初中数学教学中数形结合策略研究 -数学与应用数学专业

摘要

本研究聚焦于初中数学教学中数形结合策略的应用与优化，旨在探索提升学生数学思维能力和问题解决能力的有效途径。随着新课程改革的深入推进，数形结合作为重要的数学思想方法，在培养学生直观想象和逻辑推理能力方面具有独特优势。研究采用行动研究法、课堂观察法和问卷调查法，选取某市三所初级中学的12个班级作为研究对象，开展为期一学期的教学实验。通过对比实验组与对照组的学习效果，发现运用数形结合策略的实验组学生在几何证明、函数图像理解等核心知识点的掌握程度上显著优于传统教学组，其数学学习兴趣和自信心也得到明显提升。研究创新性地构建了“概念引入－图形表征－抽象概括－应用迁移”的四步教学模式，并开发了配套的教学案例库和评价指标体系。结果表明，有效的数形结合策略能够促进学生对数学概念的深度理解，提高问题解决的灵活性和创造性。本研究为初中数学教师提供了可操作的教学策略和方法指导，对推动数学课堂教学改革具有重要的实践意义。

关键词：数形结合；初中数学教学；数学思维能力；教学模式

Research on the combination of number and form in junior middle school mathematics teaching

Abstract

This study focuses on the application and optimization of the combination of number and form strategies in junior middle school mathematics teaching, aiming to explore the effective way to improve students' mathematical thinking ability and problem-solving ability. With the deepening of the new curriculum reform, the combination of number and form, as an important mathematical thought method, has a unique advantage in cultivating students' intuitive imagination and logical reasoning ability. This study adopted the method of action research, classroom observation and questionnaire survey, and selected 12 classes of three junior middle schools in a city as the research ob jects to carry out a one-semester teaching experiment. By comparing the learning effect of the experimental group and the control group, it is found that the students in the experimental group who use the combination of number and form strategy are significantly better than the traditional teaching group in mastering core knowledge points such as geometric proof and function image understanding, and their interest and self-confidence in mathematics learning are also significantly improved. The four-step teaching model of "concept introduction - graphic representation - abstract generalization - application transfer" is innovatively constructed, and the supporting teaching case base and evaluation index system are developed. The results show that the effective combination of number and form can promote the students' deep understanding of mathematical concepts and improve the flexibility and creativity of problem solving.

Keywords: Combination of number and form; Junior middle school mathematics teaching; Mathematical thinking ability; Teaching mode

摘要 I

Abstract II

目录 III

1 绪论 1

1.1 研究背景与意义 1

1.2 数形结合教学研究现状分析 1

2 初中数学数形结合的理论基础 3

2.1 数形结合的概念内涵解析 3

2.2 数形结合的认知心理学基础 4

2.3 数形结合的教学价值分析 4

3 初中数学数形结合教学现状调查 6