「數學解說員」之系統設計與實作──以解釋數學解題活動促進學生數學理解能力

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謝蕙如(Hui-Ju Hsieh) 查詢紙本館藏

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網路學習科技研究所

論文名稱

「數學解說員」之系統設計與實作──以解釋數學解題活動促進學生數學理解能力
(The Design and Practice of “Math Narrator” System : To improve students’ comprehension ability by implementing explaining mathematical problem-solving activity)

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摘要(中)

數學，對大多數的學生而言是一個困難的科目，越往高年級的數學概念越為抽象，但學生卻越沒有時間深入瞭解數學概念背後所隱含的意義，在解題的過程中只會複製老師的解法和計算過程，而無法理解解題的理由及相關的數學概念。且在數學學習的過程中，老師常常無法直接和學生溝通，瞭解學生對數學概念或數學題目的想法，學生也無法得知同學的數學想法，因此，本研究提出一套結合「數學解說員」系統的解釋數學解題活動，讓學生在解題後利用文字說明自己解題的想法，以瞭解自己對數學概念的理解程度。
本研究以桃園市某國中七年級學生為研究對象，將學生分為控制組（傳統教學組）及實驗組（系統操作組），進行十次的解釋數學解題活動，並透過實踐、反思修改活動流程，希望透過解釋數學解題活動幫助學生解釋數學，以提升學生的數學理解能力。研究結果發現學生在進行解釋數學解題活動後，在解題及解釋的表現皆有進步，且低成就學生在數學溝通能力表現上有大幅進步且和控制組有顯著差異，而在瞭解學生對於該活動及系統的使用感想後發現，多數學生認為進行解釋數學解題活動可以幫助自己對於數學的學習學的更好，且可以更加的理解自己的解題想法，透過系統可以觀看同學的作品並給予同學評分、建議或讚美，能夠幫助自己及同學在數學的學習上更加有信心及成就感。

摘要(英)

Mathematics is a difficult subject to most students. The higher the grade is, the vaguer the mathematical conception can be. However, students didn’t have enough time to understand the underlying meaning of the mathematical conception. During problem solving, they copied teachers’ solution and calculation process without understanding the reasons and relevant mathematical conception. What’s more, teachers were not able to communicate with students about their thoughts about the mathematical conception and questions. Students couldn’t get to know the peers’ thought about mathematical problem, either. Therefore, this study designed an explaining mathematical problem-solving activity integrated with the “Math Narrator” system. The module allowed students using texts to explain their thought after problem-solving in order to grasp their own understanding level to mathematical conception.
The participants were the seventh graders from a junior high school in Taoyuan City. This study divided students into the control group (traditional teaching group) and the experimental group (system-using group) to conduct a ten-time explaining mathematical problem-solving activity. By practicing and revising the activity process, we hoped that this activity could help students to explain mathematics conception and improve comprehension ability. The result showed that after the activity, students get ahead in both problem solving and composing explanation. Moreover, the low achievers made enormous progress in mathematical communication ability and had significant difference in comparison with the control group. Students reported that explaining mathematical problem-solving activity was beneficial to math learning and gave them a better understanding about their thought to problem solving. Also, observing, scoring, giving suggestions and compliments to peers’ works from Math Narrator made them more confident in math learning.

關鍵字(中)

★ 解題
★ 解題溝通
★ 數學寫作
★ 範例學習

關鍵字(英)

論文目次

目錄 i
圖目錄 iii
表目錄 v
一、緒論 1
1-1 研究背景與動機 1
1-2 研究目的 2
1-3 研究問題 3
1-4 論文架構 3
二、文獻探討 5
2-1 解題溝通 5
2-2 數學寫作 7
2-3 範例學習 10
2-4 設計本位研究 14
三、系統與活動設計 17
3-1 系統開發與架構 17
3-2 系統功能介紹 18
3-3 活動流程 37
四、研究方法 41
4-1 研究設計 41
4-2 研究對象 41
4-3 研究流程 41
4-4 研究工具 48
五、研究結果與討論 57
5-1 學生在解題溝通表現之差異 57
5-2 數學解說員在課堂中之實施情況 60
5-3 學生對於數學解說員活動與系統感想與看法 72
六、結論與未來展望 79
7-1 結論 79
7-2 研究限制 81
7-3 未來工作 81
參考文獻 84
附錄一、每周活動題目 90
附錄二、數學溝通能力測驗（前測） 93
附錄三、數學溝通能力測驗（後測） 103
附錄四、數學解說員活動問卷 113

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指導教授

陳德懷

審核日期

2016-7-26

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