設計高中數學建模課程之研究

Abstract

迎接嶄新時代的來臨，以數學建模的觀點來提升高中數學教學與學習之發展，是培養學生所需之數學能力與素養的重要方法之一；提升高中數學建模能力，有助於為國家高等教育及科技人才培育奠定穩固的基礎。 本論文主要是探討高中數學建模課程的教材設計，與融入教學活動之教學實驗等兩大主軸。第一部分進行實驗教材之設計示例；第二部分為理論驗證之行動研究，研究方法採實驗教學法與訪談法。 研究結果發現，在教材設計的基準需符合下列原則：兼顧教材的模型建構、學習經驗關聯性、模型共享與重製性。另外，在融入教學活動的歷程中，發現教師本身逐漸重視課本教材與生活經驗的連結，課堂教學方式也由主導講授角色變為兼具引導及參與討論的角色，注重情境多元性的建模策略，且該角色亦提升教師本身設計新的建模教材的能力；再者，建立教材資源基礎的成果，有助於教師參與實作的信心，並促進教師反思與檢討其教學方法，進而發展出一套高中數學建模教學之模式。最後，在學校實施數學建模課程，搭配充足資訊媒材與數學讀物，不僅可提升學生本身建模能力，亦可促進其應用數學知識在已建立模型的比較與連結，進而解決實際的數學問題。

There is no doubt that mathematics play the most important role in the development of modern technologies. A student with well-trained logic thinking and the ability of modeling a real world problem in senior high school is essential for him or her to face the challenge in the future. Therefore promoting mathematical modeling abilities in senior high school will be able to build up a solid foundation for higher education. This thesis is mainly to study two topics：(1) Designing mathematical modeling materials, and (2) running the experiment of inserting materials into senior high school teaching. The first part is carrying on designing teaching materials and presentation of solid examples and the second part is the teaching activity inquired by experimentation and interviews. The research finds that the designing standard in the teaching material has to follow Lesh's principles such as Model Construction principle, the Reality Principle, and Construct shareability and usability principle etc. Besides, in the process, we find that the teacher who gradually values the combination of teaching materials and real-life experience also becomes a role by predominance with leading and participating in a discussion, paying more attention to pluralistic scenario modeling strategies, and also raised to design new modeling teaching materials. Furthermore, the foundation of teaching material resources which contributes to teachers participating in confidentially, also promoting introspection and examination on teaching method, later on, developing teaching patterns of senior high school mathematical modeling. Finally, concerning the school provides students mathematical modeling curriculum which like research curriculum with sufficient IT media and mathematics readings, not only promotes their modeling abilities, but also makes them apply mathematics accomplishment to connect and compare with developed models, then to solve practical mathematical problems.