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研究生:黃渼淳
研究生(外文):HWANG MEI-CHWEN
論文名稱:高中生指數概念及運算錯誤類型分析之研究
指導教授:蕭龍生蕭龍生引用關係
學位類別:碩士
校院名稱:國立高雄師範大學
系所名稱:數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2001
畢業學年度:90
語文別:中文
論文頁數:118
中文關鍵詞:指數錯誤類型學業成就
相關次數:
  • 被引用被引用:24
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  • 下載下載:88
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論文摘要
本研究之主要目的是從不同學業成就的觀點出發﹐以探討高中生指數概念及指數運算的錯誤類型﹐並探討學生發生錯誤的原因。
本研究對象為高雄市某私立高中高三學生﹐研究者分別依學生學業成就高﹑中﹑低三群中各抽取一個班級﹐共146名學生為研究樣本。研究工具為自編之指數概念及運算測驗。
本研究經由紙筆測驗了解學生概念發展及運算錯誤情形﹐並對無法了解解題想法的學生進行面談﹐經由資料分析後﹐提出下列幾點結論﹕
1.學生前階段指數概念錯誤﹐導致以後指數概念發展錯誤。
2.學生因平方根﹑根式運算﹑因式分解﹑文字符號及乘法概念模糊﹐影響指數概念的學習。
3.學生對其他學科概念不清楚﹐影響指數應用問題的作答。
4.學生對指數律誤用情形不少﹐尤以一個題目運算中若運用到二個或二個以上指數律時﹐誤用情形更嚴重。
5.不同學業成就的學生在「正整數指數」﹑「零指數」及「實數指數」三類概念的理解上﹐不完全有顯著的差異。
6.不同學業成就的學生在「負整數指數」﹑「正實數的n次方根的存在性與唯一性」及「有理指數」三類概念的理解上﹐均有顯著的差異。
7.對於各試題的答對率﹐多依學業成就的高低漸次下降。顯示學業成就高的學生仍然較少有學習困難。
8.對於指數應用問題﹐學業成就高的學生會盡量作答﹐學業成就中﹑低等的學生﹐空白人數明顯增加。
目 錄
第一章 緒論1
第一節 問題背景與研究動機1
第二節 研究目的及待答問題3
第三節 研究假設3
第四節 名詞解釋3
第五節 研究限制4
第二章 文獻探討5
第一節 認知發展理論之研究5
第二節 解題歷程的探討12
第三節 數學概念與運算的學習17
第四節 數學概念與運算錯誤類型之研究24
第五節 數學概念與運算錯誤原因之探討27
第三章 研究方法32
第一節 研究設計32
第二節 研究對象32
第三節 研究工具33
第四節 實施步驟37
第五節 資料處理與統計40
第四章 結果與討論41
第一節 三組不同學業成就學生的指數概念41
第二節 三組不同學業成就學生的指數運算能力70
第三節 三組不同學業成就學生對指數應用的瞭解情形90
第五章 結論與建議97
第一節 研究結論97
第二節 研究建議100
參考文獻102
附錄A112
附錄B116
附錄C117
附錄D118
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