小学数学问题解决中图示策略的培养与应用研究

Research on the Cultivation and Application of Graphical Strategies in Solving Primary School Mathematics Problems

摘要: 义务教育数学课程标准(2022年版)将“问题解决”作为数学核心素养的重要组成部分，强调培养学生运用直观手段分析和解决问题的能力。图示策略作为连接具体形象思维与抽象逻辑思维的关键中介，是提升小学生数学问题解决能力的核心工具。本研究采用文献研究法、问卷调查法、访谈法、课堂观察法及动态追踪法，对吉林省4所不同类型小学的23名数学教师和92名3~5年级学生展开调研，系统诊断当前小学数学图示策略教学与应用的现状。研究发现，当前教学存在教师教学碎片化、学段衔接断层、学生应用被动化及城乡资源差异显著等核心问题。基于皮亚杰认知发展理论及本土化教学实践，本研究构建了“认知唤醒–方法掌握–实践应用–创新优化”四阶段层级递进的图示策略培养模型，并设计了分学段、分题型、分区域的差异化应用路径。教学实验结果表明，该模型能有效提升学生主动运用图示的意识，使中年级学生应用题解题正确率提升26.7%，为小学数学问题解决教学提供了可复制的实践框架。

Abstract: The Mathematics Curriculum Standards for Compulsory Education (2022 Edition) regards “problem-solving” as an important component of core mathematical literacy, emphasizing the cultivation of students’ ability to analyze and solve problems using intuitive means. Graphical strategies, as a key intermediary connecting concrete image thinking and abstract logical thinking, are core tools for enhancing primary school students’ mathematical problem-solving ability. This study adopted literature review, questionnaire survey, interview, classroom observation and dynamic tracking methods to investigate 23 mathematics teachers and 92 students from Grades 3 to 5 in 4 different types of primary schools in Jilin Province, and systematically diagnosed the current situation of graphical strategy teaching and application in primary school mathematics. The research finds that current teaching has core problems such as fragmented teaching by teachers, disconnection between learning stages, passive application by students, and significant urban-rural resource differences. Based on Piaget’s cognitive development theory and localized teaching practice, this study constructed a four-stage hierarchical progressive graphical strategy cultivation model of “cognitive awakening-method mastery-practical application-innovative optimization”, and designed differentiated application paths by learning stage, question type and region. The teaching experiment results show that the model can effectively enhance students’ awareness of actively using diagrams, and increase the accuracy rate of application problem solving for middle-grade students by 26.7 percentage points, providing a replicable practical framework for primary school mathematics problem-solving teaching.