分层教学视域下高中数学学困生解题思维障碍转化策略研究

Research on Transformation Strategies of Problem Solving Thinking Barriers for Senior High School Students with Learning Difficulties from the Perspective of Layered Teaching

摘要: 新高考改革背景下，高中数学知识的抽象性、逻辑性显著增强，班级学生数学基础与思维能力分化日趋明显，学困生解题思维障碍问题突出。传统统一化教学忽视学生认知差异，造成学困生出现审题信息提取困难、知识概念理解碎片化、逻辑建模能力不足、解题畏难心理等多重困境。本研究以最近发展区理论、差异化教学理论、认知负荷理论为基础，结合认知灵活性、认知诊断相关研究成果，梳理高中数学学困生四类典型解题思维障碍，将思维障碍与学科教学知识(PCK)相结合，构建课前学情诊断、课堂阶梯探究、课后梯度训练、分层发展性评价四维一体化分层教学干预路径，并以导数求函数单调区间为课例开展教学分析。研究表明，分层精准干预能够搭建思维支架，降低学困生认知负荷，修复断裂的解题思维链条，改善学困生数学学习状态。本研究属于案例实践研究，后续可借鉴准实验范式、认知诊断工具进一步检验策略实践效果，为高中数学差异化育人提供实操参考。

Abstract: Under the background of the new college entrance examination reform, the abstraction and logic of high school mathematics knowledge have significantly increased, and the differentiation of students’ mathematical foundation and thinking ability within the class has become increasingly obvious. The problem of students with learning difficulties in solving problems has become particularly prominent. Traditional uniform teaching ignores students’ cognitive differences, resulting in multiple difficulties for students with learning difficulties, such as difficulty in extracting information from the problem statement, fragmented understanding of knowledge concepts, insufficient logical modeling ability, and fear of solving problems. This study is based on the theory of the zone of proximal development, the theory of differentiated teaching, and the theory of cognitive load, combined with relevant research results on cognitive flexibility and cognitive diagnosis. It sorts out four typical types of thinking obstacles for students with learning difficulties in high school mathematics, combines the thinking obstacles with subject teaching content knowledge (PCK), and constructs a four-dimensional integrated stratified teaching intervention path of pre-class learning situation diagnosis, classroom step-by-step exploration, post-class gradient training, and stratified developmental evaluation. And it conducts teaching analysis using the example of finding the monotonic intervals of a function. The research shows that stratified and precise intervention can build thinking scaffolds, reduce the cognitive load of students with learning difficulties, repair the broken thinking chain for solving problems, and improve the learning state of students with learning difficulties in mathematics. This research belongs to a case practice study. In the future, it can draw on quasi-experimental paradigms and cognitive diagnosis tools to further test the practical effect of the strategy, providing practical reference for differentiated education in high school mathematics.