臺灣博碩士論文加值系統

本研究旨在利用Parker（1995）所提出百分比認知分析脈絡，編製一份百分比的學習表現評量，以了解國小六年級學生在百分比概念上的學習表現情形，以了解未知數位置與情境脈絡的影響，及學生在不同情境脈絡及不同未知數位置下的表現，並以研究者所提出之「百分比問題認知成份」來解釋其表現，且針對各問題進行逐題分析。
研究樣本共選取台南縣、市各2所學校，共11班，395位學生為樣本施測。以電腦軟體ITAN及SPSS8.0進行試題和統計分析，統計考驗為完全受試者內設計二因子變異數考驗、單純主要效果考驗及杜凱氏HSD法的事後比較，所得之研究結論如下：
1.全體學生在三個未知數的平均通過率以比較量未知最好，基準量未知最差。
2.全體學生在九個脈絡的平均通過率以「部分/整體」及「甲為乙的多少﹪小」的問題最高，「比原來減少了多少﹪」的問題最低。
3.未知數位置與情境脈絡間有交互作用。
4.在不同未知數位置中「倍數關係」基模的問題皆比「差異量比較」基模的問題容易。
5.在不同脈絡中，不需選擇基準量的問題為容易，以使用「尋找基準量」基模最困難，但在脈絡A「增加的問題」、脈絡B「增加的問題」、脈絡D「比少的問題」三個脈絡中以使用「判斷基準量」基模最為困難。
6.學生在判斷比較量和基準量上的錯誤是較常見的錯誤。
7.需要計算比較量和基準量的差的問題學生較無法掌握。

The purpose of this research was to develop a performance assessment of percent concept from Parker''s（1995）cognitive mathematical analysis of percent in context which measured pupils'' learning performance and pupils'' performance on the questions of three possible unknowns and nine different contexts. Moreover, the investigator analyzed each question by " The Cognitive Components of Percent Concept" to explain pupils'' performance.
There were 395 6th grader from four elementary schools of Tainan City and Tainan County. Two-way analysis of variance, simple main effect, and a posteriori comparisons of Tukey method with ITAN and SPSS8.0 were adopted to analyze the data.
The main finding were as follows:
1.On the questions of unknown comparative amount was superior to on the questions of unknown base.
2.With the condition of different context, the subjects received highest scores on the question of "part/whole" and "smaller is ﹪"and got lowest scores on the question of "decrease by ﹪".
3.There were interactions between the three possible unknowns and nine different contexts.
4.On the questions of unknowns comparative, the schema of "multiplicative relationship" was easier than the schema of " comparing difference".
5.In nine different context, the easiest was the schema of not choosing the base, and the hardest was the schema of " finding the base". However, in the context of " increase to ﹪of", " increase by ﹪", and "smaller by ﹪", the hardest was the schema of "determining the base".
6.The common mistake was found in determining the comparative percentage and the base.
7.It was difficult for most students that questions were counted the difference between the comparative percentage and the base.

目次
第一章 緒論…………………………………….…………………1
第一節 研究動機…………………………………………………...……2
第二節 研究目的及研究假設………………………………..………….5
第三節 名詞解釋………………………………………………..……….7
第二章 文獻探討………………………………………………...10
第一節 百分比的意義………………………………………………….10
第二節 百分比的知識及作業………………………………………….23
第三節 解題能力之相關研究………………………………………….37
第四節 百分比的知識結構.....................................................................53
第三章 研究設計……………...........……………………………57
第一節 研究對象及研究工具………………………………………….57
第二節 資料分析……………………………………………………….64
第三節 研究限制.....................................................................................66
第四章 結果與討論……………………………………………...68
第一節 國小六年級學生百分比的學習表現.....…………...………….68
第二節 未知數位置與百分比脈絡交互作用對解題表現之影響........................................................…………...………….75
第三節 相同未知數位置中不同脈絡之表現.…………………...…….79
第四節 相同脈絡中不同未知數位置之表現........…………………...103
第五節 逐題表現分析........…………………………………………...109
第五章 結論與建議......…………………………..…………….156
第一節 結論………………………….…………….....……….156
第二節 建議.................………………………………….…….161
參考書目………………………………...………………………..165
中文部分………………………………………………………………...165
英文部分………………………………………………………………...169
附錄………………………………………………..……………...178
附錄一 百分比的學習表現評量……………………………………...178
附錄二 題目鑑別度指數............……………………….....………......182
附錄三 原始分數與百分等級及直線轉換標準分數對照表………...183
附錄四 百分比的學習表現評量選項設計…………………………...184
表次
表2-2-1 簡單加減法文字題之類型………………………………………….29
表2-2-2 百分比問題的雙向細目表………………………………………….33
表2-3-1 未知數問題的認知成份…………………………….……………....43
表2-3-2 模式一難度分析………………………………………….………....43
表2-3-3 模式二難度分析………………………………………………….…44
表2-3-4 模式三難度分析…………………………………………….………44
表2-3-5 各年級兒童的答對比率…………………………………………….45
表2-3-6 各層次兒童的解題能力預測…………………………………….…46
表2-3-7 各題目的知識基模………………………………………….………47
表2-4-1 百分比問題的認知成份…………………………………….………56
表3-1-1 受試樣本人數統計表....………………………….…………………57
表3-1-2 百分比問題雙向細目表…………………….………………………59
表3-1-3 「百分比的學習表現評量」之題目分析摘要表….…………………62
表3-1-4 受試各班之效標關聯效度……………………….…………………63
表4-1-1 全體與各組學生的通過比率.............................................................69
表4-2-1 各細格通過率................………………………………………….....76
表4-2-2 完全受試者內設計二因子變異數分析摘要表….…………………77
表4-2-3 單純主要效果的變異數分析摘要表.....................................………78
表4-3-1 比較量未知中各脈絡的事後比較......……………….......................80
表4-3-2 比較量未知中各問題難度排序..............………………….……......81
表4-3-3 比值未知中各脈絡的事後比較......………………….……………..88
表4-3-4 比值未知中各問題難度排序..............………..….…………………89
表4-3-5 基準量未知中各脈絡的事後比較......………………….………..…95
表4-3-6 基準量未知各問題難度排序..............………………………….......96
表4-4-1 各脈絡下的事後比較....................................................…………...103
表4-5-1 第1題選項分析.............…………………………………………...110
表4-5-2 第2題選項分析.............…………………………………………...112
表4-5-3 第3題選項分析.............…………………….………………….….114
表4-5-4 第4題選項分析.............………………….………………………..116
表4-5-5 第5題選項分析.............………………………….………………..118
表4-5-6 第6題選項分析.............…………………….…………………..…119
表4-5-7 第7題選項分析.............………………….…………………..……121
表4-5-8 第8題選項分析.............…………………….……………………..122
表4-5-9 第9題選項分析...............…………………...….……………….…124
表4-5-10 第10題選項分析.............……………………………………...…125
表4-5-11 第11題選項分析.............……………………………………...…127
表4-5-12 第12題選項分析.............………………………………………...129
表4-5-13 第13題選項分析.................…………………….………………..131
表4-5-14 第14題選項分析.................………………………………...........133
表4-5-15 第15題選項分析.................………………………………...........134
表4-5-16 第16題選項分析.............………....…….…………………......…136
表4-5-17 第17題選項分析.............………………….…………………..…138
表4-5-18 第18題選項分析...........………………….………………………140
表4-5-19 第19題選項分析.............…………………………………..….....142
表4-5-20 第20題選項分析.............………………….…………………..…143
表4-5-21 第21題選項分析...............……………………………..…...........145
表4-5-22 第22題選項分析.............………………….……………......……146
表4-5-23 第23題選項分析.............…………….……………………..........148
表4-5-24 第24題選項分析............…………………….…………………...149
表4-5-25 第25題選項分析............………………….…………………...…151
表4-5-26 第26題選項分析............……………….…………………….......153
表4-5-27 第27題選項分析……..........………….…………………….........154
圖次
圖2-1-1 分數的五種意義……………………………………….........………16
圖2-1-2 教材地位………………………………….…………………………22
圖2-2-1 百分比問題的九種脈絡圖….……………………………………....30
圖4-2-1 相同未知數位置下各脈絡表現情形的折線圖.……………………75
圖4-3-1 比較量未知中各問題難度折線圖..................................………..….82
圖4-3-2 比值未知各問題難度折線圖...................................……………..…90
圖4-3-3 基準量未知各問題難度折線圖...............................……………......97
圖4-5-1 測驗分數百分比折線圖............................………………………...109
圖4-5-2 第1題選項分析長條圖..............................……………………......111
圖4-5-3 第2題選項分析長條圖...................................…………………….113
圖4-5-4 第3題選項分析長條圖......................................…………………..114
圖4-5-5 第4題選項分析長條圖......................................…………………..116
圖4-5-6 第5題選項分析長條圖......................................………………..…118
圖4-5-7 第6題選項分析長條圖......................................…………………..120
圖4-5-8 第7題選項分析長條圖......................................………………..…121
圖4-5-9 第8題選項分析長條圖......................................……………......…123
圖4-5-10 第9題選項分析長條圖....................................………………..…124
圖4-5-11 第10題選項分析長條圖..........................................………......…126
圖4-5-12 第11題選項分析長條圖..........................................………..........127
圖4-5-13 第12題選項分析長條圖..................................…………………..129
圖4-5-14 第13題選項分析長條圖...............................……………….........131
圖4-5-15 第14題選項分析長條圖.......................................………….........133
圖4-5-16 第15題選項分析長條圖..........................................………..…....135
圖4-5-17 第16題選項分析長條圖.............................………………….......137
圖4-5-18 第17題選項分析長條圖................................………………........139
圖4-5-19 第18題選項分析長條圖................................…………………....141
圖4-5-20 第19題選項分析長條圖...................................….........................142
圖4-5-21 第20題選項分析長條圖............................………………............144
圖4-5-22 第21題選項分析長條圖......................................……………......145
圖4-5-23 第22題選項分析長條圖....................................……......………..147
圖4-5-24 第23題選項分析長條圖.................................………………...…148
圖4-5-25 第24題選項分析長條圖.....................................…………….......150
圖4-5-26 第25題選項分析長條圖.............................……………………...151
圖4-5-27 第26題選項分析長條圖...........................…………………….....153
圖4-5-28 第27題選項分析長條圖................................…………………....155

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