To Be Presented in the 11th Asian Technology Conference in Mathematics
December 12-16, 2006, Hong Kong SAR, China

The Lesson of Cellular Automata

Kazumi Yamada
Faculty of Education and Human Sciences
Niigata University


The lesson of cellular automata

The mathematics of a discrete system like a cellular automaton is suitable for training the mathematical thinking method and logical thinking capability which are not in traditional mathematics education. In the introductory contents of the mathematics of a discrete system, since the object to investigate is finite, junior high school students can learn mathematics applying a trial-and-error method by drawing figures on paper. However, they should come to feel difficulty and a limit for pursuing, while drawing figures. After all, they probably will become necessary to experiment using computers. For example, when they investigate change of cells of the Game of Life, which is a special case of a two-dimensional cellular automaton, using papers containing grids , since time is taken too much, computers are needed.

Usefulness of a lesson of the mathematics of a discrete system

The mathematics of a discrete system has the very deep back. In addition, even if it is introductory contents which can be understood to them, it has very rich contents. By learning a cellular automaton and a fractal, they understand that the complicated phenomenon of nature is acquired by repeating simple modification repeatedly. As a result, their view to a natural phenomenon is changed gradually. Moreover, they meet with the mathematics not using a formula, and are surprised.

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