高中立体几何解题困难与对策研究

发布时间：2018-03-12 07:21

本文选题：立体几何　切入点：解题　出处：《鲁东大学》2015年硕士论文　论文类型：学位论文

【摘要】：新课程标准要求“数学教学要注重问题解决，注重数学应用，注重数学交流，注重数学思维方法，注重培养学生的态度情感和自信心。”数学不是对于真实事物或现象的直接研究,而是以抽象思维的产物作为直接的研究对象。数学思维能力的培养是数学教学的核心任务之一，而思维能力培养通过问题解决得以实现。事实上，数学界一直公认问题是数学的心脏，所以，，问题解决一直被看做是数学教育和学习的核心。问题解决包含两个方面的内涵：一是发现问题、提出问题；二是解决问题，后者具体到中学教学即为数学解题。立体几何是高中数学的重要组成部分，立体几何学习对学生认识世界、发展几何思维，培养空间想象能力和逻辑推理能力具有重要意义。目前，高中立体几何教学仍然存在问题：学生不能理解几何的概念、定理，推理能力弱，立体几何解题困难等等。立体几何解题教学的主要任务是思维培养。有学者把数学思维分为“概念式思维”和“解题式思维”。“解题式思维”是波利亚解题方法的核心部分，他的系列名著《怎样解题》、《数学的发现（一、二）》、《数学与猜想》，阐释了“怎样解题表”，“掌握数学就意味着善于解题”等解题教学思想，其中“怎样解题表”代表了《怎样解题》的精华，“怎样解题表”把问题解决过程中有效的智力活动按照正常人的思维，分成了四个阶段:弄清问题、拟定计划、实现计划及回顾。波利亚解题方法形成了一个完备的解题教学体系。本文立足于立体几何解题教学，研究立体几何解题困难和应对策略以及在立体几何教学中培养数学思维等问题。解题教学方面，主要探讨波利亚解题方法的理解和应用；而在思维培养研究方面，探讨如何使学生掌握正确的思维方法，养成良好的思维习惯和思维品质。本文设计调查问卷、测试卷，对立体几何学习过程中，解题困难、学生思维能力等方面进行调查，在此基础上探索立体几何解题和数学思维培养的方法和措施。依据教学理论的研究和调查分析的结果，本文设计了教学案例，对解题教学和思维培养进行实践探索。
[Abstract]:The new curriculum standard requires that "Mathematical teaching should pay attention to problem-solving, mathematical application, mathematical communication, and mathematical thinking methods." Pay attention to cultivating students' attitude, emotion and self-confidence. "Mathematics is not a direct study of real things or phenomena, but the product of abstract thinking as a direct research object. The cultivation of mathematical thinking ability is the core of mathematics teaching Ren Wuzhi." And the ability to think is achieved through problem-solving. In fact, mathematics has always recognized that problems are the heart of mathematics, so, Problem solving has always been regarded as the core of mathematics education and learning. Problem solving includes two aspects: one is to find problems and put forward problems, the other is to solve problems, the latter is to solve problems in middle school. Solid geometry is an important part of senior high school mathematics. Learning solid geometry plays an important role in understanding the world, developing geometric thinking, cultivating spatial imagination and logical reasoning. There are still some problems in the teaching of solid geometry in senior high school: students can not understand the concept of geometry, theorems, weak reasoning ability, difficulties in solving solid geometry problems, and so on. The main task of teaching three-dimensional geometry problem solving is the cultivation of thinking. Some scholars divide mathematical thinking into "conceptual thinking" and "problem-solving thinking". "problem-solving thinking" is the core part of Polia's problem-solving method. His series of masterpieces, how to solve problems, the Discovery of Mathematics (1, 2), and Mathematics and conjecture, explain the teaching ideas of how to solve problems, and how to master mathematics means to be good at solving problems. "how to solve problem list" represents the essence of "how to solve problem". "how to solve problem Table" divides the effective intellectual activities in the process of problem solving into four stages according to normal people's thinking: to find out the problem, to draw up a plan. Implementation plan and review. Bolia problem solving method formed a complete problem solving teaching system. Based on the teaching of solid geometry problem solving, this paper studies the difficulties and strategies of solving solid geometry problems, as well as the cultivation of mathematical thinking in the teaching of solid geometry. In the teaching of solving problems, the understanding and application of Bolia's method of solving problems are mainly discussed. In the research of thinking cultivation, this paper discusses how to make students master correct thinking methods and develop good thinking habits and thinking qualities. This paper designs questionnaires and test papers, which is difficult to solve problems in the process of learning solid geometry. On the basis of the investigation of students' thinking ability, the methods and measures of solving three-dimensional geometry problems and cultivating mathematical thinking are explored. According to the results of research and analysis of teaching theory, this paper designs a teaching case. To solve the problem teaching and the thinking cultivation carries on the practice exploration.
【学位授予单位】：鲁东大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

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