Application of Polya’s “How to Solve Problems” in junior high school mathematics problem solving teaching —— Take the 17th question of Jiangxi Middle School Mathematics paper in 2024 as an example
波利亚“怎样解题表”在初中数学解题教学中的应用——以2024年江西中考数学卷第17题为例

摘要

数学教育家乔治·波利亚提出的“怎样解题表”作为系统化解题方法论，为揭示数学思维规律提供了重要理论框架。本研究基于波利亚解题理论，选取2024年江西中考数学试卷第17题为研究对象，通过课堂观察与案例分析相结合的研究方法，系统呈现“理解问题-拟定计划-执行计划-检验反思”四阶段理论在中考试题解答中的具体实践路径。研究发现，解题表通过可视化思维过程能有效提升学生的问题表征能力与策略选择意识，但在迁移应用环节仍存在元认知监控不足等问题。通过还原解题过程中的思维路径与偏差分析，本研究提出教学改进建议，教师应注重解题过程的显性化指导，通过搭建“问题脚手架”发展学生自我提问能力，进而促进数学核心素养的培育。研究结果为初中数学解题教学提供了可操作的理论实践范式，对发展学生系统性思维品质具有现实指导意义。

Abstract

The “how to solve the problem table” proposed by mathematics educator George Polya, as a systematic solution methodology, provides an important theoretical framework for revealing the law of mathematical thinking. Based on the Polya problem-solving theory, this study takes the 17th question of the 2024 Jiangxi High School Entrance Examination mathematics paper as the research object. Through the research method combining classroom observation and case analysis, this study systematically presents the specific practical path of the four-stage theory of “understanding the problem-making a plan-executing the plan-checking and reflecting” in the solution of the high school entrance examination questions. The study found that the problem-solving table could effectively improve students’ problem representation ability and strategy selection awareness by visualizing the thinking process, but there were still some problems such as insufficient metacognitive monitoring in the transfer application. By analyzing the thinking path and deviation in the process of problem solving, this study puts forward suggestions for teaching improvement. Teachers should pay attention to the explicit guidance of the problem solving process, develop students’ self-questioning ability through the construction of “problem scaffolding”, and then promote the cultivation of core mathematical literacy. The research results provide an operational theoretical practice paradigm for the teaching of junior high school mathematics problem solving, and have practical guiding significance for the development of students’ systematic thinking quality.