以註解算式引導小學數學文字題擬題之鷹架設計

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翁瑜璘(Yu-lin Weng) 查詢紙本館藏

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網路學習科技研究所

論文名稱

以註解算式引導小學數學文字題擬題之鷹架設計
(Scaffold of Annotated Arithmetic Expression Directed Posing of Elementary Mathematic Word Problems)

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摘要(中)

本研究主旨為探討國小四年級學生使用註解算式擬題法之擬題活動實施狀況與對解題能力的影響。在本次的實驗中，研究者設計出一種以解題為出發點的擬題鷹架，其中引用了解題樹(solution tree)的概念及表徵方式，編製成為本次實驗中所使用的擬題素材(鷹架)稱為「註解算式擬題法」。為瞭解此擬題素材的實施狀況，本研究首先以紙本擬題活動探討其帶來的效益。在使用紙本擬題的過程中，學生以個人擬題的方式進行擬題發揮創作。於資料的分析上，主要為透過文字題解題評量的前、後測成績、教室觀察、訪談、擬題作品分析、教學回饋問卷做質性及量化的統計分析，來觀察兩組學生的學習歷程，並瞭解學生於 (1)解題能力；(2)擬題作品品質與特色；(3)學習經驗；(4)學習動機上的影響與成效。
研究結果發現，學生使用註解算式擬題法可以順利的擬出正確的題目，於作品品質上有好的表現。且學生在學習的過程中有正向的學習態度及學習動機，並且此方法也提昇了學生的解題能力。在探討完此擬題素材於紙本上的成效後，研究者亦進行引用註解算式擬題為內容之電腦輔助擬題系統的測試與初探。此系統之功能主要為改善於紙本擬題活動中產生的限制與缺點，亦增加主題情境，使擬題活動的進行可以更順暢與完整。而此系統於本次實驗中順利的引導學生完成出題、題目分享、互相解題與評題的活動，也使擬題活動更加生動有趣。

摘要(英)

This research aimed to investigate the influence of Annotated Arithmetic Expression Problem-Posing material on fourth grade students’ problem-posing and problem-solving ability. The posing scaffolding is designed base on the concept and representation of solution tree. In order to understand the effects of this problem-posing material, the first experiment is executed by individual text learning. The statement analysis is done on pre-tests and pose-tests of mathematical-solving ability. Students’ compositions and feedbacks about problem-posing are collected. The experimenter explore the following themes：(1) Students can pose the word problem by material successfully. (2) The opuses of students are correct and can be solved by others. (3) The learning motivation and attitude of students are positive. (4) Problem-posing teaching technique seems to affect students’ problem solving ability.
After the experiment, the computer-based problem-posing system with Annotated Arithmetic Expression is implemented in the traditional classroom. The aim of this system is to improve the drawback and the limits of text experiment. This system can work successfully and vividly in guiding students to complete the activities of problem posing, opuses display, and peer problem solving.

關鍵字(中)

★ 文字題
★ 擬題
★ 解題
★ 解題樹

關鍵字(英)

★ Problem-posing
★ Problem-solving
★ Solution tree
★ Word problems

論文目次

摘要 ........................................................................................................................................ i
Abstract ...................................................................................................................................... ii
致謝 ......................................................................................................................................... v
目錄 ..................................................................................................................................... vii
表目錄 ...................................................................................................................................... ix
圖目錄 ....................................................................................................................................... x
第一章緒論 .............................................................................................................................. 1
1-1 研究背景與動機 ........................................................................................................ 1
1-2 研究目的 .................................................................................................................... 3
1-3 研究問題 .................................................................................................................... 4
1-4 名詞釋義 .................................................................................................................... 4
1-5 章節架構 .................................................................................................................... 7
第二章文獻探討 ...................................................................................................................... 8
2-1 擬題的定義與教育上的重要性 ................................................................................ 8
2-2 數學擬題的類型 ...................................................................................................... 10
2-3 擬題相關研究 .......................................................................................................... 12
2-4 數學解題的意義與文字題解題歷程 ...................................................................... 18
第三章活動設計與實驗方法 ................................................................................................ 24
3-1 紙本擬題教材設計 .................................................................................................. 24
3-1-1 教材內容大綱設計 ...................................................................................... 25
3-1-2 教材設計與理念 .......................................................................................... 27
3-2 研究對象 .................................................................................................................. 34
3-3 研究設計與實施流程 .............................................................................................. 36
3-4 資料蒐集與評量標準 .............................................................................................. 42
3-4-1 文字題解題前後測評量 .............................................................................. 42
3-4-2 擬題作品評量表 .......................................................................................... 46
3-4-3 教學回饋問卷 .............................................................................................. 48
3-4-4 訪談內容大綱 .............................................................................................. 49
3-5 資料的處理與分析 .................................................................................................. 53
viii
第四章研究結果與討論 ........................................................................................................ 56
4-1 學生解題能力之影響 .............................................................................................. 57
4-2 擬題作品分析 .......................................................................................................... 62
4-3 擬題學習經驗 .......................................................................................................... 72
4-4 擬題學習動機 .......................................................................................................... 88
第五章系統設計 .................................................................................................................... 90
5-1 系統設計理念 .......................................................................................................... 90
5-2 系統環境架構 .......................................................................................................... 93
5-3 系統流程 .................................................................................................................. 93
5-4 系統內容 .................................................................................................................. 94
5-5 研究觀察 ................................................................................................................ 103
第六章結論與未來工作 ...................................................................................................... 106
6-1 結論 ........................................................................................................................ 106
6-2 未來工作 ................................................................................................................ 110
參考文獻 ............................................................................................................................... 114
附錄
附錄一學習經驗量表 .................................................................................................. 120
附錄二學習動機量表 .................................................................................................. 122
附錄三註解算式擬題法(實驗組) –「擬題方法」一步驟教材內容 ........................ 124
附錄四註解算式擬題法(實驗組) -「擬題素材」一步驟教材內容 ......................... 127
附錄五註解算式擬題法(實驗組) - 二步驟教材內容 ............................................... 131
附錄六算式擬題法(控制組) -「擬題方法」一步驟教材內容 ................................. 133
附錄七算式擬題法(控制組) -「擬題素材」一步驟教材內容 ................................. 136
附錄八算式擬題法(控制組)- 二步驟教材內容 ........................................................ 140

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指導教授

陳德懷(Tak-wai Chan)

審核日期

2008-7-14

推文