数学建模思想融入函数教学的实践研究

发布时间：2018-06-23 03:00

本文选题：数学建模思想 + 函数教学　；参考：《陕西师范大学》2015年硕士论文

【摘要】：本文通过理论和实践两方面的共同研究,采用文献综述的方法了解了数学建模在国内以及国外的发展概况,进而探讨了将数学建模思想融入函数教学的作用、步骤及方法。数学建模在学生学习数学的兴趣、数学的学习方法、数学解题思想以及综合实践能力等方面发挥了巨大作用。同时又对影响中学数学建模开展的各种因素进行了分析,了解到在中学中阻碍数学建模发展的主要因素大致来源于四个方面：教师、学生、家长、社会。在研究方式上本人采取了问卷调查、访谈及实验验证等措施,主要针对学生学习数学的兴趣、数学学业成绩、数学学习能力展开调查。调查结果与本人所设想的基本上一致,总体来看,学生对数学建模还是很感兴趣的,而数学建模对学生的学业成绩也有所帮助,不仅如此,在数学学习能力方面学生也有了明显的提高。以此为基础,本文特别之处在于结合教材开发案例,本人特采取改编课本上原有例题和习题的方式作为数学建模的案例给学生讲解,一方面使学生比较容易接受,另一方面也使学生亲身感受到数学建模与实际生活的联系,使他们切身感受到数学建模的神奇之处,进而感受到数学的美。在融入方式上本人提出了“分步切入”思想,即纵向思维上分为三步,主要以年级作为区分标准,而横向思维上采取渐进式切入的方式,以学生的数学思维程度来划分,这个需要教师来把握。除此之外本文还讨论了有关开发数学建模第二课堂的观点。这一内容主要在高二和高三来进行,利用学生寒暑假的时间,通过学生自由组队的方式开展数学建模课外活动,题目由老师提供或者学生自拟。总之,一切论证都说明了在中学开展数学建模教学是必要的,更是可行的。而中学内容错综复杂,所以本人特选取函数作为研究内容,加之数学建模所含内容也是一个庞大的体系,本文以其思想的融入为主,大大简化了这一过程,仅仅探究了数学建模思想在函数教学当中的融入,希望对数学建模融入中学教学提供少许推动力,使更多的人认识到数学建模,体会到数学建模的优势,进而主动学习它,这样数学建模才能真正进军中学并占有一席之地。虽然对于融入方式已有一些人提出了很多,但本人认为最行之有效的方式就是寓数学建模思想于函数教学之中。
[Abstract]:Through the research of theory and practice, this paper uses the method of literature review to understand the development of mathematical modeling both at home and abroad, and then discusses the function, steps and methods of integrating mathematical modeling ideas into function teaching. Mathematical modeling plays an important role in students' interest in learning mathematics, mathematical learning methods, mathematical problem solving ideas and comprehensive practical ability. At the same time, it analyzes the factors that affect the development of mathematical modeling in middle schools, and finds out that the main factors that hinder the development of mathematical modeling in middle schools come from four aspects: teachers, students, parents, and society. In the way of research, I have taken measures such as questionnaire, interview and experimental verification, mainly aimed at students' interest in learning mathematics, mathematics academic achievement and mathematics learning ability. The results of the survey are basically consistent with what I have imagined. In general, students are very interested in mathematical modeling, and mathematical modeling is also helpful to students' academic performance, not only that. In mathematics study ability aspect student also has the obvious enhancement. On the basis of this, the special point of this paper is that combining with the case of textbook development, I take the way of adapting the original examples and exercises from the textbook to explain to the students as a case of mathematical modeling. On the one hand, I make it easier for the students to accept it. On the other hand, it also makes students feel the relationship between mathematical modeling and real life, makes them feel the magic of mathematical modeling, and then feel the beauty of mathematics. In the way of integration, I put forward the idea of "step by step", that is, the longitudinal thinking is divided into three steps, which mainly takes grade as the criterion of differentiation, while the horizontal thinking adopts a progressive approach, which is divided by the degree of students' mathematical thinking. This needs to be grasped by the teacher. In addition, this paper also discusses the development of mathematical modeling the second classroom views. This content is mainly carried out in the second and third year of senior high school. Using the time of the students' summer and winter, the extracurricular activities of mathematical modeling are carried out through the way of the students forming teams freely. The subjects are provided by the teachers or written by the students themselves. In a word, all the argumentation shows that it is necessary and feasible to carry out mathematical modeling teaching in middle school. And the content of middle school is complicated, so I select function as the research content, and the content of mathematical modeling is also a huge system, this paper, mainly with the integration of its ideas, greatly simplifies this process. It only explores the integration of mathematical modeling idea in function teaching, hoping to provide a little impetus for mathematics modeling to be integrated into middle school teaching, so that more people can realize mathematical modeling, understand the advantages of mathematical modeling, and learn it actively. In this way, mathematical modeling can really enter the middle school and have a place. Although some people have put forward many methods of integration, I think the most effective way is to incorporate mathematical modeling ideas into function teaching.
【学位授予单位】：陕西师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

【参考文献】