Yuzita Yaacob
Department of Industrial Computing
Faculty of Technology and Information Science
National University of Malaysia
and
Michael J. Wester
Department of Mathematics and Statistics
Center for High Performance Computing
University of New Mexico, USA
and
Stanly Steinberg
Department of Mathematics and Statistics
Cancer Research and Treatment Center
University of New Mexico, USA

This paper presents a prototype of a computer learning assistant ILMEV (Interactive Learning - Mathematica Enhanced Vector calculus) package with the purpose of helping students to understand the theory and applications of integration in vector calculus. ILMEV is built on the important pedagogical concepts (interactivity, visualization and experimentation), computer based learning theory (behaviorism, cognition and humanism), simple logical steps in problem solving (with some explanations), and an easy to use interface. Vector calculus was chosen as the subject area because even mathematically talented students in engineering and science find this subject difficult. No computer algebra system has algorithms to automatically solve all but the most elementary problems of this type that appear in textbooks. To overcome this, we implemented a prototype of ILMEV, which can compute closed form solutions to many two dimensional textbook examples without substantial user intervention. ILMEV succeeds because it contains algorithms for reducing the integrals appearing in vector calculus to sums of iterated integrals. The typical presentation of this material in textbooks was reorganized and subsequently a model was created which presented an overview of many of the important integrals that appear in vector calculus. This model provides a framework for developing the complete content of ILMEV and other vector calculus packages.

KEYWORDS
computer algebra system (CAS), educational technology, information sciences, teaching methods, vector calculus.