr Vortrag acdca DYNAMIC GEOMETRY SYSTEMS AS TEACHING TOOLS IN TEACHER EDUCATION Abstract: In South African schools, synthetic geometry with its strict order of theorems following definitions following axioms, dominates the curriculum. The senior scholars are initiated into the statement-required to prove-proof format for theorems and problems in the hope that this discipline will stand them in good stead for life skills or for abstract mathematics. In either case the aim is to generate logical and sequential thought. In contrast, the junior students are encouraged to explore ideas using low technological tools such as compass, straightedge and templates. The students explore concepts visually, prior to formulating definitions. The students subsequently take an active part in the formulation of definitions and theorems. Dynamic geometry systems allow a similar process of visual stimulation to precede formal axiomatic constructions at secondary and tertiary level, in particular in programmes for teacher education. Through these systems the students can explore complex ideas and theorems, investigate change and invariance, conjecture and hypothesize prior to or in the place of engaging with the formal rigorous mathematics. Introducing new concepts in this way and encouraging reflection may also produce the insight needed to understand the dichotomy between visualisation and sequential thought or “intuition” versus “rigour” when learning and teaching geometry. ====>> Wednesday 06th of February 2002 08:23:09 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Igor Gachkov Karlstad University, Senior lecturer Majas vag 15, 65638 Karlstad / Sweden Igor.Gachkov@kau.se Mitvortragende: Vortrag: Discrete Mathematics: Boolean algebra and Set theory with TI-89 Vortrag derive The packages ”Boolean algebra” and “Set theory” are a program packages, which was created especially for TI-89 and is used for teaching in course of Discrete Mathematics based on a traditional textbook Ralph P. Grimaldi, Discrete and Conbinatorial Mathematics an Applied Introduction, fourth edition. Actually this package is a natural development and a further edition of the package ”Boolean.m” in MATHEMATICA, which has been used by the author during a long time for teaching in this course.[1][2] The packages ”Boolean algebra” and “Set theory” for TI 89 contains programs which allow to display different steps with illustrative explanations calculation in the Boolean algebra and Set theory.[3] Calculators allow to change the teaching process by replacing of MATHEMATICA with TI-89 due to their safety, low price and because they are easy to use and are possible to develop and provide. Of course MATHEMATICA has more powerful calculating possibilities, but calculators are very flexible, and can therefore be used during lectures in big rooms without technical facilities. References: 1. I.B.Gachkov ”Teaching Discrete Mathematics with Computer Algebra: A New Approach to Modern Algebra and Error-Correcting Codes”, El. Proceedings of the Conf.of Applications of Computer Algebra IMACS-ACA\'97 , Hawaii, http://www.math.unm.edu/ACA/1997/ Proceedings/education/Hulth_abstract.txt (in cooperation with K. Hulth) 2. I.B.Gachkov ”The algorithms of discrete mathematics and graph theory with MATHEMATICA and TI-83,89” 6th IMACS Conference on Applications of Computer Algebra (June, 25-28, 2000) Proceedings 3. I.B.Gachkov ”Teaching in discrete mathematics with TI-83”. TiM-2000 The Techniques in Mathematical Teaching, University of Dalarna, Falun, Sweden 27 – 29 October 2000. Proceedings (in Swedish) ====>> Wednesday 06th of February 2002 09:12:52 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Andreas Griesmayer TU-Graz Institut fuer Softwaretechnologie Inffeldgasse 16b, 8010 Graz / Austria agriesma@ist.tu-graz.ac.at Mitvortragende: Vortrag: Tools fuer die interaktive Spezifikation von Problemen Vortrag acdca deutsch Seit der Einfuehrung von algebraischen Systemen (CAS) in die mathematische Ausbildung hat sich die Bedeutung der Spezifikationsphase erhoeht. CAS-Tools bieten eine gute Rechnerunterstuetzung, stellen aber keine Hilfe bei der Spezifikation zur Verfuegung: Auswaehlen einer Funktion mit den passenden Parametern muss nach der Spezifikation gemacht werden. Das Ziel des ISAC-Projekts ist ein \"educational CAS\", das alle Phasen unterstuetzt: modellieren, spezifizieren und loesen. Zum Zweck der interaktiven Spezifikation wird in ISAC das mathematische Wissen in einem dreidimensionalen Universum entlang der Axen \"domains\", \"problem types\" und \"methods\" verwaltet. Der Vortrag behandelt das Problem bei einer so grossen und komplizierten Wissensbasis die UEbersicht zu behalten sowie entsprechende Tools um dies zu bewerkstelligen. Es werden bereits implementierte Tools zum Durchsuchen der Problemtyp-Achse und dem interaktiven Spezifizieren vorgestellt. Weiters werden neue ISAC-features zum Spezifizieren und Loesen von Problemen durch Aufteilung in Teilprobleme praesentiert. ====>> Wednesday 06. February 2002 09:44:27 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Wilfried Herget Univ. Halle-Wittenberg Ulestr. 9, 06114 Halle / Germany herget@mathematik.uni-halle.de Mitvortragende: Vortrag: A PICTURE TELLS A STORY OF WELL OVER 1,000 WORDS Workshop acdca beide “Maths means calculating!” – All right, but that is certainly not the whole story: there is far more to mathematics than that! In this talk, some unusual open-ended problems are presented which may be used at secondary school. Here, calculating is not the main focus of attention, but rather the steps before all the calculations: “Here is a situation. Think about it!” (Henry Pollak) The true value of such a problem and its solution lies in the pleasure you have derived from courageously taking your own steps, from being creative and bold in search of the right answers, and from experiencing what it is like to find a rough solution by yourself, instead of reverently looking up to the answer, or getting somebody else to work it out for you. ====>> Wednesday 06. February 2002 11:17:29 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Stefan Karnel Institute für Software Technologie, TU Graz , / skarnel@ist.tu-graz.ac.at Mitvortragende: Vortrag: Computer Algebra für Brüche -- angepasst an Ausbildungszwecke Vortrag acdca deutsch Rechnen mit Brüchen ist ein grundlegender Teil des Mathematikunterrichts. Erklärungen zum Bruchrechnen beziehen sich dabei hauptsächlich auf die bekannten Rechengesetze zum Kürzen, zum Addieren, usw. Computer Algebra Systeme (CAS) jedoch verwenden zum \'Bruchrechnen\' nicht diese Gesetze, sondern Verallgemeinerungen des euklidischen Algorithmus. Im multivarianten Fall sind diese Algorithmen jenseits dessen, was im Mathematikunterricht normalerweise gelehrt werden kann. Somit stehen die etablierten CAS-Algorithmen im Konflikt mit der Zielsetzung des ISAC-Projektes: Dieses zielt auf ein \'educational CAS\', welches in Schritten arbeitet, die dem Benutzer auf Anfrage zur Erklärung mitgeteilt werden. Solche Erklärunge sollen beim Bruchrechnen also die bekannten Rechengesetze betreffen. Der Vortrag präsentiert \'simluiertes Rewriting\' als Lösungs des Problems beim Bruchrechnen, trotz Verwendung etablierter CAS-Algorithmen dennoch Erklärungen auf die bekannten, elementaren Rechengesetze zurückzuführen. Anforderungen seitens Interaktivität an \'simuliertes Rewriting\' werden diskutiert, und die Implementierung dieser neu entwickelten Technik in ISAC demonstriert. ====>> Wednesday 06. February 2002 08:14:17 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Peter Flynn Department of Science and Maths Education, The University of Melbourne, Australia , 3010 Melbourne / Australia p.flynn@pgrad.unimelb.edu.au Mitvortragende: Vortrag: Technical and Pedagogical Challenges in Constructing CAS-Permitted Examination Questions: Some Principles Vortrag acdca The advent of CAS-permitted mathematics subjects in upper-secondary school systems present many technical and pedagogical challenges to examination authorities and textbook authors. A study of questions from non-CAS examinations suggests that CAS renders some traditional questions redundant for technical and/or pedagogical reasons and for others, it shifts the balance of abilities assessed. In a technical sense, CAS influences many facets of examination question design such as structure, language, explicitness, accessibility to users of different CAS and marking schemes. On a pedagogical level, careful consideration needs to be given to the nature and bandwidth of mathematical abilities we want (and are able) to assess in CAS-permitted examinations. One mathematical activity requiring careful scrutiny is the assessment of proof especially when the construction of the proof is achieved mainly by symbolic manipulation and/or use of algebraic or trigonometric identities. Many non-CAS examinations contain question parts structured around instructions such as ‘show that’ or ‘prove’ and these are likely to be affected by CAS. In this paper, the suitability for the future use of ‘show that/prove’ questions is scrutinised from this dual perspective and reasons for any lack of suitability are highlighted. As CAS can alter the number and nature of required intermediate steps to such questions, a set of principles for the language and structure of ‘proof’ questions will be proposed and discussed using international examples and data from The University of Melbourne’s CAS-CAT project. ====>> Thursday 07th of February 2002 12:30:18 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Peter Flynn Department of Science and Maths Education, The University of Melbourne, Australia , 3010 Melbourne / Australia p.flynn@pgrad.unimelb.edu.au Mitvortragende: Vortrag: Technical and Pedagogical Challenges in Constructing CAS-Permitted Examination Questions: Some Principles Vortrag acdca The advent of CAS-permitted mathematics subjects in upper-secondary school systems present many technical and pedagogical challenges to examination authorities and textbook authors. A study of questions from non-CAS examinations suggests that CAS renders some traditional questions redundant for technical and/or pedagogical reasons and for others, it shifts the balance of abilities assessed. In a technical sense, CAS influences many facets of examination question design such as structure, language, explicitness, accessibility to users of different CAS and marking schemes. On a pedagogical level, careful consideration needs to be given to the nature and bandwidth of mathematical abilities we want (and are able) to assess in CAS-permitted examinations. One mathematical activity requiring careful scrutiny is the assessment of proof especially when the construction of the proof is achieved mainly by symbolic manipulation and/or use of algebraic or trigonometric identities. Many non-CAS examinations contain question parts structured around instructions such as ‘show that’ or ‘prove’ and these are likely to be affected by CAS. In this paper, the suitability for the future use of ‘show that/prove’ questions is scrutinised from this dual perspective and reasons for any lack of suitability are highlighted. As CAS can alter the number and nature of required intermediate steps to such questions, a set of principles for the language and structure of ‘proof’ questions will be proposed and discussed using international examples and data from The University of Melbourne’s CAS-CAT project. ====>> Thursday 07th of February 2002 12:38:26 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Dante Silva AMA Computer University 2299 Pasong Tamo Extension, 1233 Makati / Philippines dantesilva2000@yahoo.com; mpjustan@amaes.edu.ph Mitvortragende: Mario Balancio Russell Diona Elena Velasco Vortrag: AN APPROACH TO IMPROVING A COURSEWARE ON ANALYTIC GEOMETRY Vortrag acdca The instructional use of computers remains a pervading study among educators. Concerned with methodologies and technologies appropriate to the teaching of Analytic Geometry which are more responsive to the needs of the time and the background of the learners, the researchers developed a courseware on Analytic Geometry that integrates an interactive multimedia software. The project had three phases. Phase I involved the design and the development of the courseware. Phase II dealt on the evaluation of the software module. Phase III involved its deployment in the Internet. During Phase II, two groups were formed: the control group and the case group. Through the test item analysis performed on the past departmental final examinations in Analytic Geometry, the researchers identified circle and parabola as the relevant specific topics for the study. This paper shall dwell on two matters: the design of the courseware; and the development and evaluation of the software module named CircleandParabola@Net as an aid to teaching circle and parabola. Phase II of the study showed positive results. Learning took place after the students were exposed to the software module. The use of the software module is significantly more effective than the lecture-discussion method of presenting the lessons based on the students’ achievement test. ====>> Thursday 07th of February 2002 02:53:12 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Yuriko Baldin Universidade Federal de São Carlos Rod. Washington Luiz km 235, 13565-905 São Carlos, SP / BRAZIL yuriko@dm.ufscar.br Mitvortragende: Vortrag: Analysing the limitations of technology in teacher prepartion courses Vortrag acdca Recently, many nice examples of technology-based classrooms and activities can be seen in the literature. Most of them are successful experiments or descriptions of activities with some specific software. With the advances on the research on new teaching methodologies, a new generation of mathematics teachers, either prospective or in-service, should be trained to use efficiently the information already available from different sources. In fact, one of the objectives of modern teacher preparation courses is to prepare teachers with skills to analyze the existing material as well as to create their own activities. In this context, we raise some questions to be put into discussion: a) \"Are the teachers being prepared to realize the limitation of technology in teaching activities and to analyze the possible causes?\" b) \"Are the teachers being prepared to recognize any conceptual troubles in technology-based activities and to propose solutions?\" The aim of this presentation is to analyze these questions through a comparative study of the capabilities of CAS, DGS and graphic calculators, based on concrete examples of mathematical content. We think that a discussion on these questions would improve the understanding of the role of technology in the educational context and its importance on the formation of teachers. ====>> Thursday 07th of February 2002 12:35:45 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Test Kutzler ACDCA , / b.kutzler@eunet.at Mitvortragende: Vortrag: Test with Derive 5 Vortrag acdca Blablabla ====>> Thursday 07th of February 2002 02:29:20 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Elvira Dr. Malitte Martin-Luther-Universität, Fachbereich Mathematik/Informatik , 06120 Halle / D malitte@mathematik.uni-halle.de Mitvortragende: Vortrag: Mit dem Sinus auf der Spur des Mondes Vortrag acdca deutsch Aus der Tageszeitung können Daten für Mondaufgang und Monduntergang gesammelt werden. Dabei stellt sich die Frage: \"Wie verändert sich die Mondscheindauer im Laufe der Zeit?\" Ausgehend von realem Datenmaterial wird eine Aufgabensequenz vorgestellt, die schrittweise zu einer angemessenen mathematischen Beschreibung hinleitet. Sowohl die Aufbereitung der vorliegenden Daten, die zunächst nur im Stunden-Minuten-Format vorhanden sind, als auch die mathematische Auseinandersetzung mit der funktionalen Beziehung \"Tag -> Mondscheindauer\" stellen grundlegende Aspekte der Aufgabensequenz dar. Die grafische Veranschaulichung führt zur Idee der Sinuskurven-Anpassung, diese Idee wird Schritt für Schritt durchdacht und realisiert. Der Grafikrechner erweist sich dabei als angemessenes und leistungsfähiges Werkzeug, mit dem die Aufgabe zu einem interessanten, vielgestaltigen Auftrag wird. Die Aufgabe ist sowohl in der Phase der Erarbeitung der Sinusfunktion geeignet als auch zum Festigen, Wiederholen oder selbstständigen Üben. Verzichtet man auf die Anpassung einer Sinuskurve an die Ausgangsdaten, d.h. stellt man den funktionalen Zusammenhang als solchen in den Mittelpunkt, so ist eine Bearbeitung bereits ab Klasse 7 denkbar. ====>> Thursday 07. February 2002 02:40:43 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Tena Golding Southeastern Louisiana University SLU Box 10370, 70402 Hammond, LA / USA tgolding@selu.edu Mitvortragende: Vortrag: Assessing Geometric Concepts with the Digital Camera Vortrag acdca The proposed session will discuss a digital camera project used in a geometry class for future elementary school teachers. The project, “Geometry is All Around Us,” was designed to help assess students’ ability to connect the course material to their everyday surroundings. This end-of-semester group project required at least 10 different photographs reflecting 10 different geometric concepts that had been covered in class. The geometric properties of each photo had to be stated in the form of a caption, story, etc. When the projects were shared with the rest of the class, rich discussions not only helped reinforce some concepts and help clarify possible misconceptions but also served as a nice review for the final exam. Since the format of the final project was left up to the students, the various submissions included posters, scavenger hunts, storybooks, I-spy games, etc. which provided a variety of very creative presentations. During the proposed session sample projects will be shared as well as the rubric for the evaluation of the project. Students’ reactions to the project will also be discussed. ====>> Thursday 07th of February 2002 07:02:03 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Andrei Kirillov Moscow Power Engineering Institute Krasnokazarmennaya, 105835 Moscow / Russia KirillovAI@mpei.ru Mitvortragende: Vortrag: The package AcademiaXXI integrating Word and Derive Vortrag derive AcademiaXXI is a package for educational, scientific, and technology purposes. Tha package consists of 7 modules: STEM Plus (Student Teacher Engineer Mathematics), CLab (Computer Laboratory), TablES (Tables for Economics and Statistics), TestAc (Tests with computers), TutAc (Tutorial tools), FreeSoft (Compilers and all that), TeXWord (Publishing tools). Microsoft Word is the user interface in all modules. It is integrated with Derive. A user can send formulas from Word to Derive and obtain the Derive results as parts of the Word documents. Several programs that establish such Word--Derive interaction improve some Word and Derive options. For example, computations with approximate numbers like 1.234 +-0.0023 are possible. The modules STEM Plus, CLab, and TablES have many options for calculations in the Word tables and are more effective than Exel in this field. Derive is used to produce the tests and to verify the test results in the module TestAc. In the tutorial packages based on TutAc, Derive helps the students to solve the problems. The examples of tutorial packages based on TestAc and TutAc are given in other presentations to this conference. ====>> Thursday 07th of February 2002 07:11:55 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Olga Zimina Moscow Power Engineering Institute Krasnokazarmennaya, 105835 Moscow / Russia ZiminaOV@mpei.ru Mitvortragende: Vortrag: Computer tutorial packages based on STEM Plus from AcademiaXXI Vortrag acdca The tutorial packages are presented that teach students linear algebra, analytic geometry, calculus, and other topics of mathematics. They are based on the modules TutAc and TestAc from the package AcademiaXX that integrates Word and Derive. The tutorial packages can be used in the personal computers and via Internet. Classromm examples are given that show that the packages enable new methods for teaching mathematics. The packages are integrated with textbooks in the so coled tutorial complexes. The experience of using such complexes in the distant education is presented. ====>> Thursday 07th of February 2002 07:26:33 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Olga Zimina Moscow Power Engineering Institute Krasnokazarmennaya, 105835 Moscow / Russia ZiminaOV@mpei.ru Mitvortragende: Marina Bourkovskaya Vortrag: Automated preparation and verification of tests using TestAC from AcademiaXXI Vortrag acdca MS Word is integrated with Derive in the module TestAC to produce a package that enables to automatically generate the test variants and to verify the student answers to the tests step by step. MS Word is the user interface in TestAc. Therefore, the test variants are the Word documents and the sudent answers are the Word documents too. Special programs that establish the Word--Derive interaction can take formulas from the Word documents, send them to Derive for verification and represent the Derive results in the student documents as teachers usually do it in Russia. Several examples are given of the student works and their verification by TestAc. ====>> Thursday 07th of February 2002 07:40:56 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Otto WURNIG Institute of Mathematics (University of Graz) Heinrichstrasse 36, A-8010 GRAZ / AUSTRIA otto.wurnig@uni-graz.at Mitvortragende: Vortrag: Using PC and TI-92 in teaching linear regression and correlation on different levels in the grammar school. Vortrag acdca After the recent reforms of the curricula in mathematics, statistics and the use of the computer were fixed in different grades of the grammar schools. This offers a good possibility to develop such difficult concepts as linear regression and correlation on different levels of precision. In grade 8 the pupils make the first steps towards Two-Variable-Statistics. Without a computer the pupils of grade 8 plot the data x and y as coordinate pairs per hand. By doing so they sometimes realize e.g. that y has the tendency to be directly proportional to x. This makes the pupils try to draw a straight line which fits the points. If a computer is available in the classroom, you can demonstrate the solution of this problem easily with the help of a software program like MATHEASS. After the input of the coordinate pairs you get the function term of the approximation curve, the coefficient of determination, the correlation coefficient and the standard deviation together with the diagram. It is very important not to take sets of data out of the school books only. I allow the students of grade 8 to work with their own data (length and mass) or help them to find an actual event (referendum \"Veto against Temelin\") to test the correlation. If all the pupils use the TI-92 the med-med regression is a new possibility to find the regression line: In this case it is only necessary to know about the concept of linear function. Later on, in grade 11 or 12, the students can find real data with the help of CBL (calculator-based laboratory) in an experimental way in Physics and find the regression type in Mathematics. With the computer or TI-92 the students can plot the two regression lines very quickly and with the two slopes they find a new aspect of the concept of determination. ====>> Thursday 07th of February 2002 11:00:57 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Marissa Justan AMA Computer University 59 Panay Avenue , 1100 Quezon City / Philippines mpjustan@amaes.edu.ph Mitvortragende: Vortrag: Programming Permutation Multiplication in Derive Vortrag derive Various studies on interconnection networks have gained interests in recent years. The quality of an interconnection network is often investigated by assessing its degree and diameter. These properties are important as a network’s diameter corresponds to the worst communication delay for broadcasting messages in the network while the degree describes the largest number of connections made to an individual processor. Recent developments of technologies have given us the prospect to new approaches in both the research and the teaching of the subject. One approach is computing the diameter by permutation multiplication. However, there are not many tools to support this process. In this paper, we shall illustrate permutation multiplication in the context of computing the diameter of an interconnection network and we shall show a Derive function that was developed to assist in teaching the concepts to the undergradute level. ====>> Friday 08th of February 2002 08:07:27 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Valeriu ANISIU University \"Babes-Bolyai\" Cluj, ROMANIA Kogalniceanu 1, 3400 Cluj-Napoca / ROMANIA anisiu@math.ubbcluj.ro Mitvortragende: Vortrag: Solving linear systems containing parameters with DERIVE Vortrag derive In any Computer Algebra System, a linear system of equations containing parameters is solved only generically. For example, for a simple system as 2x+3y=5, 4x+ay=10, only the solution x=5/2, y=0 is obtained, even if for a=6 the system has an infinity of solutions. The situation in this example is however simple, because the determinant equals 2a-12 and the parameter value a=6 can be examined separately. But for a null determinant or in the case of non square systems, the \"singular\" cases are harder to find. The purpose of this paper is to obtain a general DERIVE function which is able to deal with such systems. The main idea is to use a customized version of the function ROW_REDUCE which returns the Gauss-Jordan form of a matrix and the singular values of the parameters. The paper also contains the DERIVE programs and examples. ====>> Friday 08th of February 2002 12:09:56 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Frantisek Mraz Department of Mathematics, University of South Bohemia Jeronymova 10, 37115 Ceske Budejovice / Czech republic mraz@pf.jcu.cz Mitvortragende: Vortrag: Project Oriented Problems with Maple in Teachers Training sonstiges acdca The educational system in the Czech republic has a good level, which has been maybe even very good as regards fact knowledge of pupils. The system has been, however, criticized because of too much of memorizing and routine work. As the process of education has been usually inertial, a required improvement should be done, apart from other things, by some changes in teachers training. The presentation gives an information about project oriented problems which have been used in teachers training curriculum at our department. To improve our approach the experience of other participants would be useful. The idea is to give projects which solution needs to combine knowledge of different courses. The next goal is to stimulate experimentation and modelling, and to provide students with the space for their own discoveries. Therefore, several projects include randomly generated or parametric data. Students should construct problems with their own input data, too. To reach the above goals Maple has been used as it facilitates experimentation and enables to extend significantly the range of problems that cannot be solved successfully by hand calculation. ====>> Friday 08th of February 2002 02:38:41 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Rafael Barbastefano Fundação Getulio Vargas Praia de Botafogo, 190, 22253900 Rio de Janeiro / Brazil rafael@fgv.br Mitvortragende: Luiz Carlos Guimarães Elizabeth Belfort Bruno Rothgiesser Vortrag: MathChat: using CAS in synchronous distance education Vortrag acdca The last ten years have seen an enormous increase in the use of Computer Algebra packages in teaching mathematics, to the extent of developing specialized interfaces to facilitate their use in specific courses and pedagogical applications. Most educational experiments with CAS are intended for the student on campus, at special purpose facilities. We developed an interface to use CAS for Distance Education called MathChat. It is designed so that the student will have access to the same level of facilities whether on campus, at home or anywhere he/she can connect to the internet. It provides an environment where three complementary means of input are available: a text area similar in most respects to what is available in a \"normal\" chatroom, an area where command lines can be uploaded to the server, and a formula generation area, where the user can upload formulas and mathematical symbols. The result is displayed to the participants of the chat in a single window, much like a conventional chatroom, except that the messages will include a flexible array of mathematical expressions, graphs, and even animations. We will present the software and discuss its use in distance education courses for high school teachers. ====>> Friday 08th of February 2002 04:11:54 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Vladimíra Petrašková Department of Mathematics, UNIVERSITY OF SOUTH BOHEMIA Jeronýmova 10, 371 15 Èeské Budìjovice / Czech Republic petrasek@pf.jcu.cz Mitvortragende: Jindøich Klùfa Vortrag: Teaching mathematical analysis with Maple. sonstiges acdca Presently there is a discussion in the Czech Republic concerning the role of computer in teaching of mathematics. Supporters of mathematical programs believe that students are unnecssarily overloaded with theory and that they try to reduce it. On the contrary, opponents of computer teaching refer to a mindless application of these programs, which results in the fact that the students are convinced that every thing can be algorithmized.There is such a reality that mathematical programs can enable a student to solve respective problem. However without knowledge of respective theory, the student is not always able to reach a correct solution. Many times, with the help of computer, he can also come to a meaningless conclusion. The content of the lecture is a model lesson of the workshop of mathematical analysis with the application of mathematical software, i.e.of Maple program. ====>> Friday 08th of February 2002 05:24:35 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Sergey Biryukov Moscow State Pedagogical University Malaya Pirogovskaya, 29, 119992 Moscow / Russia svb3@hotmail.ru Mitvortragende: Vortrag: Dimensionless products derivation in DERIVE Vortrag derive Dimensional analysis is very helpful as a complex natural science problems solving support. The use of dimensional products usually reduce the dimension of the problem to be solved and thus dramatically reduce the number and complexity of the real world and computer simulations. As the number of dimensional products sets are dozens for real problems and the derivation of each product need several high order determinants CAS DERIVE was used for dimensional matrix generation, base units powers calculation and clear mathematical form representation. The appropriate utility DIM_PROD is written. Its main function DIM_PROD() argument is a two column matrix of parameters names and its dimension. The result is a vector of sets of independent dimensional products expressed in parameters names. The utility supports TI-92+ - like units notation, default units customization, units conversion and equations reduction to the dimensionless form. ====>> Friday 08th of February 2002 05:45:31 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Sergey Biryukov Moscow Pedagogical State University Malaya Pirogovskaya, 29, 119992 Moscow / Russia svb3@hotmail.ru Mitvortragende: Valery Kuzminikh Vortrag: The role of random perturbations and control vector restrictions in the problem of spacecraft optimal control Vortrag derive The problem of the spacecraft trajectory optimization in the presence of random perturbations of the control vector is usually solved by the reduction to the boundary problem of Bellman equation. We extended the above problem with the restricted orientation of control vector – the system of linear equations. Bellman’s equation is transformed to the quasilinear parabolic PDE and an approximate symbolic solution for the case of initial function that is quadratic in adjustment parameters is derived. CAS DERIVE was helpful in substitutions and symbolic manipulations, especially bulky 3D Poisson integral integration. The result is visualized in 3D with DERIVE and the role of perturbations and restricted direction of control vector is analyzed. ====>> Friday 08th of February 2002 05:52:04 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Sergey Biryukov Moscow Pedagogical State University Malaya Pirogovskaya, 29, 119992 Moscow / Russia svb3@hotmail.ru Mitvortragende: Dmitry Guskov Igor Makarov Vortrag: Deriving Real World Data Vortrag derive The main aim of our current project is to make a CBL-like (CBL is a Calculator Based Laboratory by Texas Instruments Inc.) system using DERIVE and regular computer input/output ports (Game, LPT, COM) and such regular devices as mouse, joystick, sound card, WEB-camera etc. Three examples of laboratory works are presented: “Fresnel Equations”, ”Damped Oscillations”, ”Alternating Current Circuits”. The first one uses DERVE for DOS, original data collecting program (Pascal) and a keystroke simulator Scancode. The 2nd and the 3d uses DERIVE for Windows and original (Kylix for 2nd) and commercial (Sound card based oscilloscope for the third) data collection programs and Hotkey keystroke simulator. ====>> Friday 08th of February 2002 05:55:09 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Jean-François Nicaud IMAG-Leibniz 46, avenue Félix Viallet, 38031 Grenoble / France Jean-Francois.Nicaud@imag.fr Mitvortragende: Denis Bouhineau Thomas Huguet Vortrag: The Aplusix-Editor Vortrag acdca The Aplusix-Editor is a computer system (also called Edix in some papers) that aims at filling a gap, among systems for algebra, between tutors like MathXpert and PAT, and Computer Algebra Systems (CAS). Here is the gap: on one hand, tutors allow the student to solve problems by applying small local commands to sub-expressions (e.g., combine like terms, extract a common factor). In the best cases, the system can help the student to solve problems step by step and can give some explanation, but the system is problem-directed and limited to a particular domain defined by the tutor. On the other hand, CAS are general purpose systems for doing mathematics without any concern/insight for a particular domain-problem. CAS allow the student to solve problems in one step by applying strong global commands (e.g., factor a polynomial, solve an equation). Neither help, nor explanations are available. In both systems, the student cannot produce his/her own steps according to his/her own tempo and have them just verified by the system. With the Aplusix-Editor, the student produces his/her own steps with the help of an editor of algebraic expressions. At each input, when the typed expression is well-formed, the system calculates the equivalence between the expression at the current step and the expression at the previous one, and tells the result to the student by drawing an equivalence link that is crossed in red when there is not equivalence. The editor is an advanced two-dimension editor that has better algebraic properties than the few current ones (e.g., MathType or the editor of Mathematica). The equivalence is currently calculated for a class of expressions including polynomials, systems of linear equations, equations and inequalities of one variable with a degree less or equal 3. The Aplusix-Editor has been experimented with two groups of 9th grade students: a regular class and a group of volunteers in a controlled experiment out of the class. The results are very positive: the students learned some algebra and liked to use the system. We are currently working to add features to the Aplusix-Editor to get an educational CAS. These features are small local commands like tutors’ ones and strong global commands like CAS ones. The presentation will include a demonstration of the system. ====>> Friday 08th of February 2002 06:32:21 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Antonio R. Quesada Department of Theoretical & Applied Mathematics, The University of Akron , 44325-4002 Akron, Ohio / USA aquesada@uakron.edu Mitvortragende: Vortrag: On Reforming an Introductory Linear Algebra Course With a TI-92 Vortrag derive This talk will present the results of a three-semester experience with reforming a traditional Linear Algebra course via the use of a TI-92 symbolic calculator. The principles that guided the experience were: 1. Going from the concrete to the abstract, 2. A hands-on, inquiry based approach was used, and 3. The use of technology to: a) facilitate exploration of many relevant applications, b) to discover through experimentation important theoretical results, c) to bridge over cumbersome calculations thus gaining access to relevant algorithms traditionally excluded from our Linear Algebra curriculum, and d) to reduce the time spent and numerical mistakes while students are learning the implementation of algorithms. The basic themes of an introductory Linear Algebra course were maintained, but the approach was changed to a matrix-oriented course. The emphases were on conceptual understanding, on problem solving, and on providing a variety of motivating applications. These were aimed to demonstrate the pervasive use of Linear Algebra in many applied disciplines and its role as an essential tool for scientists in industries. Moreover, the use of special purpose programs and scripts allowed for the inclusion of new topics. ====>> Friday 08th of February 2002 07:51:57 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: James Schultz Ohio University 117 McCracken Hall, 45701 Athens, OH / USA schultz@ohio.edu Mitvortragende: Vortrag: To CAS or not to CAS? -- that is NOT the Question! Vortrag acdca Building on a historical perspective of hand-held technology use, the presentation will provide examples of appropriate uses of CAS, as well as very similar examples where CAS is not the most effective tool. Finally it reexamines the initial question in light of these examples, leading instead to the questions \"When to CAS?\" and \"With whom to CAS?\". Examples will span mathematics for ages 12 to 19. ====>> Friday 08th of February 2002 08:05:00 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Alla Stolyarevska Computer science&mathematics Lenin 39, 126, Kharkov / Ukraine stolyare@altavista.com Mitvortragende: Vortrag: The using of Prolog programming language as a Computer Algebra System Workshop acdca Last years the tendency of genesis of Prolog programming language is observed. Prolog as widely known Lisp allows to manipulate a formula symbolically. We used the Prolog while processing knowledge and the data submitted as symbolical structures. Within a framework of the course of informatics at Kharkov G. S. Skovoroda Pedagogical University the following topics are considered: realization of recurrent and iterative algorithms (calculation of sums, fast degree, Fibonacci numbers), operation with polynomials, other tasks. The course is oriented on those students of mathematics and physics faculty who are getting acquaintance with the methods of declarative programming. The introduction of methods of declarative programming was carried out in different academic groups within several years for the students of different age categories. And the greatest successes at training the undergraduates were achieved. ====>> Friday 08th of February 2002 08:29:26 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Norma A Noguera California State University, Long Beach 1250 Bellflower Boulevard, 90840 Long Beach, California / USA nnoguera@csulb.edu Mitvortragende: mutindi ndunda Vortrag: Making Mathematics Accessible for All Students Using Technology Vortrag derive A common idea between minority and under-represented students who struggle with the learning of mathematical knowledge is that mathematics is a luxury that they cannot afford. Mathematics is a strategic keystone for the economic and cultural development of a nation. In addition, mathematics is a part of any new technological invention. When it is well taught it gives the child the opportunity to develop not only critical thinking skills, but also to learn about the connections between mathematics, science, social studies, etc. The presenters will share their research results working with CAS and Geometer\'s Sketch Pad at the middle, high school and college level. ====>> Friday 08th of February 2002 08:46:41 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: John Olive The University of Georgia 105 Aderhold Hall, 30602 Athens, GA / USA jolive@coe.uga.edu Mitvortragende: Vortrag: Exploring the Dynamic Geometry of Calculus with Geometer\'s Sketchpad 4.0 Workshop acdca Version 4 of the Geometer\'s Sketchpad Dynamic Geometry software (GSP 4) has a new powerful algebraic interface whereby functions can be entered as algebraic expressions and graphed on coordinate axes. These expressions can be constructed from dynamic measures or parameters, associated with geometric constructions or just free-standing. The symbolic derivative of any function can also be obtained and graphed in GSP 4. However, unlike other graphing software, the function graphs can be used as geometric objects. Thus tangent lines to a free point on the curve can be constructed as a true tangent or as the limit of a secant line. Such a construction can provide students with insights concerning the derivative of a function as the slope of the tangent line at any point on the function. Using the new iterate transformation, polygons can be constructed to illustrate the area under a curve and provide calculations of the Riemann sum integral. The workshop will introduce participants to these powerful new features of GSP 4 and involve them in exploring these concepts of calculus through custom-made dynamic sketches. ====>> Friday 08th of February 2002 11:00:28 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Regis OCKERMAN T3 Belgium Achterstraat 30, B 9190 Stekene / Belgium regis.ockerman@pi.be Mitvortragende: Vortrag: Drawing Julia Fractals on the TI 92 Workshop derive Drawing Julia Fractals on the TI 92 Considering the function f(z) = z^2 + c , in the complex plane, is an interesting application of the theory of complex numbers. It is also the source of the Julia Fractals. After a small theoretical introduction, we start with the example c = -0.75 which brings us to the San Marco fractal. Taking advantage of the easy way of working with complex numbers and the graphic possibilities on the TI 92 we develop a program for drawing the fractal. This works pretty fast, considering that a TI 92 is not a Pentium III or IV. This program can draw Julia fractals for any (complex) value of c, belonging to the “apple basket of Mandelbrot”. Some familiarity with the TI 92 is an advantage. Programming knowledge is not required. ====>> Friday 08th of February 2002 11:08:21 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Patricia Cretchley University of Southern Queensland , 4350 Toowoomba / Australia cretchle@usq.edu.au Mitvortragende: Vortrag: Mathematics and Technology: how integrated is this learning partnership? Vortrag derive Recent research by the author and others has revealed remarkably weak correlations between early undergraduate students\' confidence in their ability to do and learn mathematics, and their confidence in using computers, in a range of technology-enriched mathematics learning programs. Clearly this phenomenon has implications for educators who seek to integrate technology effectively into the learning of mathematics. This paper reports on a pilot investigation of the influences that these and related attitudes may have, when students face tasks commonly encountered in early undergraduate mathematics. The study used well-established scales to establish the range of confidence levels for 176 students in a typical Australian first-year undergraduate mathematics Linear Algebra and Calculus course. A representative focus group of 30 students was identified for observation late in the semester, and their attempts (handwork and technology) at eight specific tasks were captured in their usual computer laboratory sessions, where they could use a computer or graphics calculator. The tasks were kept simple, constructed so that the available technology was of varying degrees of use, and required techniques that encapsulated the essence of the much wider range encountered over the semester: solving systems of linear equations, finding determinants, and calculating definite integrals. Students\' responses were assessed to establish two outcomes: how appropriate their choices of approach were, and the degree to which they were empowered by the use of technology. Levels quantifying these \"approach\" and \"empowerment\" outcomes were established for each student, and are illustrated on a scatter-plot. The plot distinguishes between four distinct quadrants of students: those who are confident in both the learning of mathematics and their ability to use computers, those who are not confident in either, and those who are confident in one of the two areas, but not the other. Their responses to technology are compared, implications are considered, and possible directions for further research are discussed. An Appendix gives the scales used to measure mathematics confidence, confidence in the use of computers, and attitudes to technology in the learning of mathematics, with Cronbach alpha reliability ratings. ====>> Saturday 09th of February 2002 07:18:24 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Yuzita Yaacob lecturer National University of Malaysia, 43600 Bangi / Malaysia yy@ftsm.ukm.my Mitvortragende: Noraini Hassan Khairina Atika Mohd Zawawi Hasni Amiruddin Vortrag: Interactive Learning – Mathematica Enhance Calculus (ILMEC) courseware: A Pedagogical Tool to Enhancing Calculus Education in Malaysia Vortrag acdca Traditional mathematics courses emphasize the learning of mathematics through rote work, memorization and mastery of hand methods of solving problems. Although this can result in creating a good human calculator, it is not conducive to in-depth and substantive understanding of mathematical concepts ([1], [2]). In the last decade, there has been a revolution in the teaching and learning of mathematics, both within mathematics and in its related disciplines, due to the introduction of Computer Algebra Systems (CASs) such as Maple and Mathematica. However, an educational problem remains in smoothly integrating a CAS into the whole experience of teaching and learning of mathematics [3]. This project presents ILMEC, a multimedia courseware using a CAS, to serve three roles in the teaching and learning of Calculus. Specifically, the courseware can aid in the [4] (i) mathematical concept and skill development by empower students to deal with multiple representations (numeric, symbolic and graphic) [5], visualization [6], interactivity, experimentation and exploration, (ii) mathematical problem solving by enhancing the ability to focus on the process of problem solving instead of the computational aspect only and solve realistic problems instead of being restricted to contrived problems having “nice solutions”, and (iii) mathematical reasoning by empower students to input different values in order to form conjectures and apply inductive reasoning, and motivate students to think logically to perform a desired task [7]. [1] Scheftic, C. (1996). Teaching Anecdotes and Philosophy [Online]. Available: http://www.geom.umn.edu/~Scheftic/ [1999, July 23] [2] University of Illinois at Urbana-Champaign and Ohio State University. (1997). Calculus & Mathematica [Online]. Available: http://www~cm.math.uiuc.edu/ [1999, July 23]. [3] Keady, G. and Hocking, G. (1996). CAUT Proposal…Combining Computer Algebra Systems and the Internet [Online]. Available: http://www.maths.uwa.edu.au/~keady [1999, July 12]. [4] Kimmins D. and Bouldin E. 1996. Making Mathematics Come Alive With Technology. Seventh Annual Conference on College and Learning, Jacksonville, Florida, USA. [5] Kimmins D. 1989. Curriculum and Evaluation Standards for School Mathematics. National Council of Teachers of Mathematics (NCTM). [6] Klotz E. 1991. Visualization in Geometry: A Case Study of a Multimedia Mathematics Education Project. In Zimmerman W. and Cunningham S. (Eds), Visualization in Teaching and Learning Mathematics (pp. 95:104). Washington D. C.: Mathematical Association of America. [7] Maor D. 1993. An Interpretive Study of the Development of Students Inquiry Skills in a Computerized Classroom. Unpublished doctoral dissertation, Curtin University, Perth, Western Australia. ====>> Saturday 09th of February 2002 09:24:52 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: magda fayek Faculty of Engineering-Cairo university Univ. Avenue, 12612 Giza / Egypt magdafayek@hotmail.com Mitvortragende: Assem Deif Vortrag: A Web-based Tutoring system for calculus Vortrag acdca A web based calculus tutoring system is being developed in Arabic. Our experience at Cairo university is briefed. The intention is to merge our discussion e-group with the tutoring software so that the student stays in one environment. The system presents the text in a well organized form providing flexible navigation facility to move around as required and also directing the students to related topics at other locations. At proper points applets can be triggered to illustrate some concepts such as the applet for demonstrating the effect of taking different number of terms in the Taylor series and/or another that demonstrates how the area of a circle is estimated. An additional utility is the link to the e-group, which enables the student to put questions and get answers from the professor. It also enables the student to browse through previously asked questions and their answers, which are stored in the database. Questions sent by students are first filtered by the professor before adding them to the data base, categorized with respect to the topics or chapters they are related to. Such a link represents a valuable feedback to the professor from his students. This kind of e-learning falls within the broad context of computed-assisted instruction. ====>> Saturday 09th of February 2002 10:05:52 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Piotr Zarzycki Department of Mathematics, University of Gdañsk Wita Stwosza 57, 80-952 Gdañsk / Poland matpz@univ.gda.pl Mitvortragende: Vortrag: From visualizing to proving Vortrag derive Benefits of visualizing mathematics by technology like TI 92+ and mathematically oriented software (DERIVE 5 and CABRI II) are undisputable. On the basis of some examples we would like to show that visualizing techniques could help students to analize certain mathematical problems better and give them a strong support in finding formal proofs for considered problems. We present some tasks taken from school algebra, geometry, number theory and probability; for these problems it is easier for students to pass the bridge between visual and formal solutions. We conclude that the role of technology is essential in building up associations between graphs, drawings and other tools used for the formal proofs. ====>> Saturday 09th of February 2002 10:26:31 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Dr. Sonnhard Graubner Untere Hauptstrasse 86, 09228 Wittgensdorf / Sachsen Sonnhmath@aol.com Mitvortragende: Vortrag: Using Computer Algebra in triangle Geometry Vortrag acdca englisch We demonstrate how computer algebraic methods can be employed to solve problems from classical geometry. An inner point of a plane triangle is called a Brocard point iff the straight lines connecting it with the vertices from three equal angles with the adjacent sides.Any plane triangles containes two Brocard oints. We investigate whether there are triangles for which both Brocard points are situated on the incircle line. By an analytical ansatz we obtain a system of algebraic equations which are subsequently solved using the Groebner package included in the Maple system. The main result is that there exist (up to simularity) exactly four triangles with the required property. Two of them are isoceles and constructible by compass and ruler.The approach allows to attack a wide class of geometrical incidence problems which could not be handled manually due to their algebraic complexity. ====>> Saturday 09. February 2002 05:21:04 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Djordje Kadijevich Mathematical Institute, Serbian Academy of Sciences and Arts Kneza Mihaila 35, 11001 Belgrade / Yugoslavia djkadij@mi.sanu.ac.yu Mitvortragende: Vortrag: Towards a CAS promoting links between procedural and conceptual mathematical knowledge Vortrag acdca Promoting links between procedural and conceptual mathematical knowledge is an important goal of mathematics education that is by no means easy to achieve. As regards CAS-based mathematics education, such a state may partly be caused by some limitations of the available CAS environments. By examining a sample of expressions, functions, equations and inequalities, underlined are possible requirements for a CAS promoting links between the two knowledge types. The requirements suggest how these environments may be refined in years to come to produce a CAS that is more pedagogically oriented. ====>> Saturday 09th of February 2002 06:09:13 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Dusan Pagon University of Maribor Koroska c. 160, SI-2000 MARIBOR / Slovenia dusan.pagon@uni-mb.si Mitvortragende: Vortrag: Analysis of simple branching trees with TI-92 Vortrag derive In the complex plane we start at the center of the coordinate system with a vertical segment of the length one unit. Then we turn to the left and to the right for a positive angle t, not exceeding 90 degrees, and add two new segments of length r<1. The last two steps are repeated infinitely many times, to obtain a self similar fractal object, which we call simple branching tree (SBT). Typical questions about SBT are like: at what relation between r and t the branches of our tree will meet (overlap), and what will be the boundary curve, when there is no overlapping. The integration of algebraic and geometric tools that graphic calculator TI-92 posesses, allow us to find the answers to most of these questions. For instance, by summation of geometric progressions, an explicit connection between r and t is found for the boundary case and the obtained polynomial equations are solved numerically. ====>> Saturday 09th of February 2002 07:35:05 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Walther Neuper Institut für Softwaretechnologie, TU Graz Inffeldg. 16b, 8010 Graz / A neuper@ist.tugraz.at Mitvortragende: Vortrag: Re-engineering von Algebra-Systemen zum Mathematik-Lernen Vortrag acdca deutsch Derzeit verfügbare Computer Algebra Systeme (CAS) bringen die ?white-box? Phase des Mathematikunterrichtes in Schwierigkeiten: Lehrer müssen den Schüler verbieten, das Studium von Konzepten durch ?CAS-Knöpfe Drücken? abzuschneiden. Das ISAC-Projekt zielt auf die Entwicklung eines Softwaresystems, das Mathematik als Methode des schrittweisen Lösens von Problemen aus Technik und Wissenschaft erfahrbar macht, wobei jeder Schritt begründbar ist. Diese Schritte betreffen die Spezifikations- wie die Rechen-Phase, und sie können sowohl automatisch vom System vorgeführt werden, als auch vom Studenten eingegeben (und vom System überprüft) werden. Diese Zielsetzung von ISAC erfordert ein Re-engineering von CAS, und auch gewisse Erweiterungen. Der Vortrag präsentiert die grundlegenden Entwurfsentscheidungen samt den Prinzipien ihrer Realisierung durch Methoden der ?symbolic computation?, diskutiert die Vorteile und Beschränkungen aus diesen Entscheidungen, und demonstriert ausgewählte Beispiele mittels der bereits in ISAC implementierten Funktionalitäten. ====>> Saturday 09. February 2002 08:27:59 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Matthias Goldgruber Institut f\"ur Softwaretechnologie, TU Inffeldg. 16b, 8010 Graz / A goldy@sbox.tugraz.at Mitvortragende: Vortrag: Eine explizite Hierarchie von Typen elementarer Gleichungen Vortrag acdca deutsch Algebra Systeme erweisen sich als höchst leistungsfähig im Zuordnen einer Gleichung zur passenden Lösungsmethode -- es ist eine vergeudete Lerngelegenheit, dass sie dies automatisch und vor dem Benutzer verborgen tun. Das ISAC-Projekt zielt auf ein Mathematiksystem, das seine Schritte in Interaktion mit dem Benutzer durchführt. Im Fall des Gleichungslösens sind dies u.a. die explizite Spezifikation des Gleichungstyps, sowie die Auswahl der zur Lösung der Gleichung vorgesehene Methode. Der Vortrag stellt das Konzept der in ISAC entworfenen Hierarchie von allgemeinen Problemtypen am Beispiel von Gleichungstypen vor, erklärt kurz die zur Implementation verwendeten grundlegenden Techniken aus \'Symbolic Computation\' (matching, rewriting, term orders), und demonstriert die in ISAC verfügbare neuartige Funktionalität interaktiven Spezifizierens mit Benutzerführung. Die Beschreibung der Problemtypen erfolgt in ISAC mit Hilfe der üblichen Formelsprache und getrennt vom restlichen System; deshalb kann die Hierarchie mit beliebigen Problemen aus speziellen Unterrichteinheiten erweitert werden. ====>> Saturday 09. February 2002 08:33:08 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Alan Krempler Institut f\"ur Softwarertechnologie, Techn.Universit\"at Inffeldg.16b, 8010 Graz / A alan@oeh.tu-graz.ac.at Mitvortragende: Vortrag: Zum Design eines elektronischen Arbeitsblattes für Mathematik Vortrag acdca deutsch Algebra Systeme bieten ausgezeichnete graphische Benutzeroberfächen, die Formeln darstellen wie von händischem Rechen gewohnt, und die Rechenarbeit gut in Übersicht halten lassen. Unterlegt man der Rechenarbeit einen exakteren formal-logischen Rahmen, wie er im ISAC-Projekt vorgesehen ist, so entstehen auch an die Benutzeroberfläche zusätzliche Anforderungen. Der Vortrag diskutiert die folgenden Anforderungen an ein elektronisches Arbeitsblatt und demonstriert die in ISAC implementierten Lösungen: (1) Darstellung der logischen Zusammenhänge zwischen den Teilen einer Rechnung, z.B. die Weitergabe von Annahmen aus der Lösung eines Teilproblems, oder die Voraussetzung für die Anwendung einer Rechenregel (etwa: Nenner <> 0). (2) Integration von \'Browsern\' über die Wissensbasis: Problemtypen zur Spezifikation einer Aufgabe, dafür verfügbare Lösungsmethoden, für gewisse Lösungsschritte anwendbare Rechenregeln sind zu sichten und auszuwählen. (3) Strukturierte Darstellung des spezifizierten Problems und der Lösungsschritte in dem Ausmaß an Details, die der Benutzer in einer bestimmten Situation braucht und einstellen kann. ====>> Saturday 09. February 2002 08:38:15 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Heinz Klemenz Gymnasium Wetzikon Reutlingerstr. 11b, 8404 Winterthur / Schweiz hklemenz@geosoft.ch Mitvortragende: Vortrag: Plattformunabhängiges Computerwerkzeug für dynamische Raumgeometrie Vortrag acdca deutsch Die konstruktive Raumgeometrie ist in den letzten Jahren an den Gymnasien immer mehr in den Hintergrund gedrängt worden. Eine ersatzlose Streichung der konstruktiven Aspekte der räumlichen Geometrie wäre aber verhängnisvoll. Das computergestützte Konstruieren mit Raumgeometrie-Software erlaubt dieser Tendenz entgegenzuwirken, indem durchaus anspruchsvolle Aufgaben mit entsprechenden 3D-Werkzeugen elegant gelöst werden können, ohne fundierte Kenntnisse der Darstellenden Geometrie zu besitzen. An vielen Gymnasien in der Schweiz hat sich diese Alternative mittlerweile auch in den Lehrplänen etabliert. Im Vortrag wird das Programm GeometerPRO vorgestellt, welches die in gängigen 2D-Programmen (Euklid, Cabri, Cinderella, etc) enthaltenen Konzepte (Zugmodus, Ortslinien, etc.) in den Raum überträgt. Die Software ist in der Sprache Java programmiert, wird dadurch auf den schulrelevanten Betriebssystemen verfügbar sein und erlaubt den Datenaustausch zwischen verschiedenen Plattformen. ====>> Saturday 09. February 2002 09:19:06 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Marianna Goroneskul Kharkov Air Force Military Institute Mohnachanskay, 87/35, 61189 Kharkov / Ukraine larin@kharkov.ukrtel.net Mitvortragende: Vortrag: Computer Algebraic System MAPLE in the process of teaching higher mathematics Workshop acdca The process of teaching higher mathematics on the basis of laboratory research work with the use of CAS Maple contributes to improvement of students’ mathematical grounding as well as purposeful formation of their cognitive and research activity. The developed content of the educational and methodical complex includes the content of laboratory works using CAS Maple. The mathematical software can be used by higher mathematics teachers in the process of teaching higher mathematics in the institutes of higher education. The mathematical software can be used by teachers training students in higher mathematics on the basis of laboratory works in the institutes of higher education as well as by students preparing for practical training and credits, for carrying out mathematical researches. Having analyzed the modern state of the problem of the use of new computerized tools in institutes of higher education the conclusion was made that the didactic abilities of mathematical software allow to regard to CAS-Maple as a method of teaching higher mathematics. It’s an active tool and means for teachers to equip students with knowledge, to develop their educational, research and cognitive activity. That is the main goal of development and introduction of the laboratory works system on the basis of CAS Maple into the process of teaching. The laboratory works are intended for studying of the part “Integral and differential calculus of one-variable function.” In our opinion the above mentioned laboratory works system based on CAS Maple is primarily to help teachers to organize the teaching process in the way that ensures active mastering of higher mathematics material by students and promotes ability to avoid false generalizations and baseless analogies, teaches to compare, to reveal similarity and differences of concepts and modes of thinking. And as a result, it promotes a great deal the formation of students’ thinking culture. The use of teaching method on the basis of mathematical software through introduction of laboratory works system into process of teaching mathematics is to form students’ research skills, generalized conceptual systems, methods of mental activity and is based on making cognitive activity more active. ====>> Saturday 09th of February 2002 10:03:14 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: DARJA SILAN Mr.S . biologist PRZANJSKA 17, 1117 Ljubljana, Slovenia / SLOVENIA Darja.Silan@guest.arnes.si Mitvortragende: SELMA STULAR JULIJANA PALCIC Vortrag: DYNAMIC OF SOME BIOLOGICAL ACTIVITIES WITH TI-CBL SYSTEM sonstiges acdca The teachers of natural sciences at the Joze Plecnik Grammar School Ljubljana-Slovenia, are participating in the international project Comenius. We would like to contribute our experiences using CAS environments in particular TI-92. We believe that mathematical experiments supported by the TI-CBL system can be enhanced by various aspects of the biological and physical problems. Our poster represent a carbon dioxide production during germination of various seeds, metabolism of yeast (Saccharomyces sp.), larval and adult stages of mealworm (Tenebrio molitor). In biological laboratory exercises for students, theese experiments are basical but also very demonstrative for better understanding how the different organisms do their metabolism of energy rich substances during aerobic respiration. ====>> Saturday 09th of February 2002 10:04:56 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Robert Decker University of Hartford 200 Bloomfield Ave, 06117 West Hartford, Connecticut / USA rdecker@mail.hartford.edu Mitvortragende: Vortrag: Building Interactive Mathematics Software Vortrag acdca Computer algebra systems are not strong at “fast feedback” exploration. In order to see how a parameter change affects the graph of a function or differential equation one must edit and then reissue a command, which is slow and inconvenient. Tcl/Tk is a free platform independent (mac, windows, linux, unix) language that can be used to quickly build interactive mathematics programs. I have created a number of helper functions (components) which make it even easier for a mathematics educator to create little programs to illustrate particular concepts. These interactive programs can be used as stand-alone programs or as front-ends to computer algebra systems (explore and then transfer the work to the computer algebra system). I will demonstrate some interactive graphing programs that illustrate parameter changes for functions and differential equations, changes in initial conditions for differential equations (it becomes very easy to generate a complete phase portrait when done interactively), and interactive data fitting. I will also discuss benefits to both teachers and students with this approach, and some possible research directions in mathematics education related to this “write and then use” interactive software approach. ====>> Saturday 09th of February 2002 10:46:52 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: rian Morphett Mentone Grammar 63 Venice Street, Mentone, 3194 Melbourne / Australia brian_morphett@hotmail.com Mitvortragende: Vortrag: Using CAS (TI 92+) as an integral tool for learning/teaching mathematics in the secondary school. Vortrag derive The real challenge to using CAS in the secondary mathematics classroom is to perceive it as an integral part of the teaching/learning process rather than an \'add-on\' to the more traditional pedagogical methods that rely heavily on algebraic manipulation to the detrement of seeing the \'big picture\' and leave little time for developing useful applications that students can readily use. Using introductory calculus as a model, CAS will be used to develop the early concepts and algorithms of calculus. This will draw into question the traditional approach of introducing this topic late in the secondary curriculum. It will also suggest that the traditional sequence of topics in this area is not the best way to approach the introduction of calculus when CAS is integrated as a teaching tool. Finally, oral and written assessment procedures, using CAS, will be examined, while still require students to understand and use the fundamental algorithms and logic. ====>> Sunday 10th of February 2002 12:28:57 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: rian Morphett Mentone Grammar 63 Venice Street, Mentone, 3194 Melbourne / Australia brian_morphett@hotmail.com Mitvortragende: Vortrag: Using CAS (TI 92+) as an integral tool for learning/teaching mathematics in the secondary school. Vortrag derive The real challenge to using CAS in the secondary mathematics classroom is to perceive it as an integral part of the teaching/learning process rather than an \'add-on\' to the more traditional pedagogical methods that rely heavily on algebraic manipulation to the detrement of seeing the \'big picture\' and leave little time for developing useful applications that students can readily use. Using introductory calculus as a model, CAS will be used to develop the early concepts and algorithms of calculus. This will draw into question the traditional approach of introducing this topic late in the secondary curriculum. It will also suggest that the traditional sequence of topics in this area is not the best way to approach the introduction of calculus when CAS is integrated as a teaching tool. Finally, oral and written assessment procedures, using CAS, will be examined, while still requiring students to understand and use the fundamental algorithms and logic. ====>> Sunday 10th of February 2002 12:36:38 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Sergey Rakov vice Rector, Kharkov State Pedagogical University Blukhera, 2, 31168 Kharkov / Ukraine Rakov_S@ukr.net Mitvortragende: Victor Gorokh Vortrag: Information Technologies and Analytic Geometry Vortrag derive The book \"Information Technologies in Analytic Geometry\" deals with programming in Derive Environment for analytic solutions of the typical problems in analytic geometry. It covers such topics: ú Vector Algebra (The Orthocenter of the Tetrahedron, etc.), ú Lines and Planes (The Bisect Line of the Trihedral Angle, Square of the Surface Triangle), ú Convex Sets (Convex Hulls, Graphical Solutions of the Systems of Inequalities), ú Surfaces in space (Oplet Curves at the Surfaces, Conic and Cylindrical Surfaces), ú 2nd Order Curves and Surfaces (Intersection Lines and Intersection Points), ú Common Theory of 2nd Order Surfaces (Expert System in 2nd Order Surfaces), ú Geometric Transformations (The Library Of Geometric Transformations of Figures at the Plane, Full Library Of Ornament Constructions at the Plane, etc.) The book includes solutions of the typical problems, collections of problems and hints for their solutions. May be used as in the Analytic Geometry course at the university level as well as in pro-fessional mathematical work as a guide to programming practice in Derive Environment and the library of utilities. ====>> Sunday 10th of February 2002 05:20:42 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Bill Blyth Department of Mathematics, RMIT University , Melbourne / Australia bill.blyth@rmit.edu.au Mitvortragende: Vortrag: Finite Element Methods: Presentation and Animation using Maple Vortrag acdca Maple is widely used in our courses. The role of Maple varies considerably from a small support activity to \"immersion\". We teach a Finite Element Methods course to a large number of engineering students in their third or fourth year. Most of this FEM course uses Maple to do all of the computation and students are provided with Maple files which they need to edit in order to complete the assignments. The final part of the courses uses commercial FEM software. This paper discusses how Maple is used as the presentation medium (as well as the computational tool) in lectures for the Maple part of the course. This includes an animation of the error for a collocation method solution of a Boundary Value Problem (BVP)as the collocation points are changed. This animation cannot be achieved by a naive use of the animate command - the required methodology to produce a more complex animation is discussed. ====>> Sunday 10th of February 2002 10:37:35 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Karsten Schmidt FH Schmalkalden Blechhammer, 98574 Schmalkalden / Deutschland kschmidt@fh-sm.de Mitvortragende: Anke Köhler Vortrag: Einsatz von CAS und symbolischen Taschenrechnern an Hessischen Schulen Vortrag derive deutsch Es sollen Ergebnisse einer im März 2002 durchgeführten Befragung an allen Hessischen Gymnasien, Real- und Gesamtschulen vorgestellt werden. In dieser Untersuchung geht es einerseits um die Erfassung des Ist- Zustandes bezüglich der PC-Ausstattung der Schulen und dem tatsächlichen Einsatz leistungsfähiger Taschenrechner im Mathematik- Unterricht. Andererseits soll festgestellt werden, wie gut sich Lehrkräfte mit symbolischen Taschenrechnern und CAS auskennen und wie häufig sie solche Hilfsmittel persönlich (z.B. zur Unterrichtsvorbereitung) benutzen. Darüber hinaus wird untersucht, ob die Lehrkräfte beim Einsatz von symbolischen Taschenrechnern und CAS mehr Vorteile oder mehr Nachteile sehen und ab welcher Klassenstufe sie leistungsfähige Taschenrechner im Mathematik-Unterricht einsetzen würden, wenn sie die Entscheidung selbst treffen könnten. Die Ergebnisse werden verglichen mit denen einer ähnlichen Befragung an allen Gymnasien, Regel- und Gesamtschulen in Thüringen, die im Frühjahr 2001 durchgeführt worden war. ====>> Sunday 10. February 2002 12:30:27 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Eno Tonisson University of Tartu Liivi 2, 50409 Tartu / Estonia eno@ut.ee Mitvortragende: Vortrag: Equivalence of equations and computer algebra systems Vortrag acdca In connection with the spread of computer algebra systems (and algebraic calculators), the natural question arises: how to change the requirements and emphases of mathematics syllabuses? One possible domain that might be given more consideration in the future is checking the equivalence of equations. In this paper, we examine the solving strategies of school algebra equations and give much attention to equivalence checking. In order to find the solution of an equation, it is often necessary to change it to an equivalent equation. Sometimes it is recommended to use operations which do not guarantee equivalent equations (the extraneous solutions may appear, for instance). To what extent are the computer algebra systems applicable in checking the equivalence of equations? An overview is provided of the capabilities of the currently widespread systems (Derive, Maple, Mathematica and MuPAD). We also examine some possibilities of integrating checking the equivalence of equations in computer algebra systems more fully into the educational process. We present different schemes that describe the teacher\'s and student\'s activities in different situations. ====>> Sunday 10th of February 2002 02:22:14 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Palmira Mariz Venna International School Wagramer Str., 1220 Vienna / Austria pmariz@vis.ac.at Mitvortragende: Vortrag: Dynamic Geometry in Classroom Workshop acdca Geometer’s Sketchpad is a powerfull Dynamic Geometry Software that became an important tool for the study of high school geometry. This software enable teachers to use different approches to geometry topics and provides a wide range of teaching strategies: explorations of open-ended problems, guided investigations, construction activities,.... GSP is also a useful tool to produce teaching materials such as worksheets. The aim of this workshop is to introduce participants to the main features of GSP through exploration of sample classroom activities. Previous knowledge of the program is not required. ====>> Sunday 10th of February 2002 04:50:07 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Josef Lechner Bundesgymnasium Amstetten Anzengruberstr.6, A-3300 Amstetten / Österreich lejos@aon.at Mitvortragende: Vortrag: Von der Binomialverteilung zur Normalverteilung Vortrag derive beide Der Vortrag gibt eine Zusammenfassung der Möglichkeiten und Veränderungen, die sich durch den Einsatz eines CAS im Stochastikunterricht ergeben. Vor dem Hintergrund eigener Unterrichtserfahrungen wird insbesondere auf die erweiterten Möglichkeiten zur Visualisierung von Problemstellungen und auf die veränderte Behandlung operativer Hürden bei der Normalverteilung (Verzicht auf die Standardisierung) eingegangen. Es soll gezeigt werden, wie CAS (hier Derive 5 und TI-92 Plus) eingesetzt werden können, um Schülerinnen und Schülern zu helfen tragfähige Grundvorstellungen wichtiger Begriffe innerhalb der beurteilenden Statistik zu entwickeln. ====>> Sunday 10. February 2002 05:01:39 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Josef Böhm International DERIVE & TI-92 User Group D´Lust 1, 3042 Würmla / Österreich nojo.boehm@pgv.at Mitvortragende: Vortrag: Programming in DERIVE - Some Introductory Examples Workshop derive beide In this workshop we will use some examples to inform the participants about the possibilities how to connect the power of a CAS with the flexibility of a programming language. Special impact is given how to treat local and global variables. The chosen examples will cover problems from within secondary school level, because it is our opinion, that programming should become - again - part of math education. We can do this now without changing the platform using DERIVE 5. ====>> Sunday 10. February 2002 05:57:57 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Josef Böhm T^3-Österreich D´Lust 1, 3042 Würmla / Österreich nojo.boehm@pgv.at Mitvortragende: Vortrag: The History of the International DERIVE & TI-92 User Group Vortrag derive englisch The DUG was founded in 1991 as a group of DERIVE enthusiasts. Some years later it was opened for TI-92 users, too because of the very close relationship between DERIVE and the TI-92 CAS-implementation. In this lecture we will give a summary of the DUG-history, which is in a tight connection with the DERIVE history, starting with DERIVE version 1.06 accompanied by demonstrations of some highlights and remarkable contributions from 45 DERIVE & TI-92 Newsletters. ====>> Sunday 10. February 2002 06:08:05 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Max-Günter Schröfel Gymnasium Antonianum Bohmkestr. 3, 33154 Salzkotten / Deutschland Max-Guenter.Schroefel@fernuni-hagen.de Mitvortragende: Vortrag: Splines mit dem TI92 (DERIVE) Vortrag derive deutsch Es werden zunächst zwei Anwendungsbeispiele für Splines vorgestellt: a) Glatte Flächen über Stützpunkte werden in der Autoindustrie verwendet. Dieses Vorgehen wurde im Unterricht nachempfunden werden, indem wir bei einer Motorhaube drei Stützpunkte und die Neigung der Windschutzscheibe festhielten. Daraus wurde die glatte Projektionskurve der Motorhaube mit Hilfe von Splines ermittelt. b) Zwei Autobahnstücke sollen mit einer Straße verbunden werden. Die Abfahrtspunkte, ein Umgehungspunkt und die Autobahnrichtungen werden festgehalten, daraus wird dann der Straßenverlauf bestimmt. In der Theorie der Splines ist das Hauptziel das Gleichungssystem zu reduzieren, um es besser berechnen zu können. Dabei konzentriert man sich auf eine Unbekannte des Polynoms, die andern werden dann mit Hilfe dieser berechnet. In den Beispielen wird bei der Berechnung der Splines das Lösen des umfangreichen Gleichungssystems dem TI 92 überlassen, die Arbeit für den Anwender besteht in der Erstellung der großen Matrizen. Im zweiten Teil soll nun gezeigt werden, wie die Splinematizen vom Rechner erstellt werden können. Es wird der systematische Aufbau der Splinematrizen untersucht und kleinere Teilmatrizen aufgespürt, die letzlich auf drei 4x1-Matrizen und Nullmatrizen zurückgeführt werden. Die Splinematrizen werden mit einer Hand voll Matrizenoperationen zusammen gesetzt. Nach der Lösung des Gleichungssystems werden dann die Splinepolynome bestimmt. Es wird ein Beispiel mit drei Punkte, der Anfangs und Endsteigung gegeben. Durch Programmierung könnte alles automatisiert werden. ====>> Sunday 10. February 2002 07:17:35 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Jon Sims Williams Dept Engineering Maths, Bristol University University Walk, BS8 1TR Bristol / UK Jon.Sims.williams@bris.ac.uk Mitvortragende: Vortrag: Conolidating Learning through Self-Help Testing Vortrag acdca In the popular culture right across Europe, mathematics is often seen as a hard subject that is largely irrelevant to the bulk of today\'s youth. When these same people get into employment however, they find they need more mathematics but now they must teach themselves or follow a distance-learning course. Reading examples in textbooks may leave the reader feeling he understands, but it is only though being tested on unseen problems that a student can consolidate his understanding. This paper describe a way in which such students can be offered the opportunity to test themselves. The TAL database of classified questions allows students to generate tests on the topics they are studying though a web-interface from home. These automatically generated tests allow students to validate their skills against a standard, eg the SEFI syllabus, and to get feedback on questions they cannot do. Often the hints provided in feedback on questions are not adequate, so we can direct the student using the question classification system to support material that will give them targeted help with background understanding that may be the cause of their difficulties. ====>> Sunday 10th of February 2002 07:24:05 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: LAGRANGE Jean-baptiste IUFM de Reims France 5, rue Yves Montand, 35590 St Gilles / FRANCE lagrange@univ-rennes1.fr Mitvortragende: Vortrag: CASYOPEE, a symbolic environment for secondary students and teachers Vortrag acdca This presentation is based on the work of a French team of math educators, teachers and computer scientists supported by the National Institute for Pedagogical Research. It starts from a reflection about the integration of CAS (Computer Algebra Systems) in schools and the support that the development of new software environments might bring. We reflected on a general approach of the design of environments around a CAS Kernel and we are currently developing and experimenting two prototypes. Our approach is based on two principles. The first principle is about the mathematical knowledge that the use of CAS should develop. CAS is basically an \"expression transformer\" and, to use CAS properly, students should think of functions from the recognition of equivalent expressions. In order that students get this \"transformation sense \", emphasis has to be put on algebraic proof. The second principle deals with the learning situation. Our aim in a software development around a CAS kernel is to provide the student means to organise efficiently his(er) resolution of problems on functions and to give the teacher means to foresee student’s resolution. The two prototypes are oriented towards tasks. One is the study of functions, the other is the calculation of limits. Beside generic graphing, numeric and symbolic facilities, they include specific capalitities for each task and for algebraic proofs. Extensive parametrisation functionalities are offered to help the teacher in the preparation of the student’s resolution. ====>> Sunday 10th of February 2002 08:05:44 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: David Sjostrand Elof Lindälvs gymnasium Varlagard 1, S-434 32 Kungsbacka / Sweden david@ydsa.se Mitvortragende: Vortrag: A Computer Integrated Mathematics Teaching at the Swedish Natural Science Program Vortrag derive Powerful computers and easy to use mathematics soft wares enables a modern, fun and interesting mathematics teaching. Since autumn 2000 we integrate the use of computers in all math courses at the Natural Science Program at Elof Lindälvs gymnasium, Kungsbacka, Sweden. Students are working projects and self dependent. Traditional written tests have to some extent been replaced by project tasks. The students participate in compulsory national tests. We will present samples of project tasks. The use of computers in mathematics teaching has inspired us to have another view of mathematics teaching at secondary school level. We will argue that · Students can attain a lot of understanding of graphs by using interactive Excel sheets created with the help of DERIVE. 3D-plotting can and should be included. · Computer algebra makes it possible let students solve problems that are more demanding algebraically than earlier – they get the chance to see so much algebra that their understanding of it might increase. · Once the students have understood the basic idea of derivatives you can let them solve differential equations numerically. Evaluation of definite integrals can be regarded as solving differential equations. · Computer algebra and spreadsheets make analytical geometry more interesting and powerful – you can easily deal with complicated algebraic formulas and see that they really are true. · The computional power of computers makes it possible to include mathematics that traditionally has not belonged to school mathematics in secondary school mathematics. Students can for example evaluate not only simple integrals but even double and triple integrals exactly and numerically. ====>> Sunday 10th of February 2002 08:38:33 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: David Sjostrand Elof Lindälvs gymnasium Varlagard 1, S-434 32 Kungsbacka / Sweden david@ydsa.se Mitvortragende: Vortrag: A Computer Integrated Mathematics Teaching at the Swedish Natural Science Program Vortrag derive Powerful computers and easy to use mathematics soft wares enables a modern, fun and interesting mathematics teaching. Since autumn 2000 we integrate the use of computers in all math courses at the Natural Science Program at Elof Lindälvs gymnasium, Kungsbacka, Sweden. Students are working projects and self dependent. Traditional written tests have to some extent been replaced by project tasks. The students participate in compulsory national tests. We will present samples of project tasks. The use of computers in mathematics teaching has inspired us to have another view of mathematics teaching at secondary school level. We will argue that · Students can attain a lot of understanding of graphs by using interactive Excel sheets created with the help of DERIVE. 3D-plotting can and should be included. · Computer algebra makes it possible let students solve problems that are more demanding algebraically than earlier – they get the chance to see so much algebra that their understanding of it might increase. · Once the students have understood the basic idea of derivatives you can let them solve differential equations numerically. Evaluation of definite integrals can be regarded as solving differential equations. · Computer algebra and spreadsheets make analytical geometry more interesting and powerful – you can easily deal with complicated algebraic formulas and see that they really are true. · The computional power of computers makes it possible to include mathematics that traditionally has not belonged to school mathematics. Students can for example evaluate not only simple integrals but even double and triple integrals exactly and numerically. ====>> Sunday 10th of February 2002 08:40:07 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Lyudmyla Bilousova Kharkiv State Pedagogical University Artema str, 29, 61078 Kharkiv / Ukraine belousova@kgpu.sa.net.ua Mitvortragende: Vortrag: Assessment of Pupils\' Knowledge in Mathematics Vortrag acdca Advantages of testing method for assessment of pupils’ knowledge and the diagnostics of its structure are widely known: objective results, along with technological convenience and a lot of information obtained. Those are the reasons why both educators and pupils are interested in testing. We have developed some sets of tests on different topics in mathematics curriculum for secondary school. The following two kinds of tests have been developed: 1. Tests with tasks of different levels of difficulty. Those tests cover all parts and all levels of the subject topic chosen for testing. 2. Tests with answers of different levels. In this case each task corresponds to a particular element of the topic and the answers suggested for pupils\' analysis reflect the increasing level of mastering the material. Our tests have been used for thematic testing in Kharkiv secondary schools and enabled the teachers to realize the teaching function of testing. Also, those tests enhanced pupils\' interest in the subject, made a solid basis for creating a system of individual monitoring for pupils\' progress in learning, and, in addition, supplied us with some valuable information concerning the quality of teaching in Kharkiv schools. ====>> Sunday 10th of February 2002 08:45:47 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Tatyana Byelyavtseva Kharkiv State Pedagogical University Artema str, 29, 61078 Kharkiv / Ukraine byelyavtseva@kgpu.sa.net.ua Mitvortragende: Vortrag: Teaching Divisibility of Numbers with Computer Technology Vortrag acdca Divisibility of numbers is studied in different parts of secondary school algebra. Teachers notice that pupils usually experience difficulty in studying this topic. To help pupils to study this topic quickly and easily the program “Divisibility of Numbers” has been developed. This program can be used for two purposes: for learning and for testing. While pupils learn new material the program supply them with all the relevant information on divisibility of numbers. The program also gives pupils the opportunity to do some exercises on divisibility. When pupils test their knowledge the program gives them a number of tasks and correct (as well as records) their activity. The methods of using this program in classes on algebra has been developed. The program “Divisibility of Numbers” has been successfully used in secondary school. The results showed that the use of the program helped to increase pupils’ understanding of the topic and made the process of learning much more enjoyable. ====>> Sunday 10th of February 2002 08:48:15 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: David Sjostrand Elof Lindälvs gymnasium Varlagard 1, S-434 32 Kungsbacka / Sweden david@ydsa.se Mitvortragende: Vortrag: A Computer Integrated Mathematics Teaching at the Swedish Natural Science Program Vortrag derive Powerful computers and easy to use mathematics soft wares enables a modern, fun and interesting mathematics teaching. Since autumn 2000 we integrate the use of computers in all math courses at the Natural Science Program at Elof Lindälvs gymnasium, Kungsbacka, Sweden. Students are working more with projects in a self dependent way. Traditional written tests have to some extent been replaced by project tasks. The students participate in compulsory national tests. We will present samples of project tasks. The use of computers in mathematics teaching has inspired us to have another view of mathematics teaching at secondary school level. We will argue that · Students can attain a lot of understanding of graphs by using interactive Excel sheets created with the help of DERIVE. · 3D-plotting can and should be included. · Computer algebra makes it possible let students solve problems that are more demanding algebraically than earlier – they get the chance to see so much algebra that their understanding of it might increase. · Once the students have understood the basic idea of derivatives you can let them solve differential equations numerically. Evaluation of definite integrals can be regarded as solving differential equations. · Computer algebra and spreadsheets make analytical geometry more interesting and powerful – you can easily deal with complicated algebraic formulas and see that they really are true. · The computional power of computers makes it possible to include mathematics that traditionally has not belonged to school mathematics in secondary school mathematics. Students can for example evaluate not only simple integrals but even double and triple integrals exactly and numerically. ====>> Sunday 10th of February 2002 08:50:19 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Angel Balderas University of Querétaro, Mexico Cerro del Cubilete 113, 76090 Querétaro / Mexico balderas@sunserver.uaq.mx Mitvortragende: Vortrag: Integrating Derive in the didactics of Laplace Transform Vortrag derive We present a didactic pathway of integration of CAS type software, specifically Derive, for the teaching and learning of the Laplace Transform in the context of differential equations courses at university level, working with 19 years old students. Some phenomena linked with this integration are evidenced, such phenomena are related with teacher\'s preparation and with student\'s creativity. Some didactic problems due to the passage of doing math in a paper and pencil environment to doing math in information technology environment are discussed. We present the implementation with Derive of different processes associated with the topic: from calculating transforms to calculating inverse transforms, from the solution of differential equations to the solution of systems of differential equations, from the use of special functions to the use of the convolution theorem. Each one of the exposed ideas has been experienced in regular courses with students of different engineering careers. ====>> Sunday 10th of February 2002 09:27:42 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: David Bowers Suffolk College Rope Walk, IP4 1LT Ipswich / United Kingdom david.bowers@suffolk.ac.uk Mitvortragende: Vortrag: Computer algebra within a spreadsheet-style environment Workshop derive Spreadsheets have long been a useful tool for analysing mathematical problems numerically, and computer algebra systems allow us to approach problems symbolically. In this workshop we demonstrate how the Texas Instruments TI-92 goes some way to incorporate computer algebra into a simple spreadsheet environment. Examples of some unexpected applications will be investigated. Firstly the basic functions and operations of the TI-92 Data/Matrix Editor are reviewed. Then various activities covering a range of mathematical areas are proposed. The first of these deal with numerical applications of the type that may be familiar to users of spreadsheets in the mathematics classroom, and serve to illustrate the spreadsheet-style use of the Data/Matrix Editor. The subsequent activities introduce some features of computer algebra systems that hitherto have not been available within a spreadsheet environment. Participants are encouraged to review the activities and their usefulness for demonstrating and investigating mathematical concepts in new ways, to consider the advantages and technical limitations of the Data/Matrix Editor for this purpose, and to speculate on the future development of algebraic spreadsheets. ====>> Sunday 10th of February 2002 09:55:49 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Philip Oostenbroek Marist College Ashgrove 82 Moola Rd, 4060 Ashgrove / Australia philoostenbroek@yahoo.com Mitvortragende: Vortrag: Creating Favourable Attitudes in Mathematics in 12 year old boys. Vortrag acdca A series of activities and projects designed to create favourable attitudes in primary mathematics through the use of basic facts and geometry. Students will appreciate that Mathematics can be fun and is used in all aspects of life. Basic computer programs using Draw, Excel and Word and Powerpoint can be used. ====>> Sunday 10th of February 2002 11:36:32 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Bernnard Cunningham LakeVille Community Schools; Delta College; Mott Community College 135 Madison St., 48768 Vassar, Michigan / USA bcunning@gfn.org Mitvortragende: Vortrag: Use the Program Editor of the TI-89/92 Calculator to write a program to solve cubic equations. Workshop derive The workshop will begin with a brief history lesson on the mathematicians that were responsible for the development of the cubic formula. To equalize all participants, programming the quadratic formula will be the first activity. This will address Input/Output (I/O) and Control (CTL) submenus as well as the capabilities of a word processor in copying and pasting. The cubic formula will then be analyzed and a plan of attack will be developede for the writing of this program. (The old flow chart plan of attack.) The participants will be allowed some time to write their programs. To close the activity, programmers will be allowed to show their programs. Now, if time permits, this workshop will turn to a lecture on the proof of the cubic formula. ====>> Sunday 10th of February 2002 11:40:55 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Bernard Cunningham LakeVille Community Schools; Delta College; and Mott Community College 135 Madison St., 48768 Vassar, Michigan / USA bcunning@gfn.org Mitvortragende: Vortrag: Symbollic Math Guide - Two Years of Data on an Introduction to Integrated Math Course Vortrag derive In the winter & spring of 2001, the students at LakeVille High School in Otisville, Michigan, USA were involved in the piloting of the SMG Application in two ways. A Precalculus class helped evaluate the application before it became public with a very critical eye. The second phase was the involvemnet of 90 students who would not be classified as model students. These 90 students were enrolled in a class entitled \"Introduction to Integrated Mathematics\". A pre-test was given. The students were then introduced to the TI-92 calculator and the SMG Application. After some time a post test was givne (which was identical to the pre-test) The data is very interesting. The second set of data will be from the 2001-02 school year with 50 students from the same titled class. At the conclusion of presentation of the data from both years the floor will be open for questions and discussion of the Symbollic Math Guide Application. ====>> Sunday 10th of February 2002 11:50:27 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Michael Pemberton The University of Queensland Coopers Road, 4072 ST LUCIA, BRISBANE / AUSTRALIA mrp@maths.uq.edu.au Mitvortragende: Vortrag: CAS-aided Mathematical Modelling:an immersion course using PBL Vortrag acdca CAS-aided Mathematical Modelling:an immersion course using PBL Mike Pemberton, Mathematics Department, University of Queensland, Australia This paper reports on a course for biological and physical science students where Maple was used in all forms of teaching - in all lectures, tutorials and exams - something which has not been done before. All topics were introduced by real life problems which led both to discussions of the associated theory and computer implications. The course had five chapters - (1) Problems of optimization, where four problems introduced students to the need for understanding the difference between local and global maxima and minima, using Maple procedures to see the dependence of optimum solutions on parameters, approximations and the need for Maple for algebraic simplification and computation. (2) Biological and business models - epidemics, daily temperature, seasonal variation and trend, additive and multiplicative models; the Economic Order Quantity (EOQ) models, sensitivity analysis and discount models - using Maple to both set up and solve these problems (3) Functions of several variables, using Maple for graphs and contours of functions of two variables, partial derivatives; relative and percentage error with many examples from physical chemistry and biology. (4) The Area Problem - how to approach calculating areas, integration techniques, numerical integration and extensive use of Maple to find harder integrals. (5) Differential and difference equations - models of exponential increase and decrease; growth by generation; migration and seasonal growth; Logistic growth; models of epidemics like AIDS; Future value, annuities and mortgages - using Maple\'s dsolve and rsolve to solve and then plot solutions for these problems. Students learned the necessary Maple as they went along and each tutorial was in the computer laboratory where they learned some new Maple and then used it in real life examples. In lectures Maple was used extensively and we, as a class, often discussed tutorial problems that had problems and how to overcome them. The exams were in front of the computer and students could bring along their Maple manual that I wrote especially for them and any other notes they might want. Evidently, with this approach, it is possible to discuss a wide and often difficult range of problems with students who are not mainstream mathematicians very successfully and all students reported that they had at last understood the need for theory to underpin these ideas, whereas before it had just been a boring and irrelevant subject. ====>> Monday 11th of February 2002 01:11:42 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Michael Pemberton The University of Queensland Coopers Road, 4072 ST LUCIA, BRISBANE / AUSTRALIA mrp@maths.uq.edu.au Mitvortragende: Vortrag: Modelling Air-resistance using Maple Vortrag acdca Modelling Air-resistance using Maple Mike Pemberton, Mathematics Department, University of Queensland, St. Lucia, Brisbane, Australia This workshop takes the participants through an assignment given to my engineering and science students to investigate how to model air-resistance. First students drop plastic bottles containing various quantities of water from buildings of various heights to test which of four models is most applicable - air-resistance is proportional to (1) the velocity (2) the square of the velocity and whether (3) per unit mass or (4) directly. Participants will be given the data collected by my students and use Maple to solve each differential equation and test the solutions for validity. For the second part, students use the same bottle, hang it on an elastic string, pull it down and release it. Students then observe the subsequent motion and try to fit the best model to it - linear or non-linear. Participants will use Maple to solve each differential equation, animate them and then watch to see how well the animation matches the physical motion. Seit Wien so weit von Australien ist, so glaubte ich, ich sollte zwei Arbeiten präsentieren. Ich hoffe, dass dies eine gute Idee und in Ordnung ist. Mike Pemberton, Mathematics Department, University of Queensland, St. Lucia, Brisbane, Australia This workshop takes the participants through an assignment given to my engineering and science students to investigate how to model air-resistance. First students drop plastic bottles containing various quantities of water from buildings of various heights to test which of four models is most applicable - air-resistance is proportional to (1) the velocity (2) the square of the velocity and whether (3) per unit mass or (4) directly. Participants will be given the data collected by my students and use Maple to solve each differential equation and test the solutions for validity. For the second part, students use the same bottle, hang it on an elastic string, pull it down and release it. Students then observe the subsequent motion and try to fit the best model to it - linear or non-linear. Participants will use Maple to solve each differential equation, animate them and then watch to see how well the animation matches the physical motion. Seit Wien so weit von Australien ist, so glaubte ich, ich sollte zwei Arbeiten präsentieren. Ich hoffe, dass dies eine gute Idee und in Ordnung ist. ====>> Monday 11th of February 2002 01:15:59 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Judith Hector Walters State Community College 500 S. Davy Crockett Pkwy, 37813 Morristown, TN / USA Judy.Hector@ws.edu Mitvortragende: Vortrag: Problem Solving, Programming and Pedagogy Vortrag derive Good problem solvers are in short supply for careers in science, mathematics, engineering and technology (SMET). This paper reports on how teaching programming on TI-89/92 calculators enhances student problem solving skills and mathematical understanding. The author has taught computer programming for SMET students at an American high school and a two-years college (first two years of university.) She uses a high level computer language (FORTRAN) on a main frame in parallel with TI-89/92 language. The structured programming topics include top-down design, step-wise refinement and algorithm development. The paper discusses pedagogical issues and suggests a sequence of instruction to develop understanding of uses of iteration and recursion. In learning programming, students read, flowchart and modify already developed programs before solving problems with programs they develop themselves. CAS software offers preprogrammed approaches to problems such as root finding and numerical differentiation and integration. One reason for teaching programming is so that a student will be able to apply such software to non-routine problems. ====>> Monday 11th of February 2002 01:22:57 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Roger Peck California State University, Bakersfield 9501 Stockdale Highway, 93311 Bakersfield, California / USA rpeck@csub.edu Mitvortragende: Vortrag: Teaching Statistics on the Internet Vortrag acdca This presentation will discuss how the Internet can be incorporated into a statistics course. The presenter has been using the Web in all his courses for the past eight years and has been teaching courses completely on the Web for the past four years. Using the Internet when teaching Statistics can have benefits to student learning. For example, since the interaction between students and faculty is almost entirely written, questions and answers are better thought out than when the spoken word is used. Student interaction can be facilitated by using email or discussion groups. There are many data sets available on the Internet that can be used in the classroom for teaching or projects. This presentation will explore some well-known sites where data can be found and used in an introductory statistics course. ====>> Monday 11th of February 2002 02:45:42 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Peter Jones School of Mathematical Sciences, Swinburne University John St, 3122 Hawthorn / Australia pjones@swin.edu.au Mitvortragende: Vortrag: Exploring the potential of a hand-held computer algebra system using a classic problem Vortrag acdca In this presentation, the classic ‘volume of a box’ problem will be used to illustrate the alternative solution strategies available to students when they have everyday access to graphics calculators with symbolic algebra capabilities. In the process, and using the traditional pencil and paper solution as a benchmark, an attempt will be made to identify those mathematical skills that remain critically important when students have everyday access to such technology. This is of relevance to future curriculum development when graphics calculators with symbolic algebra capabilities become the norm in the classroom. ====>> Monday 11th of February 2002 03:03:23 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Valentyna Pikalova Kharkiv State Pedagogical University Artema 29, 61002 Kharkiv / Ukraine vpikalova@hotmail.com Mitvortragende: Vortrag: The Role of Macros in Teaching Geometry: Developing Students\' Algorithmic Skills Vortrag acdca Dynamic Geometry Software (DGS) enables students to define such objects as points, lines (or segments, rays and vectors, circles or arcs) and construct geometric figures that depend on them by classical construction tools -- straight edge and compass, linear transformations etc. But one of the most important issues is that learner can create new geometric tools by using macro techniques. On one hand additional tools gave student new opportunities in problem solving. On the other hand macro constructions in DG environment involves learner into the framework of algorithms. Students are taught to decompose complex algorithms into units for constructing geometrical objects and record macros. Also analysis of capabilities of pre-recorded macros by tracing greatly improves learners\' activity. Development of macro constructions plays an important role in forming student\'s algorithmic culture as well as in efficiency of solving geometrical tasks. The article focuses on the methodological questions of macros implementation in teaching and learning geometry in secondary school. ====>> Monday 11th of February 2002 03:14:31 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Julie Saunders Royal Melbourne Institute of Technology Swanston Street, 3000 Melbourne / Australia julie.saunders@rmit.edu.au Mitvortragende: Bill Blyth Vortrag: Using CAS as a Pedagogical Tool in the Training of Pre-service Mathematics Teachers Vortrag acdca The Mathematics department at RMIT delivers a mathematics course to pre-service secondary mathematics teachers. The course aims to strengthen the students\' understanding of the more advanced secondary Mathematics curriculum topics and to extend their knowledge in areas such as complex variables, differential equations and power series. Use of the computer algebra system Maple is incorporated into the delivery of the course. The objective here is to use the CAS as a tool to help consolidate the students\' understanding while also exposing them to the potential of such tools for their own teaching in the future. Here, we present examples from the Maple worksheets used and summarise the findings of a feedback survey consisting of questionnaires, student journals and structured interviews. We found that the students favoured the use of pen and paper exercises alongside Maple work on the Complex Variables topic. In a Maple worksheet demonstrating Newton\'s Law of Cooling, we found that the CAS was able to provide the scaffolding in the form of computation of derivatives, allowing the students to focus on the modelling process. The students also highlighted the visualisation aspects of a worksheet on Taylor Series as revealing to them more clearly the concept of Radius of Convergence. ====>> Monday 11th of February 2002 07:01:09 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Peter Lüke-Rosendahl Bismarckschule Hannover Im bultfeld 53/54, 30966 Hemmingen / Deutschland PeterLR@web.de Mitvortragende: Vortrag: Berührkreis dreier Kreise am Beispiel der Sichel des Archimedes Vortrag acdca deutsch Möglichkeiten, Grenzen und Verbindungen im Gebrauch von DGS und CAS werden exemplarisch vorgeführt. Gesucht ist der Kreis, der die drei Kreise der Sichel des Archimedes (Shoemakers knife) gleichzeitig berührt. Durch \"Trial and Error\" in DGS wird die Basis für eine mögliche Untersuchungsrichtung aufgezeigt, die dann mit CAS realisiert wird. ====>> Monday 11. February 2002 12:07:13 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Giora Mann Levinsky College of education , 76868 Beit Chanan / Israel giorama@macam98.ac.il Mitvortragende: Nurit Zehavi Shafik Halifa Vortrag: VECTORS IN CAS – A PORTFOLIO FOR TEACHERS Vortrag derive VECTORS IN CAS – A PORTFOLIO FOR TEACHERS Giora Mann, Nurit Zehavi, and Shafik Halifa The Weizmann Institute of Science Rehovot 76100, Israel Nurit.zehavi@weizmann.ac.il Abstract In the local high school curriculum a course on vectors was introduced, about 15 years ago, in order to integrate algebra and geometry in an advanced level course. The teachers often complained, that “when students learn about the direction vector they tend to loose the direction”. The aim of the MathComp project at the Weizmann Institute is to broaden opportunities for learning and to promote greater mathematical understanding by using a Computer Algebra System (CAS). Within this framework, we have developed a portfolio for teachers, Vectors in CAS. We will demonstrate how teachers learn to customize the portfolio to their privileges, in terms of the mathematical content, the explicitness of the text, and the visual representation. The examples are taken from a unit dealing with the distance between lines in 3D space, through various representations. The CAS environment enables students and teachers to reflect on previously learned related topics, as well as to formalize and appreciate the concept of the distance between two geometric figures. ====>> Monday 11th of February 2002 01:51:28 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Giovannina Albano Dip. Ingegneria dell\'Informazione e Matematica Applicata via Ponte don Melillo, 84084 Fisciano - SA / Italy albano@diima.unisa.it Mitvortragende: Matteo Desiderio Vortrag: Improvements in teaching and learning using CAS Vortrag derive In this work we wish to present an innovative proposal for a differential equations course supported by software tools. The aims we have placed in such experience are principally three: - we are interested in showing the students of the concrete applications of the daily life that can be described and interpreted through the use of the differential equations, discovering in such a way, the real adhesion between experience and mathematical environment, giving motivation to the students for the study of the subject; - we want to add the interactive use of mathematical software to the traditional used didactic methodologies: in fact studies recently performed have put in evidence than the interactive use of such tools allows to arrive at a superior abstraction level in the solution of mathematical problems, avoiding more easily the happen of misconception due to the creation of wrong mental models; - we want to stimulate the student to have a more critical attitude towards the solution of the problem described by a differential equation. It is well known in fact that the differential equations represent a base tool in the mathematical modelling in varied applicative fields as physic, astronomy, economic sciences and others. According to the problem which has determined the equation and to the kind of differential equation which is wanted to solve, we wish that the student to establish in critical way if it is necessary to find a solution qualitative or quantitative, in the second case if it must be precise or approximate, and in this last hypothesis he must establish the wanted approximation level, to be able, on the basis of this, to choose an opportune solving method. In fact, a preliminary study of the equation can suggest the most suitable numerical method and vice versa an experimental study by numerical methods can provide information about qualitative appearances of the solution. ====>> Monday 11th of February 2002 03:28:06 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Marlene Torres-Skoumal Vienna International School Strasse der Menschenrechte, 1220 Wien / Austria marlenes@aon.at Mitvortragende: Vortrag: Curricula and Assessment Model for the integration of CAS into the high school program Vortrag acdca The Vienna International School has been integrating computer algebra systems into its MYP (Middle Years Program) curricula for the past four years. Curricula and assessment criteria has been rewritten to reflect the changes in learning objectives brought about by this new technology. This presentation will highlight the VIS model for the use of technology in classroom teaching and assessing. The model classifies curricula and assessment into three main categories: technology free, technology supported, and technology focused. The technology free parts attempt to assess the numerical and algebraic components of the curricula that are not obfuscated by computation. In addition, technology neutral topics are assessed under this caption. The technology supported areas focus upon those numerical, graphical, or experimental skills which can be executed using analytical methods, but would be tedious and time consuming otherwise. Students can freely choose between paper and pencil methods taking time element into account, or can rely upon the technology to assist when necessary. Their judgment as to the appropriate use of the technology would form part of the assessment criteria. The technology focused areas bring into the classroom possible concepts or problem types that are unapproachable or have no (accessible) analytical solutions. This would include sophisticated problem solving, investigations, and mathematical modelling. Samples of assessment of the above three areas, including student samples, will be shared with the participants. ====>> Monday 11th of February 2002 06:36:12 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Kurt Kreith Dept of Mathematics, Univ of California , 95616-8633 Davis, CA / USA kkreith@math.ucdavis.edu Mitvortragende: Vortrag: Re-thinking the Algebra Curriculum in the Computer Age Vortrag acdca Technology has implications for both how we teach and what we teach. To address the latter question, it is of interest to focus on a topic central to the standard algebra curriculum, the solution of quadratic equations. More important than the ability to solve such equations are the mathematical ideas one encounters in the process. In the computer age, the solution of quadratic equations can provide a basis for conveying concepts other than factoring and completing the square. Finding square roots by \"divide and average\" constitutes an intuitive form of Newton\'s method, and calculators such as the TI-83 give this a geometric representation in terms of cobweb diagrams (rather than tangent lines). Now it is possible (at a pre-calculus level!) to extend Newton\'s method from x^2 - c = 0 to the general quadratic equation. In this process, the student encounters important concepts such as \"fixed point\" and \"contraction mapping\" while taking a modern, technology-based approach to a classical topic. The fact that technology provides an alternative to \"solution in terms of radicals\" has important implications. It enables the student to approach cubic and higher order polynomial equations with practical tools. It also enables the teacher to relate the wonderful world of fractals to topics central to the school curriculum. ====>> Monday 11th of February 2002 06:39:15 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Johann Engelbrecht University of Pretoria , 0186 Pretoria / South Africa jengelbr@scientia.up.ac.za Mitvortragende: Ansie Harding Vortrag: Internet Calculus: How does Big Brother watch? Vortrag acdca The instructor stays mainly in the background when presenting an internet course and does not have the hands on opportunity to motivate students and check daily progress. Yet, it is still largely the instructor\'s responsibility to present a successful course and to help maximise the opportunity of every student to succeed. It is therefore important to monitor the progress of students and act when required. One possible tool for doing this is to employ co-operative learning where students are divided into small groups and are responsible for assignments and projects as a group, thus letting the group synergy act as a catalyst for performance. Another tool that can be used for letting the student monitor his or her own progress is that of internet quizzes. We discuss our experience in using these two tools. We investigate the benefits and difficulties and the overall success. ====>> Tuesday 12th of February 2002 06:56:17 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Moses Eben CEEP (Liberia) Carey Street, P.O. Box 20-4364, Monrovia, Liberia, 1000 Monrovia / Liberia ceeplbr@yahoo.com Mitvortragende: David Dahn n/a n/a n/a n/a Vortrag: INTERNET AS AN TEACHING AID Vortrag acdca This paper presents the Internet as an teaching aid. It will discuss the Interbet as it helps to give the ability to think thus informed in decision-making; enhance skill in communication so one can develop a defending argument or work effectively in groups; hence, produce quality work after acquiring and using information. Further, we will explain that as an information source, it is a site in which the relations between the state, society, community and individual are worked and reworked thus a real teaching aid. Finally, the Internet shapes and fashions the kind of people that one can become. ====>> Tuesday 12th of February 2002 09:26:13 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Carl Leinbach Gettysburg College 300 N. Washington Street, 17325 Gettysburg, PA / USA leinbach@cs.gettysburg.edu Mitvortragende: Vortrag: Programming with TI-Interactive! Workshop derive TI-Interactive is a general purpose tool for doing mathematical investigations. It allows students to use a PC-based platform to perform many of the functions of a TI graphing calculator: do scientific calculations, define variables and evaluate formulas, do statistical analyses, graph functions, do parametric and polar plots, etc. In addition, it allows them to connect to any website containing data and copy that data into a TI-Interactive! work sheet for statistical analysis. It also allows for connectivity with a TI-calculator to copy data collected by the TI-Ranger or TI-CBL. In short, it is a powerful tool with much of the functionality of a TI-83 for use in a mathematics classroom. TI-Interactive! also has a powerful Computer Algebra System that contains most of the functionality of the TI-89/92 plus. This all is packaged in a way that allows students to create nicely formatted and displayed interactive documents that can display their results. What is not as well known is that TI-Interactive! also allows a user to write programs in a large subset of TI-Basic. In this workshop participants will be given an introduction to programming within the context of TI-Interactive! . After a brief introduction to the available programming structures and some of the programming operators that are available and others that are not available, they will write some simple functions starting with an interval characteristic function (which can be done without programming). The workshop will continue to develop some more interesting functions and also show how TI-Interactive! can graph these user-programmed functions (a process that is not immediately obvious). The culmination of the workshop will be an illustration of how to draw the graph of a slope field and an Euler and Runge-Kutta approximation to a function defined in terms of a rate of change. ====>> Wednesday 13th of February 2002 01:59:19 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Carl Leinbach Gettysburg College 300 N. Washington Street, 17325 Gettysburg, PA / USA leinbach@cs.gettysburg.edu Mitvortragende: Vortrag: Growing Ideas with a CAS Vortrag derive We are living in a computing environment that stresses Object Oriented Programming. While the user of a particular object may have some idea about how it works, most of the details are hidden from the user. In Mathematics the idea of hiding information about a process is seen as a violation of the goals of mathematical pedagogy. However, as mathematics teachers, we do hide information from our students. We have been doing it for years! We do it in the form of presenting simplified models that take into account only that part of the real world process that can be modeled and solved using the mathematical theory and techniques the student is capable of applying. This form of information hiding may be more dangerous than that hidden by the computer scientist. It leaves the students with an incomplete understanding of the underlying process that they are attempting to describe. It subverts one of the reasons for studying mathematics - providing a better understanding of our world and how it operates. In this presentation we will consider a case of the flight of a batted baseball (a ball of diameter approximately 7.6 cm made of thread wrapped around a cork core and wrapped in a stitched leather covering). We will begin the investigation assuming that the flight of the ball is a parabola. However, data collected on the flight of a batted ball find that the parabolic model does not describe this situation. A cubic curve gives a good approximation to particular curves, but the coefficients tell us little or nothing about the underlying phenomenon. To really understand the phenomenon we will need to construct a physical model that involves rates of change. This is where the information hiding comes in to play. Most students do not have the background to do this. The CAS the students have at their disposal can help them construct their model and give a general result that can predict the flights from arbitrary initial inputs. The net result is that students can do the modeling process, and the CAS can generate the results. Thus, we will watch the idea grow from a simple, but incorrect, quadratic curve model through the attempt to use regression techniques to gain understanding to the (still simplified) model using rates of change. ====>> Wednesday 13th of February 2002 02:24:46 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Esther Openhaim Levinsky College Jasmin 12 , 44355 Kfar-Saba / Isreal esther_o@netvision.net.il Mitvortragende: Vortrag: Using CAS for Developing Students’ Reflection and Reasoning – Vortrag derive Using CAS for Developing Students’ Reflection and Reasoning – A Case Study on the Subject of Polynomial Interpolation Computer-Based environments challenge instructors to design new tasks for mathematics education, because it turns out to be unreasonable to continue to emphasis mathematics’ instruction only on teaching skills (symbol manipulation), when a powerful supportive tool such as Derive5 (a mathematics assistant) can perform better and quicker. For the purpose of enhancing students’ mathematical knowledge, and communications skills, and develop their advanced mathematical thinking we developed a sequence of CAS–based assignments for high school and pre-service students. Derive5 serves as a convenient dynamic tool for making complicated and tedious computation, and so release the user to devote himself to more essential aspects of the mathematics: raising conjectures, investigations, reflection and reasoning. The topic “Polynomial Interpolation” was chosen because of its’ mathematical richness, and its’ applicability to the current computer world. To rouse the student curiosity we start the workshop by presenting a stimulating question: ‘Do you have any idea how a computer calculates the values of a given built-in function such as sin(x) so quickly and so accurately?’ By observing and documenting students’ laboratory work we followed their cognitive paths from visual interpretation of the approximation process to formal reasoning. Dealing with this issue of Polynomial Interpolation exposes the way polynomial interpolation is actually used for the purpose of building \" simple\" built-in computer functions. It added a new viewpoint on the basic idea of approximation and the values of adjacent solutions. At the end of the workshop students are able to construct acceptable approximations for a built-in function justifying any product they might have made. The challenging questions that are posed during the workshop stimulate discourses about various assumptions, which lead to further research work. Consequently it appears that the new CAS-based tasks open for learners a window on new intellectual connections and supports students in building on their own meaning in ways, which converge towards mathematical ways of knowing. The paper discusses the underlying didactical principles of the workshops’ design, convey the goals of two assignments, and describe the lab work of two high school students including their reflection and reasoning on their research process. ====>> Wednesday 13th of February 2002 07:21:57 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Esther Openhaim Levinsky College Jasmin 12 , 44355 Kfar-Saba / Isreal esther_o@netvision.net.il Mitvortragende: Vortrag: Using CAS for Developing Students’ Reflection and Reasoning –A Case Study on the Subject of Polynomial Interpolation. Vortrag derive Computer-Based environments challenge instructors to design new tasks for mathematics education, because it turns out to be unreasonable to continue to emphasis mathematics’ instruction only on teaching skills (symbol manipulation), when a powerful supportive tool such as Derive5 (a mathematics assistant) can perform better and quicker. For the purpose of enhancing students’ mathematical knowledge, and communications skills, and develop their advanced mathematical thinking we developed a sequence of CAS–based assignments for high school and pre-service students. Derive5 serves as a convenient dynamic tool for making complicated and tedious computation, and so release the user to devote himself to more essential aspects of the mathematics: raising conjectures, investigations, reflection and reasoning. The topic “Polynomial Interpolation” was chosen because of its’ mathematical richness, and its’ applicability to the current computer world. To rouse the student curiosity we start the workshop by presenting a stimulating question: ‘Do you have any idea how a computer calculates the values of a given built-in function such as sin(x) so quickly and so accurately?’ By observing and documenting students’ laboratory work we followed their cognitive paths from visual interpretation of the approximation process to formal reasoning. Dealing with this issue of Polynomial Interpolation exposes the way polynomial interpolation is actually used for the purpose of building \" simple\" built-in computer functions. It added a new viewpoint on the basic idea of approximation and the values of adjacent solutions. At the end of the workshop students are able to construct acceptable approximations for a built-in function justifying any product they might have made. The challenging questions that are posed during the workshop stimulate discourses about various assumptions, which lead to further research work. Consequently it appears that the new CAS-based tasks open for learners a window on new intellectual connections and supports students in building on their own meaning in ways, which converge towards mathematical ways of knowing. The paper discusses the underlying didactical principles of the workshops’ design, convey the goals of two assignments, and describe the lab work of two high school students including their reflection and reasoning on their research process. ====>> Wednesday 13th of February 2002 07:24:22 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: John Shepherd Mathematics Department, Royal Melbourne Institute of Technology PO Box 2476V, 3001 Melbourne / Australia jshep@rmit.edu.au Mitvortragende: Vortrag: Solving Perturbation Problems via Maple Vortrag derive Perturbation techniques have been applied for many years in the construction of approximate solutions to nonlinear problems arising in applications in applied mathematics and engineering science. Such techniques break down nonlinear problems into a series of (mostly) linear sub-problems, and such packages as Maple are ideally suited to the recursive solution of these. This talk will discuss how Maple may be used in undergraduate courses to analyze a range of perturbation problems of interest. Approximate solutions will be constructed using Maple, and where possible, the extent to which these approximations represent the exact solution will be explored. ====>> Thursday 14th of February 2002 04:40:14 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Tatyana Oleinik , / Ukraine Olejnik@kgpu.sa.net.ua Mitvortragende: S. Gorkova V. Yevdokimov Vortrag: DEVELOPMENT OF DECISION-MAKERS COMPETENCIES Vortrag acdca This paper presents the results of special courses given to undergraduate students with mathematics and computer science as subjects. A general purpose of our study theoretical framework is to mould teachers’ competencies as reflective decision-makers and lifelong learners. It is evident that today the problem of changing a person’s social level demands special attention: only a widely educated person with SOFT SKILLS is able to flexibly restructure the direction and essence of his or her activity. According to this, students have to learn new learning techniques that will question how they currently decide problem and even what they currently believe about learning and decision-making. This is very important for posing questions, analyzing and at last understanding of what is happening. In other words, master specialists have to find clear and fruitful ways to characterize and carefully consider possibilities or alternatives for action and thoughtful assessment of choices made and implemented. ====>> Friday 15th of February 2002 03:16:50 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: COUSQUER Eliane University of Sciences and Technology of Lille Campus Lille1, 59655 Villeneuve d\'Ascq / France Eliane.Cousquer@univ-lille1.fr Mitvortragende: CARON Pierre André MIDENET Anne Vortrag: Initial Training of Teachers of Mathematics and collaborative work Workshop acdca Initial Training of Teachers of Mathematics and Collaborative Work in the IUFM Author Eliane Cousquer Head of the LAMIA laboratory (IUFM Nord Pas de Calais France) Eliane.Cousquer@univ-lille1.fr For several years, Technologies of Communications have been intensively used by the trainers in mathematics of the training college I.U.F.M. of the North of France. Use of the e-mail for the memoirs of maths, use of WEB resources for the history of mathematics, an on- line bibliographic data base, a data- base of memoirs and web sites created by trainers : the C.R.E.A.M, a center of pedagogical resources for the trainees; Mathadoc (A6-3), the electronic schoolbag of the secondary school teacher that the teacher can modify it the way he wants.; LILIMATH : discovery workshops for a use in the classes received in 1998 the first prize of a national competition (cervod) of software tools for training; FUNCTIONS allows an individual following-up of the works of the pupils (fourth price in that same competition) ; GEOWEB, a site presenting some creations made by the pupils themselves on the solving of some open problems of geometry, has received in 2001 a national price for innovative methods. All these groups of teachers use e-learning software for their network. In 2001-2002, a new program for the training in technologies has begun, in link with the memoirs. The trainers are themselves engaged in creation of ressources and animation of networks, and a workshop with the trainers engaged in the memoirs will analyze this new training. This program is part of a program called FORMASCIENCES, with laboratories of the North of France; the essential points of this program are the following : use of simulations in sciences, real teaching program, with references to distributed cognition and collaborative work. This communication will give the essential point of this program and a paper will analyze the first year of training. Keys-words : initial training , cooperative and collaborative work, distributed cognition, network. LAMIA http://www.lille.iufm.fr/labo/prologlabo.html On line programs http://www.lille.iufm.fr/labo/laboProjetsReal.html On line bibliography http://www.lille.iufm.fr/dep/math/resdoc/index.htm on line memoirs of math http://www.lille.iufm.fr/dep/math/mempro/index.htm ====>> Friday 15th of February 2002 10:47:56 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Johann Wiesenbauer Technische Universität Wien , / J.Wiesenbauer@tuwien.ac.at Mitvortragende: Vortrag: Primality Testing and Factoring Large Numbers with DERIVE Workshop derive englisch Primality Testing and Factoring Large Numbers with DERIVE Proposal for a workshop by Johann Wiesenbauer, Vienna According to Gauss \"the problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic.\" Today these problems have also become crucial with respect to some highly topical encryption methods, such as e.g. the RSA-cryptosystem. This could also serve as the starting point to deal with the following basic questions in the classroom: (1) How can we recognize whether a given integer N is prime or not? (2) How can we find a nontrivial factor of N in the latter case? As for the first problem, many computer algebra systems e.g. DERIVE make a compromise by using probabilistic primality tests. For example, the so-called Miller-Rabin test (essentially based on Fermat´s Little Theorem) is used in most CAS. Other important probabilistic primality tests use certain properties of Lucas sequences. Of course, if absolute security is needed, one has to resort to deterministic primality tests, which are far more timeconsuming in general though. In particular, deterministic primalitity tests for Mersenne and Fermat numbers are given. The factorization problem is much tougher by comparison. Here are some of the factorization methods which I am going to talk about in my workshop: (1)Trivial division: Before applying more complicated methods one should search for small prime factors of the given number N. (2) Pollard´s \"rho\" method: One of the simplest factorization methods which also most CAS make use of. It is based on the famous „birthday paradox“. (3) Pollard´s (p-1)-method: Very efficient, if p-1 factors into many small primes for some prime factor p of N. (4) The Elliptic Curve Method (ECM): This method was announced by Lenstra, Jr., in 1985, and uses facts from the theory of Elliptic Curves. ====>> Sunday 17. February 2002 09:17:09 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Klaus Aspetsberger Pädagogische Akademie des Bundes in Oberösterreich Kaplanhofstrasse 40, 4020 Linz / Österreich aspetsberger@aon.at Mitvortragende: Brigitta Aspetsberger Vortrag: Data Collection and Mathematical Reasoning: An Attempt of Cross Curriculum Teaching in Natural Science Courses Vortrag derive beide Cross curriculum reasoning is a principal objective of natural science courses in Austrian high schools. However in reality the students have problems to understand laws from physics and chemistry written in mathematical terms and to apply them to real situations. In math courses students often do not see the necessity for introducing new mathematical concepts. Examples demonstrating the use of these new concepts are often quite artificial and the students have even problems to understand these examples. Carrying out experiments in science courses the students have the possibility to produce their own data and to analyse them by mathematical reasoning. However, they have to learn experimenting, how to obtain good results, how to document their work and to write reports and how to work in groups. CBL from Texas Instruments is a Calculator Based Laboratory which allows to collect data during physical and chemical experiments. Data are stored directly to a calculator e.g. the TI-92 for graphical visualisation and further manipulation. CBR from Texas Instruments is a motion detector which allows to gather a large amount of data points from an object in motion. CBL, CBR and TI-92 support data collection and manipulation. However careful experimenting is absolutely important for obtaining good quantitative results, which are necessary for functional modelling of experimental data. We report about experiments being carried out in the years 1999 to 2002. In several different classes consisting of students at the age of 16 to 18 experimenting with the CBL and TI-92 was integrated within regular classes. About 50% of the students were girls. A special course for high ability students at the age of 14 was installed during the school year 2000/01 also carrying out experiments with CBL. In 2000 a group of students were testing the water quality during regular classes using CBL and ion selective probes from Vernier. We also report about experiences made during several in-service teacher training courses introducing CBL, CBR and TI-92 to math and science teachers within the last two years. It was surprising to see that they had problems similar to the students when treating experimental data. ====>> Sunday 17. February 2002 09:47:33 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: wolf schlichthorn , / wolschl@t-online.de Mitvortragende: Vortrag: Anforderungen an CAS für den Unterricht in Berufs- und Berufsfachschulen Vortrag acdca deutsch test ====>> Sunday 17. February 2002 10:41:20 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Irene Penesis Department of Mathematics, Royal Melbourne Institute of Technology PO Box 2476V, 3001 Melbourne / Australia irene.penesis@rmit.edu.au Mitvortragende: John Shepherd Vortrag: First-year Undergraduate Mathematics using Maple Vortrag derive This paper discusses the application of the package Maple to an elementary course on the modelling of nonlinear phenomena in the real world using differential equations, as presented to first year undergraduate students at RMIT. While the differential equation solving abilities of Maple are used extensively, more emphasis is directed toward nonlinear problems for which an exact solution is not available, and other techniques of analyzing the (unknown) solution must be relied upon. In such cases, Maple\'s ability to represent the solution via phase-plane methods is used , and such a geometric representation is valuable in assessing the solution structure of the problem. ====>> Sunday 17th of February 2002 01:23:02 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Irene Penesis Department of Mathematics, Royal Melbourne Institute of Technology PO Box 2476V, 3001 Melbourne / Australia irene.penesis@rmit.edu.au Mitvortragende: John Shepherd Vortrag: First-year Undergraduate Mathematics using Maple Vortrag derive This paper discusses the application of the package Maple to an elementary course on the modelling of nonlinear phenomena in the real world using differential equations, as presented to first year undergraduate students at RMIT. While the differential equation solving abilities of Maple are used extensively, more emphasis is directed toward nonlinear problems for which an exact solution is not available, and other techniques of analyzing the (unknown) solution must be relied upon. In such cases, Maple\'s ability to represent the solution via phase-plane methods is used , and such a geometric representation is valuable in assessing the solution structure of the problem. ====>> Sunday 17th of February 2002 01:24:07 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Irene Penesis Department of Mathematics, Royal Melbourne Institute of Technology PO Box 2476V, 3001 Melbourne / Australia irene.penesis@rmit.edu.au Mitvortragende: John Shepherd Vortrag: First-year Undergraduate Mathematics using Maple Vortrag derive This paper discusses the application of the package Maple to an elementary course on the modelling of nonlinear phenomena in the real world using differential equations, as presented to first year undergraduate students at RMIT. While the differential equation solving abilities of Maple are used extensively, more emphasis is directed toward nonlinear problems for which an exact solution is not available, and other techniques of analyzing the (unknown) solution must be relied upon. In such cases, Maple\'s ability to represent the solution via phase-plane methods is used , and such a geometric representation is invaluable in assessing the solution structure of the problem. ====>> Sunday 17th of February 2002 01:24:56 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Irene Penesis Department of Mathematics, Royal Melbourne Institute of Technology PO Box 2476V, 3001 Melbourne / Australia irene.penesis@rmit.edu.au Mitvortragende: John Shepherd Vortrag: First-year Undergraduate Mathematics using Maple Vortrag derive This paper discusses the application of the package Maple to an elementary course on the modelling of nonlinear phenomena in the real world using differential equations, as presented to first year undergraduate students at RMIT. While the differential equation solving abilities of Maple are used extensively, more emphasis is directed toward nonlinear problems for which an exact solution is not available, and other techniques of analyzing the (unknown) solution must be relied upon. In such cases, Maple\'s ability to represent the solution via phase-plane methods is used , and such a geometric representation is invaluable in assessing the solution structure of the problem. ====>> Sunday 17th of February 2002 01:25:20 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Franz Schlöglhofer Universität Linz, Institut für Mathematik Altenbergerstr. 69, 4040 Linz / Austria f.schloeglhofer@utanet.at Mitvortragende: Vortrag: Wahrscheinlichkeitssimulationen zum \"Ziehen ohne Zurücklegen\" Vortrag acdca deutsch Simulationen von stoachastischen Prozessen sind in der Wahrscheinlichkeitsrechnung sehr wichtig. Man erhält zwar als Ergebnisse nur relative Häufigkeiten statt Wahrscheinlichkeiten und Mittelwerte anstelle von Erwartungswerten, kommt aber mit den Modellen oft weiter als es mit theoretischen Berechnungen möglich ist, weil nicht in jedem Fall schwierige kombinatorische Überlegungen angestellt werden müssen. Im Vortrag werden hauptsächlich Beispiele zum \"Ziehen ohne Zurücklegen\" behandelt. Dafür wurden Prozeduren in DERIVE 5 geschrieben, die als Grundlage für die Berechnungen im Unterricht direkt verwendet werden können. ====>> Sunday 17. February 2002 09:06:47 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: David Jeffrey U. Western Ontario , / djeffrey@uwo.ca Mitvortragende: Michel Beaudin Rob Corless Vortrag: Row reduction for computers Vortrag derive We describe why computer users should ask for Turing factors, rather than reduced row echelon form or LU decomposition. We then demonstrate a program for the TI-89 and illustrate the applicability of Turing factors by solving some typical problems that have caused difficulties in our lectures. ====>> Monday 18th of February 2002 08:32:04 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: wolfgang schlichthorn Georg-von-Langen-Schule(BBS) Holzminden , / wolschl@t-online.de Mitvortragende: Vortrag: Anforderungen an ein schüler- und damit auch kundenorientierte CAS sonstiges derive beide Meine Schüler (bei denen ich DERIVE einsetze) besuchen die Sekundarstufe I(Berufsfachschule Wirtschaft)sowie die Kaufm. Berufsschule(Industriekaufleute) Ich würde folgene Probleme, die sich nicht nur auf DERIVE beziehen, anschneiden wollen: 1.Verständnishindernisse durch fremdsprachige Anweisungen, unnötige Amerikanismen und Sprachsprünge bzw. Sprachdoppelungen.Pädagogisch gestaltete Benutzerführung. 2. Die Nicht-Einhaltung der gesetzlich vorgeschriebenen bzw. kaufmannisch üblichen Datendarstellung stört den Unterrichtsablauf: statt 44,342,345.67€ muß es 44.342.345,67€ lauten. Außerdem wird die Datenübernahme(die automatisierte ist teilweise unmöglich) aus Anwendungen nur durch deren erneute Eingabe möglich, d.h. die Schüler kämpfen mit der Software und nicht mit dem Problem. 3. Einige mit DERIVE im erfolgte Anwendungen aus dem Unterichtsbereich ====>> Tuesday 19. February 2002 03:41:17 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Richard Tamfu Konfor MATHEMATICS TEACHER G.B.H.S KUMBO, P.O.BOX 85 KUMBO / CAMEROON hospital_banso@kastanet.org Mitvortragende: NDZELEN CHRISANTUS AJIM CHRISOGONUS RICHARD KONFOR Vortrag: MATHEMATICS TEACHING IN ANGLOPHONE CAMEROON Vortrag acdca I WANT TO LECTURE THE SITUATION OF MATHEMATICS TEACHING IN ANGLOPHONE CAMEROON. ====>> Tuesday 19th of February 2002 07:26:20 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Hajime Yamashita Professor, Waseda University 1-6-1 Shinjyuku, 169 Tokyo / JAPAN yamashit@mn.waseda.ac.jp Mitvortragende: Vortrag: Educational Evaluation Applying Fuzzy Theory Vortrag acdca Generally speaking, our educational evaluation for students might be somehow subjective because the final decision is based on individual instructer who has taught the class. In order to revise such a situation with fuzziness, we have developed the objective evaluation method applying fuzzy theoery. It acutually uses approximate reasoning which practically has developed at the end of last century. This evaluation method should be useful (1) for grading the students in Mathematics class, (2) for classifying the students through the placement-test and so on. In this article, the author would not only describe the evaluation method but also illustrate its practical effectiveness with the case study in Mathematics education. ====>> Wednesday 20th of February 2002 08:00:34 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Hajime Yamashita Professor, Waseda University 1-6-1 Shinjyuku, 169 Tokyo / JAPAN yamashit@mn.waseda.ac.jp Mitvortragende: Vortrag: Educational Evaluation Applying Fuzzy Theory Vortrag acdca Generally speaking, our educational evaluation for students might be somehow subjective because the final decision is based on individual instructer who has taught the class. In order to revise such a situation with fuzziness, we have developed the objective evaluation method applying fuzzy theoery. It acutually uses approximate reasoning which practically has developed at the end of last century. This evaluation method should be useful (1) for grading the students in Mathematics class, (2) for classifying the students through the placement-test and so on. In this article, the author would not only describe the evaluation method but also illustrate its practical effectiveness with the case study in Mathematics education. ====>> Wednesday 20th of February 2002 08:04:43 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Hans-Jürgen Elschenbroich Studienseminar S II Neuss Mainstr. 85, 41469 Neuss / Germany elschenbroich@t-online.de Mitvortragende: Vortrag: Dem Höhenschnittpunkt auf der Spur Vortrag acdca deutsch Mit Hilfe Dynamischer Geometrie-Software (hier Cabri II) kann nicht nur zu einem einzelnen Dreieck der Höhenschnittpunkt konstruiert werden, sondern es kann seine Ortslinie untersucht werden, wenn die Gestalt des Dreiecks verändert wird. Wird die Ecke C auf einer Parallelen zu AB bewegt, ergibt sich eine Parabel. Der Nachweis, dass so die erzeugte Linie tatsächlich eine Parabel ist, erfolgt über klassische Abstandsüberlegungen. Derartige Aufgaben waren über Jahrzehnte aus dem Unterricht verschwunden, sind aber noch in Schulbüchern aus den 50er Jahren zu finden! Es wird gezeigt, wie diese klassischen Ansätze mit Dynamischer Geometrie-Software wiederbelebt werden können. Anschließend werden die Ergebnisse auf quadratische Funktionen in der SI-üblichen Funktionsschreibweise angewandt. So werden ausgehend von einem elementaren Problem Querverbindungen von Algebra und Geometrie mit Hilfe von DGS (wieder) aufgebaut, Aspekte, die aus unserem Mathematikunterricht fast verschwunden sind. ====>> Monday 25. February 2002 06:20:36 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Hans-Jürgen Elschenbroich Studienseminar S II Neuss Mainstr. 85, 41469 Neuss / Germany elschenbroich@t-online.de Mitvortragende: Vortrag: Dynamisch Funktionen entdecken Vortrag acdca deutsch Funktionen sind ein wichtiges Themengebiet in der Sekundarstufe I. Üblicherweise werden sie als Teil der Algebra unterrichtet und neue Technologien werden höchstens genutzt, um die Graphen zu plotten. Auf diese Weise bekommen die Schüler eher ein statisches Bild von Funktionen. Mit Dynamischer Geometrie-Software (hier Euklid-Dynageo) ist jedoch ein dynamischer Zugang möglich! Die Schüler können zum einen die unabhängige Variable x variieren und untersuchen, wie verändert sich y und wie entsteht der Funktionsgraph als Ortslinie von P(x/y). Sie können weiter die Parameter a, b, c variieren und beobachten, welche Auswirkungen das für den gesamten Graphen hat. Dies lässt sich einfach mit Schiebereglern durchführen, die Auswirkungen sind unmittelbar zu sehen. Auf diese Weise erhalten die Schüler ein neues Werkzeug, um Eigenschaften von Funktionen zu entdecken. Das soll am Beispiel quadratischer Funktionen exemplarisch gezeigt werden. ====>> Monday 25. February 2002 06:33:46 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Lisa Townsley Benedictine University 5700 College Rd, 60532 Lisle / USA ltownsley@ben.edu Mitvortragende: Vortrag: Multimedia Classes: Can ther ever be too much techno? Vortrag derive Abstract: Have you ever had a 4-technology day in the classroom? Did your students witness you using the calculator, CAS, handouts and projection devices, with a side trip to the WWWeb? The speaker talks about some experiences she and her colleagues have had with multiple technology platforms in the classroom, including the good, the bad, and the ugly. The best stories are those of students presenting talks using multiple platforms. ====>> Wednesday 27th of February 2002 05:20:52 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Lisa Townsley Benedictine University 5700 College Rd, 60532 Lisle / USA ltownsley@ben.edu Mitvortragende: Vortrag: Second-Generation Technology Teachers Vortrag acdca Abstract: The speaker’s department has been heavily involved with technology, particularly CAS and graphics calculators, since 1990. What are some of the issues which arise when so few of the original faculty remain? Should a department retain the same pedagogical goals after a change of faculty? What are the components of a successful transition? With 5 new faculty in and out of the department (of 5) over the last 5 years, the speaker has a LOT of anecdotal evidence on successful and unsuccessful strategies for mentoring second-generation technology teachers and modifying a department strategic plan to reflect the strengths and interests of new faculty. ====>> Wednesday 27th of February 2002 05:22:23 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Rainer Dr. Heinrich Pestalozzi-Gymnasium Dresden Pestalozziplatz 22, 01127 Dresden / Deutschland Raihein@aol.com Mitvortragende: Vortrag: Ein Fach verändert sich - Erfahrungen mit der verpflichtenden Einführung von Grafikrechnern in Sachsen. Vortrag acdca deutsch Im \"Zentralabiturland\" Sachsen (Bundesrepublik Deutschland) wurde im Jahr 1996 für alle Schüler ab Klasse 8 die Nutzung des grafikfähigen Taschenrechners verbindlich vorgeschrieben. Im Vortrag sollen Erfahrungen und Auswirkungen dieses Schrittes auf den Mathematikunterricht gezeigt werden. Diese betreffen Inhalte, Aufgabenkutltur und didaktische Gestaltung des Unterrichts, Konsequenzen für die Bewertung und Zensierung und auf Schüler- und Lehrertätigkeiten. Insbesondere soll die Positionierung zum Basiswissen für Mathematik, die sich nicht an traditionellen Linienführungen von Lehrplänen orientiert, vorgestellt werden. ====>> Wednesday 27. February 2002 06:39:36 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Anna Savchenko Skovoroda State Pedagogical University , / Ukraine ntb@uab.karkov.com Mitvortragende: Vortrag: Distance Learning Course in Mathematics for Economists Vortrag derive The working out of a distance learning mathematics course for the economists is perspective direction of Ukrainian educational reforms. Training high skilled economists, who have a deep understanding of applied mathematics, will stimulate researches on problems market economy. The logical content of this course based on the analysis of reason-consequence links of mathematical conceptions and their economical interpretations. The computer algebra system Derive is used as an intellectual partner of a student in the process of economical problem solution. The main goal of the mathematical problems is the formation of modeling and research skills of modern economic systems by collaborative and cooperative works (“projects”). The mathematical problems are connected to real situations, for example, researching of productivity of work, cost price of production, profitability, optimum plan, rationality of manufacture etc. The strategies of educational Technology of Critical Thinking Development is used for realizing new educational approach, for example: team works, working together, brain storming, clustering, debates, “Jigsaw” etc. First stage of our results has published in textbook \"The solution of problems with the economical content using CAS Derive\" in Project \"Development of critical thinking as a component of establishing of an open society\" of Skovoroda State Pedagogical University. ====>> Wednesday 27th of February 2002 08:41:14 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Al Maturo Leysin American School , 1854 LEYSIN / Switzerland AMATURO@las.ch Mitvortragende: Vortrag: TI-92 Plus Calculator Workshop for Beginners Workshop acdca This workshop is designed to teach one how to use the Texas Instruments TI-92 Plus Calculator with hands on exercises. We will also use the TI-89 Calculators, but there is no difference in their capability; they only look different. Al Maturo will demonstrate the capability of the TI calculators as well as offer exercises to allow the user, you, a chance to learn \'hands on‚\' how to use this classroom tool. He uses the TI calculators when appropriate in the classroom. The workshop is designed for the new user, or for those with little experience with the TI-92 Plus. Calculators will be provided for those without one, but feel free to bring your own. Note: I am already presenting the TI-83 Plus Calculator. I regret that I am making this submission late. ====>> Monday 04th of March 2002 06:23:51 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Hildegard Urban-Woldron Pädagogische Akademie der Erzdiözese Wien Gentzgasse 52/I/4, 1180 Wien / Österreich hildegard.urban@chello.at Mitvortragende: Vortrag: CBR und CBL im fächerübergreifenden Unterricht /Mathematik - Physik- Informatik Vortrag derive deutsch Anhand einer exemplarischen Einführung wird der Umgang beim Messen mit einzelnen Sensoren und die anschließende Auswertung der Daten in Verbindung mit einem TI-Rechner erläutert. Experimentell ermittelte Daten werden nach ihrer grafischen Veranschaulichung der Theorie und dem Modell gegenübergestellt. Die Einsatzmöglichkeiten des CBR und CBL im Unterricht zum Experimentieren, Veranschaulichen, Analysieren, Modellieren und Interpretieren bereichern durch anwendungsorientierte Fragestellungen und fächerübergreifende Betrachtungen die Unterrichtsarbeit in hohem Maße. Beziehungen der Daten können numerisch und grafisch erforscht, mit mathematischen Funktionen assoziiert und mit repräsentativen Funktionen modelliert werden. Dabei kann die physikalische Bedeutung der einzelnen Parameter erkundet und in der Folge ein tiefergehendes Verständnis erzielt werden. ====>> Monday 04. March 2002 09:34:24 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Hildegard Urban-Woldron Pädagogische Akademie der Erzdiözese Wien Mayerweckstraße 1, 1210 Wien / Österreich hildegard.urban@chello.at Mitvortragende: Vortrag: CBR und CBL im fächerübergreifenden Unterricht /Mathematik - Physik- Informatik Vortrag derive deutsch Anhand einer exemplarischen Einführung wird der Umgang beim Messen mit einzelnen Sensoren und die anschließende Auswertung der Daten in Verbindung mit einem TI-Rechner erläutert. Experimentell ermittelte Daten werden nach ihrer grafischen Veranschaulichung der Theorie und dem Modell gegenübergestellt. Die Einsatzmöglichkeiten des CBR und CBL im Unterricht zum Experimentieren, Veranschaulichen, Analysieren, Modellieren und Interpretieren bereichern durch anwendungsorientierte Fragestellungen und fächerübergreifende Betrachtungen die Unterrichtsarbeit in hohem Maße. Beziehungen der Daten können numerisch und grafisch erforscht, mit mathematischen Funktionen assoziiert und mit repräsentativen Funktionen modelliert werden. Dabei kann die physikalische Bedeutung der einzelnen Parameter erkundet und in der Folge ein tiefergehendes Verständnis erzielt werden. ====>> Monday 04. March 2002 09:35:32 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Dennis Pence Department of Mathematics, Western Michigan University Kalamazoo, 49008 Michigan / USA dennis.pence@wmich.edu Mitvortragende: Vortrag: Good Things with Piecewise-Defined Functions on the TI-92Plus Vortrag derive englisch All too often, piecewise-defined functions are used to show discontinuity in a mathematics course, and then they never appear again. This leaves the mistaken impression that only “bad things” happen when you work with such functions. We will explore some “good things” that can be done with piecewise-defined functions. This material will be appropriate for precalculus, calculus, and linear algebra courses. There are three ways to specify a piecewise-defined function on the TI-92 family of CAS calculators. If there are only two or three pieces, the when( command generally provides a simple way to do this. Functions defined by a single when( command or two nested when( commands are displayed nicely in pretty print in the home screen. Expressions involving the when( command can be differentiated nicely (the pieces have the same defining logical tests), but integration does not work as well (because these defining logical tests are not necessarily well ordered). More than three pieces are most easily implemented in a function-type program using the IF-THEN-ELSE IF-ELSE IF.....ELSE control structure. Unfortunately we lose the nice display in pretty print, symbolic differentiation, and integration because there can be no symbolic understanding of what you might have done inside a program. A third way involves the sign( function, which is the derivative of the absolute value function. This built-in piecewise-defined function oddly cannot be symbolically differentiated but integrates nicely. ====>> Wednesday 06. March 2002 09:11:56 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Alfred Rosing Dahlkeweg 24, 59227 Ahlen / BRD AHRosing@t-online.de Mitvortragende: Vortrag: Modellierung von kontinuierlich ablaufenden Prozessen durch diskret dyn. Modelle Workshop derive deutsch Es soll demonstriert/untersucht werden, wie in der Umwelt ablaufende Prozesse, die gewöhnlich durch e-/ln-Funktionen beschrieben werden, durch iterative Modelle (diskrete Dynamik) beschrieben werden können, die den realen Vorgang gut nachbilden. Als Beispiel verweise ich auf meinen Beitrag, der Grundlage für den Workshop sein soll, in den TI-Nachrichten, Ausgabe 02/2001. Das Beispiel zeigt wie verschiedene Bereiche der Mathematik - z.B. Geometrie, Algebra, Algorithmik - mit einander in Beziehung treten. Alfred Rosing ====>> Monday 11. March 2002 08:57:21 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Rüdeger Baumann Gymnasium Ernestinum Celle Italien. Garten 15, 29221 Celle / Deutschland baumann-celle@t-online.de Mitvortragende: Vortrag: Algorithmische Geometrie mit Derive (Vortrag + Workshop) sonstiges derive deutsch An Beispielen aus der Analytischen Geometrie bzw. Vektorgeometrie wird gezeigt, wie sich dieses Gebiet der Oberstufenmathematik mit Hilfe eines Computeralgebra-Systems (etwa Derive) zu einer Algorithmischen Geometrie weiterentwickeln lässt. Die Schüler erstellen Konstruktionen in Gestalt von Algorithmen (bzw. Derive-Programmen) und beweisen deren Korrektheit. Es ist zu diskutieren, ob das (die Rechenmacht des) Computeralgebra-System(s) auch durchschnittlichen Schülern das selbständige Finden von Konstruktionen und Beweisen erleichtert oder allererst ermöglicht, wie diese sich von den herkömmlichen Beweisen und Konstruktionen unterscheiden und was vom \"Geist der Geometrie\" dabei noch übrig bleibt. Whorkshop: Die Teilnehmer sollen angeregt bzw. angeleitet werden, anhand von Aufgaben aus der Analytischen Geometrie / Vektorgeometrie bzw. Linearen Algebra eine (im Sinne des Vortrags) CAS-unterstützte Methodik des Konstruierens und Beweisens zu entwickeln. ====>> Monday 11. March 2002 09:42:09 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Oswaldo Lezama Universidad Nacional de Colombia Ciudad Universitaria, DC Bogotá / Colombia olezama@matematicas.unal.edu.co Mitvortragende: Patricia Barragán Wilson Castro Schweitzer Rocuts Vortrag: Algebra Conmutativa On Line Vortrag acdca An online course in algebra conmutativa (in sapanish) is presented. The course includes lessons in Latex, online evaluations, chat, java applets for computing Gröbner basis. The url of the course is: http://www.virtual.unal.edu.co/cursos/ciencias/15930/index.html ====>> Wednesday 13th of March 2002 09:35:04 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: IFTIKHAR HUSAIN UNIVERSITY HIGH SCHOOL, NEWARK PUBLIC SCHOOLS, NEW JERSEY, USA 1701 VAN NESS TERRACE, 07083 UNION, NEW JERSEY / USA INAZ786@YAHOO.COM Mitvortragende: Vortrag: EXPLORING ALGEBRA WITH CREATIVE DESIGNS Workshop acdca Teaching in the new millennium challenges teachers at all grade levels to engage students in leaning for greater depth and meaning. The fast growing graphing calculator technology is a great help in all mathematics classes to meet these challenges. The creative design technique helps students to enhance visual thinking. It helps students to understand and apply Algebra and Geometry concepts in a creative and enjoyable way. The visual illustrations, the creative designs, inspire and motivate students in the learning process. The Power Point Presentation, based on unique creative designs technique, discuss several designs with mathematical equations. The participants, in the second half of the session, use TI-83 or TI-83Plus graphing calculator and create designs based on linear functions with or without restricted domains,quadratic functions, higher degree polynomial functions, trigonometric functions,and conics and much more if time permits. With creative design techniques I am able to reveal the visual beauty of mathematical art as never seen before. ====>> Thursday 14th of March 2002 12:10:06 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Gert Kadunz Universität Klagenfurt Universitätsstr. 65, A-9020 Klagenfurt / Österreich gert.kadunz@uni-klu.ac.at Mitvortragende: Vortrag: Möglichkeiten und Grenzen von Modulen bei DGS-Einsatz Vortrag acdca deutsch Die einschlägige fachdidaktische Literatur zum Einsatz von DGS im Mathematikunterricht untersucht besonders die Bedeutung und Verwendung des Zugmodus. Der Konstruktion und der differenzierten Verwendung von Modulen (Makros) wird weniger Augenmerk geschenkt. Der Vortrag stellt eine mögliche Klassifikation der Verwendung von Modulen vor, beschreibt das Verhältnis dieser Verwendung zur Verwendung des Zugmodus und weist auf Grenzen des Moduleinsatzes hin. ====>> Sunday 17. March 2002 11:26:17 AM <<==== --------------------------------------------------------------------------- Hauptvortragender: Edith Schneider University of Klagenfurt, Department of Didactics of Mathematics Universitaetsstrasse 65-67, 9020 Klagenfurt / Austria edith.schneider@uni-klu.ac.at Mitvortragende: Vortrag: CAS and Experimental Learning Vortrag acdca englisch The availability of technological tools as CAS offers the possibility of outsourcing operative (algorithmical, routine) activities (which require often a very great deal of time and work) to the \"mathematical expert\" CAS. Thereby it gets possible to use experimental working also in maths classes in a sensful and adequate manner. Many concrete proposals for teaching mathematics base on such experimentation (including keynotes as: investigating, exploring, discovering, heuristical approaches, …). The black-box/white-box-principle formulated by H. Heugl refers to this possibility offered by CAS. Within the lecture it is planned to scrutinize the significance of experimental working closely from the point of view of mathematical education of students of general educating high schools. From this perspective a few possibilities of experimental learning in CAS-supported maths classrooms (as for instance investigating characteristics of mathematical concepts, discovering mathematical rules, exploring CAS as a mathematical learning environment, …) and their relevance for maths classes should be discussed exemplarily by means of concrete examples. ====>> Tuesday 19. March 2002 08:48:57 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Bernhard Kutzler , / b.kutzler@eunet.at Mitvortragende: Vortrag: Test Vortrag acdca Test ====>> Tuesday 19th of March 2002 09:29:11 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Edith Schneider University of Klagenfurt, Department of Didactics of Mathematics Universitaetsstrasse 65-67, 9020 Klagenfurt / Austria edith.schneider@uni-klu.ac.at Mitvortragende: Vortrag: CAS and Experimental Learning Vortrag acdca englisch The availability of technological tools as CAS offers the possibility of outsourcing operative (algorithmical, routine) activities (which require often a very great deal of time and work) to the \"mathematical expert\" CAS. Thereby it gets possible to use experimental working also in maths classes in a sensful and adequate manner. Many concrete proposals for teaching mathematics base on such experimentation (including keynotes as: investigating, exploring, discovering, heuristical approaches, …). The black-box/white-box-principle formulated by H. Heugl refers to this possibility offered by CAS. Within the lecture it is planned to scrutinize the significance of experimental working closely from the point of view of mathematical education of students of general educating high schools. From this perspective a few possibilities of experimental learning in CAS-supported maths classrooms (as for instance investigating characteristics of mathematical concepts, discovering mathematical rules, exploring CAS as a mathematical learning environment, …) and their relevance for maths classes should be discussed exemplarily by means of concrete examples. ====>> Tuesday 19. March 2002 09:40:14 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Werner Peschek University of Klagenfurt, Dept. of Didactics of Mathematics Universitaetsstr. 65-67, 9020 Klagenfurt / Austria werner.peschek@uni-klu.ac.at Mitvortragende: Vortrag: Modules, Black Boxes and the Principle of Outsourcing Vortrag acdca englisch Modules are important tools for human thinking, modularity is an important strategy for structuring and organizing individual as well as social knowledge. This strategy has also highly influenced the development and organization of computers and occurs here in different forms. It is remarkable, that this fundamental idea was rather seldom taken up and analyzed in the didactical CAS-discussion up to now (contributions of H. Heugl, E. Lehmann or E. Schneider are rather exceptions). One reason for this reserve might be the feeling of uncertainty about the question, if it is acceptable (from a didactical point of view) to use CAS-modules without knowing their internal operational sequences (\"black boxes\"). In the so called \"White-Box/Black-Box-Principle\" (B. Buchberger) this is opposed, the \"Principle of Outsourcing\" (W. Peschek) comes to a positive answer. Within this lecture, I will try to point out some aspects of modularity, which could be relevant for the use of computers in mathematics education (and lead to a sophisticated answer for the question mentioned above), I will present different occurrences and forms of modules and discuss E. Schneider´s categorizing of CAS-modules and last but not least I will reflect on possibilities of a sensible use of CAS-modules in mathematics education. ====>> Thursday 21. March 2002 05:26:40 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Steven Schonefeld Tri-State University , 46703 Angola, Indiana / U.S.A. sschonefeld@mchsi.com Mitvortragende: Vortrag: Picturing a Complex Function (25 minute talk) Vortrag acdca In this paper, we explore some two-dimensional curves, which enhance our understanding of a complex function, f(z). We follow the usual convention of letting z = x + iy (where x and y are reals and i is the square root of negative one). With this z = x + iy notation, we get a one-to-one correspondence between each point, (x, y), in the Euclidean plane and each complex number. When z = x + iy, x is called the real part of z and y is called the imaginary part of z. The DERIVE function RE(z) returns the real part of z and IM(z) returns the imaginary part of z. That is, x = RE(x + iy) and y = IM(x + iy). When we plot the implicit curves given by RE(f(x + iy)) = 0 and IM(f(x + iy)) = 0, the points of intersection will be the zeros of f(z). We explore the families of curves given by ABS(f(x + iy)) = n, for n positive and PHASE(f(x + iy)) = k, for k between -pi and pi. Finally, we show the surprising result that these two families of curves are orthogonal. ====>> Monday 25th of March 2002 07:54:44 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Steven Schonefeld Tri-State University , 46703 Angola, Indiana / U.S.A. sschonefeld@mchsi.com Mitvortragende: Vortrag: Picturing a Complex Function (25 minute talk) Vortrag derive In this paper, we explore some two-dimensional curves, which enhance our understanding of a complex function, f(z). We follow the usual convention of letting z = x + iy (where x and y are reals and i is the square root of negative one). With this z = x + iy notation, we get a one-to-one correspondence between each point, (x, y), in the Euclidean plane and each complex number. When z = x + iy, x is called the real part of z and y is called the imaginary part of z. The DERIVE function RE(z) returns the real part of z and IM(z) returns the imaginary part of z. That is, x = RE(x + iy) and y = IM(x + iy). When we plot the implicit curves given by RE(f(x + iy)) = 0 and IM(f(x + iy)) = 0, the points of intersection will be the zeros of f(z). We explore the families of curves given by ABS(f(x + iy)) = n, for n positive and PHASE(f(x + iy)) = k, for k between -pi and pi. Finally, we show the surprising result that these two families of curves are orthogonal. ====>> Monday 25th of March 2002 07:56:37 PM <<==== --------------------------------------------------------------------------- Hauptvortragender: Györgyi Führer-Nagy Westungarische Universitaet Ady E. u.5,, 9400 Sopron / Ungarn fuh@emk.nyme.hu Mitvortragende: Vortrag: Ausrechnen Einer Regressionskurve mit TI-83 Vortrag derive deutsch Ausrechnen Einer Regressionskurve mit TI-83 Györgyi Führer-Nagy (Sopron, Ungarn) In Kreisen der Jäger ist es bekannt, dass die Schnecke von des Muffelwildes staendig, im höheren Alter aber langsamer, wächst und deren Länge sich einem Maximumwert A nähert. (Verschiedene Jagdgebiete haben verschiedene Lebensbedingungen, und damit ist auch Qualität der Jagdtrophäen verschieden.) Die Veränderung der Länge der Schnecke versuchen wir mit einer Kurve modellieren. Die Gleichung dieser Kurve ist: y = A(1 -abx) wobei x das Alter (Jahre), y die Länge (cm) und A die theoretisch maximale Laenge (für das untersuchte Land) zeigen. In Wirklichkeit ist es eine in die exponenziale veränderbare Regression, einfach mit y* = abx = 1-y/A Classische Bestimmung dieser Regression ist ziemlich müchsam. Wenn uns ein Taschenrechner TI-83 zur Verfügung steht, wird alles deutlich einfacher. Programm für Ausrechnen der Tabellenwerten und Coeffizienten der Exponenzialkurve ist schon in Grundoperationen gegeben! ====>> Friday 05. April 2002 02:23:14 PM <<==== ---------------------------------------------------------------------------