臺灣博碩士論文加值系統

本研究目的在探究國小六年級學童解題錯誤類型並接受基模化影片結合電腦教學解多步驟代數文字題之列式教學之成效。一般學生對於數學文字題解題的學習，因解讀題意能力不足，又理解力較差，致使學生工作記憶超過負荷，因此造成在列式、計算錯誤等情形提高。本研究對象為台中市某國小六年級二個班五十七名學生，研究設計採用準實驗研究法（quasi-experimental design）中含實驗組及控制組的「前後測控制組設計」（pretest-posttest control group design）配合電腦輔助教學進行數學多步驟代數文字題列式之教學課程，並且分析受試者在解題歷程中的表現及結果。
本研究結果綜述如下：
一、實施「基模化影片教學」能有效幫助學生思考及解多步驟文字題，有助於降低六年級學生進行數學多步驟代數文字題的錯誤率及解題成效。
二、實施「基模化影片教學」進行數學多步驟代數文字題列式及解題的教學成效顯著優於傳統解題教學。
三、實施「基模化影片教學」對於六年級學生進行數學多步驟文字題列式及解題有學習保留之成效。
四、實施「基模化影片教學」有助於六年級學生降低各類型解題錯誤率
五、實施「基模化影片教學」能提升六年級學生對於數學的學習興趣。

This study was aimed to explore the error types of sixth graders solving word problems and the effect of using schema-based video to solve multiple-step algebraic word problems. Algebraic multi-step word problems tended to overload the working memory of students. Students might also have reasoning difficulty and reading comprehension problems. There were fifty-seven sixth-grade students in two classes in Taichung City participating in the study. The researcher used pretest-posttest control group design which was a quasi-experimental design with computer-assisted instruction. It was found that the schema-based video was effective for teaching multi-step algebra word problems, and the results satisfactory.
1.Implementing schematic video teaching could help students think effectively, solve multiple-step word problems, decrease the error rate of six- graders ’ solving multiple-step algebraicword problems and enhance the effectiveness of solving problems.
2.Implementing schematic video teaching in in solving multiple-step algebraicword problems and the effectiveness of solving problem teaching was superior to traditional teaching in solving problems.
3.Implementing schematic video teaching to six-graders’ solving multiple-step word problems and the effectiveness of solving problems could have the retention of learning effectively.
4.Implementing schematic video teaching could decrease the erreo rate of different types of solving problems.
5.Implementing schematic video teaching could promote six-graders’ interest in learning mathematics.

中文摘要.......................................................................................................ⅰ
英文摘要...................................................................................................... ii
目錄......................................................................................................... iii
表目錄........................................................................................................ v
圖目錄...................................................................................................... viii
第一章　緒論....................................................................................................1
　第一節　研究動機...............................................................................................1
　第二節　研究目的...............................................................................................2
　第三節　名詞解釋...............................................................................................3
　第四節　研究範圍與限制..........................................................................................4
第二章 文獻探討.................................................................................................5
　第一節　文字符號代數解題........................................................................................5
　第二節　基模與文字題............................................................................................9
　第三節　數學文字題解題錯誤原因相關研究............................................................................11
第四節 基模化影片系統教學相關研究...............................................................................17
第三章 研究方法.................................................................................................19
第一節　研究對象..............................................................................................19
　第二節　研究架構與實驗設計......................................................................................19
　第三節　研究工具...............................................................................................24
　第四節　資料分析與處理..........................................................................................29
第四章 研究結果與討論............................................................................................32
第一節　多步驟文字題解題表現之錯誤分析............................................................................32
第二節　基模化影片多步驟代數文字題列式解題系統對國小六年級學生代數文字題列式解題之結果分析.................................48
第三節 基模化影片多步驟代數列式解題系統對國小六年級學生代數文字題列式解題表現之社會效度分析...............................53
第四節 研究者之教學心得........................................................................................56
第五節　綜合討論...............................................................................................56

第五章 結論與建議 ...............................................................................................64
第一節　結論..................................................................................................64
　第二節　研究限制...............................................................................................66
　第三節　建議..................................................................................................67
參考文獻.................................................................................................... 69
中文部份 ..................................................................................................... 69
英文部份 ..................................................................................................... 71

表目錄
表 3-1 基模化影片多步驟代數文字題列式解題系統內容分析.......................... 26
表 4-1 原數未知文字題錯誤率.............................................................................. 39
表 4-2 中間數未知文字題錯誤.............................................................................. 41
表 4-3 原數未知文字題錯誤率.............................................................................. 43
表 4-4 中間數未知文字題錯誤率.......................................................................... 45
表 4-5 甲丁兩試卷統計量表........................................................................... 48
表 4-6 甲丁兩試卷t檢定............................................................................. 49
表 4-7 組別統計量表................................................................................. 49
表 4-8 獨立樣本t檢定................................................................................ 50
表 4-9 實驗組成對樣本統計量….......................................................................... 51
表 4-10 實驗組成對樣本t檢定.................................................................................51
表 4-11 對照組成對樣本統計量.............................................................................. 52
表 4-12 對照組成對樣本t檢定.............................................................................. 53
表 4-13 二十八位受試者填答「學生反應調查表」之結果.................................. 54

圖目錄
圖3-1 實驗設計圖......................................................................... 21
圖3-2 實驗教學階段圖..................................................................... 23
圖3-3 基模化影片多步驟代數文字題列式解題系統結合電腦之架構………......... 24
圖3-4 基模化影片多步驟代數文字題列式解題系統主畫面................................. 25
圖3-5 點選主畫面電器行選項後進入子畫面....................................................... 28
圖3-6 電器行-基模化動態影像影片…............................................................. 28
圖4-1 列式錯誤範例圖示...................................................................... 33
圖4-2 計算錯誤範例圖示...................................................................... 34
圖4-3 誤植數字錯誤圖示...................................................................... 35
圖4-4 遺漏算數錯誤圖示...................................................................... 36
圖4-5忽略結果錯誤圖示....................................................................... 37
圖4-6其他錯誤圖示........................................................................... 38
圖4-7原數未知文字題列式錯誤率折線圖………..................................................... 39
圖4-8原數未知文字題計算錯誤率折線圖............................................................. 40
圖4-9原數未知文字題粗心錯誤率折線圖............................................................. 40
圖4-10中間數未知文字題列式錯誤率折線圖....................................................... 41
圖4-11中間數未知文字題計算錯誤率折線圖....................................................... 42
圖4-12中間數未知文字題粗心錯誤率折線圖....................................................... 42
圖4-13原數未知文字題列式錯誤率折線圖........................................................... 43
圖4-14原數未知文字題計算錯誤率折線圖........................................................... 44
圖4-15原數未知文字題粗心錯誤率折線圖........................................................... 44
圖4-16原數未知文字題其他錯誤率折線圖........................................................... 45
圖4-17中間數未知文字題列式錯誤率折線圖....................................................... 46
圖4-18中間數未知文字題計算錯誤率折線圖....................................................... 46
圖4-19中間數未知文字題粗心錯誤率折線圖....................................................... 47
圖4-20中間數未知文字題其他錯誤率折線圖....................................................... 47
圖4-21實驗組與對照組原數未知錯誤率折線圖................................................... 57
圖4-22實驗組與對照組中間數未知錯誤率折線圖............................................... 58
圖4-23第一題型顯示圖..................................................................... 59
圖4-24第二題型顯示圖..................................................................... 59
圖4-25第三題型顯示圖..................................................................... 60
圖4-26第四題型顯示圖..................................................................... 60
圖4-27第五題型顯示圖..................................................................... 61
圖4-28第六題型顯示圖..................................................................... 61
圖4-29實驗組與對照組在原數未知多步驟文字題答對平均數長條圖................ 62
圖4-30實驗組與對照組在中間數未知多步驟文字題答對平均數長條圖............ 62

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