波利亚的解题理论在高中导数教学中的应用

发布时间：2018-04-24 20:19

本文选题：波利亚 + 导数　；参考：《东北师范大学》2015年硕士论文

【摘要】：波利亚的《怎样解题》一书出版30后的1980年,波利亚的解题方法流传到我国,被我国学者大力赞扬,它主张的内容与我国现阶段的课程标准相符合,导数是数学中非常重要的一个概念,它连接了高中数学和大学数学,在高中阶段想要很好的掌握导数的概念,对它能够灵活应用是有一定难度的。这部分出现了大量的学困生,因此我将对波利的解题方法用于高中数学导数教学之中。本文主要分三部分内容,第一部分介绍波利亚的解题方法,其中包括他的解题表,他将归纳类比用于解题之中,在问答中应用启发法使学生解决问题,以及数学解题中的四种经典模型。第二部分研究波利亚的解题方法在高中导数应用的可行性,并对此进行评价。第三部分为波利亚解体理论下导数几何性质单调性的教学的实证研究。
[Abstract]:Polya's "how to solve the problem" after the publication of the book 30 in 1980, Polya's problem solving method spread to our country, has been greatly praised by Chinese scholars, its content is in line with the current stage of our country's curriculum standards, the derivative is a very important concept in mathematics, it connects high and middle mathematics and university mathematics, in high school stage is very good. It is difficult to apply the concept of derivative, and it is difficult to apply it flexibly. In this part, there are a lot of students with learning difficulties. So I will use the method of solving the problem of Polly in the derivative teaching of high school mathematics. This paper is divided into three parts. The first part introduces Polya's solution method, including his solution table, he will sum up the analogy In the question of solving the problem, we apply the heuristic method to solve the problem in the question and answer, and the four classical models in the mathematical problem solving. The second part studies the feasibility of Polya's solving method in the high school derivative application and evaluates it. The third part is the empirical study on the monotonicity of derivative geometric properties under Polya's disintegration theory.

【学位授予单位】：东北师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

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