Teaching And Learning Or Mathematical Modeling In High Schools

What is the purpose of education, especially the mathematical education? At least, it should make people who accept the education more knowledgeable and more capable when they face to problems The traditional (mathematical) education method over emphasizes student's ability to memorize the knowledge on the book or to solve the problems which have known solutions. This method may be a good way to train student's analytic ability; however, it has little effect to enhance student's creativity and practicality which are necessary for students to solve the problems that they face to everyday [Stemberg]. There is a big gap between the goals of education and what the traditional method could really achieve; especially now the value of applying mathematics to real problems gets more and more recognition. Indeed, it is the ultimate goal of education to train students to fit in with the needs of the society and solve the real problems for the society. Therefore, the Mathematical Modeling Training, which teach students how to solve problems by building mathematical models, is getting more and more attentions from educators worldwide. It becomes a focal point of education system reform, in universities and high schools, in China and other countries.This thesis presents an overview of the Mathematical Modeling Teaching and learning practice in high schools. The key parts of this thesis are Chapter Four, Five and Six, in which the three key elements of mathematical education in Mathematical Modeling, i.e. content, student and teacher, are discussed In the first chapter, two examples are used to illustrate the drawbacks of current education methods and the reasons causing such drawbacks. Chapter Two introduces the concept and activities of Mathematical Modeling Training through the practice of mathematical education reform worldwide. Chapter Three describes the concept of the mathematical model, the relation between the mathematical model and the prototype, and other relevant concepts. Chapter Four gives the definition of Mathematical Modeling; introduces the application of Mathematical Modeling in high school education; describes the principles, procedures and methods of Mathematical Modeling, summarizes the contents and current status of Mathematical Modeling in high school education as well as the difference between the Mathematical Modeling and the Application Problems. Chapter Five discusses the high school Mathematical Modeling Training from learning psychology point of view, and extends the discussion to the end of problem solving. Chapter Six details the educational activities and models of high school Mathematical Modeling Training. Chapter Seven presents the results of a small scale test and its data analysis. Chapter Eight is the conclusion and closing statementThe author wishes to thank Dr. Shengyuan Zhang of Mathematics Department, Fujian Normal University. Without his guidance, this thesis would not have been possible.