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“数形结合”是求解数学问题的一种常用的思维方法。教师在教学中经常引导学生创设“数形结合”的情景,不仅可以沟通数与形的内在联系,把代数式的精确刻划与几何图形的直观描述有机地结合起来,而且有利于开拓学生解题思路,发展形象思维能力。“数形结合”的方法一般来说可分为以下三种:①将几何论证转化为代数运算的“解析法”;②利用数(式)来研究形的“以数(式)论形法”;③利用形来研究数(式)的“以形促数(式)法”。下面举例分别加以说明。
“Number and shape combination” is a common way of thinking for solving mathematical problems. Teachers often guide students in the teaching to create a “number and shape combination” scenario, which can not only communicate the intrinsic relationship between numbers and shapes, but also combine organically accurate algebraic descriptions with the intuitive description of geometric figures, and is beneficial for students to solve problems. Ideas, develop image thinking ability. The method of “association of numbers and shapes” can be generally divided into the following three types: 1) transforming geometric arguments into “analysis methods” of algebraic operations; 2 using numbers (formulas) to study the “patterns of numbers” method “3. Using formulae to study numbers (formulas) ”to promote the number (formula) method." The following examples illustrate them separately.