教师专业知识是教师质量的保障，教师专业知识的研究是教育研究的重要主题，数学教师的专业知识是从数学学科对教师专业知识的关注。面向教学的数学知识（Mathematical Knowledge for Teaching，简称MKT）理论于2008年缘起美国，成为近年来数学教师知识研究领域的热点话题。了解数学教师的知识构成和发展现状，是进一步推进和深化新一轮课改实践与实验的需求。然而，由于不同时期、不同研究者的关注点不同，导致MKT各成分概念内涵和外延不够清晰等，这些问题仍待澄清。同时，教师MKT作为一种实践性知识，研究中不仅应关注教师MKT现状特征，更应关注教师MKT在教学实践中的表现。 为此，本研究的主要研究目标在于探明不同类型小学数学教师MKT特征及其教学实践表现。在此基础上，进一步探讨小学数学教师MKT与教学实践表现的关系，并对不同类型小学数学教师的专业培训提出相应的建议。 围绕研究目标，本研究以分数主题为例拟解决如下三个主要子问题： 第一，如何构建小学数学教师MKT分析框架？ 第二，不同类型小学数学教师MKT及其各维度有什么特征和差异？ 第三，不同类型小学数学教师MKT各维度在教学实践中有怎样的表现？ 本研究采用量化研究和质性研究相结合的方式，结合问卷调查法、专家评定法、视频录像分析法、访谈法等研究方法，对小学数学教师MKT进行系统研究。具体包括四个子研究： 子研究一针对构建小学数学教师MKT分析框架展开研究。在第二章文献研究，尤其是鲍尔团队研究的基础上，初步建立小学数学教师MKT分析框架。该分析框架在构建过程中进行了三轮“专家评定+焦点小组讨论”，MKT二级维度内涵得到更清晰地刻画，三级指标上也做了较完备的划分。在此分析框架的指导下开发了用于量化研究和质性研究的工具，分别是小学数学教师MKT问卷、课堂教学中教师MKT表现水平分析框架。 子研究二试图回答不同类型小学数学教师MKT及其各维度的特征和差异。研究结合抽样目的性原则和便利性原则，从中国大陆东部沿海地区、中部平原地区、华北地区、西部地区四个不同区域中的直辖市、地级市、县、乡镇、农村随机抽取小学数学教师1051名，实施小学数学教师MKT问卷调查。采取SPSS软件将998份有效问卷从四类教师MKT及各维度上进行了特征分析和差异性分析。 子研究三探究了不同类型小学数学教师MKT各维度在教学实践中的表现。通过分层目的抽样，从量化研究对象中选择了代表四个类型的四位教师。通过子研究一中拟定的课堂教学中教师MKT表现水平分析框架，分别对这四位教师所执教的《分数的意义与性质》单元中关键的五个课时共20节课堂录像进行分析，探究了不同类型小学数学教师MKT各维度在教学实践中的表现。 子研究四探讨小学数学教师MKT特征与教学实践表现的关系。试将子研究二、三进行联系，将教师MKT特征与其教学实践表现进行一致性、差异性和关联性分析。 本研究主要得出以下六条结论： （1）本研究在鲍尔团队研究基础上构建了小学数学教师MKT分析框架，一级指标为SMK（学科知识）与PCK（学科教学知识），二级指标为CCK（一般内容知识）、SCK（专门内容知识）、HCK（眼界内容知识）、KCS（内容与学生的知识）、KCT（内容与教学的知识）以及KCC（内容与课程的知识），三级指标是在教师的行为层面上用“行为动词+内容”的形式刻画出了共44个行为指标。本分析框架对于量化分析或质性分析均具有参考性，且可操作性较强。 （2）四类教师在MKT整体得分上，从高到低的排列顺序为：专家教师、高级熟手、普通熟手、新手教师，且在SMK与PCK两大维度以及六个子维度的得分上具有显著差异。在CCK方面，新手教师得分显著低于其他三类教师；在HCK方面，专家教师得分显著优于其他三类教师。 （3）在MKT各子维度上，四类教师得分不均衡。新手教师的SCK与KCS最弱；普通熟手的CCK显著优于其他子维度；高级熟手与专家教师在CCK、SCK、KCS上具有显著优势。 （4）教学实践上，新手教师表现为CCK维度上缺乏准确性；普通熟手表现为能调用有限的SCK与KCS；高级熟手表现为能充分调用SCK与KCS；专家教师在KCC与HCK的运用上表现出独到的洞察力。 （5）教师MKT知识是教学实践的基础，然而教师在MKT某一子维度上的较高得分并不能保证其对应维度上好的教学实践表现，尤其对新手教师而言，将HCK转化到教学实践方面更难。 （6）MKT的两大维度（SMK与PCK）之间以及六个子维度之间均显著相关，且在SMK与PCK两个维度间，SCK与KCS起到中心关联作用。 最后，根据研究结论，本研究从如何利用小学数学教师MKT分析框架指导教学实践、不同类型教师MKT的培训、教师自我发展等方面提出了相应的建议。

Teachers' professional knowledge is the guarantee of teacher quality, and the research on teachers' professional knowledge is an important topic of education research. Mathematics teachers' knowledge focuses on teachers' professional knowledge in the mathematics discipline. The theory of Mathematical Knowledge for Teaching (MKT) is oriented in the United States since 2008, and has become popular in the field of mathematics teachers' knowledge research in recent years. A better understanding of the knowledge composition and its relationship with teacher professional development is the need to further promote and deepen the newly curriculum reform. However, researchers concern differently in different periods, which raise questions such as unclear connotation and extension of various components of MKT. As a practical knowledge, MKT should not only focus on the current characteristics of teachers' knowledge, but also on their practical performance. Therefore, the main goal of this study is to explore the characteristics of MKT of different types of primary school mathematics teachers and their teaching practice. Further, it discusses the relationship between MKT of primary school mathematics teachers and teaching practice, and puts forward corresponding suggestions for the professional training of different types of primary school mathematics teachers. This study aims at exploring the research questions as followed: Firstly, how to construct the MKT analysis framework for primary school mathematics teachers? Secondly, what are the characteristics and differences of MKT and its dimensions among different types of primary school mathematics teachers? Thirdly, how do different types of primary school mathematics teachers' MKT dimensions perform in teaching practice? In this study, a mixed research method was adapted, which combined quantitative analyse with qualitative analyse, along with questionnaire survey, expert evaluation, video and interview analysis. To answer research question 1, this study constructs a MKT analysis framework for primary school mathematics teachers. Based on the literature review in Chapter II, especially the research of Ball team, a first MKT analysis framework for primary school mathematics teachers was constructed. After three rounds of "expert evaluation+focus group discussion" were carried out, the connotation of MKT's dimensions was more clearly depicted and the tertiary indicators were more completely divided. With this analysis framework, quantitative survey tools and qualitative research tools are developed, namely the MKT questionnaire test tools for primary school mathematics teachers and the analysis framework for teachers' MKT performance level in classroom teaching. To answer research question 2, the characteristics and differences of MKT and its dimensions of different types of primary school mathematics teachers, considering the research purpose and research convenience, 1051 primary school mathematics teachers were randomly selected from four regions of Chinese Mainland, namely, municipalities directly under the central government, prefecture level cities, counties, towns and villages in the eastern coastal area, the central plain area, the North China area and the western area, and the MKT questionnaire test for primary school mathematics teachers was carried out. Using SPSS22 software, 998 valid questionnaires were analyzed from MKT and various dimensions for four types of teachers' characteristics and differences. To answer research question 3, explored the performance of various dimensions of MKT of different types of primary school mathematics teachers in teaching practice. The strategy of combining purposive random sampling with convenient sampling was adopted to conduct stratified purposive sampling. Four teachers were selected from the quantitative research objects, representing four types respectively. Through the proposed analysis framework of teachers' MKT performance level in classroom teaching, classroom video analysis was conducted on the five key class hours in the unit of the meaning and nature of scores of four teachers, and the performance characteristics of different types of teachers' MKT dimensions in classroom teaching practice were explored. Based on the anlaysis above, this study explored furtherly the relationship between MKT characteristics and teaching practice performance of primary school mathematics teachers,,and analyze the consistency, difference and correlation between teachers' MKT characteristics and their teaching practice. Six conclusions come below: （1）This research constructs the MKT analysis framework for primary school mathematics teachers based on Ball's research. The first level indicators are SCK and PCK, and the second level indicators are CCK, SCK, HCK, KCS, KCT, KCC. The third level indicators depict a total of 44 behavior indicators in the form of "behavior verb+content" at the level of teachers' behavior. This analysis framework is practical and inspired for quantitative analysis and qualitative analysis. （2）About the overall MKT scores of the four types of teachers, their performance order ranges from high to low as: expert teachers, senior proficient, ordinary proficient, novice teachers, and there are significant differences in the scores of SMK and PCK and six sub dimensions. The score of novice teachers in CCK is significantly lower than those of the other three types of teachers, and the score of expert teachers in HCK is significantly higher than those of the other three types of teachers. （3）About the sub dimensions of MKT, the scores of the four types of teachers are uneven. The novice teachers' SCK and KCS are the weakest, the ordinary proficient teachers' CCK is significantly better than other sub dimensions, and the advanced proficient teachers and expert teachers have significant advantages in CCK, SCK and KCS. （4）As for teaching practice, the novice teachers are week in accuracy in CCK dimension; The common skilled hand can call limited SCK and KCS; The advanced proficient can fully call SCK and KCS; The expert teachers showed unique insight in the application of KCC and HCK. （5）Teachers' MKT knowledge is the basis of teaching practice. However, teachers' higher scores on a certain sub dimension of MKT cannot guarantee their good teaching practice performance on the corresponding dimension. Especially for novice teachers, it is more difficult to transform HCK into teaching practice. （6）The two dimensions (SMK and PCK) and the six sub dimensions of MKT are significantly correlated with each other, and the SCK in SMK and KCS in PCK play a central role, with a high correlation between them. Finally, according to the research conclusion, this study also puts forward some corresponding suggestions on how to adapt the MKT analysis framework of primary school mathematics into guiding teaching practice, as well as teacher training for different types of teachers' MKT, and teachers' self professional development.