高中数学结构不良问题的分层教学与指导策略研究

Research on Stratified Teaching and Guidance Strategies for Ill-Structured Problems in High School Mathematics

摘要: 随着课程改革推进，结构不良问题逐渐成为高中数学考查的重点。这类问题条件开放、解法多样，对传统统一教学模式构成挑战，易导致学生思路固化与探究能力不足。本文以建构主义学习理论、最近发展区理论、分层教学理论以及结构不良问题解决的心理机制研究为支撑，分析此类问题的特点，结合高考真题，提出并阐释分层教学的实践策略，并通过教学案例设计验证策略的实践价值，旨在为高中数学教师开展结构不良问题教学提供可操作的参考方案，助力学生数学核心素养的全面发展。

Abstract: With the advancement of curriculum reform, ill-structured problems have gradually become a key focus in high school mathematics examinations. These problems feature open conditions and diverse solutions, posing a challenge to the traditional uniform teaching model and often leading to students’ fixed thinking patterns and insufficient exploration abilities. This paper, supported by constructivist learning theory, the zone of proximal development theory, stratified teaching theory, and research on the psychological mechanisms of solving ill-structured problems, analyzes the characteristics of such problems, combines real college entrance examination questions, proposes and explains practical strategies for stratified teaching, and validates the practical value of these strategies through the design of teaching cases. The aim is to provide high school mathematics teachers with an operational reference plan for teaching ill-structured problems and to promote the comprehensive development of students’ core mathematical literacy.