数学建模思想融入高中数学教学的实践研究

发布时间：2018-05-01 09:31

本文选题：中学数学建模 + 数学建模思想　；参考：《西华师范大学》2017年硕士论文

【摘要】：21世纪是信息技术与大数据的时代,这些都与数学有着密切的联系。为了顺应时代的发展,数学的应用性被推到了我们面前,数学知识应用到生活实际一直以来都是广大从事数学相关人员研究的课题之一。数学建模充当了数学知识与现实生活的桥梁,数学建模思想就有着举足轻重的作用。数学建模是应用数学知识的有效手段之一,掌握应用数学知识是新时代对人才必然的要求。从小学数学就是学习必不可少的一门课程,但是从前面一些学者的研究情况来看很多学生对数学知识的应用能力还是比较欠缺的。基于这些现实本文主要围绕三个问题进行研究,问题1:高中生以及数学教师对数学建模的了解情况;问题2:有没有更好的方式、方法让学生能够更好的接受、学习数学建模;问题3:数学教师如何才能更好地进行数学建模教学。笔者主要应用文献分析法、问卷调查和访谈分析相结合进行研究。了解数学建模思想融入数学教学在国内外的发展情况及相关理论;通过调查发现很多高中生和数学教师对数学建模都是不了解的,并且觉得数学建模和他们有距离;并对影响高中开展数学建模活动的因素从学生、教师、家长、社会几个方面进行分析,发现高考压力和对数学建模不了解是主要因素。为了改变这种现状,将数学建模思想融入高中数学教学是行之有效的方式;在融入的过程中注意学生实际学习特点,采取先局部,再整体的方式,循序渐进。高中数学知识被分为几大板块,相应的数学建模也可以分为九种类型:集合模型、函数模型、向量模型、几何模型、统计与概率模型、数列模型、不等式模型、导数模型、综合模型。根据不同类型设计与教材知识紧密联系的数学建模题目,学生与教师一起完成这些题目的同时,了解数学建模及数学建模思想,感受数学建模的步骤。根据课程标准中对数学建模的要求、学生的实际情况,结合一些研究者的研究成果,笔者提出:(1)将数学建模思想融入到高中数学教学中应遵循的几个原则:以学生为主体;关注数学能力的提升;渗透数学思想方法;关注学生全面发展;结合学生的实际情况。(2)将数学建模思想融入到高中数学教学的选题范围:从课本中改编而来的数学建模题目;教师根据日常生活自己编写的数学建模题目;学生根据自己生活提出的数学建模题目。(3)从三方面谈数学建模思想融入到高中数学教学的实践策略,学生方面:培养学生观察身边事物的习惯;培养学生团结协作能力;培养学生阅读能力和语言表达能力;培养学生收集有效信息的能力;培养学生综合应用知识的能力。教师方面:结合学生实际创设好的问题情境,选择适合高中生的数学建模题目;注重自我提升,树立终身学习意识;建立良好的师生关系。其他方面:学校要给学生提供良好数学建模条件;家庭、社会方面要关注孩子的全面发展。(4)设计了两个将数学建模思想融入到高中数学教学的教学案例:椭圆的定义及其标准方程;等比数列求和公式的推导。
[Abstract]:Twenty-first Century is the age of information technology and large data. These are closely related to mathematics. In order to conform to the development of the times, the application of mathematics has been pushed to us. The application of mathematical knowledge to the reality of life has always been one of the subjects engaged in the research of mathematics related personnel. Mathematical modeling has acted as a mathematical knowledge and present. The idea of mathematical modeling plays an important role in the bridge of real life. Mathematical modeling is one of the effective means of applying mathematics knowledge. Mastering applied mathematics knowledge is a necessary requirement for talents in the new era. From primary school mathematics, it is an indispensable course for learning, but a lot of students are viewed from the research situation of some previous scholars. The application ability of mathematical knowledge is still relatively short. Based on these realities, this paper mainly focuses on three problems, the problem 1: high school students and mathematics teachers to understand the mathematical modeling; question 2: has a better way to allow students to better accept, learn mathematical modeling; problem 3: mathematics teachers how to The author is able to better carry out the teaching of mathematical modeling. The author mainly applies the literature analysis method, the questionnaire survey and the interview analysis to study the development of mathematical modeling ideas into the development of mathematics teaching at home and abroad and related theories; through the investigation, many high school students and mathematics teachers are unaware of the mathematical modeling, and feel that the mathematical modeling is not understood. Mathematical modeling and their distance, and the analysis of factors affecting high school mathematical modeling activities from the students, teachers, parents and society, found that the pressure of the college entrance examination and the mathematical modeling are the main factors. In order to change this situation, it is an effective way to integrate mathematical modeling into high school mathematics teaching. In the process of entry, we should pay attention to the students' actual learning characteristics, take the local, and then the whole way, step by step. The high school mathematics knowledge is divided into several big plates, and the corresponding mathematical modeling can be divided into nine types: set model, function model, vector model, geometric model, statistics and probability model, series model, inequality model and derivative model, A comprehensive model. According to the mathematical modeling subject closely related to the knowledge of different types of design and the knowledge of the teaching materials, the students and the teachers complete these topics together, and understand the mathematical modeling and mathematical modeling ideas, and feel the steps of the mathematical modeling. According to the requirements of the mathematical modeling in the curriculum standards, the actual situation of the students, and the research of some researchers. The author puts forward that: (1) the principles of integrating mathematical modeling into high school mathematics teaching: taking students as the main body, paying attention to the promotion of mathematical ability; penetrating mathematical thinking methods; paying attention to the overall development of students; combining with the actual situation of the students. (2) integrating the mathematical modeling ideas into the topic selection range of high school mathematics teaching: The mathematical modeling topic adapted from the textbook; the mathematical modeling title of teachers according to their daily life; students' mathematical modeling topics based on their own life. (3) from three aspects of mathematical modeling ideas into the practical strategies of high school mathematics teaching, students: training students to observe the habits of things around the students; cultivate students Unity and cooperation ability; cultivate students' reading ability and language expression ability; cultivate students' ability to collect effective information; cultivate students' ability to apply knowledge in a comprehensive way. Teachers: combining students with practical problem situations, choosing mathematical modeling topics suitable for high school students, and paying attention to self promotion and setting up lifelong learning consciousness; Jian Liliang Good relationship between teachers and students. Other aspects: the school should provide students with good mathematical modeling conditions; family and social aspects should pay attention to the overall development of children. (4) two teaching cases are designed to integrate mathematical modeling ideas into high school mathematics teaching: the definition of ellipse and its standard formula; isometric sequence and formula derivation.

【学位授予单位】：西华师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6

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