本研究主要的目的在探討七年級學生在學習三種多邊形內角和解題方法後,對學生形成一般化解題公式的影響以及推論一般化解題公式的過程可能遭遇之困難。研究對象為桃園縣楊梅市某七年級數學學習低成就三十位學生。本研究使用動態幾何軟體設計出三種解決多邊形內角和的方法,分別是除了使用課本所教授「切割多邊形成多個三角形以求多邊形內角和」方法,另外還多加了「堆砌三角形以求多邊形內角和」與「多邊形內一點與各頂點做連接線以求多邊形內角和」兩種解題方法。研究結果為: 1. 傳統課本的解題方法對學生求解固定邊數的多邊形內角和較容易,但非課本討論的解題方法(多邊形內一點與各頂點做連接線以求多邊形內角和)對看出多數形邊數與內角和的關係是較容易的。 2. 學生推導多邊形內角和一般化公式的困難,除了是因為沒有掌握構成多邊形邊數與三角形個數的關係之外,最大的困難仍是對文字符號意義的不了解。
The study aimed to explore the influence of the 7th graders to formulate the general formula after learning one of the solutions to the Angle Sum of Polygon. The researcher also examined the difficulties of the ratiocinated process. The chosen participates were the 30 lower achiever students at a selected junior high school in Taoyuan County in Taiwan. The research designed three solutions to angle sum of polygon with dynamic geometry software. It included the first solution of “computing angle sum of polygon by cutting polygon to triangles” from the textbooks; the second solution of “to compute angle sum of polygon by piling triangles”; and the third solution of to calculate angles by making lines between one point in the polygon and the other vertexes”. Results of the study generated from qualitative way as following: 1. Traditional solutions were easier for participants when solving the Angle Sum which had fixed sides, such as the Angle Sum of quadrilateral, pentagon, hexagon, and heptagon. However, from the result of findings, the third solution was helpful for participants to solve the questions of Angle Sum of Polygon. 2. The difficulties of the ratiocinated process that participants encounter included two aspects. In addition to the incomprehensible relationship between the side of Polygon and the amount of triangle, the participants could not realize the meaning of words or phrases literally caused the biggest baffle.