基于跨学科视角的二项式定理教学设计与实践探究

Research on the Teaching Design and Practice of the Binomial Theorem Based on an Interdisciplinary Perspective

摘要: 二项式定理作为高中数学计数原理模块的核心内容，是多项式乘法的延伸与计数原理的重要应用，同时为后续二项分布的学习奠定基础，在高中数学知识体系中起到承上启下的关键作用。下文以人教A版(2019)选择性必修第三册《二项式定理》第一课时为研究对象，立足《普通高中数学课程标准(2017年版2020年修订)》要求，结合高二学生的认知特点，从跨学科教学视角出发，对二项式定理的教学设计进行系统探究。通过融合语文、历史、德育等多学科元素，采用“情境创设–探究发现–归纳证明–应用拓展”的教学路径，突破二项式系数推导的教学难点，渗透数学抽象、逻辑推理、数学建模等核心素养，实现数学学科能力与学生综合素养的协同提升。同时，对教学过程中的核心问题进行反思与优化，为高中数学定理类课程的跨学科教学提供实践参考。

Abstract: As a core content of the counting principle module in high school mathematics, the binomial theorem is an extension of polynomial multiplication and an important application of the counting principle. It also lays the foundation for the subsequent study of the binomial distribution, playing a crucial role in connecting and advancing the knowledge system of high school mathematics. This paper takes the first class of “Binomial Theorem” in the third volume of the elective series of the People’s Education Edition A (2019) as the research object. Based on the requirements of the “General Senior High School Mathematics Curriculum Standards (2017 Edition, 2020 Revision)”, and in combination with the cognitive characteristics of high school sophomores, it systematically explores the teaching design of the binomial theorem from the perspective of interdisciplinary teaching. By integrating elements from multiple disciplines such as Chinese, history, and moral education, and adopting a teaching approach of “situation creation-exploration and discovery-induction and proof-application and extension”, it breaks through the teaching difficulty of deriving binomial coefficients, and permeates core qualities such as mathematical abstraction, logical reasoning, and mathematical modeling, achieving a coordinated improvement in students’ mathematical discipline abilities and comprehensive qualities. At the same time, it reflects on and optimizes the core issues in the teaching process, providing practical references for the interdisciplinary teaching of theorem-based courses in high school mathematics.