| The content about History of Mathematics has been as a course selected of new curriculum in senior high school, which stands out the meaning and value of History of Mathematics. But how to melt History of Mathematics into main Mathematics curriculum and play its function plentifully do not has viable strategies. It is a key point of Mathematics education and a efficient approach to promote Mathematics Curriculum reformation and development to excavate cultural connotation and instructive value of History of Mathematics and to convert the historiography-modality into education-modality of History of Mathematics.In the 17th century, the famous mathematician Descartes(1596-1650) founded the Analytical Geometry, which is one of the landmark of history of Mathematics. The Plane Analytical Geometry based on Analytical Geometry is key Mathematics course in senior high school. Therefore, studying these all above will be provided with some historical meaning, academic value, and realistic meaning, practical value also.There are 3 main points this research will cover concretely: (1) cultural connotation of the mathematical idea of Descartes;(2) the teaching strategies in the analytical geometry of the secondary school based on the mathematical idea of Descartes;(3) a simple introduction of the effect of the teaching strategies.The basic conclusions of the research are as following:1. The mathematical idea of Descartes is a whole culture system: (1)exterior culture environment: Revival of Learning, high develop of manufacture, a lot of problems come forth in the science and mathematics, the conceptions and methodology of mathematics had changed a lot.(2)the value of science: introduced the variable and coordinate conception into mathematics, began a new era of modern mathematics; provided an effective mathematical instrument for the natural science; founded the mechanization scheme of geometry attest; made a drastic breakthrough of the science methodology; formed the framework of symbolic logic. (3) core configuration: curve and equation are the kernels; the mapping principle is the basic character; the transforming between the algebra and geometry is the main method.(4)the contrail of the creative activities: the pursuit of mathematical value is the basis; the taste instinct is the power of creation; the effective choose and combination is the basic approach; (5) aesthetics exhibition: contracted and harmonious of mathematical ideas and method.(6)individual qualities: the firmly faith of symbolic logic; the spirit of suspicion, animadvert and creation; inheriting and comprehensive spirit; the ceaseless pursuit of the value of life2. According to the mathematical idea of Descartes, the teaching strategies in the analytical geometry of the secondary school can be as follow: (1) Drive the culture as a whole: make the factors in the mathematical idea of Descartes as a whole teaching power, then drive the analytical geometry teaching in the secondary school as a whole. (2) Core conception: make the culture connotation of mathematical idea of Descartes as the fodder. (3) Analysis the configuration: conformity the algebra and geometry. (4) Convert between the two models: convert between the algebra model and geometry model in analytical geometry, which, is the practice of analysis the configuration3. The main conclusions of the teaching practice of the strategies are as following: (1) It is good for inspiring the motivation of the students' learning; (2) It is good for the students to obtain, assimilate and consolidate the basic conception of analytical geometry; (3) It is good for the students' intuitivism, abstractivism, former consciousness and data handling; (4) It is good for the student's dialectic-thinking ability. (5) It is good for the students to comprehend, obtain and apply the basic idea of analytical geometry.4. Based on the research, there are some suggestions as follow: (1) Adjusting the Curriculum Standard: to explain the main curriculum aims of analytical geometry; to consider the conics as compulsory; to increase the main content of coordinate commutation. (2) Textbook development: to enhance the history content of analytical geometry; to adjusting the arrange sequence and present approach of analytical geometry content, put the conception of curve and equation in front of the beeline and equation. (3) Teachers' teaching: to build up the mathematical notion, curriculum notion and teaching notion of culture, and consider the basic idea of analytical geometry as a whole culture system; to pay attention to the learning interesting of the students; to train the students' intuitionistic consciousness. (4) To increase the requirement of plane geometry curriculum aims in junior schools.The innovations of this research are as follow: 1 .Preparatoryly discussd the culture connotation of the mathematical idea of Descartes; try to analysis the contrail of the creative activities of Descartes and the logical conjunction between the cognition model and mental model. 2. Discussed the teaching strategies in the analytical geometry of the secondary school based on the mathematical idea of Descartes. 3. Analyzed mathematical ideas from the view of mathematical culture and epistemology, and give prominence to "excavate" and "convert", this is also a kind of new method in the research of mathematical history in mathematical education.The theoretics value of this research is deepened the understanding of the culture connotation and educational value of mathematical idea of Descartes, and provide some reference for the research on the history of mathematical ideas; the practice point is provide some suggestion for the curriculum and teaching reform of analytical geometry in the secondary school; provide a instructing case for the new curriculum reform; provide some reference for the adjusting of the high-school curriculum standard, textbook writing and teachers' teaching, provide a exemplification for the reaching on the mathematical history in mathematical education.
|
PDF Full Text Request