学生在进入高三一轮复习后，常出现题目讲过后不久就会遗忘的现象，且笔者所在学校的数学习题课形式单一。为改变单一的教学模式，笔者依据波利亚的解题理论进行了本文研究，旨在将教师讲解转变为通过提问引导学生解答，将教师大包大揽转变为给予学生适当的帮助。

本研究以波利亚的“怎样解题”表为基础。该表精炼地概括了一般的数学解题程序，具有很强的可操作性，且主要针对求解题，对证明题的解题步骤没有进行详细说明。笔者依靠波利亚的解题理论，结合笔者教学班级的实际学情，修改整合了求解题的解题步骤，并结合笔者自身经验，归纳概括出了证明题解答步骤，形成了本文的理论基础。两类问题解答步骤如下：

针对求解题：一、审清题设，标记条件；二、转化条件，寻找关系；三、代数运算，书写步骤；四、检查总结。

针对证明题：一、审清题设，挖掘条件；二、转化倒推，整理思路；三、依靠定理，严格书写；四、回顾反思。

笔者基于上述步骤，在解析几何和立体几何的习题课中进行了教学设计和教学实践，并根据课堂实录进行了教学反思。

After entering the third round of senior high school review, students often forget the topic soon after the lecture, and the mathematics exercises in author's school are in a single form. In order to change the single teaching mode, the author carries on this research according to Polya's problem-solving theory, aiming to change the teacher explaining herself into guiding the students to answer by asking questions, and giving the students proper help.           

This study is based on Polya's "how to solve it" list. This list concisely summarizes the general mathematical problem-solving process, which has a powerful operability. It mainly aims at problems of construction, and does not explain the solving steps of problems to prove. Based on Polya's problem-solving theory, combined with the actual situation of the author’s teaching class, the author revised and integrated the problem-solving steps, and combined with the author’s experience, the author summed up the solving steps of problems to prove. Finally, the author formed the theoretical basis of this paper. The steps to answer the two types of questions are as follows:            

For problems of construction: First, figure out the conditions and mark them; Second, transform the conditions and find the relationship; Third, use algebra operation and write steps; Fourth, check and summarize.           

For problems to prove: First, figure out the conditions and dig them; Second, transform the conditions and derive relations from the end; Third, write strictly according to theorems; Fourth, review and rethink.           

Based on the above steps, the author designs and practices the teaching in the exercises course of analytic geometry and solid geometry, and reflects on the teaching according to the course video.