A Study of Teaching Materials for Inquiring into the Cause of Graphical Misrepresentaions on a Graphing Calculator : Graphical Misrepresentations in Rose Curves of Polar Equations

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  • グラフ電卓のグラフ誤表示の原因を探究する教材研究 : 極方程式における正葉曲線の誤表示
  • グラフ デンタク ノ グラフ ゴヒョウジ ノ ゲンイン オ タンキュウスル キョウザイ ケンキュウ キョクホウテイシキ ニ オケル セイヨウ キョクセン ノ ゴヒョウジ

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Abstract

The purpose of this research is to develop teaching materials for inquiring into the cause of graphical misrepresentations in rose curves of polar equations on the graphing calculator. Firstly, we surveyed the previous research about graphical misrepresentations on the graphing calculator to stimulate students' enthusiasm for learning. Secondly, we developed teaching materials that students used to explore the reason why a graph of γ=10sin100θ is displayed in the same way as a graph for γ=10sin4θ using hand-held graphing calculators. Finally, we analyzed the problem solving methods that students used to clarify potential problems with this teaching material. The following results were obtained: (1) Educational usage of graphical misrepresentations of polar equations on the graphing calculator is a new educational concept that has not been explored in previous research. (2) Students found the cause of graphical misrepresentations in connection with previous knowledge of trigonometric functions from their mathematical activities. (3) We concluded that this teaching material can be used to enhance the understanding of periodicity of trigonometric functions and the discrete nature of the graphing calculator.

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