数形结合思想在几种典型数学问题中的应用研究

Research on the Application of the Thought of Combination of Numeral and Form in Some Typical Mathematical Problems

摘要: 数形结合思想是中学数学中一种重要的思想，对于学生数学思维的发展、解题能力的提高都具有十分重要的意义。数形结合思想方法是把题设中的数量关系与图形关系结合起来，实现数定形，形助数，达到更直观的效果，提高解题效率。文章基于新课程标准对数形结合思想方法的要求，探讨该思想在中学数学几类典型问题中的应用，如向量、函数、解析几何等，并针对如何开展数形结合思想方法教学提出合理建议。

Abstract: The thought of combination of numeral and form is an important thought in secondary school mathematics, which is of great significance to the development of students’ mathematical thinking and the improvement of their problem-solving ability. The thought of combination of numeral and form is to combine the quantity relation and graph relation in the question setting, so as to achieve a more intuitive effect and improve the efficiency of problem solving. This paper discusses the application of this thought in some typical problems of secondary school mathematics, such as vectors, functions, and analytic polynomials based on the requirements of the new curriculum standard to the thought of combination of numeral and form, and puts forward reasonable advice on how to carry out the teaching of combination of numeral and form.