圆作为初中数学的核心学习内容，是数学学习及其它学科学习的基础。因为初中生接触的第一个曲线形是圆，圆的基本性质较多，学生在理解和记忆方面存在困难，且与圆有关的证明计算往往知识点多、方法灵活、综合性要求高，所以初中生面对圆的相关推理证明往往束手无策。

基于上述原因，为了解学生在圆的学习中具体存在的障碍，引起障碍的原因，以及针对具体的障碍应该采取的措施，笔者对所任教学校初三的四个班级（包括三个平行班，一个实验班），共计235名学生开展了圆的学习障碍的调查研究，并选取了五位有经验的初三数学教师和存在圆的学习障碍的三名学生进行访谈。通过调查问卷的分析和访谈结果，论文分析学生产生障碍的原因后提出转化策略，并进行教学实验检验转化策略的有效性。本研究主要进行了以下三方面的工作：

第一，以问卷调查的形式初步调查学生在学习圆的态度方法、相关知识的理解记忆掌握以及审题识图、推理过程的书写等方面是否存在障碍，再通过测试卷进一步调查学生对有关知识的理解和掌握情况，分析样本学生在学习圆内容时存在的具体障碍。

第二，通过对在教学一线且经验丰富的数学教师和存在圆学习障碍的学生的访谈，总结出学生学习圆时形成障碍的原因以及转化策略。

第三，针对前两部分的研究，提出圆学习障碍的转化策略，并进行教学实验检验转化策略的有效性。

本研究得到的主要结论是：

第一，调查研究结果表明，许多学生在圆的学习中存在相关基础知识薄弱、复杂图形的识图能力差、圆的有关性质定理和公式的掌握有欠缺以及综合运用所学知识解决问题的能力较差的障碍。

第二，针对学生存在的圆的学习障碍，相应转化策略是：

1.对勾股定理、二次根式进行重点复习，同时将对其它旧知的复习渗透到圆的教学中；

2.加强学生对圆的有关性质的识记和对学生进行识图训练从而使得学生提高识图能力；

3.及时进行圆周角及其推论的辨析、切线的判定与切线性质的辨析以及圆锥侧面积公式的剖析；

4.细化推理证明部分的教学，包括审题、总结常用辅助线的添加方法、教给学生分析题目的方法以及引导学生对推理证明的过程进行归纳总结。

As the core of junior middle school mathematics learning, circle is the basis of mathematics learning and other subjects learning. Because the first curve that junior high school students contact is circle, circle has many basic properties, students have difficulties in understanding and memory, and the proof calculation related to circle often has many knowledge points, flexible methods and high comprehensive requirements, so junior high school students are often helpless in the face of circle related reasoning proof.

Based on the above reasons, to understand the students, the obstacles exist in the circle of learning specific causes of disorder, as well as for specific disorders should take measures, the author to teach school grade four class (including three parallel class, a experimental classes), a total of 235 students conducted a round of investigation and study, the learning disabilities Interviews were conducted with five experienced mathematics teachers in grade three and three students with learning disabilities. Through the analysis of questionnaire and interview results, the paper analyzes the causes of students' barriers and puts forward transformation strategies, and carries out teaching experiments to test the effectiveness of transformation strategies.

This research mainly carries out the following three aspects:

       First, a preliminary investigation in the form of questionnaire survey the attitude of the students in the learning circle method, the understanding of the relevant knowledge memory master and the topic knowledge chart, reasoning process writing aspects such as the existence of a obstacle, again through the test further investigation the student's understanding of relevant knowledge and master the situation, analysis of samples of students in the learning circle of specific disorders.

Secondly, through interviews with experienced mathematics teachers and students with circle learning disabilities, the causes of the formation of the obstacles in students' circle learning and transformation strategies are summarized.

Thirdly, according to the first two parts of the research, the transformation strategy of circular learning disorder is proposed, and the effectiveness of the transformation strategy is tested by teaching experiment.

The main conclusions of this study are as follows:

First, the results of the investigation show that many students have some obstacles in learning circle, such as weak basic knowledge, poor ability to recognize complex graphs, lack of knowledge of theorems and formulas of properties of circles, and poor ability to solve problems by comprehensive application of knowledge.

Second, in view of students' existing learning disabilities, the corresponding transformation strategies are:

1. Review the Pythagorean theorem and quadratic roots, and infiltrate the review of other old knowledge into the teaching of circles;

2. Strengthen students' memorization of the properties of circles and train them to recognize pictures so as to improve their ability to recognize pictures;

3. Timely analysis of the circumferential Angle and its corollaries, determination of tangent line and its properties, and analysis of the formula of cone side area;

4. Refine the teaching of reasoning proof, including examining the topic, adding the method of summarizing the common auxiliary lines, teaching students the method of analyzing the topic and guiding students to summarize the process of reasoning proof.