Using Theorema for Training Math Students B. Buchberger Research Institute for Symbolic Computation Johannes Kepler University, A4232 Castle of Hagenberg, Austria Abstract Theorema goes beyond the current math software systems by providing computer-support for proving. In fact, in Theorema, all the potential for programming and computing in Mathematica is accessible but, in addition, a couple of automated provers for various areas of mathematics are provided. In the tutorial, we will give a couple of demos for illustrating how Theorema can be used for tutoring math students. We will emphasize the aspect of computer-supporting all phases of the exploration cycle when introducing a new mathematical subject to students: Starting from a vague understanding of the basic concepts in examples we go through the phase of formalization of the concepts and the phase of conjecturing properties of the new notions to the phase of proving or disproving the conjectures and finally arrive at the phase of using the new knowledge for solving problems in an algorithmic way. All phases can be computer-supported, within Theorema, in a uniform logic and software-technologic frame. We will also demonstrate the various Theorema tools for presenting and browsing proofs, for generating natural language explanatory text and for manipulating mathematical knowledge bases. The Issue of Appropriate Assessment In the Presence of a CAS Terence Etchells School of Computing & Mathematical Sciences Liverpool John Moores University Abstract If we believe that the phrase "Assessment drives the Curriculum," then the use of computer Algebra Systems (CAS) in the Teaching and Learning of Mathematics will have a minimal impact on the overall Mathematics Curriculum until the CAS becomes a legitimate tool to be used in mathematics examinations. Several papers have been written addressing the effect of the use of the CAS on the overall marks, the fairness of such use, the logistics, and other issues. The authors believe that the financial issues have been minimized with the availability of hand held CAS and the declining price of all CAS. The important issue is how the examinations can be written in a way that allows the student the option of using a CAS and tests the students' understanding of the underlying mathematical concepts and problem solving strategies. To this end, the authors give concrete examples of exams that have been given in a CAS teaching and learning environment and illustrate the allocation of marks to possible student solutions to some of these questions. The authors discuss the need to link the construction of the exam and evaluation of the exam scripts in terms of an existing classification scheme for mathematical tasks, the MATH taxonomy. The sample exam questions and proposed solutions are evaluated within this framework. Web-based answers to math questions Richard Fateman Computer Science Division University of California at Berkeley Abstract Teachers now assume that calculators will play a role in students' lives, and thus such topics as accurate square-root extraction by pencil and paper methods has faded from the curriculum. What happens when every student is internet-connected and there are web sites that answer other kinds of questions, free? We discuss our experience with tilu, http://torte.cs.berkeley.edu:8010/tilu an integral table lookup program that can do some easy and some challenging symbolic integration problems, instantly and free. Teaching Math over the Internet: a new challenge for computer algebra Erich Kaltofen North Carolina State University Raleigh, USA Abstract The Internet can be used as a vehicle to deliver education, and math courses on the Internet have been created. I have taught an Elementary Linear Algebra course on the Internet for the third time in Spring 2000. While increasing accessibility and improving overall quality, such delivery faces new challenges, pedagogical, technological, legal, and financial: * The lack of mathematics in the current browsers * The separation between computer algebra systems like Maple and Internet course management software like WebCT or WebAssign. * Maintenance of inter-person communication via threaded discussion groups and chat rooms * Copyright law * Adherence to the USA Americans with Disabilities Act (ADA) * Web server compute power and network bandwidth * All of the above have direct implications to our discipline. * In my talk, I will demonstrate my successes and discuss the challenges. Computer algebra Components for Supporting the Development of Web-based Teaching Materials Frank Postel, University of Paderborn and Andreas Sorgatz, SciFace Software Abstract In a project for the German "Schulen ans Netz e.V.", a MuPAD computing server for use in internet and intranet applications, in particular in schools, is under development. The idea is that remote clients, such as plugins for web browsers, Java applets or ActiveX controls, can connect to the server via sockets, send requests like "please compute an indefinite integral of $x^2 sin(x)$ with respect to x, receive the answer $2x sin(x)-cos(x)(x^2-2)$ from the server, and render it on the screen. Our goal is to power web-based teaching materials by a modern computer algebra system. In a project funded by the BMBF (Bundesministerium für Bildung und Forschung, German Department for Education and Research), graphical user interfaces are developed which can be used by teachers or publishers to create electronic tutorial documents with mathematical contents for interactive learning or for presentation software, such as, for example, web browsers. The components are based on the ActiveX technology for Windows platforms. In cooperation with the "Institut für Mediendidaktik" at the University of Koblenz, these tools are used to develop tutorial documents for linear algebra in schools and universities. The poster introduces the technology of the implemented computing server, corresponding Java applets, graphics and calculator ActiveX controls. It will be demonstrated how these components can easily be used within interactive teaching materials always appearing in a new shape. Also examples are given for using this technology for web computing, e.g. based on OpenMath or MathML content in the future. TI InterActive! A software tool for learning Math and Science Mohamed Omar Rayes Texas Instruments Inc. Abstract TI InterActive! is user-friendly, interactive computer software for teachers and students. TI InterActive! enables high school and college teachers and students to easily investigate ideas in mathematics and science. Teachers can enhance students' learning through interactive lessons that encourage exploration, visualization, data analysis and writing. Students can use TI InterActive! to help them master math and science concepts, improve problem solving skills, create great looking homework, access and download teacher-prepared materials from the Internet, and more. During this tutorial, we will give a live demo on the use of TI InterActive! to explore math and science topics.