Using applets in teaching mathematics

INTRODUCTION During the last several years the Department of Mathematical Sciences at the United States Military Academy has significantly increased the use of technology in the classroom. Currently students have and use the TI-89 calculator as well as MathCad 2000. These technology advances can increase a student's ability to learn objectives and concepts presented in Discrete Dynamical Systems and Introduction to Calculus, and Introduction to Calculus and Differential Equations, the first two required freshman level mathematics courses. However, these tools have an associated cost for the majority of students who must learn the hardware and/or software while trying to grasp new course material. Informal surveys of students repeatedly indicate this to be perceived as detrimental to learning. To minimize this negative effect on the learning process I have found it beneficial to use applets ("a program designed to be executed from within another application." [2, p. 1]) in classroom demonstrations, and to allow students to use them in completing suggested problems. This does not free them from the responsibility to learn the hardware/software; however, it does equip students with tools to immediately focus on concepts and learning objectives. BACKGROUND Mathcad and the TI-89 brought a wealth of power and benefits to both the instructor and student. For the instructor, both enhanced classroom demonstrations. MathCad made it much easier to graphically show the effects of modifying parameters of an equation. Attempting to accomplish the same with a blackboard and/or transparencies is a futile effort. We found much the same was true for demonstrations with the TI-89. However, the TI offered a bigger plus. Rather than simply watching what was done in class students could follow along and see the results on their screens. Because all students had access to these tools in their rooms, in theory they could repeat classroom demonstrations or explore further on their own. What does a student do who does not have a TI-89 or an expensive computer algebra system such as Mathcad? Or what about the student who does have access to these resources but cannot remember the keystrokes or correct syntax used in classroom demonstrations? Does he/she wait until the next class? More often than not, these procedural and syntactical stumbling blocks, and lack of resources become barriers to studying and self-motivated learning. Given that more than 50% of college students will be able to access the Internet from their dorm rooms and 80% or more will have access from some campus locations) [1, p. 1], a viable solution may be applets. JAVA APPLETS Our applets are written in Java and executed in a web browser. Why applets? Instructors can focus on concepts, modeling, and problem solving instead of teaching the syntax of MathCad or the keystrokes of the TI needed for procedural computations. Since there are no syntax or keystrokes to learn students start using and learning immediately. Moreover, learning concepts or lesson objectives are not by-products of having mastered certain software. In discussing this with students, one of the recurring complaints is the large amount of time required to become familiar with the software as opposed to understanding concepts. Students also say that they are more likely to use applets outside of the classroom since they do not experience the difficulties of having to learn a new program or procedure. Java is: "A simple, object-oriented, network-savvy, interpreted, robust, secure, architecture neutral, portable, high-performance, multithreaded, dynamic language." [3, p. 1] In the education arena instructors can capitalize on the portable and dynamic qualities of the language. Unlike the TI-89 and MathCad, Java applets are not tied to a specific software package or computational device. As long as students have access to the Internet/Intranet, and a Java-compliant Web browser such as Netscape Navigator or Microsoft Internet Explorer they can use applets. …