Kiyoshi Kitahara

IFSGen4 : Interactive Graphical User Interface for Generation and Visualization of Iterated Function Systems in

This paper presents a new interactive, user-friendly graphical user interface (GUI) for generation and visualization of IFS. The program, called IFSGen4LaTeX, is particularly designed for proper Open image in new window editing in a WYSIWYG mode. During a working session, IFS are created interactively from scratch and visualized by using the IFSGen4LaTeX GUI; simultaneously, its engine generates source code that, once inserted in Open image in new window and compiled, displays the same fractal images in Open image in new window Ṫhis process leads to substantial savings in CPU time and memory storage, since the resulting source code is astonishingly small, but still of excellent visual quality because the number of iterations is decided by the user.

A Simple Method of the

The authors have been developing KETpicas a bundle of macro packages for Computer Algebra Systems (CASs) to draw fine

{\rm\kern-.15em T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX}

{\rm\kern-.15em T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX}

Surface Drawing Suitable for Teaching Materials with the Aid of CAS

-pictures. Recently we have developed a new method of the surface drawing using KETpic. The equation of envelopes is used to draw ridgelines of surfaces. Also the technique of hidden line elimination is used. By these methods, we can draw 3D-graphics which are so simple that the global (i.e. sketchy) shapes of them are easily understood.

Establishment of KETpic Programming Styles for Drawing

When collegiate mathematics teachers make their original teaching materials, they often use TeX and CAS in order to insert figures and tables into the materials. TeX and CAS have their own programming languages, respectively. Programs must be written in a good style so that other people can read them. KETpic is a plug-in based on CAS to enable teachers to create figures as they like. KETpic has a programming language for drawing but its programming style is not yet established as a good programming style. In this paper we propose the requirements for a good KETpic programming style.

Creating Interactive Graphics for Mathematics Education Utilizing KETpic

In teaching mathematics, there are instances when we need to graphically present mathematical concepts and solid figures to clarify students’ understanding of them. For the last few years, we have been creating graphics that illustrate these various concepts dynamically through careful utilization of KETpic. Examples we will look at include an interactive graphic developed to clearly illustrate the line of intersection of two solid surfaces. In this case, we can easily show the cross-section of the intersection following the cut. A second example is of an interactive graphic produced in order to dynamically present the correspondence relation between the z −plane and w −plane in a complex function w = f(z). Here, by using the navigation buttons embedded in the graphic, we can demonstrate how the regions on the w −plane change in relation to the z −plane. Other graphics we have produced will also be introduced.

On Some Attempts to Verify the Effect of Using High-Quality Graphics in Mathematics Education

In this paper, we will show some of our attempts to verify the effect of using high-quality graphics in collegiate mathematics education through two types of experiments. In the first experiment, we gave a lesson on the law of logarithms usually done without using graphics. We used teaching materials containing graphics to give students some hints. To prepare the graphics, we utilized an extension of TeX capabilities for flexible page layout. Then we estimated the effects of the lesson through a statistical approach. In the second experiment, we detected the change of students’ brain activity by making behavioral observation and neuroimaging simultaneously. For this lesson, we chose the comparison of the degree of growth between two functions as the theme, and prepared some graphs for them. To generate these graphs, we utilized the programmability of the computer algebra system for automatically changing the scale. We showed them to three students and observed their responses. Simultaneously we monitored their brain activities through EEG (ElectroEncephaloGram) measurements. We observed that the judgment of these students changed when they saw a triggering figure, and some change in the trend of the EEG signal was observed at that time. From the results of these experiments, it is indicated that using effective figures in materials might have a great influence on learners’ reasoning processes.