- 學位論文
針對國民中學學生關於魔術方塊解題思維之研究
The Research of Solving Rubik's Cube for Junior High School Students
摘要
本研究探討「如何推導二階魔術方塊解題公式」的問題。目的在不利用既成公式或牽涉高等數學的情況下，如何以推理方式發展適合國中學生學習的魔術方塊解題方式。藉由平面圖型的觀察與簡單的推理層遞，導出各具特色的公式，並利用觀察圖形的方式小心驗證公式的適用性，完成解題。並使學生能藉由解題過程中訓練推理及空間觀念。本研究根據研究目的，提出以下結論。 一、 可以藉由基本的空間推理，訓練國中學生完成二階魔術方塊的解題過程，以及自行發展更有效率之解題工具。 二、 藉由引入Game Tree的概念，能自行繪製圖形驗證自定公式的適用性，同時檢驗既成公式後，確認自定公式適用範圍與既成公式相同。 三、 本研究第二章所提及的公式及推理的思路，可以直接推廣或修改後推廣至更高階的魔術方塊使用，以進行高階公式的推導工作。
並列摘要
In this research we want to discuss about ”How to derive the formula of pocket cube？”. It is our final goal that students can derive the solution of pocket cube by just elementary mathematics, not existed formula. By observing the polyhedron and the process of reasoning, we derive featured formula, then we can prove that the formula is useful for solving pocket cube problem by using game tree. So we can train students through this process and improve their space concept and ability of reasoning. The results of the research show that： 1. By using elementary space reasoning, students can complete the solving of pocket cube, and develop more effective formula by themselves. 2. By inducting game tree, students can prove whether their featured formula work or not. And we verify that featured formula is as useful as existed formula. 3. By using the same concept in this research, we can solve the problem of hyper Rubik’s cube.