臺灣博碩士論文加值系統

　　本研究以「通分」、「顛倒相乘」及「整合通分與顛倒相乘」等三種不同類型的範例教學，探討學生於分數除法之概念性知識與程序知識的學習成效，尤其關注低先備知識學生的學習。前導研究以115名五年級學生和108名六年級學生分別預試先備知識試題及概念性知識評量試題，結果顯示大部分的試題呈現難度較低，但鑑別度優良的情況，進一步進行信效度分析（效度指標為學生100學年度第二學期數學期中考成績），亦顯示試題內部一致性良好，也與數學成就有適當的相關，故本研究僅修訂少部份試題，其他試題在正式實驗則予以沿用。正式實驗的研究參與者為台北市與桃園縣各一所國小、各三個五年級班級的學生，有效樣本為148 名學生。受試者以班級為單位分派至三種不同的範例教學。教學實驗前施測先備知識；隨後進行二節（整合組）或三節（另外兩組）的範例教學，課堂讓學生兩兩異質分組，透過討論範例與各自練習解題進行學習；教學後施以分數除法的程序性知識及概念性知識試卷。結果顯示學生透過範例教學學習分數除法的概念性知識及程序性知識，其正確率達八成與九成，達到一般教學所欲達成的教學效果，然由於三組學生的表現都很好，透過共變數分析控制先備知識的影響後三種範例組別未達顯著差異。低先備知識的學生則有組別效果，以整合組學習概念性知識的成效優於顛倒相乘組，且整合或顛倒相乘組學習程序性知識的效果優於通分組，顯示對於低先備知識學生而言，整合組的範例不僅最有效率，也最有效益。本文最後對課堂中的學生行為進行描述，也討論研究限制與教學上的建議。

In this study, three different prototypes of “common denominator”, “reciprocal multiplication” , and “integration” as the worked-out examples were applied to explore the learning effect on conceptual knowledge and procedural knowledge of fraction division, especially that on the students with low prior knowledge. The pilot study pre-examined 115 5th graders and 108 6th graders via the examination of prior knowledge and conceptual knowledge. The pilot study result shows lower difficulties in accordance with better discrimination in most of the items. The analysis of internal consistency reliability fitted the goodness; criterion-related validity was qualified for the significant correlation with the mathematics-achievement scores. Therefore, the study only revised minor part of the items. Other items were expected to be adopted in the formal examination. The valid samples in the formal examination were 148, including 5th graders sampling from elementary schools in Taipei and Taoyuan. The participants divided by classes as a unit were designed to three conditions with different worked-out-example teaching instruction. The examination of prior knowledge was proceeded before the instruction. The worked-out-example instruction was then proceeded in the second (integrated group) or third (the other groups). The students were divided into heterogeneous group and they could learn via discussing the examples as well as solving the questions. The examination of fraction division with procedural knowledge and conceptual knowledge were provided after the worked-out examples. The results exhibited the anticipated learning effects on the students with 80% and 90% correct rate via learning conceptual knowledge and procedural knowledge of fraction division respectively. The difference between three groups was not significant according to ANCOVA analysis since the performance of three groups were fine simultaneously. The effect resulting from different groups occurred in the students with low prior knowledge. The effects of learning conceptual knowledge in integrated group were better than those in the reciprocal multiplication group. The effects of learning procedural knowledge in integrate group or reciprocal multiplication group were better than those in the common denominator group. In conclusion, the prototype of worked-out examples in integrated group demonstrated the best efficiency and benefit for the students with low prior knowledge. Additionally, the acts of the students in class, the restriction of the research, and the advice of instruction were all described and discussed in this article.

誌謝辭.............................................................................................................................. i
中文摘要........................................................................................................................ iii
英文摘要.......................................................................................................................... v目次........................................................................................................................ vii
表次......................................................................................................................... ix
圖次......................................................................................................................... xi
第一章 緒論………………………………………………………………………1
第一節 研究動機…….................………………………………………………1
第二節 研究問題與研究假設….................……………………………………4
第二章 文獻探討…………………………………………………………….……..5
第一節 範例教學………………………..…..…………........………………….5
第二節 分數除法……………………….…..……..........…......………………10
第三節 分數除法的教學型態………….....…........................………………..13
第四節 本研究的教學設計理念………….....…………............……………..16
第三章 前導研究…………………………………………………………………..19
第一節 方法……………………….....…………………...........……………..19
第二節 結果與分析……………...……………………….............…………23
第三節 討論……………………...………………………...........……………27
第四章 正式實驗…………………………………..……………………………29
第一節 研究方法……..………………………………….............……………29
第二節 結果與分析……..………………………………................………….40
第三節 討論………......……………………………………...................……..52
第五章 結論與建議………………………………….......………………………55
第一節 結論……...…………………………………….....……..........……….55
第二節 研究限制與未來研究方向……………………………..................…58
第三節 教學建議………………………………………...........………………59
參考文獻……………………………………………………...........………...…..61
中文部分………………........……………………………………............………61
西文部分…………......……………………………………………...............……62
附錄………………………………………………………………………………67
附錄一…….....................…………........…………………………………………67
附錄二……….................…………………………………………………………68
附錄三………….………………………....…...............…………...…………….70
附錄四……………………………………....…………............…....……………71
附錄五………………………………………....……………....................………89
附錄六………………………………………………………………..........……107
附錄七……………………………………………………….................………119
附錄八…………………………………………………………….......….......…120
附錄九……..…………………………………………………………........……122

一、中文部分
李源順、胡蕙芳（2005）：分數除法的教學實驗研究。台北市立師範學院學報（人文藝術類、社會科學類與科學教育類），36，147-182。
吳昭容、徐千惠（2010）：兒童如何在重複中找到規律？重複樣式的程序性與概念性知識。教育科學研究期刊，55，1-25。
林福來、黃敏晃、呂玉琴（1996）：分數啟蒙的學習與教學之發展性研究。科學教育學刊，4，161-196。
林碧珍（1990）。從圖形表徵與符號表徵之間的轉換探討國小學生的分數概念。新竹師院學報，4，259-347。
岳修平（2001）：教學心理學—學習的認知基礎。臺北市：遠流。
洪素敏、楊德清（2002）。創意教學∼分數的補救教學。科學育研究與發展季刊，29，33-52
涂金堂（2011）：運用「範例（worked-out example）」在國小數學問題解決的教學實驗研究。教育心理學報，43，25-50。
陳明宏、呂玉琴（2005）：國小四年級學童分數概念之診斷教學研究。國立臺北教育大學學報：數理科技教育類，18，1-32。
教育部（2008）：國民中小學九年一貫課程綱要數學學習領域。臺北市：教育部。
張英傑（主編（2011）：國小課本數學11。臺南市：南一。
游政雄、呂玉琴、吳宏毅、劉世能（2003）：台灣北部地區國小學童的分數單位量概念之研究。南師學報：數理與科學類，37，19-40。
國家教育研究院籌備處（主編）（2011）：國小數學課本。臺北市：翰林。
楊瑞智（主編）（2008）：國民小學數學第十一冊。臺北市：康軒。


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