摘 要
数形结合作为一种重要的数学思想方法，在高中数学教学中具有广泛的应用价值。随着新课程标准的实施，数学教学更加注重培养学生的直观思维和空间想象能力，数形结合成为提升学生数学素养的有效途径。本研究旨在探讨数形结合在高中数学教学中的具体应用策略及其对学生学习效果的影响。通过文献分析、教学实验和问卷调查等方法，研究发现数形结合能够显著提高学生的解题效率和理解深度，尤其是在几何与代数知识的融合应用中表现尤为突出。研究结果表明，教师在教学中合理运用图形辅助、动态演示等手段，能够有效促进学生对抽象概念的理解，增强其问题解决能力。
关键词：数形结合；高中数学教学；直观思维
Abstract
As an important mathematical thought method, the combination of numbers and shapes has wide application value in high school mathematics teaching. With the implementation of the new curriculum standard, mathematics teaching pays more attention to the cultivation of students 'intuitive thinking and spatial imagination ability, and the combination of numbers and shapes has become an effective way to improve students' mathematical literacy. The purpose of this study is to investigate the specific application strategy of number-shape combination in high school mathematics teaching and its influence on students' learning effect. Through literature analysis, teaching experiment and questionnaire survey, it is found that the combination of numbers and shapes can significantly improve students' problem solving efficiency and depth of understanding, especially in the fusion application of geometry and algebraic knowledge. The results show that teachers 'reasonable use of graphics assistance, dynamic demonstration and other means in teaching can effectively promote students' understanding of abstract concepts and enhance their problem-solving ability.
Key Words ： Combination of numbers and shapes; high school mathematics teaching; intuitive thinking
目 录
摘 要 1
1 数形结合的理论基础与教学意义 2
1.1 数形结合的基本概念与数学哲学基础 2
1.2 数形结合在高中数学教学中的重要性 3
1.3 数形结合对学生数学思维发展的影响 3
2 数形结合在高中数学教学中的具体应用 4
2.1 函数与图像的结合应用 4
2.2 几何问题中的数形结合策略 5
2.3 解析几何中的数形结合方法 5
3 数形结合教学的实践与效果评估 6
3.1 数形结合教学案例分析 6
3.2 学生对数形结合教学的反馈与认知变化 6
3.3 数形结合教学效果的量化评估与改进建议 7
4 结论 7
参考文献 9
谢辞 10
