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研究生:葉晉佳
研究生(外文):Chin-Chia Yeh
論文名稱:二位七年級資優生在數規形規的解題表現之研究
論文名稱(外文):The case studies of performance for the two seventh grade gifted students on solving number pattern problems
指導教授:劉祥通博士
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
畢業學年度:97
語文別:中文
論文頁數:105
中文關鍵詞:資優生數形規律自發性策略數學解題
外文關鍵詞:gifted studentnumber patternspontaneous strategymathematical problem solving
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摘  要
本研究旨在探討資優生在數形規律的解題表現,以立意的方式挑選兩位七年級資優生為個案。研究採個案研究法,首先依據研究目的設計結構化的工作單,工作單內容則以具有等差數列之規律的圖形為主,待學生完成工作單之後,根據學生的解題表現進行訪談。
關於個案學生在數形規律的自發性解題表現,研究發現主要的結果為:兩位個案學生均能善加利用其先備知識來擬定其解題計畫,利用除法原理來發展一階等差數列的解題策略,解題過程中展現其探索與修正解題計畫之能力,進而能成功的完成解題。

The purpose of this study was to investigate the problem solving performance on number pattern problems of the seventh grade gifted students. The two subjects were purposefully chosen according to their prior performances of problem solving. The study was a case study. The structured task was designed purposefully based on the study and it consists of the shape arranged in number pattern. The structured task-based interview technique was conducted to collect and analyze data after subject solved the structured task.
As to the subjects’ spontaneous strategies of problem solving, the results indicated that the subjects can use their prior knowledge well to design their plan, use the basic division theory to develop their problem solving strategies.It shows that they are able to design, reflect, modify and successfully solve the problems.

目次
中文摘要i
英文摘要ii
目次iii
表次 v
圖次 vi
第一章 緒論
第一節 研究動機 1
第二節 研究目的與待答問題 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 解題 6
第二節 數形規律 19
第三章 研究設計
第一節 研究方法與研究對象 26
第二節 研究架構 28
第三節 研究工具 29
第四節 資料蒐集與分析 34
第五節 研究流程 36
第四章 研究分析與討論
第一節 小安的自發性解題表現 40
第二節 小宇解題表現 61
第五章 研究結果與建議
第一節 研究結果 78
第二節 建議 82
參考文獻
中文部份 85
外文部份 88
附錄
附錄一 數形規律工作單 93

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