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題名:認知學徒制在國小數學解題教學成效之研究
作者:方吉正
作者(外文):FANG, JI-JENG
校院名稱:國立高雄師範大學
系所名稱:教育學系
指導教授:張新仁
學位類別:博士
出版日期:2000
主題關鍵詞:認知學徒制數學解題情境學習情境認知cognitive apprenticeshipproblem solving in mathematicssituated learningsituated cognition
原始連結:連回原系統網址new window
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本研究旨在探討「認知學徒制數學解題教學法」對我國國小學童之訓練成效,以作為改進數學解題教學的參考。
本研究以高雄市楠梓國小六年級學童為實驗對象,以國小六年級上學期「怎樣解題」三個單元為實驗題材,進行二十節課的教學實驗,本研究採準實驗設計中的不等組前後測設計,隨機抽取三個班級分派為「認知學徒制數學解題教學組」、「一般數學解題教學組」、以及「自行練習解題組」,其中前兩組為實驗組,後一組為控制組。三組學童均接受前測、實驗處理、立即後測、以及延宕評量等實驗程序。為評量各組的數學解題教學成效,於實驗前、實驗後立即、以及實驗後八週,實施自編之「國小數學解題測驗」、「國小數學解題遷移測驗」、「國小數學信念問卷」、以及「國小數學學習態度問卷」。並由各實驗班級級任教師推薦男女生各六名,分屬高、中、低數學程度,接受數學解題歷程有聲思考晤談,以探討三組學生在數學解題歷程中解題策略與控制策略的表現情形。
本研究獲致下列幾項主要的發現:
一、不同數學解題教學法的訓練成效差異
1.就「數學解題表現」和「數學解題遷移表現」而言,「認知學徒制數學解題教學組」在全部分項上,無論是立即後測或延宕評量,均顯著優於其他兩組。
2.就「數學信念」和「數學學習態度」各分項而言,各教學組別在立即後測或延宕評量均無顯著差異。
3.就「數學解題歷程」而言,分述如下:
⑴在「數學解題策略」方面,接受「認知學徒制數學解題教學」者在立即後測階段顯著優於「自行練習解題」者,在延宕評量階段顯著優於其他兩組學生。
⑵在「數學控制策略」方面,依數學解題歷程階段分述如下:
①在「讀題」階段:在「注意條件目標」分項上,接受「認知學徒制數學解題教學」者在立即後測階段顯著優於「自行練習解題」者,在延宕評量階段則顯著優於其他兩組學生。
②在「分析-探索」階段:接受不同教學法的學生在各分項上的表現均無顯著差異。
③在「計畫─執行」階段:在「評估執行行為」分項上,接受「認知學徒制數學解題教學」者,無論在立即後測與延宕評量階段,均顯著優於「一般數學解題教學」者。在「有效評估執行行為」分項上,在立即後測階段顯著優於「一般數學解題教學」與「自行練習解題」者,在延宕評量階段則顯著優於「自行練習解題」者。
④在「驗證」階段:在「驗證答案行為」分項上,接受「認知學徒制數學解題教學」者在延宕評量階段顯著優於其他兩組學生。
整體而言,「認知學徒制數學解題教學」對於改進國小學生「數學解題表現」最具成效,具遷移與保留效果。在「數學解題歷程」之「數學解題策略」方面無立即效果,但有保留效果。在「數學解題歷程」之「數學控制策略」方面效果較不一致,在較簡單易學的控制策略方面較具成效,如「讀題」階段的「注意條件與目標」、「在計畫-執行」階段之「評估執行行為」和「有效評估執行行為」、以及「驗證」階段的「驗證答案行為」等;在較複雜的控制策略方面則較無成效,如「讀題」階段的「評估問題難度」與「回憶相關知識或經驗」、以及「分析-執行」階段的「合理控制策略」等。至於在「數學信念」與「數學學習態度」方面,效果最不明顯。
二、在數學解題教學法與數學程度間的交互作用
1.就「數學解題表現」各分項而言,僅在延宕評量之「了解題意」分項上有顯著的交互作用,其中低程度學生以接受「認知學徒制數學解題教學」者,顯著優於其他兩組學生。
2.就「數學解題遷移表現」與「數學信念」各分項而言,不同數學解題教學法與學生數學程度之間均無交互作用,顯示不同數學解題教學法並不特別利於某一數學程度的學生。
3.就「數學學習態度」各分項而言,在「學習習慣」與「總分」項目上,在立即後測階段有顯著的交互作用。在「一般數學解題教學組」中,高程度組學生在前述兩個項目上均優於中程度組學生。在「自行練習解題組」中,中程度組學生僅在「總分」項目優於低程度組學生。而中程度組學生當中,以接受「自行練習解題」者在前述兩個項目上,優於「一般數學解題教學」者,接受「認知學徒制數學解題教學」者則僅在「學習習慣」分項優於「一般數學解題教學」者。
整體而言,數學解題教學法與數學程度間的交互作用主要顯現於「數學學習態度」之「學習習慣」分項以及「數學解題表現」之「了解題意」分項,在「數學解題遷移表現」與「數學信念」方面,均無交互作用存在。
三、不同數學程度的訓練成效差異
1.就「數學解題表現」而言,除立即後測的「了解題意」分項外,其他分項與延宕評量的所有分項上,高程度組顯著優於低程度組學生。在立即後測的「回顧解答」分項上,高程度組顯著優於中程度組學生。在延宕評量的「了解題意」、「擬定計畫」、和「執行計畫」分項上,中程度組顯著優於低程度組學生。
2.就「數學解題遷移表現」而言,無論是立即後測或延宕評量階段,高程度組在所有項目均顯著優於低程度組學生。在立即後測的「了解題意」、「擬定計畫」、和「執行計畫」分項上,中程度組顯著優於低程度組學生。在立即後測的「執行計畫」、「回顧解答」、和「總分」,以及延宕評量的「擬定計畫」、「執行計畫」、「回顧解答」、和「總分」分項上,高程度組顯著優於中程度組學生。
3.就「數學信念」而言,在立即後測的所有項目以及延宕評量的「數學知識本質」、「總分」等項目上,高程度組均顯著優於低程度組學生。在立即後測的「數學解題」、「自我效能」、以及「總分」等項目上,中程度組均顯著優於低程度組學生。
4.就「數學學習態度」而言,在延宕評量的「學習方法」、「學習習慣」、以及「總分」等項目上,高程度組均顯著優於低程度組學生。在延宕評量的「學習方法」項目上,中程度組顯著優於低程度組學生。
5.就「數學解題歷程」而言,在「數學解題策略」與「數學控制策略」方面,無論在立即後測或延宕評量階段,不同數學程度別間均無實質差異。
整體而言,數學程度與「數學解題表現」、「數學解題遷移表現」、「數學信念」、「數學學習態度」等均大致呈現正向關係,數學程度與「數學解題歷程」較無明顯關係存在。
基於上述研究發現,本研究提出下列幾項建議:
一、在數學課程教材編選方面
(一)將「認知學徒制數學解題教學法」納入未來數學課程
(二)設計問題情境由簡單漸至複雜
(三)設計數學解題提示單提供學生學習鷹架
二、在數學教學實施方面
(一)塑造多元、懷疑、批判的班級氣氛
(二)培養學生討論與發表的能力
(三)平時多培養學生獨立探究的能力
(四)加強培養學生控制策略技能
(五)利用多媒體工具以輔助教學
三、在師資培育方面
(一)訓練教師有聲思考示範解題的能力
(二)培養教師本身扮演與訓練學生多元化角色的能力
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