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研究生:張育萍
研究生(外文):Yu-ping Chang
論文名稱:兒童分數比值概念的解題活動類型
論文名稱(外文):The Solution Categories of Two Elementary students in Solving Rational as Ratio Task
指導教授:劉祥通劉祥通引用關係
指導教授(外文):Shiang-tung Liu
學位類別:碩士
校院名稱:國立嘉義大學
系所名稱:數學教育研究所
學門:教育學門
學類:普通科目教育學類
論文種類:學術論文
論文出版年:2005
畢業學年度:93
語文別:中文
論文頁數:91
中文關鍵詞:比值個案研究工作單為基礎的訪談分數
外文關鍵詞:case studyratiorational numbertask-based interview
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本研究旨在探討兩位未接受比值教學的學童,其在處理比值問題時的解題表現,並將他們的解題活動類型加以分析。研究方法採用個案研究,並藉工作單為基礎的訪談以助本研究資料的搜集,工作單問題共有9題,研究者依學生解題後的解題表現加以訪談。
研究一的小亭是一位國小五年級的學生,她在處理比值問題,習慣在兩階單位的部份整體關係思考下,從等分除的方式,找出「一份所佔的比值」,因此她在不論遇到比較量大於基準量甚至比較量小於基準量的情況,都使用此方式解題。
研究二的小奕是一位國小四年級的學生,他在處理比值問題,容易受到題目中的「語詞」–多少倍、多少、幾分之幾的使用方式而影響解題,尤其是當題目或是研究者訪談中的語詞出現「多少倍」,會讓他有「大數除以小數」的迷思產生。當使用「幾分之幾」的方式,他則都可以正確地解題,且不會有「比值有單位」的問題產生,但是當使用「多少」方式時,他則會受到「等分除」方式的使用影響,而有「比值有單位」的問題產生,惟這樣的情況不甚穩定。
The purpose of this study was to explore the problem solving performances of two elementary students, a fifth grader Ting and a fourth grader Yi, in rational as ratio task and to analyze their solution categories. The study was a case study comprising of two cases. The task-based interview was adopted in the process of data collection. There were 9 questions within the task.
The important findings of the two cases were as follows: First, Ting used the strategy based on part-whole relationship to divide and obtained the result of “the quantity of unit fraction” to get the answer of ratio problem. Using this strategy, she solved all the task questions.
Furthermore, Yi was influenced by the words and phrases of the questions- “how many times”, “how many”, and “what a b is”. When he solved “how many times” questions, he had a misconception that the dividend must be bigger than divisor. He could solve any “what a b is ” questions. He was influenced by the notion of partitive division in solving “how many” questions, so he thought that ratio is a quality not a number.
目 次
中文摘要……………………………………………………………………i
目次…………………………………………………………………………ii
表目次………………………………………………………………………iv
圖目次………………………………………………………………………v
第一章 緒論
第一節 研究背景與動機……………………………………………… 1
第二節 研究目的……………………………………………………… 3
第三節 名詞釋義……………………………………………………… 3
第四節 研究範圍與限制……………………………………………… 4
第二章 文獻探討
第一節 乘法概念域…………………………………………………… 6
第二節 單位化與基準化………………………………………………13
第三節 分數構念………………………………………………………17
第四節 比值……………………………………………………………20
第五節 比值的迷思概念………………………………………………23
第六節 數學寫作………………………………………………………24
第三章 研究方法
第一節 研究法…………………………………………………………26
第二節 研究架構與流程…………………………………………27
第三節 研究對象…………………………………………………30
第四節 研究工具…………………………………………………31
第五節 資料蒐集與分析…………………………………………33
第四章 研究結果與討論
第一節 研究一結果與討論………………………………………35
第二節 研究二結果與討論………………………………………47
第三節 綜合討論…………………………………………………65
第五章 結論與建議
第一節 結論………………………………………………………71
第二節 建議………………………………………………………76
參考書目
中文部份 …………………………………………………………81
英文部分 …………………………………………………………83
附錄
附錄一 比値未知工作單 ………………………………………86
附錄二 原案及問題對照 ………………………………………86
參考書目

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臺灣省國民學校教師研習會(1996)。國民小學數學實驗課程教師手冊第九冊。台北:研習會出版。
劉秋木(1996)。國小數學科教學研究。台北:五南。
劉祥通(2001)。實踐數學寫作活動以發展國小教師之佈題能力。台北縣:文京圖書有限公司。
劉祥通(2004)。分數與比例問題解題分析—從數學題問教學的觀點。台北:師大書苑。
劉祥通、周立勳(2001)。發展國小教師數學教學之佈題能力—以分數乘除法教學為例。科學教育學刊,9(1),15-34。
Patton,(1990)/吳芝儀、李奉儒譯(1999)。質的評鑑與研究(初版三刷)。台北縣:桂冠。
Skemp, R. R.(1987)/陳澤民譯(1995)。數學學習心理學(六版一刷)。台北:九章。
Yin, R. K.(1994)/尚榮安譯(2001)。個案研究。台北:弘智。

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