高中数学解题思维策略研究

发布时间：2018-06-14 12:14

本文选题：高中数学 + 解题　；参考：《河南师范大学》2015年硕士论文

【摘要】：在高中数学学习活动中,解题是最基本的活动之一,是实现学生对定理概念的理解,思想方法的掌握以及思维能力的提高的有效手段.掌握好一定的解题思维策略可以提高学生数学解题的效率.但由于高中数学知识较为抽象,难度较大,加之应试教育的影响,学生普遍存在机械式解题的现象,很少关心解题时的思维过程,以致在解题中经常出现各种障碍,学习效果不佳.虽然现阶段多数教师也已经意识到这个问题,在解题教学中注重思维过程的展示以及思想方法的渗透,但出于各种原因,效果也并不明显,以致教学质量难以提高.为了更好解决现阶段存在的数学解题问题,需要对学生在解题中出现的思维障碍进行系统分析,并提出相应的改进策略.这也是本文的出发点.但由于学生在解题时出现的问题不尽相同,要想有效的解决这些问题,必须从学生解题本质的思维过程出发,系统的分析存在的思维障碍,从而有针对性的提出改进策略.这是本文研究的核心问题,也是创新点.采用文献法、访谈法和案例分析法展开本次研究.在本文中,将数学解题思维过程分成了四步,分别是认真审题,理清题意;仔细分析,拟定计划;实施解题,书写规范;反思纠正,举一反三.并从这四个基本步骤入手,总结出学生在各个步骤中常见的思维障碍如下:审题阶段出现的理解性障碍、缺失性障碍;分析阶段出现的严密性障碍、灵活性障碍、策略性障碍;实施阶段出现的监控性障碍、条理性障碍以及反思阶段出现的批判性障碍.导致这些障碍形成的原因无外乎有客观和主观两个方面,但本文主要针对高中生数学解题思维障碍而制定相应的改进策略,因此侧重于主观原因的分析.最终总结出形成这些障碍的主要原因有四个方面:一是知识经验匮乏.具体表现在数学基础知识不扎实以及数学思想方法掌握不佳;二是解题习惯不良.具体表现在不注重审题、语言表达不规范和缺乏自我反思意识;三是思维定势的负影响,导致思维呆板,变通能力差;四是心理因素的影响.包括解题意愿不强、心理压力大和意志力较差.而在数学学习中,教师的教与学生的学是相辅相成的,要想有效的排除这些障碍,必须从教师和学生两个方面进行改进.教师在今后的教学应更加注重数学基础知识、数学思想方法的教学,以及审题和反思教学,同时关注学生的心理状况.学生自身也应该重视数学基础知识、思想方法的学习,养成良好的数学学习习惯,同时调整心态,树立学习数学的信心.
[Abstract]:In high school mathematics learning activities, problem solving is one of the most basic activities, which is an effective means to realize students' understanding of the concept of theorem, the mastery of thinking methods and the improvement of thinking ability. Mastering a certain thinking strategy of solving problems can improve the efficiency of solving mathematical problems of students. However, due to the abstract and difficult knowledge of mathematics in senior high school and the influence of exam-oriented education, students generally have the phenomenon of mechanical problem solving, and they seldom pay attention to the thinking process of solving problems, so that there are often various obstacles in solving problems. The effect of study is not good. Although most teachers have been aware of this problem at present, they pay attention to the display of thinking process and the infiltration of thought methods in the teaching of solving problems, but for various reasons, the effect is not obvious, so the teaching quality is difficult to improve. In order to solve the problem of solving mathematical problems in the present stage, it is necessary to systematically analyze the thinking obstacles of students in solving problems, and put forward the corresponding improvement strategies. This is also the starting point of this paper. However, because students have different problems in solving problems, in order to effectively solve these problems, we must start from the thinking process of students' essence of solving problems, systematically analyze the existing thinking obstacles, and then put forward the corresponding improvement strategies. This is the core of this study, but also innovation. Literature method, interview method and case analysis were used to carry out this study. In this paper, the thinking process of mathematical problem solving is divided into four steps, that is, to carefully examine the problem, to clarify the meaning of the question, to carefully analyze and draw a plan, to implement the problem solving, to write the standard, to reflect and correct, to draw a lesson from the other. Starting with these four basic steps, the common thinking obstacles of students in each step are summarized as follows: comprehension obstacle, missing obstacle, strictness obstacle, flexibility obstacle, strategic obstacle; Monitoring barriers, structured obstacles and critical barriers in the implementation phase. The causes of these obstacles are not only objective and subjective, but this paper mainly aims at the problem solving obstacles of senior high school students and makes corresponding improvement strategies, so it focuses on the analysis of subjective reasons. Finally, the main reasons for these obstacles are summarized: first, lack of knowledge and experience. The concrete manifestation is that the basic knowledge of mathematics is not solid and the method of mathematics thought is not good; the second is the bad habit of solving problems. The concrete manifestation is not paying attention to the examination, the language expression is not standard and lacks the self-reflection consciousness; the third is the negative influence of the thinking pattern, which leads to the thinking rigidity, the flexibility ability is poor; the fourth is the influence of the psychological factor. Including the problem-solving will is not strong, psychological pressure and poor willpower. In mathematics learning, teachers' teaching and students' learning complement each other. In order to remove these obstacles effectively, it is necessary to improve from two aspects: teachers and students. Teachers should pay more attention to the basic knowledge of mathematics, the teaching of mathematical thought method, the teaching of examining questions and reflection, and pay attention to the students' psychological condition. Students themselves should also attach importance to the study of basic knowledge and methods of mathematics, develop good learning habits of mathematics, adjust their mentality and establish confidence in learning mathematics at the same time.
【学位授予单位】：河南师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

【相似文献】