1. Introduction
As we all know, Comenius and Pestalozzi are both advocates of intuition. In modern Chinese dictionaries in China, intuition is interpreted as "direct acceptance and direct observation with the senses". Japan's Guangci Garden explains intuition as "generally not including the thinking function of judgment and reasoning, but directly grasping the function of the object".
In the Japanese philosophical dictionary, intuition is explained as "intuition is a cognitive function that directly grasps the whole picture and essence of an object". In the literature of mathematics education, intuition is directly regarded as "the ability to discover abstraction and ideal (state) from behind the concrete object of feeling". Mathematician Klein thinks that "mathematical intuition is a direct grasp of concepts and proofs".
2. Significance
Generally speaking, mathematics is regarded as a deductive discipline with strict logic. Especially based on Euclid's Elements of Geometry. However, The Elements of Geometry was developed on the basis of "intuitive geometry" in ancient Egypt and Babylon. So should the formation and development of other branches of mathematics.
The historical process of mathematics development reflects the process of human understanding mathematics-intuition and logic complement each other. In fact, in the "early Greek geometry" between "intuitive geometry" and "Euclid geometry", there is already a logical component of deductive proof. The historical process of mathematics development can reflect the process of human understanding mathematics.
3. Definition
Geometrical intuition mainly refers to describing and analyzing problems with graphics. With the help of geometric intuition, complex mathematical problems can be made concise and vivid, which is helpful to explore the solution ideas and predict the results. Geometric intuition can help students understand mathematics intuitively, and it plays an important role in the whole process of mathematics learning.
4. Introduction to Geometry
Geometry is the study of spatial structure and properties. It is one of the most basic research contents in mathematics, which has the same important position as analysis and algebra, and has a very close relationship. Geometry has a long history and rich contents. It is closely related to algebra, analysis and number theory.
Geometric thought is the most important thought in mathematics. The temporary development of each branch of mathematics tends to geometry, that is, to explore various mathematical theories with geometric viewpoints and thinking methods. Common theorems are Pythagorean Theorem, euler theorem Theorem and Stewart Theorem.