Mathematics Teaching Case Based on Constructivist Theory—Taking “Ellipse” as an Example

文章以“椭圆及其标准方程”教学为例，基于建构主义理论开展跨学科教学。圆锥曲线是高中数学重难点，椭圆传统教学中学生学习被动、难理解定义。文章阐释相关理论概念，梳理研究现状，明确价值。经教学分析确定重难点、学情及目标，将开普勒第一定律融入椭圆教学。通过情境唤起、操作探究、数形推导、应用巩固、总结提升、课后练习等步骤，提升学生课堂参与度，助力物理概念向数学定义转化，培养跨学科思维，为圆锥曲线后续教学及高中数学教学提供新思路。The article takes “ellipse and its standard equation” teaching as an example of interdisciplinary teaching based on constructivist theory. Conic curve is a difficult point in high school mathematics, and the traditional teaching of ellipse is passive and difficult for students to learn and understand the definition. The article explains the relevant theoretical concepts, sorts out the current state of research, and clarifies the value. After analyzing the teaching to determine the key points, learning conditions and objectives, Kepler’s first law is integrated into the teaching of ellipses. Through the steps of contextual arousal, operational exploration, numerical and morphological derivation, application and consolidation, summarization and enhancement, and post-course practice, the article enhances students’ participation in the classroom, facilitates the transformation of physical concepts into mathematical definitions, cultivates interdisciplinary thinking, and provides new ideas for the subsequent teaching of conic curves and the teaching of mathematics in high schools.