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中学数学思想方法及其教学研究 On the Thinking Methods and Teaching Research of Middle school Mathematics
摘要通过对《中学数学教学大纲》、有关数学思想方法的文献资料研究，以及对自己的教育实践的总结，归纳指出中学数学教学中几种常用的数学思想方法，并列举相关教学案例，对其教学作用作了较为详尽的叙述。
Abstract: By studying The Teaching Syllabus of Mathematics and the literature of Mathematics thinking methods and the summary of my teaching experience, the paper points out several common used thinking methods of Mathematics, lists relative teaching cases and gives detailed narration about its affects on teaching.

关键词：函数与方程的思想、数形结合思想、分类讨论思想、化归与转化思想、数学归纳法、待定系数法、换元法、反证法、配方法、坐标法、分析法与综合法 ）
Key words: the function and equation thought, the number shape union thought, classified discussion thought, reduction and transformation thought, mathematical induction, method of undetermined coefficients, method of substitution, reduction to absurdity, distribution method, coordinate method, analysis method, synthesis

Title: The Thoughtway and Teaching Study of Mathematics in Middle School

ABSTRACT
Based on the study of mathematics syllabus of middle school, some relative documents on mathematics thoughtways and teaching practices, the paper gives a conclusion and points out there are some commonly used thoughtways, after which the paper emulates some relative teaching cases and elaborates on its teaching efforts.
Key words: the thoughtway of function and equation
the thoughtway of combination between numeral and form
the thoughtway of discussion by classification
the thoughtway of sorting and transformation
method of mathematical induction method of undetermined coefficients
method of substitution proof by contradiction
method of completing the square method of coordinate method of analysis and synthesis

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