本研究旨在探討實施數學建模教學策略融入DDMT教學模式後，探討對9年級學生數學學習態度、數學「基本計數原理及函數」概念的學習成效，以及探討在課程實施後，學生的回饋及對教學模式的建議。研究者採用不等組前、後測準實驗研究法，進行10節課的教學實驗，主題為「外送-最佳時間之數學模型」，實驗設計分為兩組：數學建模策略融入DDMT教學模式的實驗組、控制組為教師直接教學策略下的建模教學。研究工具包含：「基本計數原理及函數」、「數學學習態度量表」之前、後測以及學生反思回饋單。資料分析方法包含：敘述性統計、成對樣本t檢定、獨立樣本t檢定、單因子共變數以及質性的分析。本研究主要結論分述如下：
(一) 以數學建模融入DDMT模式的教學在「函數概念」的學習成效優於控制組。
(二) 以數學建模融入DDMT模式的教學的學生在「樹狀圖及窮舉法」及「函數」概念上有顯著進步。
(三) 教師直接教學策略下的建模教學的學生在「樹狀圖及窮舉法」概念上有顯著進步。
(四) 數學建模教學法在DDMT教學模式下能引起學生較高層次的思考。
(五) 數學建模教學法在DDMT教學模式下在較能引發學生後設思考能力。
(六) 進行數學建模的歷程是需要長時間且連續的進行。
(七) DDMT教學模式對STEAM教育的創造力有正向的影響。
(八) 數學建模策略融入DDMT教學模式需要多位協同教師合作
(九) 數學建模策略融入DDMT教學模式歷程中須隨時緊扣核心問題

This research aimed to investigate the effects of incorporating mathematics modeling teaching strategies into the DDMT (Direct Design of Mathematical Tasks) instructional model on 9th-grade students. The study focused on their attitudes towards mathematics, learning outcomes in the "Fundamental Counting Principle and Functions" concept, and also explored student feedback and suggestions regarding the instructional approach. The researcher employed a non-equivalent pretest-posttest quasi-experimental design, conducting a 10-lesson teaching experiment with the theme "Delivery Service - Optimal Time Mathematical Model." The experiment included two groups: the experimental group received mathematics modeling integrated with the DDMT instructional model, while the control group received direct teaching strategies for modeling instruction from teachers. Research tools included pretest and posttest assessments for "Fundamental Counting Principle and Functions," the "Mathematics Learning Attitude Scale," and student reflective feedback forms. Data analysis methods involved descriptive statistics, paired-sample t-test, independent-sample t-test, one-way ANCOVA, and qualitative analysis.
The main conclusions of this study are as follows:
1. Teaching with mathematics modeling integrated into the DDMT model resulted in better learning outcomes for the "Functions" concept compared to the control group.
2. Students taught with mathematics modeling integrated into the DDMT model showed significant improvement in understanding "Tree Diagram and Exhaustion Method" and "Functions" concepts.
3. Students who underwent modeling instruction using direct teaching strategies also demonstrated significant progress in understanding the "Tree Diagram and Exhaustion Method" concept.
4. Mathematics modeling instruction within the DDMT model stimulated higher-order thinking in students.
5. Mathematics modeling instruction within the DDMT model enhanced students' metacognitive thinking abilities.
6. The process of engaging in mathematical modeling required substantial and continuous time commitment.
7. The DDMT instructional model positively influenced creativity in STEAM (Science, Technology, Engineering, Arts, Mathematics) education.
8. Implementing mathematics modeling strategies within the DDMT instructional model necessitated collaborative efforts among multiple teachers.
9. During the process of implementing mathematics modeling strategies within the DDMT instructional model, it was crucial to stay closely connected to core issues.

摘要---------------------------------------------- i
Abstract -----------------------------------------ii
致謝 ---------------------------------------------iv
目錄 ----------------------------------------------v
表目錄 -------------------------------------------vii
圖目錄 --------------------------------------------ix
第一章 緒論--------------------------------------- 1
第一節 研究動機------------------------------------1
第二節 研究目的與問題--------------------------------3
第三節 名詞釋義------------------------------------ 4
第四節 研究範圍與限制--------------------------------6
第二章 文獻探討--------------------------------------8
第一節 數學建模理論----------------------------------8
第二節 STEAM教育-----------------------------------19
第三節 數學建模與清華STEAM教育之DDMT教學模式的關聯----26
第三章 研究方法------------------------------------33
第一節 研究架構------------------------------------33
第二節 教學研究設計---------------------------------35
第三節 研究流程-------------------------------------38
第四節 研究對象-------------------------------------40
第五節 研究工具-------------------------------------41
第六節 資料蒐集與分析--------------------------------55
第四章 研究結果與分析--------------------------------58
第一節 數學建模教學在對學學習成就之影響----------------58
第二節 數學建模教學對數學學習態度之影響----------------65
第三節 學生課後反思回饋之分析-------------------------71
第五章 結論與建議------------------------------------86
第一節 研究結論--------------------------------------86
第二節 研究建議--------------------------------------89
參考文獻 ------------------------------------------92
中文部分 ------------------------------------------92
英文部分----------------------------------------------94
附錄--------------------------------------------------99
附錄一 實驗組數學建模教案------------------------------99
附錄二 控制組數學建模教案------------------------------106
附錄三 數學建模教學學習單(實驗組) -------------------113
附錄四 數學建模教學學習單(控制組) -------------------129
附錄五 數學學習成就評量(前測/後測)--------------------- 146
附錄六 數學學習態度問卷---------------------------------149
附錄七 教師教學省思表-----------------------------------151
附錄八 學生課程反思與回饋-------------------------------153
附錄九 學生回饋單有效份數之整理--------------------------154

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