类比是一种数学思想方法,将生疏的问题和熟知的问题进行比较,对生疏的问题作出猜想,并由此寻求问题的解决途径或结论。正如波利亚所说“:对平面几何和立体几何作类比,是提出新问题和获得新发现取之不竭的源泉”。下面谈一谈自己运用类比思想对平面几何与立体几何进行探究的教学过程:一、提出问题,引导思考:平面几何与立体几何的关系1.由平面几何与立体几何的相似性引发的思考,是否可以类比。平面几何和立体几何在研究对象和方法、构成图形的基本元素等方面是相同或相似的,因此,在两者之间进行类比是研究他 Analogy is a mathematical method of thinking that compares unfamiliar questions with well-known questions, guesses strange questions, and seeks solutions to problems or conclusions. As Polia said: “The analogy between plane geometry and solid geometry is an inexhaustible source of new problems and new discoveries.” Here to talk about their own use of analogy to study plane geometry and three-dimensional geometry of the teaching process: First, ask questions, guide the thinking: the relationship between planar geometry and solid geometry 1 by the geometric similarity between planar geometry and three-dimensional thinking, Is it analogical? Plane geometry and solid geometry are the same or similar in the research objects and methods, the basic elements that make up a graph, etc. Therefore, to do analogy between the two is to study him