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数学教学的主要目标是培养学生的逻辑思维能力,但直觉思维能力却在数学的发现和创造过程中发挥重要的先导作用,同时也是数学学习过程中确定解题思路的重要途径,本文仅就解题教学中如何培养学生的直觉思维能力举数例加以分析。 (一)考虑特殊值例1 △ABC的三边为 a、b、c满足关系式a~2-a-2b-2c=0 ①及a+2b-2c-3=0 ②求△ABC的最大角的度数. [分析] 按常规思路先要比较三条边的
The main goal of mathematics teaching is to train students’ logical thinking ability, but the intuitive thinking ability plays an important role in the discovery and creation of mathematics. It is also an important way to determine the problem-solving ideas in mathematics learning process. How to cultivate students’ intuition thinking ability in the problem teaching is illustrated by several examples. (I) Consider special values Example 1 The three sides of △ABC are a, b, and c. Satisfy the relationship a~2-a-2b-2c=0 1 and a+2b-2c-3=0 2 Find the maximum value of △ABC The degree of the angle. [Analysis] According to the conventional thinking, we must first compare the three sides.