A semantic explanation and symbolic computation approach for designing mathematical courseware

In this paper, we present our proposed semantic explanation and symbolic computation approach in mathematical courseware automation. To get students to understand the relationships that appear in a given mathematical problem, it is necessary to explain the meanings of a set of equations using various methods: visual explanations using 2D and 3D graphs, economical explanations using words, and mathematical explanations using math expressions. In mathematical explanations, both concrete example values and calculations in variable symbols are used, depending on the situation. To make it possible to generate such a variety of explanations, we introduce the idea of mathematical concepts and apply it in our proposed method. Our proposed semantic explanation and symbolic computation approach has enabled us to automate various versions of the explanation from many angles.