List of Lectures
 
© 2001 Mail-Button   ACDCA - Austrian Center for Didactics of Computer Algebra
  
Rüdeger Baumann (Gymnasium Ernestinum Celle, Germany)
baumann-celle@t-online.de
Algorithmische Geometrie mit Derive (Workshop)
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. 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.

Josef Böhm (DUG, Würmla, Austria)
nojo.boehm@pgv.at
Programming in DERIVE - Some Introductory Examples (Workshop)
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.

David Bowers (Suffolk College, Ipswich, UK)
david.bowers@suffolk.ac.uk
Computer algebra within a spreadsheet-style environment (Workshop)
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.

Bernnard Cunningham (Mott Community College, Vassar, Michigan, USA)
bcunning@gfn.org
Use the Program Editor of the TI-89/92 Calculator to write a program to solve cubic equations (Workshop)
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.

Homero Flores (Colegio de Ciencias y Humanidades-UNAM, Mexico City, Mexico)
ahfs@servidor.unam.mx
Geometric Proof in Upper Middle School (Workshop)
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.

Marianna Goroneskul (Kharkov Air Force Military Institute, Kharkov, Ukraine)
larin@kharkov.ukrtel.net
Computer Algebraic System MAPLE in the process of teaching higher mathematics (Workshop)
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.

Wilfried Herget (Univ. Halle-Wittenberg, Halle, Germany)
herget@mathematik.uni-halle.de
A Picture Tells a Story of Well Over 1,000 Words (Workshop)
"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.

Carl Leinbach (Gettysburg College, PA, USA)
leinbach@cs.gettysburg.edu
Programming with TI-Interactive! (Workshop)
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.

Palmira Mariz (Vienna International School, Austria)
pmariz@vis.ac.at
Dynamic Geometry in Classroom (Workshop)
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.

Al Maturo (Leysin American School, Switzerland)
amaturo@las.ch
TI-83 Plus Calculator Workshop
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.

Al Maturo (Leysin American School, Switzerland)
amaturo@las.ch
TI-92 Plus Calculator Workshop for Beginners (Workshop)
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.

Al Maturo (Leysin American School, Switzerland)
amaturo@las.ch
Statistics with List Editor with the TI-89/TI-92Plus Calculator (Workshop for Intermediate & Advanced Users)
This workshop highlights the ability of the TI-89/TI-92Plus to perform Statistical Functions using the Flash Program: Statistics with List Editor. Statistics with List Editor is a free Flash program which offers more computing capability while enhancing user-friendliness. The workshop is designed for intermediate & experienced users, but new users that attend the TI-92 Workshop for Beginners will have enough knowledge to follow along. Al Maturo will offer you exercises and a chance to learn "hands on" how to use this classroom tool. Calculators will be provided for those without one, but feel free to bring your own. Current users of the TI-89/TI-92Plus and TI-83Plus are encouraged to attend.
This a MUST SEE demonstration for all Teachers of Statistics!

Gay L. Nixon (Lynnwood, Washington, USA) gaynixon@juno.com Absolute Value: Geometrically, Algebraically and Technologically (Workshop) 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.

Regis Ockerman (Steken, Belgium)
regis.ockerman@pi.be
Drawing Julia Fractals on the TI 92 (Workshop)
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.

John Olive (The University of Georgia, Athens, GA, USA)
jolive@coe.uga.edu
Exploring the Dynamic Geometry of Calculus with Geometer's Sketchpad 4.0 (Workshop)
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.

Philip Oostenbroek (Marist College Ashgrove, Australia)
philoostenbroek@yahoo.com
Creating Favourable Attitudes in Mathematics in 12 year old boys (Workshop)
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

Michael Pemberton (The University of Queensland, Brisbane, Australia)
mrp@maths.uq.edu.au
Modelling Air-resistance using Maple (Workshop)
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.

Alfred Rosing (Ahlen, Germany)
AHRosing@t-online.de
Modellierung von kontinuierlich ablaufenden Prozessen durch diskret dynamische Modelle (Workshop)
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.

Peter Schofield (Trinity & All Saints College, Leeds, UK)
p_schofield@tasc.ac.uk
Some General-Purpose Tools for 2D- and 3D-Linear Transformation Geometry with DERIVE 5 (Workshop)
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.

Alla Stolyarevska (Kharkov, Ukraine)
stolyare@altavista.com
The using of Prolog programming language as a Computer Algebra System (Workshop)
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.

Andy Ventress (Rich Central High School, Olympia Fields, IL, USA)
rc124@hotmail.com
The Digital Camera and Mathematics - What's the Connection ? (Workshop)
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.

Johann Wiesenbauer (Technische Universität Wien, Austria)
J.Wiesenbauer@tuwien.ac.at
Primality Testing and Factoring Large Numbers with DERIVE (Workshop)
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.