高中数学教学中数学建模思想融入的实践研究(硕士)(论文21000字)
摘要
数学不是孤立的“教”和“学”，单纯的知识传授，更要注重获取知识的方法、渗透数学思想，教学生怎样学。数学建模是数学对现实的刻画，通过对现实问题的抽象、简化，归纳出一般数学模型，以此来演绎与推广新的理论，并运用于实际生活。
数学建模的思想有：①简化与描述世界。简化问题，取关键因素研究，再用简洁的数学语言描述；②揭示世界的变化规律。数学建模主要描述各个量之间的关系，特别是变量之间的变化规律；③还原对世界的认识过程。还原公式的过程可以使数学变得生动活泼；④推动数学的发展。对已知问题进一步抽象，揭示更深层次的规律，发展了的数学又可以解释更为复杂的实际问题。
本文以课程标准为纲，对普通高中必修与选修教材分析，有如下特色；注重发展数学应用意识、注重与其他学科的联系、内容设计丰富有弹性、现代信息技术融于数学课堂。通过对学生问卷调查、教师访谈，发现以下问题：①自然科学的分类导致文化的割裂；②数学教学过于体系化；③学生缺乏抽象化和数量化的训练；④教师知识传授的理念根深蒂固。为此对教师的教学启示有：①数学教学中要勤于练习实际；②讲清楚知识的来龙去脉，源与流；③多一些抽象化和数量化的训练；④透过知识传达方法、思想。
数学建模的内容体现在“发现”、“推广”、“应用”三个方面，为此数学建模思想融入教学的途径有：①“源”融入——用数学建模的观点讲授发现的过程，分析数学知识点的来源背景；②“本”融入——用数学建模的观点讲授推广的过程，表达知识本身；③“流”融入——用数学建模的观点讲授应用的过程，运用于现实问题。通过一些具体数学建模思想融入教学应用案例，总结反思：教学需透过知识传达方法、思想；注重“问题意识”的养成。
关键词：数学建模思想；高中数学教学；源本流
Abstract
Mathematics is not an isolated "teaching" and "learning", simple knowledge imparting, should pay attention to acquire knowledge method, infiltrate mathematics thought, teach the student how to learn. Mathematical modeling is the depiction of the reality in mathematics. Through the abstraction and simplification of the real problems, the general mathematical model is generalized to deduce and promote the new theory and apply it to real life.
The idea of mathematical modeling is to simplify and describe the world. Simplify the problem, take the key factor research, and then use the concise mathematical language description; To reveal the laws of change in the world. Mathematical modeling mainly describes the relationship between each quantity, especially the variation law between variables. The process of understanding the world. The process of reduction formula can make mathematics lively and lively. It promotes the development of mathematics. Further abstraction of known problems reveals deeper rules, and developed mathematics can explain more complex practical problems.
Based on the curriculum standard, this paper analyzes the compulsory and elective textbooks of ordinary high school, and has the following characteristics. It attaches importance to the development of mathematical application consciousness, attaches great importance to the connection with other disciplines, rich in content design, and integrates modern information technology into mathematics class. Through questionnaire survey and teacher interview, the following problems are found: the classification of natural science leads to the fragmentation of culture; The teaching of mathematics is too systematic; Students lack abstraction and quantitative training; The concept of teacher knowledge is deeply rooted. Therefore, the teaching implications for teachers are as follows: in the teaching of mathematics, we should be diligent in practice; To explain the context of knowledge, source and flow; More abstract and quantitative training; To convey methods and ideas through knowledge.
Mathematical modeling is reflected in the content of the "discovery", "promotion" and "application" from three aspects, therefore the way of mathematical modeling into the teaching are: (1) the "source" in - use the standpoint of mathematical modeling teaching process of discovery, the source of the mathematics knowledge background; The integration of "Ben" -- teaching the process of generalization with the idea of mathematical modeling, expressing the knowledge of mathematics itself; "Flow" integration -- the process of using mathematical modeling to teach the application and apply it to practical problems. Through some concrete mathematical modeling ideas to integrate into the teaching application case, summarize reflection: teaching needs to convey the method and thought through knowledge; Focus on cultivating students' "problem consciousness".
Key words: mathematical modeling; High school mathematics teaching; The source of this flow
目 录
摘要 i
Abstract II
第一章 绪论 - 1 -
1.1问题提出的背景 - 1 -
1.2研究综述 - 2 -
1.3研究的理论基础 - 3 -
1.3.1建构主义学习理论 - 3 -
1.3.3弗赖登塔尔教育思想 - 3 -
1.3.3多元智能理论 - 4 -
1.3.4问题解决理论 - 4 -
1.4选题的意义及研究方法 - 4 -
1.4.1选题意义 - 4 -
1.4.2研究方法 - 5 -
1.4.3研究内容 - 5 -
第二章 数学建模思想融入高中数学教学的必要性 - 6 -
2.1数学建模思想的内涵 - 6 -
2.1.1数学建模等概念 - 6 -
2.1.2数学建模思想 - 9 -
2.1.3数学建模方法论 - 9 -
2.2数学建模思想融入高中数学教学的内容 - 11 -
2.2数学建模思想融入高中数学教学的意义 - 12 -
第三章 教学中数学建模思想融入情况调查研究 - 14 -
3.1教材分析 - 14 -
3.2学生数学建模思想理解调查 - 16 -
3.2.1调查目的 - 16 -
3.2.2调查方法 - 17 -
3.2.3调查结论及分析 - 17 -
3.3教师应用数学建模思想教学调查 - 18 -
3.3.1调查目的 - 18 -
3.3.2调查方法 - 18 -
3.3.3访谈提纲 - 18 -
3.3.4调查结论及启示 - 19 -
第四章 数学建模思想融入高中数学教学的途径 - 22 -
4.1“源”——用数学建模思想分析数学知识点的来源背景 - 23 -
4.2“本”——用数学建模思想表达数学知识点本身 - 26 -
4.3“流”——用数学建模思想应用于实际问题 - 27 -
第五章 数学建模思想融入高中数学教学应用案例 - 29 -
5.1导数的概念 - 29 -
5.2等比数列前n项和公式探讨 - 30 -
5.2向量的应用 - 32 -
结 语 - 34 -
参考文献 - 35 -
致 谢 - 36 -
附录A - 37 - |
