Making Figures for Class Materials Using KETpic Based on Symbolic Thinking

Abstract

Many mathematics teachers produce original course materials with figures because their use enables students to comprehend mathematical objects. This paper presents a model for producing effective figures for use in course materials. LaTeX is often used to edit course materials and they often use computer algebra system (CAS) to insert graphical image files into the materials. We developed KETpic as a plug-in based on CAS to insert precise and expressive figures into a LaTeX document. After KETpic generates LaTeX-readable codes, the resultant figure is a monochrome, high-quality line drawing. Consequently, teachers can easily improve the quality of their materials. When they produce a figure using KETpic, they can perform mathematical operations as they consider combinations of KETpic commands as mathematical symbols. We designate this mathematical activity as symbolic thinking. By performing symbolic thinking, they need not be overly concerned about writing a program for CAS. Instead, they can concentrate on consideration of more important matters of cognition such as producing an effective figure. They require an advantageous environment in which they can easily perform symbolic thinking. This paper presents two sufficient conditions for this environment: (i) they produce new KETpic commands as the modularization of mathematical operations that they frequently use, and (ii) they create an original package of new KETpic commands. In this paper, we present some examples for these propositions using KETpic based on Scilab.