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研究生: 虞富崴
Yu, Fu-Wei
論文名稱: 探究學生在幾何任務中展現之數學創造力與視覺推理歷程及其間之關聯
Exploring the Mathematical Creativity, Visual Reasoning Process and its Relationship of Students in Geometrical Task
指導教授: 左台益
Tso, Tai-Yih
口試委員: 左台益
Tso, Tai-Yih
李源順
Lee, Yuan-Shun
呂鳳琳
Lu, Feng-Lin
口試日期: 2023/07/24
學位類別: 碩士
Master
系所名稱: 數學系
Department of Mathematics
論文出版年: 2023
畢業學年度: 111
語文別: 中文
論文頁數: 218
中文關鍵詞: 數學創造力視覺推理視覺化多元解題任務資優教育
研究方法: 個案研究法
DOI URL: http://doi.org/10.6345/NTNU202300892
論文種類: 學術論文
相關次數: 點閱:117下載:40
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  • 本研究旨在探討學生在面對幾何任務時,所展現出的數學創造力以及視覺推理歷程的關聯性,以及其數學創造力產品。為回應研究問題,本研究採取質性研究法之個案研究法,個案人數總計八位,並依照「學習階段」與「資優身分」兩個變項分為四組,並以幾何多元解題任務以及半結構式訪談大綱作為主要的研究工具。對於解題歷程的分析則參考並修改Schoenfeld(1985)的原案分析方法,而在視覺推理歷程與數學創造力產品的分析,則分別採用Zazkis等人(1996)所提出之視覺化-分析模型以及Leikin(2009)的數學創造力評分架構。
    本研究的主要研究結果顯示:(1) 解法與個體的創造性分數之決定性因素為獨創力;(2) 無論學習階段或是資優身分,皆有機會提出高創造力的解法;(3) 同一問題的不同解法下,有多元的視覺推理歷程;(4) 高創造力的解法較仰賴直觀與視覺行動;(5) 學習階段在分析行動的選擇受到知識豐富程度的限制,且高創造力解法在解題的先後順序具有差異;(6) 資優生多具備靈活思考的能力,但較缺乏對某一解法的深究;(7) 課程調整會影響資優生數學創造力的發展。
    研究最後對於教學實務與未來研究給予數點建議,並藉由對於創造力與視覺推理的研究,期許在數學教育與資優教育之間建立起連結。

    謝辭 i 摘要 ii 表目錄 iv 圖目錄 v 第壹章 緒論 1  第一節 研究背景與動機 1  第二節 研究目的與研究問題 7  第三節 名詞界定 8 第貳章 文獻探討 9  第一節 創造力與數學創造力的內涵 9  第二節 視覺化與視覺推理 21 第參章 研究方法 31  第一節 研究設計 32  第二節 研究對象 33  第三節 研究工具 36  第四節 資料收集與分析 40  第五節 研究流程 52 第肆章 研究結果 53  第一節 解題歷程分析與視覺推理分析 54  第二節 解題產品分析 150  第三節 學習階段對於數學創造力及視覺推理歷程之差異 157  第四節 資優身分對於數學創造力及視覺推理歷程之差異 167 第伍章 結論與建議 173  第一節 結論 173  第二節 未來建議 178  第三節 研究限制 182 參考文獻 183 附錄 193

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