本研究以高中“随机变量及其分布”的教学内容为例，探索如何运用高观点的知识指导该部分的教学。研究由以下三方面展开：
      一是调查随机变量及其分布的教学现状，以广州市某高中为例，一方面从教师自身的知识储备、当前存在的教学问题、教师的教学方式三个角度对一线在职高中数学教师实施访谈，另一方面是通过问卷调查学生对随机变量及其分布的学习情况。研究结论表明：教师们对概念的理解基本停留于中学教材的深度，他们未能从高等数学视角去解释某些概念背后更深层的逻辑联系；大部分学生表现出对概念似懂非懂的学习特点，导致其解题时容易以偏概全。
      二是基于高观点，深入分析2020年高中数学人教A版选择性必修第三册中关于“随机变量及其分布”的内容，按照“随机变量的定义——离散型随机变量的分布列——离散型随机变量的数字特征——二项分布——超几何分布——正态分布”的顺序开展了对核心概念的理论基础研究。研究结论表明：从定义表述上看，该版教材的定义更接近于高等数学中的一般定义。另外，本研究对部分例子的情境创设提出了高观点的思考，对相关性质的结论给出了一般的证明，并深入剖析了部分例习题体现的高观点背景。
      三是结合教学现状的结果和教材分析的理论基础，本研究选取了《离散型随机变量的概念》和《二项分布与超几何分布的区别》这两个课例进行教学设计。相较于已有的教学设计，本研究创设了学生主体、教师引导的问题探究课堂，通过问题的设置由具体到一般地推动了抽象概念的生成，并根据教学内容的需要融入了信息技术的使用，同时有梯度地设计了例习题。
      基于上述三方面的研究结论，本文提出的教学建议有两点：（1）夯实专业知识，辩证看待教材；（2）巧用信息技术，化抽象为具象。

      This study takes the teaching content of "random variables and their distribution" in high school as an example, and explores how to use the knowledge of advanced mathematics to guide the teaching. The research is carried out in the following three aspects:
      The first is to investigate the teaching status of "random variables and their distribution". Taking a high school in Guangzhou as an example, on the one hand, interviews are conducted with front-line in-service high school mathematics teachers from three perspectives: teachers' own knowledge reserves, current teaching problems, and teachers' teaching methods. On the other hand, students' learning about random variables and their distributions is investigated through questionnaires. The conclusion of the study shows that: teachers' understanding of concepts basically stays at the depth of middle school textbooks, and they fail to explain the deeper logical connections behind certain concepts from the perspective of advanced mathematics; most of the students show the characteristics of learning but not understanding the concepts, which makes them easy to take a part for the whole when solving problems.
      Secondly, based on the higher mathematics viewpoint, a theoretical study on the core concepts in "random variables and their distributions" of PEP Senior Math for China (2020 version) (optional required module Three) was carried out in the order of "definition of random variables - distribution series of discrete random variables - numerical characteristics of discrete random variables - binomial distribution - hypergeometric distribution - normal distribution". The research conclusion shows that: from the definition expression, the definition of this edition of the textbook is closer to the general definition in advanced mathematics. In addition, this study puts forward the thinking of advanced mathematics viewpoints on the situation creation of some examples, gives general proofs for the conclusions of related properties, and deeply analyzes the background of advanced mathematics viewpoints reflected in some exercises.
      Thirdly, combining the results of the current teaching situation and the theoretical basis of the textbook analysis, this study selects two examples of "The Concept of Discrete Random Variables" and "The Difference Between Binomial Distribution and Hypergeometric Distribution" for teaching design. Compared with the existing teaching design, this study created a student-centered, teacher-led problem inquiry classroom, promoted the generation of abstract concepts from concrete to general through problem setting, integrated the use of information technology according to the needs of teaching contents, and designed example exercises with a difficulty gradient.
      Based on the research conclusions of the above three aspects, there are two teaching suggestions: (1) consolidate professional knowledge and treat textbooks dialectically; (2) use information technology skillfully to turn abstract into concrete.