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題 名 | 無窮等比級數概念與運算錯誤類型之研究=A Study of Error Patterns in Infinite Geometric Series Concepts and Their Operations |
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作 者 | 謝哲仁; 林清岳; | 書刊名 | 美和技術學院學報 |
卷 期 | 22:1 2003.04[民92.04] |
頁 次 | 頁255-281 |
分類號 | 521.22 |
關鍵詞 | 無窮等比級數; 錯誤概念; Infinite geometric series; Error patterns; |
語 文 | 中文(Chinese) |
中文摘要 | 本研究之目的主要在探討高中生學習無窮等比級數後,其概念發展情形與學生運算錯誤的類型及造成錯誤之原因。研究採用紙筆測驗與面談相互配合的方式進行,藉由紙筆測驗調查學生在無窮等比級數單元之概念發展情形及運算錯誤類型,再經由面談的過程進一步了解學生解題時的想法及運算過程與犯錯的原因。紙筆測驗乃採用研究者所自編的『無窮等比級數概念及運算測驗』對高雄地區某私立高中之高三學生,共128人,實施測驗。本研究主要的發現有: 一、 學生的錯誤原因主要為:(一)因概念不清產生的錯誤。(二)受先前學習過的知識或本單元學習經驗的影響做錯誤的推論。(三)受錯誤的舊經驗影響,使用錯誤的運算規則。(四)被相似的概念原則混淆。(五)缺乏先備知識。(六)粗心計算或書寫的錯誤。 二、 受測學生有關無窮與極限的概念發展情形:(一)大多數學生對於無窮等比級數的認知,仍停留於背公式做題目的階段。(二)大多數學生以有限來類推無窮,把極限當成近似,尚未有正確的概念形成。 |
英文摘要 | The purpose of this study was to discuss how senior high school students develop the concept of infinite geometric series and to investigate the reasons for error patterns in calculating after students have learned infinite geometric series. Written tests and interviews were applied to this study. Written tests were used to examine the error patterns about infinite geometric series. Interviews were used to understand students' thoughts and the reasons why they made mistakes when calculating infinite geometric series. The written test- The Infinite Geometric Series Concept and Calculating Test- was designed and developed by the authors. The participants of this study were 128 senior students in a private senior high school in Kaohsiun. The results of this study were the following: I. The reasons of students' errors: (1) Students did not have clear concepts of infinite geometric series. (2) Students' incorrect inference was caused by previous learning experience. (3) Students used incorrect calculating rules. (4) Students felt confused by similar concepts or rules of mathematics. (5) Students lack prerequisite knowledge. (6) Students made mistakes because of carelessness or lapse. II. The testees' concepts of Infinite and Limit in this study: (1) Most students just memorized equations but did not understand infinite geometric series. (2) Most students did not have correct concepts of infinite geometric series. |
本系統中英文摘要資訊取自各篇刊載內容。