國中九年級學生三角形的外心、內心與重心單元 錯誤類型之分析研究

An Analysis of Error Patterns in Junior High School Ninth-Grade Students' Performance of Circumcenter, Incenter and Triangle Centroid

本研究的主要目的是瞭解國中九年級學生在三角形的外心、內心與重心單元的解題狀況，並歸納解題的錯誤類型，進一步探討解題的錯誤可能形成原因。研究採問卷和晤談的方式進行，以臺南市東區一所國中的九年級學生二十八名為研究樣本。藉由自編的成就測驗，以紙筆測驗調查解題狀況，根據測驗結果歸納出錯誤類型，並以晤談的方式瞭解解題錯誤的可能原因。本研究的主要結果為：全體錯誤率過半，外心錯誤率最高，內心錯誤率次之，重心錯誤率最低；根據測驗及晤談結果共歸納出七種錯誤類型及五種錯誤可能形成原因。

 

This research mainly aimed to understand ninth-grade students’ basic comprehension of Circumcenter, Incenter and Triangle Centroid and how they solved problems, analyze the error patterns in their performance of Circumcenter, Incenter and Triangle Centroid, investigate the possible reasons of their errors. The research method combined surveys and interviews. The sample included twenty eight ninth-grade students from a class in a junior high school in East District, Tainan City. Applying “achievement test”, a paper-based test developed by the researcher, to the Circumcenter, Incenter and Triangle Centroid session, this research investigated students’ performance in the achievement test and the errors in their performance. The error patterns were generalized from the result of the achievement test. Ultimately, the researcher conducted interviews with students to further understand the possible reasons for the errors they made in the achievement test. The main results were: first, the overall error rate was over fifty percent. The highest error rate occurred in Circumcenter, followed by that of Incenter, with that of Triangle Centroid the lowest. Next, there were seven error patterns in students’ performance of Circumcenter, Incenter and Triangle Centroid. In the end, there were five possible reasons for students’ errors in their performance of Circumcenter, Incenter and Triangle Centroid.