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数形结合的思想是初中数学中常用的思想方法。所谓数形结合,就是根据数量和图形之间的对应关系。通过数与形相互转化来解决数学问题的思想。初中阶段的数形结合问题常与以下内容有关:①实数与数轴上的点的对应关系;②函数与图象的对应关系;③方程与不等式的对应关系;④以几何元素和几何条件为背景建立起来的概念(如勾股定理、三角函数等);⑤统计和概率等。根据学生在不同学习阶段的认知水平和知识特点,可逐渐渗透数形结合的思想。
The idea of combination of numbers and shapes is a commonly used method of thinking in junior high school mathematics. The so-called number-shaped combination is based on the correspondence between quantity and graphics. The idea of solving mathematical problems through the transformation of numbers and shapes. The combination of number and shape in junior high school is often related to the following: 1 Correspondence between points of real number and number axis; 2 Correspondence between functions and images; 3 Correspondence between equations and inequalities; 4 Background of geometric elements and geometric conditions Established concepts (such as the Pythagorean theorem, trigonometric functions, etc.); 5 statistics and probabilities. According to the students’ cognitive level and knowledge characteristics at different stages of learning, they can gradually penetrate the idea of combination of numbers and shapes.