矩阵变换思想在高中圆与椭圆教学中的应用

The Application of Matrix Transformation Concepts in the Teaching of Circles and Ellipses in High School

摘要: 新课标对高中数学核心素养培育提出明确要求，本文系统探析2 × 2坐标变换矩阵与向量加法支撑下的矩阵变换思想，在高中圆与椭圆教学中的核心应用价值，依托教学目标、教学内容、教学过程、教学评价四维逻辑，构建系统化教学体系，对“核心素养”“结构化教学”核心概念进行可操作化界定，构建概念生成、思想迁移、素养落地三大实施策略，为高中解析几何结构化教学提供可落地、可推广的实践范式，推动学生数学核心素养的系统化发展。

Abstract: The new curriculum standards set clear requirements for cultivating core competencies in high school mathematics. This paper systematically explores the core value of matrix transformation concepts—supported by 2 × 2 coordinate transformation matrices and vector addition—in the teaching of circles and ellipses in high school. Following the four-dimensional logic of teaching objectives, teaching content, teaching process and teaching evaluation, it restructures the teaching system, operationalizes the definitions of “core competencies” and “structuring”, and proposes three major instructional implementation strategies: concept formation, conceptual transfer, and competence cultivation. It aims to provide a practical model for structured teaching in high school mathematics and promote the systematic development of students’ core mathematical competencies.