Step by step instruction of symbolic calculation

Abstract

WWW based on-line exercise system of algebra developed by the authors provides the students with individual learning of symbolic calculation. Because all problems, answers, learning histories of the students, and evaluating rules are stored in the server, the students are allowed to use the system at any time from any where through the Internet. The system accepts intermediate expressions on its way to the answer and gives them comments how different the expressions to the answer. The comment is quite helpful for the students who knows calculation rules but needs more training to master them. Such students use the system as their personal coach and do not need extra h elp on their learning.

On the other hand, the comment is rather helpless to beginners. They know so few calculation rules that they can not find the very first step in the calculation. They need some guide showing them possible operations at each stage of calculation and also showing the result of selected operation im mediately. The step by step assistant of symbolic calculation described in this paper is one of those approaches to teach fundamental mathematical operations to beginners.

The system shows a list of operations applicable to current mathematical expression which might lead the expression to the answer. Usually an operation has some options and/or parameters working with it. If a student selects one of the operations, selects options and parameters the system show s the result of the operation immediately with a comment how close the result is to the answer. As each line of the operation is the written explanation in a natural language, the student easily learn the meaning of the operation, and the effect from the result and the comment. It becomes a detailed explanation how an operation works on an expression.

The method worked well on a Mathematica notebook utilizing the Mathematica Palettes philosophy to bring Computer Algebra closer to the students. Palettes consist of activating buttons of operations which are carried out by custom Mathematica functions. It is implemented on to WWW-based system as a function of the on-line exercise system.