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研究生:莊裕庭
研究生(外文):Chuang Yu-Ting
論文名稱:國二高低數學成就學生解題之後設認知個案研究
論文名稱(外文):A case study of metacognition in mathematical problem solving of second grade junior high school students
指導教授:柳賢柳賢引用關係
指導教授(外文):LEOU SHIAN
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:2002
畢業學年度:90
語文別:中文
論文頁數:141
中文關鍵詞:解題後設認知
外文關鍵詞:problem solvingmetacognition
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本研究之目的在探討國二學生後設認知的表現對數學解題的影響。研究的對象為嘉義縣一所國中二年級學生,挑選高低數學成就學生各三名進行放聲思考解題測驗。研究採個案處理的方式以放聲思考法、晤談法、事後回溯法,對研究樣本之解題原案進行分析。研究結論如下:
一、國二學生後設認知的表現對解題歷程的影響:
(一)讀題之後,高數學成就學生因為選擇注意、組織訊息、與策略使用能力全面發揮,才能在較短的時間之內就進入了分析階段。數學知識足夠者,更可能直接跳過探索階段進入分析階段。
而低數學成就學生讀題後往往選擇注意、組織訊息、策略使用的能力有缺損,後設認知沒有全面發揮,要經歷一段長時間的探索歷程,才有機會進入分析階段,甚至跳不開探索歷程,自我情緒監控失敗,失去耐性或信心而放棄解題,此時解題階段受到後設認知與情意因素雙重影響。
(二)國二學生解題歷程很少有計劃階段,沒有完整的解題計劃、全面的考量,因此對於策略使用與解題能否成功的自我評估能力自然難以發揮。
(三)高數學成就學生的自我監控能力較強,各解題階段比較少發生一連串的失誤,解題階段的轉換也較順暢,解題歷程比較多樣化。即使解題失敗,高數學成就學生往往離成功只差一兩個步驟。
而低數學成就學生自我監控能力較弱,各解題階段常發生一連串的錯誤而未發現,解題階段的轉換也就不順暢,解題歷程比較單調。而且解題歷程往往發生了許多錯誤點,離成功有一大段差距。
(四)高數學成就學生的各項後設認知成分能力均優於低數學成就學生,因此解題歷程的進行、突破與轉換,就比較容易與順暢,解題能力較佳。因此藉著放聲思考進行後設認知教學對國二學生解題能力的增長是有助益、且需要的。
二、國二學生後設認知的表現對解題成敗的影響:
(一)一個成功的解題歷程必須由兩個以上的後設認知能力相互配合才得以實現。各後設認知成分能力環環相扣,密切配合。
(二)每道放聲思考題的關鍵能力中都含有自我監控能力,對解題成敗的影響最為深遠,對數學解題有最關鍵性的影響,表現愈好,解題成功的機率就愈高。
(三)後設認知也需要有良好情意表現的配合才能完整發揮,成功解題。由此更可確定放聲思考法與晤談法都要先與研究樣本建立夥伴關係、信賴的情感。解題教學時,不能一味只要求學生進行後設認知、解題訓練,師生的互信情感也要花時間培養,如此一來教學才會有事半功倍的成效。
第一章 緒論……………………………………….…………1
第一節 研究動機…….…...…………………………....1
第二節 研究目的……………………………………....3
第三節 待答問題…………………………………..…..3
第四節 名詞界定……………………………………....3
第五節 研究限制………………………………………4
第二章 文獻探討………………………………………...…5
第一節 後設認知理論……………………….….…......5
第二節 數學解題相關理論……………..……………..15
第三節 解題成敗因素與相關研究……………………24
第四節 數學解題與後設認知之實徵研究…………....27
第三章 研究方法與步驟………………………….……..31
第一節 研究樣本……………………………….….…..31
第二節 研究方法…………………………….…….…..31
第三節 研究工具……………………………….….…..33
第四節 實施步驟……………………………….….…..35
第五節 資料分析……………………………….….…..38
第四章 結果與討論………………………….…….………40
第一節 原案分析……………………………….….…..40
第二節 綜合討論……………………………….….…..82
第五章 結論與建議……………………………..…………90
第一節 研究結果……………………………….….…..90
第二節 研究結論……………………………….….…..93
第三節 研究建議……………………………….….…..95
參考文獻………………………………………………………….97
附錄
附錄A:國中數學第二冊成就測驗、雙向細目分析表、鑑別度、難度………..105
附錄B:放聲思考試題關鍵技能與雙向細目分析表……………………………..108
附錄C:半結構性解題後設認知行為晤談大綱與半結構性背景晤談大綱……..110
附錄D:放聲思考指導語…………………………………………………………..112
附錄E:放聲思考練習題…………………………………………………………. 113
附錄F:原案………………………………………………………………………...114
表次
表2-1 Polya之解題歷程與解題策略表………………………………………….17
表2-2 Lester之認知與後設認知數學解題表現架構……………………………19
表2-3 Schoenfeld 之解題原案巨觀分析架構表………………………………..21
表2-4 自編之解題歷程階段區分表…………………………………..…………22
表4-1 解題歷程階段紀錄表……………………………………………………82
表4-2 關鍵後設認知能力表………………………………………………………86
表4-3 數學知識與後設認知能力狀況表…………………………………………88
表5-1 解題歷程特徵表……………………………………………………………90
表5-2 後設認知差異表……………………………………………………………91
圖次
圖2-1 Flavell的後設認知模式……………………………………………………7
圖2-2 Brown的後設認知模式……………………………………………………9
圖2-3 Paris的後設認知模式……………………………………….…………....10
圖2-4 Lester的數學解題認知--後設認知模式…………………………………..19
圖2-5 原案時序表徵圖(Schoenfeld, 1985)……………………………………….22
圖2-6 Mayer的解題歷程模式…………………………………………………23
圖3-1 研究步驟實施流程圖…………………………………………………..…37
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