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研究生: 李佳奇
論文名稱: 高中生對條件機率解題策略與錯誤類型之探討
指導教授: 陳昭地
Chen, Zhao-Di
程毅豪
Chen, Yi-Hau
學位類別: 碩士
Master
系所名稱: 數學系
Department of Mathematics
論文出版年: 2001
畢業學年度: 89
語文別: 中文
論文頁數: 111
中文關鍵詞: 條件機率解題策略錯誤類型
論文種類: 學術論文
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  • 本研究的主要目的在於探討高中學生對條件機率的解題策略、錯誤類型和背後的錯誤原因。
    本研究的方法乃是藉由設計的條件機率試題問卷來探討學生的解題策略和錯誤類型,並且輔以面談的方式找出錯誤類型背後的錯誤原因;而本研究的樣本乃是選取台北縣的兩所高中高二和高三各四個班級,共計324個學生。
    本研究的主要結果為:
    一、解題策略上:(1)高二的學生習慣藉由求出事件樣本個數的方式來計算條件機率,而缺乏操作事件機率來求取條件機率的能力。(2)高三的學生雖然具有操作事件機率來求取條件機率的能力,但是他們經常忽略兩事件間的關係,而個別計算不同基礎下的兩事件機率,然後將其相乘求解。
    二、在錯誤類型上:(1)學生經常將條件機率的問題誤為交集機率的問題。(2)學生在處理條件機率的問題時,經常採用個別計算不同基礎下的兩事件機率並將其相乘求解。(3)在處理基本概念的條件機率問題時,部分高三的學生會誤用排容原理來進行解題。(4)在處理基本事件之機率不相等的條件機率問題時,學生容易經常患了等機率的偏見。(5)當解需要應用到貝氏定理的條件機率問題時,學生經常用P(B|A)或P(A B)來求 P(A|B)。(6)當解某些需要應用到貝氏定理的條件機率問題時,學生經常只考慮到條件事件的部分情況,而忽略其他情況。(7)當解某些需要應用到貝氏定理的條件機率問題時,學生經常受到事件先後發生順序的影響而忽略條件事件。(8)當解某些需要應用到貝氏定理的條件機率問題時,學生經常受到問題情境的影響,只考慮到問題中某一給定事件的比例。
    最後根據本研究之結果加以討論,並提出若干建議,希望能提供教材編輯者編寫教材及教師往後教學時的參考。

    第一章 緒論…………………………………………………………1 第一節 研究動機…………………………………………………1 第二節 研究目的…………………………………………………4 第三節 名詞解釋…………………………………………………4 第二章 文獻探討…………………………………………………….6 第一節 數學解題歷程的相關研究………………………………6 第二節 機率迷思概念的相關研究……………………………..16 第三節 條件機率迷思概念的相關研究…..……………………20 第四節 機率迷思概念與教學上的關係…..……………………21 第三章 研究方法……………………………………………………22 第一節 研究架構…..……………………………………………22 第二節 研究設計…..……………………………………………23 第三節 研究樣本…..……………………………………………23 第四節 研究工具…..……………………………………………24 第五節 研究過程…..……………………………………………26 第六節 研究限制…..……………………………………………29 第四章 研究結果與討論……………………………………………30 第一節 資料處理與統計…………………………………………30 第二節 解題策略與錯誤類型分析………………………………31 第三節 錯誤原因分析……………………………………………45 第五章 結論與建議…………………………………………………59 第一節 結論………………………………………………………59 第二節 建議………………………………………………………62 參考文獻………………………………………………………………..64 中文部分………………………………………………………….64 英文部分………………………………………………………….65 附錄……………………………………………………………………..70 附錄一 答題說明和注意事項…………………………………70 附錄二 預測試題………………………………………………71 附錄三 實測試題………………………………………………75 附錄四 各題之作答情形………………………………………77 附錄五 訪談錯誤類型之分類…………………………………93

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