数学史融入高中数学课堂教学的研究——以等比数列的前n项和公式为例

A Study on the Integration of History of Mathematics into High School Mathematics Classroom Teaching—Taking the Formulation of the First n Terms of Isoperimetric Series as an Example

摘要: 为响应教育政策对数学文化融入教学的要求，解决学生在等比数列前项和公式学习中因推导抽象导致的认知困难，研究基于历史视角探索教学优化路径。通过设计国际象棋麦粒问题的经典情境引入课题，结合多元历史文化案例梳理错位相减法、掐头去尾法、因子提取法和等比定理法四种推导方法，构建“观察猜想–逻辑证明–实践应用”的教学框架。数学史融入显著提升了学生对公式本质的理解：通过复现数学家思维路径，抽象公式被具象化为可操作的探究过程，有效降低学习难度；同时，不同文明的数学方法对比分析拓宽了学生的文化视野，激发探究兴趣，促进数学抽象、逻辑推理等核心素养的发展。数学史与课堂教学的深度融合能够优化知识建构逻辑，增强学科文化认同，为核心素养导向的教学实践提供可行范式，具有推广价值。

Abstract: In order to respond to the requirements of the education policy on the integration of mathematical culture into teaching and to solve the cognitive difficulties caused by the abstraction of derivation in the learning of the formula for the sum of the first n terms of the isoperimetric series, the study explores the path of teaching optimization based on the historical perspective. By designing the classic situation of the chess grain problem to introduce the topic, combining with multiple historical and cultural cases to sort out the four methods of derivation, namely, the method of subtracting by mistake, the method of removing the end by pinching the head and the tail, the method of extracting the factors, and the method of the equiprobability theorem, and constructing the teaching method of “Observation and Conjecture - Logical Proof - Practical Application”. The teaching framework of “Observation and Conjecture - Logical Proof - Practical Application” is constructed. The integration of the history of mathematics significantly improves students’ understanding of the essence of formulas: by reproducing mathematicians’ thinking paths, abstract formulas are visualized as operable inquiry processes, effectively reducing the difficulty of learning; at the same time, the comparative analysis of mathematical methods of different civilizations broadens students’ cultural horizons, stimulates their interest in inquiry, and promotes the development of core literacy skills, such as mathematical abstraction and logical reasoning. The in-depth integration of the history of mathematics and classroom teaching can optimize the logic of knowledge construction, enhance the cultural identity of the discipline, provide a feasible paradigm for core literacy-oriented teaching practice, and have the value of promotion.