数学是高中教育体系中的重要内容，具有高度抽象性、逻辑严密性、应用广泛性的特点，能够培养学生的理性思维、科学精神，能够促进学生的智力发展。初高中数学难度跨度大是导致学生在数学学科产生差异的重要原因之一，传统的班级授课制缺乏选择性，无法满足不同潜质学生发展的需要，而分层走班教学赋予学生选择权，能够满足学生的差异化需求，同时在新高考改革政策的推动下，数学学科实施分层走班教学已经成为普遍现象。然而数学学科实施分层教学的效果如何、其效果的具体观测维度有哪些、产生效果的原因是什么以及如何提升数学分层教学效果等问题仍需要研究，即数学分层走班教学效果的观测框架、效果及其成因有待深入研究。
首先，本研究通过问卷调查、访谈、观察与实物分析的方法，呈现了案例学校高中学数学分层走班教学的实施过程，探究了该校数学分层走班教学的效果及其成因，包括“案例学校是如何实施数学分层走班教学的”、“该校数学分层走班教学产生了哪些效果”以及“为什么会产生这样的效果”。
其次，为了深入剖析分层走斑的效果及其成因，研究者构建了包含学业方面和非学业方面共七个观测维度的效果观测框架，对该校的数学分层走班教学效果进行分析，发现既有积极的效果，也有消极的效果：①学生成绩整体有所提升，高分段的学生人数明显增多：②分层走班对于P层(Professional) 、A层(Advanced)学生的数学自我概念有积极影响：③大部分学生数学学动机增强：④分层走班教学普遍使学生数学学习压力和考试焦虑程度增大：⑤学生人际交往范围普遍扩大：⑥实施分层走班以后，大部分学生的班级归属感削弱：⑦八成左右的学生对于数学分层走班教学持满意或较满意的态度。
然后，研究者运用多元智能理论、最近发展区理论和社会比较理论分别剖析了案例学校产生积极效果的原因：①差异化的分层课程设置及更有针对性的教学：②灵活的层级调整机制：③PAR的命名避免了标签效应； ④案例学校重视优质教师队伍的培养与家长学校的构建：同时，产生消极效果的原因主要源自于分层走班赋予的“流动性”，学生与教师之间的沟通稍有减少，使学生班级归属感削弱，教师期望会影响R层学生的自我概念，层级内或层级间的比较会引发学生焦虑。
最后，总结案例学校优秀经验包括：培优补弱同发展，因材施教是根本，层级调整需合理，家长学校是关键；针对案例学校的不足提出相应的优化建议包括：教师要关注每个学生，要引导学生正确归因，构建积极的教师期望，注重班级凝聚力的建设。

Mathematics is an important part of high school education system, which has the characteristics of high abstraction, logical strictness and wide application. It can cultivate students' rational thinking, scientific spirit and promote students' intellectual development. The large span of mathematics difficulty in junior high school and senior high school is one of the important reasons for students' differences in mathematics. The traditional class teaching system is lack of selectivity, which can not meet the needs of students with different potentials. The stratified class teaching gives students the right to choose, which can meet the differentiated needs of students, It has become a common phenomenon to implement stratified class teaching in mathematics.However, there are still some problems to be studied, such as the effect of stratified teaching, the specific observation dimensions of the effect, the reasons for the effect, and how to improve the effect of stratified teaching. That is to say, the observation framework, effect and its causes of the effect of stratified teaching need to be further studied.
First of all, through the methods of questionnaire survey, interview, observation and physical analysis, this study presents the implementation process of the multi-level instruction between class of high school mathematics in case school, and explores the effect and causes of the stratified class teaching of high school mathematics in this school, including "how to implement the multi-level instruction between class of high school mathematics in case school" "What are the effects of multi-level instruction between class " and "why do they have such effects".
Secondly, in order to deeply analyze the effect and causes of multi-level instruction between class, the researchers constructed an effect observation framework including seven observation dimensions of academic and non-academic aspects, and analyzed the teaching effect of multi-level instruction between class in this school. The results show that there are both positive and negative effects: ① the overall performance of students
has been improved, and the number of students in high section has increased significantly; ② Multi-level instruction between class has a positive effect on the mathematics self-concept of P-Level (Professional) and A-level (Advanced) students; ③ Most of the students' mathematics learning motivation is enhanced; ④ Multi-level instruction between class generally increases students' mathematics learning pressure and test anxiety; ⑤ The scope of students' interpersonal communication is generally expanded; ⑥ Most students' sense of belonging to the class is weakened; ⑦ About 80% of the students are satisfied with the stratified teaching of mathematics.
Then, using the theory of multiple intelligences, the theory of zone of proximal development and the theory of social comparison, the researcher analyzes the reasons for the positive effect of the case school: ① differentiated hierarchical curriculum and more targeted teaching; ② Flexible hierarchical adjustment mechanism; ③ The naming of par avoids the label effect; ④ Case schools attach importance to the cultivation of high-quality teachers and the construction of parent schools; At the same time, the reasons for the negative effect mainly come from the "mobility" given by multi-level instruction between Class. The communication between students and teachers is slightly reduced, which weakens students' sense of class belonging. Teachers' expectations will affect the self-concept of R-level students, and the comparison within or between levels will lead to students' anxiety.
Finally, it summarizes the excellent experience of the case school, including: training the excellent, supplementing the weak, developing together, teaching students in accordance with their aptitude is fundamental, level adjustment needs to be reasonable, and parent school is the key; In view of the shortcomings of the case school, this paper puts forward corresponding optimization suggestions, including: teachers should pay attention to each student, guide students to correctly attribute, build positive teacher expectations, and pay attention to the construction of class cohesion.