本研究以學生為主要觀點，探討在台灣國小高年級的學生對於分數除法與小數除法的解釋偏好與學生被說服的原因，最後再藉由教師上課的解釋偏好為輔，希望能瞭解教師的教學偏好對學生的影響，以作為學生偏好的比較依據。本研究利用問卷的方式，調查49名國小高年級學生對於分數與小數的數學解釋的觀點，並以訪談為輔，透過訪談其中10位學生希望能更深入的瞭解學生的偏好、被說服的原因、較能理解教師使用的解釋等。本研究的結果：（一）分數除法學生偏好為圖像表徵，由於分數除法學生沒有公式可以使用，所以多數的學生選擇了教科書中最常出現的圖像表徵，較多學生認為圖像表徵比較簡單、比較基礎。（二）分數除法學生被說服的原因為圖像表徵，學生認為圖像表徵比較容易學習，因爲比較基礎，所以學生會被說服的原因多數為學習簡單，而如果要說服別人圖像表徵也比較好去解釋。（三）分數除法中學生能理解教師使用的解釋為圖像表徵，多數學生認為在剛接觸分數除法的時候會比較希望教師用圖像表徵來解釋，因為比較簡單而且較能協助學生理解基本的數學概念，然而在現今台灣的教科書也都有將圖像表徵的解釋編排在其中，因此多數的教師在教學時也會使用圖像表徵來解釋分數除法。（四）小數除法學生偏好為純數學符號表徵，由於小數在學生的日常生活中較少接觸到，所以多數學生對情境較無感，因此學生超過七成以上喜歡純數學符號表徵用直式除法直接運算。（五）小數除法學生被說服的原因為純數學符號表徵，由於學生的先備經驗整數除以整數（直式除法）導致學生對於使用直式除法的純數學符號表徵特別有印象，然而這也造成多數學生被說服的主要原因。（六）小數除法中學生能理解教師使用的解釋為純數學符號表徵，多數學生認為小數除法與整數除法使用的直式除法相同，所以在學習上學生已經有舊經驗，他們認為教師只要解釋清楚小數點的意義與數值位置關係就可以理解小數除法，所以有高達六成的學生認為教師在教小數除法時直接用直式除法比較好理解。

This study assumes students as the main point of view, the aim of the research is exploring the students' preference and the reasons why students are persuaded for fractional division and decimal division in the senior students of Taiwan's elementary school, finally, supplemented by explanation preferences of teachers, I expect to understand the impact of teachers' teaching preferences on students as a basis for comparing student preferences.
This study used a questionnaire to investigate 49 senior students of elementary school for the mathematical explanation viewpoints of fractions and decimals, and supplemented with interviews, through interviews with 10 students hoping to comprehend the student's preferences, reasons why students are persuaded, and be able to understand explanation of teachers and so on.
The results of this study:
(1) fractional division of students' preference is image representation, owing to fractional division have no formulas for students to use. therefore most of students choose the most frequently used image representation in textbooks, more students consider that image representation is simpler and more basic.
(2) The reason why the fractional division students are persuaded is the image representation. The students consider that the image representation is easier to learn. Because of the basics, most of the reasons students are persuaded are simple to learn, and if you want to persuade others that the image representation is better to illustrate.
(3) In the fractional division, the students can comprehend that the explanation used by teachers is image representation. Most of the students consider that when they first contact with fractional division, they would like that the teacher would use the image representation to explain, because it is simpler and more helpful to help students understand basic mathematical concepts. However, in Taiwan textbooks also uses explanations of image representations now, therefore, most teachers also use image representation to explain fractional division when teaching.
(4) The decimal division students' preference is mathematical symbolic representation. Because the decimals are rarely used in the students' daily life, most students have no sense of the decimal situation, so more than 70% of the students like mathematical symbolic representation direct operation by straight division.
(5) The reason why the decimal division students are persuaded is the mathematical symbolic representation. Because the student's experience of integer division(straight division), leading students to be particularly impressed with the mathematical symbolic representation of straight division. Therefore, the main reason for most students being persuaded.
(6) In the decimal division, the students can comprehend that the explanation used by teachers is mathematical symbolic representation. Most of the students consider that the decimal division is the same as the integer division using straight division. Therefore, students have already had an old experience in learning. They consider that the teacher explains the meaning of the decimal point and the numerical positional relationship, students can comprehend the decimal division, consequently, as many as 60% of the students consider when teachers uses straight division to teach decimal division, can be better to comprehend the decimal division.

第一章 緒論 1
第一節 研究背景與研究動機 1
第二節 研究目的和問題 3
第三節 名詞解釋 3
第二章 文獻探討 5
第一節 教師解釋 5
第二節 教師教學解釋與知識 7
第三節 教師解釋與信念 13
第四節 學生對於教師教學解釋的偏好 20
第五節 分數、小數的教與學 24
第三章 研究方法 35
第一節 問卷調查法 35
第二節 研究工具 38
第三節 研究對象 39
第四節 研究流程 39
第五節 資料蒐集與分析 43
第四章 研究結果與分析 44
第一節 學生對不同解釋的偏好之結果 44
第二節 學生對不同解釋中能說服自己之結果 65
第三節 學生對老師所使用不同解釋的偏好之結果 85
第四節 討論:對於學生在不同題型的研究結果 106
第五章 結論與建議 109
第一節 結論 109
第二節 建議 115
參考文獻 118
中文部分 118
西文部分 120
附錄一 國小高年級學生對分數與小數解釋的偏好之問卷 128
附錄二 預試訪談問卷 139
附錄三 學生訪談內容 141

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