The Study On Plausible Reasoning In "graph And Geometry" Field Of Mathematics In Junior High School

Reasoning is not only the basic mode of thinking in mathematics, but also the constantly used mode of thinking in people's learning and everyday life. The ability of reasoning is the essential part of understanding mathematics and the development of reasoning ability should run through the whole process of mathematics learning. Normally, reasoning is divided into two kinds: plausible reasoning and deductive reasoning. Plausible reasoning focuses on discovery which is helpful to develop students'innovative spirit. Plausible reasoning can make students understand the meaning and reasonableness of mathematics through developing ideas, exploring phenomena, justifying results and getting math guess. But for a long time, mathematical"graph and geometry"field in junior high school have paid attention on formalized method to develop students'reasoning ability and ignored the plausible reasoning training.This thesis applies method of documents, method of comparative study, method of questionnaire, etc. and gives the prominence to the key points as follows:1. According to the pertinent documents, the thesis defines the plausible reasoning. Plausible reasoning is to derive possible conclusion from existent truth by experience and intuition with the methods of induction and analogue under some circumstance of process. It analyzes the definitions, features and steps of inductive reasoning and analogical reasoning in mathematical"graph and geometry"field of junior high school and lists some cases of"graph and geometry"to explain. Because one of the main aims of reflecting axiomatic idea is to develop deductive reasoning ability, the thesis analyzes the dialectical relationship of plausible reasoning and deductive reasoning in this field. Plausible reasoning and deductive reasoning supplement each other and promote the further development of students'reasoning ability together.2. To combine with the trend of geometry course design internationally, the thesis studies the course design features of"graph and geometry"field in the third learning stage of Curriculum Standard, and discovers that the course design of"graph and geometry"field applies comprehensive geometry together with intuitional geometry, experimental geometry and deductive geometry. The definitions and propositions are discovered by plausible reasoning through intuitional geometry and experimental geometry; propositions'correctness is proved by deductive reasoning. Intuitional geometry and experimental geometry are helpful to develop students'ability of plausible reasoning. Meanwhile,"graph and geometry"field in the third learning stage of Curriculum Standard had trained formalized deductive reasoning, but now it highlights plausible reasoning and emphasizes the balanced development of plausible reasoning and deductive reasoning and develops students'innovational spirit. Curriculum Standard weakens formalized deductive reasoning, but it doesn't give up the main educational aim of geometry. In compulsory stage, it pays attention to the sense of order of thinking and doesn't overemphasize the reasoning form. However, Curriculum Standard has limitations on elaborating reasoning ability and plausible reasoning, even hasn't defined the plausible reasoning which has no unified understanding at present and hasn't mentioned the functions and value of plausible reasoning, all of which will influence the understanding of the plausible reasoning. Therefore, the thesis suggests making clear the definition, functions of plausible reasoning and the value of developing the students'innovational spirit.3. The thesis studies comparatively the"graph and geometry"field of junior high school math textbooks published by People's Education Press and Beijing Normal University Press and finds out that the textbooks pay much attention to plausible reasoning in"graph and geometry"field. The textbooks strengthen the connection to students'reality, use intuitional geometry and experimental geometry, explore the definition, basic fact and theorem by intuitional perception and operational confirmation and come to prove by deductive reasoning. Especially in the junior high school math textbook published Beijing Normal University Press, all the propositions listed in Curriculum Standard are all explored first, and then established axiomatic system to demonstrate. The process of exploring definition, basic fact and theorem develops the students'plausible reasoning ability. However, there are different opinions on the arranged mode of intuitional geometry, experimental geometry and deductive geometry are showed respectively is whether good or not for geometry teaching, especially if too much intuitional geometry and experimental geometry can make geometry lose its original systematicness and preciseness. Therefore, the author proposes some writing suggestions on textbooks based on the constructivism theory and the writing experience of junior high school math textbooks.4. The thesis takes questionnaire on the plausible reasoning teaching and find out the elements which influence the plausible reasoning teaching. They are as follows: Curriculum Standard has limitation on elaborating plausible reasoning; the textbooks pay much attention to plausible reasoning in"graph and geometry"field, but the content arrangement has limitations; the teachers and students realize the importance of plausible reasoning, but they don't use plausible reasoning to deal with geometry questions in the usual teaching and learning. The author suggests the teaching mode of plausible reasoning based on the constructivism theory, Piaget's Theory of Cognitive Development of Children and Freudenthal's math learning theory and further explains with cases; proposes five suggestions on developing students'plausible reasoning ability according to the definition of plausible reasoning and the course design features of"graph and geometry"in junior high school.