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研究生: 吳原榮
Wu, Yuan-Jung
論文名稱: 國中生數學符號素養的創造思考表現
Middle School Students’ Performance in Creative Thinking of Mathematical Symbolic Literacy
指導教授: 謝豐瑞
Hsieh, Feng-Jui
口試委員: 謝豐瑞
Hsieh, Feng-Jui
鄭英豪
Cheng, Ying-Hao
楊凱琳
Yang, Kai-Lin
王婷瑩
Wang, Ting-Ying
謝佳叡
Hsieh, Chia-Jui
口試日期: 2024/06/21
學位類別: 博士
Doctor
系所名稱: 數學系
Department of Mathematics
論文出版年: 2024
畢業學年度: 112
語文別: 中文
論文頁數: 169
中文關鍵詞: 形成過程詮釋過程數學符號素養數學創造思考數學過程應用過程
英文關鍵詞: Formulate Process, Interpret Process, Mathematical Symbolic Literacy, Mathematical Creative Thinking, Mathematics Processes, Employ Process
研究方法: 調查研究
DOI URL: http://doi.org/10.6345/NTNU202401247
論文種類: 學術論文
相關次數: 點閱:103下載:16
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  • 本研究透過根據PISA數學問題解決形成、應用和詮釋三過程的具體活動設計題目,探討在此三過程中,台灣國中生在符號及其運算中的數學創造思考表現。研究對象兼採立意及方便抽取樣,為在台灣北部和南部各取兩所中等程度以上的國中,在其中32個8年級班級中隨機抽取的210位學生參與研究,其中男生104位,女生106位。研究採問卷調查法,並根據從兩個角度評估學生的創造思考:,一是為學生回答答案的特質;二是,另一為創造思考中基於流暢性、變通性和與獨創性三項的傳統指標,為此,。題目設計與傳統研究創造思考所設計的題目有兩大差異,一為題目乃素養導向試題,二為題目提供了可創造無限多種答案的解答空間以激發學生的創造思考。設計的開放性題目允許學生提出多種可能的創意答案。
    研究結果顯示,當題目設計強調激發學生鼓勵創造性思考維時,大多數學生能夠提出多個適當且多樣的答案。特別是在形成階段過程的題目中,超過80%的學生能提出三個不同的適當答案。然而,當題目限制使用特定、難度較高的數學物件時,學生的數學難度的增加會影響學生提出創造性答案的能力,尤其是當題目限制使用特定數學物件時,這一點在應用過程中的表現尤為明顯,顯示出學生在面對更高挑戰時,創造作答表現明顯力的展現可能會受限。
    不論在哪一個在數學過程中,學生的創造思考表現皆依序為流暢性、變通性和獨創性的順序下降。針對流暢性思考,學生在各數學過程中的表現差異不大;針對變通性思考,學生在詮釋階段過程的表現最佳;針對獨創性思考,學生在形成階段過程的表現最佳。此外,在詮釋過程中,雖然大部分學生能提供至少兩個可接受的答案,但創造出第三個或更多答案的學生比例顯著下降,指出表示這一過程對學生而言可能的創造思考可能更具挑戰性。
    另一個重要發現是,當學生被鼓勵提出具有高差異度和獨特性的答案時,許多學生展現了出色的結合式創造思考能力,提出了遠超預期的創新解答。研究透過K-means群集分析將學生依各數學過程分群,還發現,研究結果顯示,不論是整體學生或分群學生,男女性別對各數學過程中學生學生的整體創造思考表現以及高低數學創造性思考群集上並皆無顯著影響差異。

    This study, based on the three processes of formulate employ, and interpret from PISA mathematical problem-solving, designs tasks to explore the mathematical creative thinking performance of Taiwanese junior high school students in the context of symbols and their operations. The study employs both purposive and convenient sampling, selecting two moderately performing junior high schools each from northern and southern Taiwan. From 32 eighth-grade classes, 210 students were randomly selected to participate. The research uses a questionnaire survey method and evaluates students' creative thinking from two perspectives: the characteristics of students' answers and three indicators of creative thinking—fluency, flexibility, and originality. The task design differs from traditional creative thinking research in two major ways: the tasks are competence-oriented and provide a solution space that allows for infinite answers to stimulate students' creative thinking.
    The results show that when the task design emphasizes stimulating students' creative thinking, most students can propose multiple appropriate answers. Particularly in the formation process tasks, over 80% of students were able to propose three different appropriate answers. However, when tasks limited the use of specific, more challenging mathematical objects, students' performance was significantly constrained. In any mathematical process, students' creative thinking performance decreased in the order of fluency, flexibility, and originality. For fluency, there was little difference in students' performance across the various mathematical processes. For flexibility, students performed best in the interpretation process, and for originality, students performed best in the formation process. Additionally, in the interpretation process, although most students could provide two acceptable answers, the proportion of students who created a third answer significantly decreased, indicating that this process might be more challenging for students' creative thinking.

    Another important finding is that when students are encouraged to propose highly diverse and unique answers, many students exhibited outstanding combinatory creative thinking abilities, presenting innovative solutions beyond expectations. Using K-means cluster analysis to group students by each mathematical process, the results show that, regardless of the overall or clustered students, there were no significant gender differences in students' creative thinking performance in any mathematical process.

    第一章 緒論 1 第一節 研究動機 1 第二節 研究背景 2 第三節 研究目的與問題 6 第四節 名詞解釋 8 第二章 文獻探討 9 第一節 創造力與創造思考 9 一、遠端聯想(Remote Associates,聯結論) 12 二、發散性思考(Divergence thinking) 15 三、遠端聯想與發散性思考 16 四、學校教育的創造力 17 第二節 數學創造力 19 第三節 數學創造力評量 23 第四節 PISA數學素養 28 一、PISA 2022數學素養框架 28 二、PISA 2022數學素養定義 29 三、數學推理 31 四、問題解決三過程 32 第五節 國中生的應用符號素養剖析 35 第三章 研究方法 41 第一節 研究架構 41 第二節 研究設計 43 一、研究工具 43 二、研究樣本 47 三、資料收集與分析 48 第四章 研究結果 57 第一節 形成、應用、詮釋數學符號素養的創造思考特質 57 一、形成過程 57 二、應用過程 63 三、詮釋過程 72 第二節 數學三過程中數學符號素養的流暢性、變通性、獨創性 82 一、形成過程中創造思考指標的樣貌 82 二、應用過程中創造思考指標的樣貌 90 三、詮釋過程中創造思考指標的樣貌 98 第三節 各數學過程中創造思考指標統計描述 106 一、數學創造思考各數學過程信度分析 106 二、各數學過程中三創造思考指標與總分間的相關係數 106 第四節 各數學過程中學生的創造力分數及群集表現特質 111 一、形成過程學生的創造思考分數及群集表現特質 111 二、應用過程學生的創造思考分數及群集表現特質 116 三、詮釋過程學生的創造思考分數及群集表現特質 120 四、學生整體的創造思考分數表現討論 124 第五節 各數學過程中創造思考性別表現的差異 129 一、各數學過程中創造思考性別表現的差異 129 二、各數學過程性別在數學高低創造思考的差異 132 第五章 研究結論 135 第一節 根據研究結果反思研究架構與工具設計 135 第二節 創造思考與數學過程交互之表現 138 第三節 學生整體的創造思考分數表現特質 140 一、創造思考分數表現分析 140 二、學生答題特質分析 140 三、 性別在創造思考的影響 142 第六章 未來應用與研究限制 143 第一節 從研究發展而言 143 一、研究發展 143 二、創造力總分的計算與分析 144 三、未來研究方向 144 四、創造思考指標的拓展 144 第二節 從促進教學發展策略而言 145 一、課程與教學的啟發 145 二、豐富預備知識與練習 148 三、建立創造思考支持環境 149 參考文獻 151

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