A Study of the Effectiveness of Mathematical Activities in Rose Curves of Polar Equations Using a Graphing Calculator

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  • グラフ電卓を活用した極座標における正葉曲線に関する数学的活動とその有効性
  • グラフ デンタク オ カツヨウ シタ キョク ザヒョウ ニ オケル セイ ヨウ キョクセン ニ カンスル スウガクテキ カツドウ ト ソノ ユウコウセイ

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The purpose of this study is to evaluate the effectiveness of mathematical activities in graphing polar equations. Using hand-held graphing calculators, students observed many graphs of polar equations r=10sin nθ and explored the properties of the graphs. After their explorations, they analyzed the properties and reasoned mathematically about them by themselves. The following results were obtained : (1) Students found various properties of the graphs of polar equations from their mathematical activities. (2) Some students formulated generalizations and evaluated their conjectures about the observed properties. (3) Students learned new contents of polar coordinates in connection with previous knowledge of trigonometric functions. (4) The authors conclude that the graphing calculator is an effective tool for mathematical activities.

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