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