Research And Enlightenment On Mathematical Way Of Thinking In College Entrance Examination Of Mathematics

At present exercises-stuffed teaching method, which has many disadvantages, is still being widely used among the secondary school maths teaching. However, education should aim to encourage students'potential and improve their overall ability. In the reform of curriculum, examinaing students'capacity has become a core subject in the entrance examination, We must be aware that only when students have a further understanding of the nature and implications of mathematics based on a solid grasp of mathematical knowledge and concepts, can they improve their capacity and enhance their comprehensive mathematical literacy. The mathematical way of thinking is often embedded in the materials and exercises, which calls for careful excavation. In this context, it is necessary to study the mathematical way of thinking inherent in the mathematics test paper since the resumption of the entrance examination .In this paper, theoretical research method and empirical research method are combined to reveal the core concepts of mathematical thinking. Using literature method and on the basis of modern teaching theory, educational psychology, instructional design principles and so on,the paper is an analysis of argumentation and theoretical generalization. In order to study the typical mathematical way of thinking reflected in the types, forms, manners, and extent, etc.of math problems, empirical research has been carried out on the basis of theoretical analysis. The paper contains the following five main parts:Chapter I (Introduction): mainly to raise questions and theoretical research .Chapter II: mainly to describe the typical mathematical way of thinking in high school. Chapter III: to do research about the national college entrance examination mathematics papers from 1978 to 2001 and Jiangsu mathematics entrance examination papers from 2002 to 2009 and classify them into three categories: from 1978 to 1983, six years of the initial stage; from 1984 to 1999, sixteen years of exploration and stability; from 2000 to 2009, a decade of development.Chapter IV: to do further research about the mathematical way of thinking embodied in the type, form, manner and extent (scope, span, difficulty)of Jiangsu entrance examination in the past decade (2000 ~ 2009), make the statistical analysis and draw the conclusion that: (1) The types: the way of combining numbers with forms, the way of classified discussion, the way of functions and equations, the way of generalization and specialization, the way of reduction theorem and the way of analog. These are the six typical mathematical way of thinking that are reflected in Jiangsu entrance examination papers in the past decade, in which the way of combining numbers with forms, the way of classified discussion, and the way of functions and equations are reflected more fully. (2)The forms: the above six kinds of typical mathematical way of thinking are reflected in the fill-in, multiple-choice and questions, in which the way of combining numbers with forms, the way of classified discussion, and the way of functions and equations are more reflected.(3) The manners: most of the mathematical ways of thinking are intrinsic in the mathematics questions which won't appear before carelly dug.(4) The extents: according to the statistics based on the scope, span, difficulty, the problems have reflected a certain scope, span and difficulty.On this basis, after comparing the mathematical ways of thinking reflected in Shanghai entrance examination papers and Jiangsu entrance examination in the last decade (2000 ~ 2009), we can draw a conclusion: Mathematical thinking reflected in Shanghai and Jiangsu math college entrance examination, the types and the manners are almost the same, while in terms of scope, span, and difficulty, Shanghai papers reflect them more fully, especially the ideas of combining numbers with forms.Chapter V: experience and reflection. In the course of the research, it is necessary to study a large number of College Entrance Examination papers so as to extract the implicit way of thinking. Due to time constraints and limited capacity, the study is not so perfect. However, follow-up topics have come up.