基于HPM视角的一次函数教学案例研究

A Case Study of Linear Function Teaching from the Perspective of HPM

摘要: 一次函数是初中数学中学生由“常量”向“变量”过渡的重要内容，也是后续函数学习的重要基础。然而当前教学存在方式单一、学生理解困难、文化渗透不足等问题。基于此，本文从数学史与数学教育融合(History and Pedagogy of Mathematics，简称HPM)的视角出发，在建构主义学习理论和历史发生原理的指导下，对一次函数概念教学进行教学设计研究。通过梳理一次函数从古代比例思想到近代函数概念形成的发展脉络，提炼适合课堂教学的历史素材，并结合初中生认知特点，设计包含情境引入、历史再现、概念抽象和应用巩固等环节的一次函数教学案例。研究认为，在一次函数教学中合理融入数学史，有助于呈现数学知识的形成过程，促进学生对概念本质的理解，同时在教学中渗透数学文化，提升学生的学习兴趣与数学核心素养。

Abstract: Linear function is a key topic in junior high school mathematics that helps students transition from “constant quantities” to “variables”, and also lays an important foundation for subsequent function learning. However, current teaching suffers from problems such as monotonous methods, difficulties in students’ understanding, and insufficient integration of cultural elements. Against this background, this paper conducts a teaching design study on the concept of linear function from the perspective of the integration of the History and Pedagogy of Mathematics (HPM), guided by constructivist learning theory and the genetic principle of history. By sorting out the development of linear function from the ancient idea of proportion to the formation of the modern function concept, this study extracts historical materials suitable for classroom teaching. Combined with the cognitive characteristics of junior high school students, a teaching case of linear function is designed, including situational introduction, historical representation, concept abstraction, application and consolidation. The study concludes that appropriately integrating the history of mathematics into linear function teaching helps to present the formation process of mathematical knowledge, promote students’ understanding of the essence of concepts, infiltrate mathematical culture into teaching, and enhance students’ learning interest and core mathematical literacy.