1. As the name suggests, geometric intuition refers to two things: one is geometry, here geometry refers to graphics; the other is intuition, where intuition does not only refer to things directly seen (directly seen) (is a level), and more importantly, thinking and imagining based on what we see now and what we saw before. To sum up, geometric intuition is to rely on and use graphics to think and imagine mathematics. It is essentially an imaginative ability developed through graphics. Einstein: tH_ (Einstein, 1879-1955) once said a famous saying: "Imagination is more important than knowledge, because knowledge is limited. Imagination summarizes everything in the world, promotes progress, and it is the evolution of knowledge. The source of it. Strictly speaking, imagination is a real factor in scientific research. "Geometric intuition allows us to realize the greatest benefits it brings in the relationship chain of "mathematics-geometry-graphics". This is just as Hilbert (1862-1943), the greatest mathematician of the 20th century, mentioned in his famous book "Intuitive Geometry", graphics can help us discover and describe research problems; they can help us seek Ideas for solving problems; can help us understand and remember the results. The value of geometric intuition in studying and learning mathematics can be seen from this.

2. From another perspective, geometric intuition is concrete, not nihilistic, and it is closely connected with the content of mathematics. In fact, many important mathematical contents and concepts, such as numbers, measurements, functions, and even high school analytic geometry, vectors, etc., have a "dual nature", having both "characteristics of numbers" and "characteristics of form". Characteristics", only by understanding them from two aspects can we understand them well and grasp their essential meaning. Only in this way can these contents and concepts become vivid and vivid, making it easier for students to accept and use them to think about problems and form geometric intuitive abilities, which is often referred to as the "combination of numbers and shapes." In this curriculum reform, the emphasis on geometric transformation is not only a change in content, but also a change in the guiding ideology of the design geometry course. This will be the direction of the development of geometry courses. Let graphics "move" and study, reveal, and learn the properties of graphics in "movement or transformation". In this way, on the one hand, it deepens the essential understanding of the properties of graphics; on the other hand, it also improves the geometric intuition ability. . It can also be seen that it is very important to cultivate students' geometric intuition in the compulsory education stage.

3. Geometric intuition and "logic" and "reasoning" are also inseparable. Geometric intuition is often supported by logic. It is not just what you see? But what do you think about through the graphics you see? What do you imagine? This is a very important and valuable way of thinking in mathematics. Geometric intuition combines what you see with what you have learned before, and through thinking and imagination, you can guess some possible conclusions and arguments. This is also reasonable reasoning, which lays the foundation for rigorous proof of conclusions.

Some objects of mathematical research can be "visible and tangible", while many objects of mathematical research are "invisible and intangible" and are abstract. This is a basic principle of mathematics. Features. However, those abstract objects in mathematics are by no means rootless trees or sourceless water. Their "roots and sources" must be concrete. For example, we cannot see "seven-dimensional space", but we know that "white light is composed of seven colors of light: red, orange, yellow, green, cyan, blue, and violet." This can be understood. The "visible source" of the "seven-dimensional space" is the "physical object" and foundation that helps us associate. In mathematics, we need to rely on "one-dimensional, two-dimensional, and three-dimensional space" to imagine and think about "high-dimensional space" problems. This is geometric intuition or geometric intuition ability: geometric intuition is very important in researching and learning mathematics. It can also be regarded as the most basic ability. We hope that mathematics teachers will pay attention to it and help students continuously improve this ability in daily teaching.