研究生: |
范喻婷 |
---|---|
論文名稱: |
國小六年級擬題的數學創造力表現之研究 A Study on Mathematical Creativity in Problem-Posing Among Sixth-Grade Elementary School Students |
指導教授: |
許慧玉
Hsu, Hui-Yu |
口試委員: |
鄭英豪
Ying-Hao Cheng 陳建誠 Jian-Cheng Chen |
學位類別: |
碩士 Master |
系所名稱: |
竹師教育學院 - 數理教育研究所碩士在職專班 Mathematics & Science Education Master Inservice Program |
論文出版年: | 2025 |
畢業學年度: | 113 |
語文別: | 中文 |
論文頁數: | 96 |
中文關鍵詞: | 擬題 、數學創造力 、流暢性 、靈活性 、獨創性 、多元評量 |
外文關鍵詞: | Problem Posing, Mathematical Creativity, Fluency, Flexibility, Originality, Multiple Assessment |
相關次數: | 點閱:18 下載:0 |
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本研究旨在探討國小六年級學生於擬題任務中所展現的數學創造力表現,採用Leikin等人(2009)所提出之創造力評估模型,從流暢性、靈活性與獨創性三個向度切入,分析學生在不同題型中的創造表現與思維特徵。研究設計三個擬題任務,分別為「零錢問題」、「分數問題」與「成分問題」,題目結合生活經驗與課程內容,期能激發學生的數學表達與創意思考。
本研究以桃園市六個班級之國小六年級學生為研究對象,採便利取樣進行施測,蒐集學生的擬題作品後進行量化評分與質性分析。研究結果顯示,多數學生在擬題任務中具備基本的流暢性表現,能產生一定數量的正確題目;而在靈活性與獨創性方面,則因題目結構與開放程度不同而展現出顯著差異。其中,「零錢問題」因貼近生活情境,能有效激發學生的延伸與改寫能力;「分數問題」則有較多學生展現跨概念整合的能力;「成分問題」雖相對抽象,但部分學生能由圖像與數據中發展出具創意的題目。
進一步分析各創造力指標間之關聯,結果發現獨創性與總體創造力表現具有高度正相關,顯示創新能力為數學創造力的重要關鍵。靈活性與獨創性亦呈現中度正相關,反映多樣思維在創意發展中的關鍵角色;而流暢性則與其他指標關聯較低,顯示題數的多寡不應作為唯一評量依據。
本研究指出,擬題活動有助於提升學生的數學創造力,亦彰顯評估學生創造表現時應關注質與量的多重面向。同時,針對創造力評估模式的應用與擬題分類標準之建立,也提出理論反思與實務建議,期能作為未來教學與研究之參考。
This study aims to investigate the mathematical creativity demonstrated by sixth-grade elementary students through multiple problem-posing tasks. Based on the creativity assessment model proposed by Leikin et al. (2009), this research evaluates students' performance across three dimensions: fluency, flexibility, and originality. Three problem-posing tasks were designed, namely "money problem," "fraction problem," and "composition problem," each integrating real-life scenarios and curriculum content to stimulate students’ mathematical thinking and creative expression.
The participants were sixth-grade students from six classes in Taoyuan City, selected through convenience sampling. After collecting the students’ problem-posing responses, both quantitative scoring and qualitative analysis were conducted. The findings revealed that most students exhibited basic fluency, generating a reasonable number of mathematically valid problems. However, notable differences emerged in flexibility and originality depending on the task type and its level of openness. The "money problem" facilitated higher creative engagement due to its familiarity with students’ daily life; the "fraction problem" encouraged conceptual integration; while the "composition problem," although more abstract, led some students to develop highly creative responses through interpreting visual and numerical data.
Further analysis indicated that originality had a strong positive correlation with overall mathematical creativity, underscoring the importance of innovation in creative problem-posing. Flexibility and originality also showed moderate correlation, highlighting the value of diverse thinking strategies. In contrast, fluency had a weaker correlation with the other dimensions, suggesting that the number of problems posed should not be the sole indicator of creativity.
This study concludes that problem-posing activities play a significant role in promoting students’ mathematical creativity and advocates for multidimensional evaluation that values both quantity and quality of responses. In addition, theoretical reflections and practical recommendations are provided regarding the refinement of creativity assessment models and the classification of student-generated problems, offering insights for future research and classroom implementation.