教师专业知识的培养与发展一直是国内外研究者关注的热点，国内教师资格考试改革的大背景下，研究教师专业知识的重要性日益彰显。本研究进行了两方面工作： 第一，利用层级分析法归纳国家教师资格认证中《数学学科知识与教学能力》考试大纲的测量框架，运用于15-17年四套真题，得到真题在知识点覆盖率、考点频数和分值比重分布上的特点，同时归纳高中数学教师专业知识考核框架。研究表明： (1)测量框架由数学学科知识、数学教育理论知识及数学教育实践知识三部分组成。 (2)四套真题在知识点覆盖率上平均为65%，偏低；在考点频数和分值比重上，数学学科知识模块所占比例远高于考试大纲比例要求，数学教育理论知识与数学教育实践知识的比例则低于考试大纲要求。 第二，基于国家教师资格考试大纲及真题的分析，选取某重点师范院校的数学师范生作为样本，讨论数学师范生的专业知识。研究表明： (1)师范生数学学科知识与数学教育理论知识不存在相关关系；数学学科知识与数学教育实践知识存在显著正相关；数学教育理论知识与数学教育实践知识存在较弱相关关系。 (2)对数学教育实践知识最具预测性的影响因子是数学学科知识，其次是数学教育理论知识。 (3)15级与16级数学师范生三部分专业知识的表现上存在差异，在数学教育理论知识上的差异最大。 (4)进一步研究三部分专业知识与在校课程学业成就的关系，数学学科基础课程学业成就和三部分专业知识成绩呈显性正相关，但数学教育类基础课程学业成就与三部分专业知识成绩不存在相关关系。 据此，提出如下思考和建议： (1)将数学学科知识与数学教育理论、实践知识分为三个科目进行考查以解决知识覆盖率低的问题。融合高中数学知识于高等数学中考查，体现知识的来龙去脉，调整试卷中数学教育理论知识与实践知识的比重。 (2)数学学科知识不是成功教学实践所需要的全部，但是教学实践的必要条件，对教学实践知识有显著的解释能力。职前教师的培养应该以数学学科知识为主。数学教育理论知识对数学教育实践知识有影响，短期内不易看出成效。

Under the background of the reform of domestic teacher qualification examination, the importance of researching teachers' professional knowledge has become increasingly prominent. This research has carried on two aspects: firstly, we summarize the professional knowledge framework of senior high school mathematics teachers based on the outline of the National Teacher Qualification Examination, Secondly, we selected students from a normal university as a sample to test, which we called mathematics pre-service teachers. Analyzed the relationship between their professional knowledge. What’s more, we puts forward some thoughts and suggestions on the reform of National Examination and the training of pre-service teachers considering the academic achievements of normal school students in curriculum learning. The first research work used hierarchical analysis method, said: (1) The measurement framework is composed of three parts: mathematics subject knowledge, mathematics education theory knowledge and mathematics education practice knowledge. (2) The coverage rate of the four sets of real questions is 65% on average, which is on the low side. On the frequency and score of the test points, the real questions are subject-oriented, and the proportion of knowledge modules in mathematics subject is much higher than that of the examination syllabus, while the proportion of theoretical knowledge and practical knowledge in Mathematics Education is lower than that of the examination syllabus. Strengthen the knowledge of higher mathematics and weaken the knowledge of high school mathematics. The second study focuses on the relationship between mathematics pre-service teachers' professional knowledge, and discusses the correlation between test scores and mathematics teachers' academic achievement in school curriculum. (1) There is no correlation between mathematics subject knowledge and mathematics education theory knowledge of normal school students; there is a significant linear correlation between mathematics subject knowledge and mathematics education practice knowledge; there is a weak correlation between mathematics education theory knowledge and mathematics education practice knowledge. (2) The most important predictor of practical knowledge in mathematics education is knowledge of mathematics, followed by theoretical knowledge of mathematics education. It can be seen that in order to enhance the practical ability of pre-service teachers, it is the key to help pre-service teachers construct a perfect knowledge system of mathematics. (3)There are differences in the performance of different parts of professional knowledge among different grades of mathematics normal students. The greatest difference is the theoretical knowledge of mathematics part. (4) There is a positive correlation between the academic achievement and the test result, but there is no correlation between the academic achievement and the test result. Accordingly, the following thoughts and suggestions are put forward: (1)It is suggested that the syllabus of the National Examination should be refined, and the knowledge of mathematics, the theory of mathematics education and practical knowledge of mathematics education should be examined in different sub-subjects to solve the problem of low knowledge coverage. When proposing tests, we should integrate senior high school mathematics knowledge into higher mathematics, reflect the origin and development of knowledge, and adjust the proportion of theoretical knowledge and practical knowledge of mathematics education in examination papers. (2)The relationship between professional knowledge of students in normal school enlightens that knowledge of mathematics subject is a necessary and insufficient condition for practical knowledge of mathematics education, so pre-service teacher training stage should still focus on knowledge of mathematics subject. The theoretical knowledge of mathematics education has an impact on the practical knowledge of mathematics education. It is not easy to see the effect in a short time. It should permeate into every stage of teachers' teaching career.