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在中学几何教学中,我们要注意研究学生的心理特点,特别要研究初学几何的学生对几何图形感知的心理因素。本文就这方面谈几个问题。一、图形的错觉初学几何的学生观察图形时常常会产生错觉。例如对图1中的两个三角形,他们凭眼睛的感知,只承认△ABC是等腰三角形,否认△A′B′C′是等腰三角形。产生错觉的原因是:在△A′B′C′中垂直位置的线段A′B′好象比水平位置的线段B′C′短了一点。这种错觉叫做垂直线和水平线错觉。又如图2中线段AB好象比线段CD短一点,这也是一种错觉,叫做谬勒——莱依尔错觉。在应用同一法则证明几
In the middle school geometry teaching, we should pay attention to study the psychological characteristics of the students, in particular, to study the geometry of the geometry of students beginners psychological factors of perception. This article discusses several issues in this regard. First, the illusion of graphics Beginner geometry students often observe the graphics have a wrong impression. For example, for the two triangles in Fig. 1, they perceive △ ABC as an isosceles triangle only by their eyes 'perceptions, and deny △ A'B'C' as an isosceles triangle. The reason for the illusion is that the line segment A'B 'in the vertical position in ΔA'B'C' seems to be a little shorter than the line segment B'C 'in the horizontal position. This illusion is called illusion of vertical lines and horizontal lines. Another example is the line AB in Figure 2 seems a bit shorter than the line segment CD, which is also an illusion, called Mi Le - Lai Yier illusion. In the application of the same law to prove a few