变式教学最早来源于前苏联心理学界关于几何教学的争论，后受到我国心理学研究者 的关注，便逐步引入应用于课堂教学，在教学实践中得到推广。在上世纪 70、80 年代， 顾泠沅等人基于实践探索，对变式教学进行了系统概括，形成了变式教学理论。 变式教学指在课堂教学中，教师给学生提供不同形式的直观资料或者事例以说明事物 的本质属性，或是在不同维度变化同类事物的非本质特征以突出事物的本质特征的教学。 在数学课堂中，教师合理的运用变式教学，能够帮助学生由表及里，深度学习，架构有意 义的教学。但是目前国内对变式教学的关注更多聚焦在理论研究，包括变式问题与变式训 练的探讨、变式素材的运用等等，而结合课例研究，从变式教学理论的视角看待一节课的 研究并不多。 针对这个问题，本研究在查阅和学习变式教学与变异教学理论文献的基础上，以过程 性变式的三个环节和四种变异范式为主要框架，采用案例分析法，选取四位特级教师的五 节三年级《分数的初步认识》课例，对其教学过程进行了课例分析。同时，对三位来自不 同地区、有着不同教龄、但都有三年级执教经验的一线教师就其在《分数的初步认识》教 学中如何开展变式教学进行了访谈与分析。 通过研究发现，在教授《分数的初步认识》的教学过程中，四位优秀教师都非常灵活 而且巧妙的使用了变式教学。虽然执教的课题一样，教学步骤也相似，但在过程性变式的 三个环节中又各有特色，帮助学生由浅入深，逐步认识、理解、掌握分数的概念。研究还 发现对比范式多用于概念形成环节、类合和分离范式多用于概念形成阶段、融合范式多用 于概念深化阶段。 基于课例分析和访谈，本研究提出了如下建议。第一，要关注教学中的过程性变式， 让学生体验学习的过程；第二，在变式教学中，变式的数量要适度、变式的难度要有梯度、 变式要提高学生的参与度；第三，在变式教学中，重视反例的使用；第四，小学数学教师 要有自己的教育观，从整个数学知识的框架和系统看待在有限的一节课上“教什么”，才 能更好的应用好变式教学。

The variant teaching originated from the controversy about geometry teaching in the psychology of the former Soviet Union. After being concerned by psychologists in China， it was gradually introduced into classroom teaching and promoted in teaching practice. In the 1970s and 1980s， Gu Yu and others based on practical exploration， systematically summarized the variant teaching，and formed the theory of variant teaching. Variant teaching means that in the classroom teaching， the teacher provides students with different forms of visual materials or examples to illustrate the essential attributes of things， or to change the non-essential features of similar things in different dimensions to highlight the essential characteristics of things. In the mathematics classroom， the teacher's reasonable use of variant teaching can help students to learn from the table and the depth， and to construct meaningful teaching. However，at present，the focus on variant teaching in China is more focused on theoretical research，including the discussion of variant problems and variant training， the use of variant materials，etc， combined with the case study， from the perspective of the theory of variant teaching. There are not many studies on class. In response to this problem，based on the literature review and learning of the variant teaching and mutation teaching theory， this study takes the three links of the process variant and the four variant paradigms as the main framework， and uses the case analysis method to select four special teachers. The five-third grade "Preliminary Understanding of Scores" is a case study of the teaching process. At the same time， three front-line teachers from different regions who have different teaching ages but all have three years of teaching experience interviewed and 3 analyzed how to carry out the variant teaching in the teaching of "Preliminary Understanding of Scores". Through research，it is found that in the teaching process of the "Preliminary Understanding of Scores"， four excellent teachers are very flexible and clever use of variant teaching. Although the teaching tasks are the same，the teaching steps are similar，but they have their own characteristics in the three links of the process variants，helping students to understand， understand and master the concept of scores from the shallower to the deeper. The study also found that the comparative paradigm is mostly used in the concept formation，the combination and separation paradigm is mostly used in the concept formation stage，and the fusion paradigm is mostly used in the concept deepening stage. Based on the case analysis and interviews ， this study proposes the following recommendations. First，we must pay attention to the procedural variants in teaching，let students experience the process of learning. Second，in the variant teaching， the number of variants should be moderate， the difficulty of the variant should be gradient，and the variant should improve the students. Participation; third，in the variant teaching，pay attention to the use of counterexamples; fourth， primary school mathematics teachers must have their own educational concept，and view the "teaching" in a limited class from the framework and system of the entire mathematical knowledge. In order to better apply the variant teaching.