基于HPM的数学建模思想融入高中数学的教学设计——以等差数列的前n项和公式为例

The Mathematical Modeling Idea Based on HPM Is Integrated into the Teaching Design of High School Mathematics—Taking the First n Terms and Formulas of Arithmetic Series as an Example

摘要: 数学知识的学习过程是学生在已有基础上主动建构的过程。数学史与数学文化有效融入数学知识的学习有助于学生更好地经历数学知识层层深化的过程，感受到深厚的数学文化。同时，通过还原数学家解决问题过程为主线的情境，有助于提升学生的问题解决与创新能力。本节课精心选取我国古代杨辉良马图的数学史，通过设计问题串，促使学生主动发现问题、提出问题、分析问题和解决问题。

Abstract: The learning process of mathematical knowledge is a process that students actively construct on the existing basis. The effective integration of mathematical history and mathematical culture into the study of mathematical knowledge helps students to better experience the deepening process of mathematical knowledge and feel the profound mathematical culture. At the same time, it is helpful to improve students’ problem-solving and innovation ability by restoring the situation in which mathematicians solve problems. This lesson carefully selects the mathematical history of ancient Yang Huiliang Horse Map in our country, and encourages students to actively discover, propose, analyze and solve problems by designing problem strings.