基于波利亚理论的高考圆锥曲线解题思维策略研究

发布时间：2019-01-03 10:58

【摘要】：圆锥曲线是中学数学知识的一个核心交汇点,内容综合、解法灵活、思维抽象,它既是高考的热点题型,又是颇难解决的重点问题。学习圆锥曲线不仅可以培养学生数形结合、等价转换、函数与方程、分类讨论等数学思想,也能加深学生对代数与几何之间的联系的理解。本文以高考圆锥曲线解题思维策略作为研究目标,采用文献研究、统计分类、调查、分析等研究方法。首先对高考圆锥曲线的试题特征以及圆锥曲线的解题思维策略进行相关的文献综述,为研究提供理论基础;接着对高考圆锥曲线知识点进行分类统计,对试题来源、试题类型进行分析总结,为解高考题作准备;通过调查,了解学生对高考圆锥曲线试题的掌握情况,总结分析学生解题时遇见的障碍;根据分析所得的试题特征和解题障碍,结合波利亚的“怎样解题表”,提出圆锥曲线解题思维策略;最后,尝试应用圆锥曲线解题思维策略解决问题。本文研究结论包括:(1)统计了近五年全国高考圆锥曲线的知识点考察情况,了解试题背景,分析总结试题特征,为后续研究提供基础;(2)结合圆锥曲线的具体情况,对波利亚解题表分析解读,提出圆锥曲线波利亚解题步骤。再结合圆锥曲线的试题特征和解题障碍,针对性地提出四种圆锥曲线解题思维策略:“定义”审题;“性质”推论;“运算”转化;“图像”验证。
[Abstract]:Conic curve is a core intersection of mathematics knowledge in middle school. It is the key problem which is difficult to solve and is the hot topic type of college entrance examination. It is the content synthesis, the solution is flexible, the thought is abstract, it is not only the hot topic type of the college entrance examination, but also the key problem. Learning conic curves can not only cultivate mathematical ideas such as combination of number and form, equivalent transformation, function and equation, classification and discussion, but also deepen students' understanding of the relationship between algebra and geometry. This paper takes the thinking strategy of conic problem solving in college entrance examination as the research goal, and adopts the research methods of literature research, statistical classification, investigation, analysis and so on. First of all, the characteristics of the test questions of the conic curve of the college entrance examination and the thinking strategy of solving the conic curve are reviewed, which provides a theoretical basis for the study. Secondly, the knowledge points of conic curve of college entrance examination are classified, and the sources and types of test questions are analyzed and summarized, so as to prepare for solving the questions of college entrance examination. Through the investigation, we can understand the students' mastery of the conic curve test of the college entrance examination, and summarize and analyze the obstacles encountered by the students in solving the problems. According to the analysis of the characteristics of the test questions and the problem solving obstacles, combined with Poolia's "how to solve the problem list", the paper puts forward the conic curve problem solving thinking strategy, and finally, attempts to use the conic curve problem solving thinking strategy to solve the problem. The conclusions of this paper are as follows: (1) the knowledge points of the conic curve of the national college entrance examination in recent five years are investigated, the background of the examination questions is understood, the characteristics of the examination questions are analyzed and summarized, which provides the basis for the follow-up study; (2) according to the concrete situation of conic curve, this paper analyzes and interprets the Bolian problem solving table, and puts forward the steps of solving conic curve problem. Combined with the characteristics and obstacles of conic curve, four thinking strategies of conic curve are put forward: "definition", "nature" corollary, "operation" transformation and "image" verification.
【学位授予单位】：广州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6

【参考文献】