基于数学联结力的高中数学教学法探究——以“圆锥曲线”教学为例

Exploration of High School Mathematics Teaching Method Based on Mathematical Connectivity—Taking the Teaching of “Conic Sections” as an Example

摘要: 数学联结力是衡量学生数学核心素养的重要隐性指标，对培养学生知识迁移与复杂问题解决能力具有重要意义。本文在介绍数学联结力内涵基础上，阐释了数学联结力关于知识联结紧密性、表征方式多样性、方法应用创新性的核心特征；结合高中数学教学实际，提出知识系统化、思维可迁移、应用层次化的教学应用原则；以高中圆锥曲线教学为例，构建概念联结、方法迁移、创新应用、思想升华四阶段教学策略，形成培养学生数学联结力的完整教学框架。帮助学生构建结构化知识体系，促进学生数学综合能力与创新思维发展。实现从“解题”到“悟理”的认知跃迁。

Abstract: Mathematical connectivity is an important implicit indicator for measuring students’ core mathematical literacy and plays a significant role in fostering their ability to transfer knowledge and solve complex problems. Based on an introduction to the concept of mathematical connectivity, this paper elaborates on its core features, including the tightness of knowledge connection, the diversity of representation methods, and the innovativeness of method application. In light of the actual situation of high school mathematics teaching, the paper proposes the teaching application principles of systematizing knowledge, making thinking transferable, and stratifying application. Taking the teaching of conic sections in high school as an example, a four-stage teaching strategy of concept connection, method transfer, innovative application, and ideological elevation is constructed, forming a complete teaching framework for cultivating students’ mathematical connectivity. This helps students build a structured knowledge system and promotes the development of their comprehensive mathematical abilities and innovative thinking, achieving a cognitive leap from “problem-solving” to “understanding principles”.