| 摘要: | 數學是基本能力評估的重要項目，也是國民教育中不可或缺的基礎課程之一。在當今的時代，數學的學習不再是為了應對考試，更是培養學生的邏輯思維、問題解決能力以及創新潛能的重要途徑，因此，提升學生學習數學的興趣、增強學生的自我效能、降低學生的數學焦慮感以及建立自主學習習慣是教學的重要目標。
本研究採用設計研究方法，主要專注於教材與教學活動的創新設計。研究對象為桃園市某國小的五、六年級學生共 23 位及數學教師 1 位。我們使用數學興趣問卷、數學焦慮問卷和數學自我效能問卷進行前後測，採用描述性統計及魏克生符號檢定來分析結果，並輔以訪談進行討論。
在教學設計方面，我們引入開放性數學問題思考模式，並安排學生進行登台活動。教材設計結合開放性問題的理念，著重於解題的思考過程而非單一答案。我們在問題中設置多個啟發性問題點，引導學生多角度思考，激發探究欲望，培養發現問題、分析問題和解決問題的能力。同時，我們採用小組合作的方式解題，鼓勵學生從不同角度思考，產生多種可能的答案。
研究結果顯示，開放性問題融入課堂教學活動對於數學興趣、數學自我效能以及數學焦慮面向均無顯著影響。然而，本研究強調開放性問題在數學教育中的重要性，它不僅能激發學生的創造力、探究精神和批判性思考能力，更有助於提高他們的數學自我效能感。結合毅力數學的理念，我們認為這種教學方法有潛力培養學生持續面對挑戰的能力，提升他們對數學學習的長期興趣和投入。本研究為開放性問題在數學教育中的應用提供了新的視角，為未來相關研究和教學實踐奠定基礎，彰顯了其在創新數學教育方面的價值和貢獻。;Mathematics is a crucial component of basic ability assessment and an essential foundational course in national education. In today′s era, learning mathematics is no longer just about passing exams, but an important path to cultivate students′ logical thinking, problem-solving abilities, and innovative potential. Therefore, enhancing students′ interest in learning mathematics, strengthening their self-efficacy, reducing math anxiety, and establishing self-directed learning habits are important teaching objectives.
This study adopts a design research methodology, focusing primarily on innovative design of teaching materials and educational activities. The research subjects include 23 fifth and sixth grade students and one mathematics teacher from an elementary school in Taoyuan City. We used mathematics interest questionnaires, math anxiety questionnaires, and math self-efficacy questionnaires for pre- and post-tests. Descriptive statistics and Wilcoxon signed-rank test were used to analyze the results, supplemented by interviews for discussion.
In terms of instructional design, we introduced an open-ended mathematical problem thinking model and arranged for students to participate in presentation activities. The
curriculum design incorporates the concept of open-ended problems, emphasizing the thought process of problem-solving rather than single answers. We set multiple thought-provoking points in the problems, guiding students to think from multiple angles, stimulating their desire to explore, and cultivating their abilities to discover, analyze, and solve problems. Simultaneously, we adopted a group collaboration approach to problem-solving, encouraging
students to think from different perspectives and generate multiple possible answers.
Research results show that integrating open-ended problems into classroom teaching activities had no significant impact on mathematics interest, math self-efficacy, or math anxiety. However, this study emphasizes the importance of open-ended problems in mathematics education. They not only stimulate students′ creativity, spirit of inquiry, and critical thinking skills but also help to improve their math self-efficacy. Combining the concept of grit mathematics, we believe this teaching method has the potential to cultivate students′ ability to persistently face challenges, enhancing their long-term interest and engagement in mathematics
learning. This study provides a new perspective on the application of open-ended problems in mathematics education, laying a foundation for future related research and teaching practices, and highlighting its value and contribution to innovative mathematics education. |
