基于波利亚“怎样解题”表的解题与教学探究——以一道平面几何公开问题为例

Problem Solving and Teaching Inquiry Based on Bollea’s “How to Solve Problems” Table—Taking an Open Problem of Plane Geometry as an Example

摘要: 解题教学，即解题活动的教学。数学解题的教与学是数学教学的重要内容，因此教会学生解题是数学教学中的核心问题。本文基于一道平面几何的公开问题，运用波利亚的“怎样解题”表来分析解决问题，通过解题的四个步骤及合理的推理过程，清晰明了的得出结果，培养师生运用波利亚解题理论的意识，从而提高教师的教学能力以及学生解决数学问题的能力。

Abstract: Problem solving teaching is the teaching of problem solving activities. Teaching and learning of mathematical problem solving is an important part of mathematics teaching, so teaching students to solve problems is the core of mathematics teaching. This article is based on a public problem of plane geometry, using polya analysis of how “problem solving” table to solve the problem, through the four steps of problem solving and the reasonable inference process, clear results, cultivating the consciousness of teachers and students use polya problem solving theory, so as to improve teachers’ teaching ability and the students’ ability of solving math problems.