基于波利亚数学解题思想的数列解题研究
发布时间：2019-05-13 13:35
【摘要】：数列在高考中有着非常重要的位置。本文通过文献研究、问卷调查、访谈及个案跟踪等研究方法对高三学生数列问题解题状况进行调查分析,将波利亚解题数学模式运用到高中数列问题的求解与教学实践当中,力求能够改善学生高中数列问题求解状况,在高考中取得好成绩。本文主要分为四大部分：(一)对高中学生进行关于数列问题解题状况调查,发现其解题过程不符合波利亚数学解题模式。(二)基于波利亚解题模式的研究,提出数列求解模式的四个步骤：①认真审题,获悉显隐性条件②观察数列特征,寻求有用的思路③用好数学思想方法④解题回顾(三)基于波利亚解题模式进行数列重点题型的求解实践,归纳总结重点题型的解题方法技巧。让学生体会解题思维过程和数学思想方法。(四)基于波利亚解题模式给出数列解题教学建议：①重视并用好概念及性质②观察数列特征、启发引导学生找解法③用好数学思想方法、优化解题思维过程④解题回顾。并给出数列习题解题课的教学设计。本文的研究不仅仅是波利亚解题模式的推广,也对一线教师的教学和高中生的解题有着非常重要的指导意义。
[Abstract]:The sequence of numbers plays a very important role in the college entrance examination. Through literature research, questionnaire survey, interview and case tracking, this paper investigates and analyzes the problem solving situation of the series of problems for senior high school students, and applies the mathematical model of Polya problem solving to the solving and teaching practice of the series of problems in senior high school. Strive to improve the high school series of problem-solving situation, in the college entrance examination to achieve good results. This paper is divided into four parts: (1) the high school students are investigated about the problem solving of series of problems, and it is found that the process of solving problems does not accord with Pollya mathematical problem solving model. (2) based on the study of Polya's problem-solving model, four steps of solving the series of problems are put forward: (1) carefully examining the problem and learning that the hidden condition 2 observes the characteristics of the sequence of numbers, Find useful ideas 3 make good use of mathematical thinking method 4 Review of problem solving (3) solve a series of key problem types based on Polya problem solving mode, summarize the key problem solving methods and skills. Let the students experience the thinking process and mathematical thinking method of solving problems. (4) based on Polya problem solving mode, this paper gives some suggestions on how to solve problems in series of numbers: (1) pay attention to and use the concept and nature of 2 to observe the characteristics of series of numbers, enlighten and guide students to find a solution and make good use of mathematical thinking methods, and optimize the thinking process of solving problems. (4) Review of problem solving. The teaching design of the course of solving problems in several series of exercises is given. The research in this paper is not only the promotion of Polya problem-solving model, but also has a very important guiding significance for the teaching of front-line teachers and the problem-solving of senior high school students.
【学位授予单位】：西北大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：G633.6
本文编号：2475930
[Abstract]:The sequence of numbers plays a very important role in the college entrance examination. Through literature research, questionnaire survey, interview and case tracking, this paper investigates and analyzes the problem solving situation of the series of problems for senior high school students, and applies the mathematical model of Polya problem solving to the solving and teaching practice of the series of problems in senior high school. Strive to improve the high school series of problem-solving situation, in the college entrance examination to achieve good results. This paper is divided into four parts: (1) the high school students are investigated about the problem solving of series of problems, and it is found that the process of solving problems does not accord with Pollya mathematical problem solving model. (2) based on the study of Polya's problem-solving model, four steps of solving the series of problems are put forward: (1) carefully examining the problem and learning that the hidden condition 2 observes the characteristics of the sequence of numbers, Find useful ideas 3 make good use of mathematical thinking method 4 Review of problem solving (3) solve a series of key problem types based on Polya problem solving mode, summarize the key problem solving methods and skills. Let the students experience the thinking process and mathematical thinking method of solving problems. (4) based on Polya problem solving mode, this paper gives some suggestions on how to solve problems in series of numbers: (1) pay attention to and use the concept and nature of 2 to observe the characteristics of series of numbers, enlighten and guide students to find a solution and make good use of mathematical thinking methods, and optimize the thinking process of solving problems. (4) Review of problem solving. The teaching design of the course of solving problems in several series of exercises is given. The research in this paper is not only the promotion of Polya problem-solving model, but also has a very important guiding significance for the teaching of front-line teachers and the problem-solving of senior high school students.
【学位授予单位】：西北大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：G633.6
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