Because, when painting, there are many things that need the imagination of three-dimensional space.

A person with strong abstract ability and spatial imagination ability, is he good at math? The deeper you learn mathematics, the more abstract it becomes. You are only in Grade Two. Some math classes in universities are really abstract. It unifies what you seem irrelevant, highly generalized and highly abstract, and makes me vomit blood.

And you have a strong spatial imagination, so much the better. A little deeper mathematics requires good spatial thinking ability (just for calculation), a bunch of inexplicable abstract spaces. I learned badly myself, but I think it's beyond my imagination.

How to effectively enhance the spatial imagination? The following is an article to improve middle school students' spatial imagination. Please refer to!

How to Cultivate Students' Spatial Imagination Ability

Yi Jianhui, Guzhen High School, Zhongshan City, Guangdong Province

The ability of spatial imagination in middle school mathematics mainly refers to the ability of students to observe, analyze, abstract and innovate the spatial form of objective things.

The space of middle school mathematics research is the real space of people's life. Specifically, it includes the spatial form reflected by one-dimensional (straight line), two-dimensional (plane) and three-dimensional (three-dimensional) graphics. With the growth of students' age, they can constantly acquire and master various spatial perceptions and spatial representations from their daily life experience, and at the same time, they are constantly accumulating various words to express spatial relations, so that their spatial essentials are constantly improved and enriched.

In middle school mathematics learning, the cultivation of spatial imagination ability includes the following aspects:

1. Very familiar with the shapes, structures, properties and relationships of basic geometric figures such as lines, surfaces and spaces in geometry. I can draw, remember and reproduce the shape and structure of basic graphics correctly in my mind without physical objects or graphics, and analyze the positional relationship and measurement relationship between basic elements of graphics.

2. Be able to use rib graphics to reflect and think about objective things or use words and formulas to express spatial shapes and positional relationships.

3. Can distinguish between basic graphics and more complex graphics, and can analyze the relationship between basic graphics and basic elements.

4. According to the nature of geometric figures, we can create geometric figures that meet certain conditions and properties through thinking.

All the above aspects are based on the ability of observing, analyzing and understanding the essence of graphics and drawing. It is worth emphasizing that the ability to read and draw pictures is not only spatial imagination, but also closely related to general ability and skills in using drawing tools. Therefore, to cultivate students' spatial imagination ability, we should consider various factors and cooperate with each other to get good results.

In my opinion, we should cultivate students' spatial imagination ability from the following aspects:

1. By enriching students' space experience, the problem of difficult introduction to geometry is solved.

The difficulty of getting started in geometry teaching has always been a big problem in mathematics teaching. Because when students begin to learn geometry, they must go through a turning point in their understanding-the transition from algebra to geometry. This change has caused two difficulties for beginners: first, the learning of objects has changed from numbers to shapes, and students have to change from the operation of symbolic information to the operation of graphic information; Second, the way of thinking changes from calculation to reasoning, and students should change from quantitative analysis of things to qualitative analysis of their spatial forms.

For the beginners of geometry, they don't understand this change and the purpose of learning geometry, which shows their inadaptability in learning. In particular, the middle school geometry class soon entered the demonstration stage, and at this time, the intellectual development level of many students has not yet reached the stage of formal logic operation. Therefore, it is difficult for them to understand formal and strict logical reasoning, especially some seemingly obvious facts that need mathematical proof. I am not used to geometric reasoning, nor can I describe it in geometric language, which leads to my fear of geometric learning. With the deepening of learning, the concept of geometry is increasing day by day, and the requirements of reasoning and argumentation are higher. The above situation will be more serious, which will make geometry learning an obstacle, and there will be differentiation in learning. Some people will walk in front of obstacles, so as to experience the true meaning of proof, gain the joy of success and enhance their confidence in learning mathematics. On the contrary, some people are stumped and lose confidence in math learning.

Overcoming the difficulty of getting started in geometry is the key to geometry learning. An effective method is to enrich students' spatial experience and enlarge their spatial vocabulary between learning geometric concepts, so that they can have a certain foundation for understanding geometric concepts. Because in essence, geometry, like any other experimental science, originates from the actual needs of human social life, so geometry learning must be based on the experience of real space.

2. Improve students' logical thinking ability through the study of reasoning geometry.

The cultivation of students' spatial imagination ability is closely related to the cultivation of logical thinking ability. Specifically, we can start from the following aspects.

(1) Understanding the basic concepts of geometry is the premise of cultivating logical thinking ability.

Paying attention to the teaching of basic concepts is the general requirement of mathematics teaching, and it also has special significance and specific requirements for geometry teaching. In practical teaching, we should guide students to analyze the composition of concepts and grasp the essential characteristics of concepts, so that students can not only understand concepts literally, but also understand and master related concepts by reciting the essential definitions and analyzing the essential characteristics. Not only that, but also help students to distinguish the relationship between concepts, systematize the geometry knowledge they have learned, and always pay attention to sorting out related concepts and their properties, so as to bring them into a good knowledge structure and improve students' cognitive structure. For example, after learning the concept of "right triangle", some students only know that the right triangle is being placed, but after changing the position of the right angle in the right triangle, they think it is not a right triangle. The reason is that the concept lacks a considerable number of variant patterns. Of course, this also shows that these students have a low level of representation generalization, which affects the concretization of knowledge.

(2) Learning and mastering geometric language is the key to cultivate students' logical thinking ability.

Geometric languages often use reasoning languages. In the process of learning geometry, students are required to learn and master its usage, especially the equivalence of various variants. For example, "point A is on a straight line" is equivalent to "a straight line passes through point A"; "Two straight lines are perpendicular to each other" is equivalent to "the angle formed by two straight lines is 900 degrees" and so on. In practical teaching, some students can't understand some words in geometry. For example, many students don't understand the meaning of "three planes intersect each other"; "There is only one plane behind two intersecting straight lines", "You and only" cannot be understood, and so on. Especially in geometry learning, we often have to turn some geometric languages into mathematical expressions to prove it. For example, "proving that the sum of the interior angles of a triangle is 1800" is usually translated into proving "ABC of a known triangle, proving: ∠A+∠B+∠C= 1800". I think how to break through the above obstacles can students make great progress in geometry learning.

3. Improve students' spatial imagination ability by cultivating students' mathematical thinking quality.

The development of students' spatial imagination ability is closely related to the improvement of their mathematical thinking quality. It can be said that cultivating students' mathematical thinking quality is the starting point to improve students' spatial imagination ability. To this end, we can start from the following two aspects.

(1) Let students master the knowledge they have learned and cultivate the profundity and agility of thinking by solving multiple questions.

In the process of learning geometry, without the profundity of thinking, it is impossible to accurately explain graphic information and make correct reasoning and judgment; Without the flexibility and agility of thinking, it is impossible to flexibly convert and operate non-graphic information and visual information, and it is also impossible to imagine the space for movement and change.

Through the training of multiple solutions to one question, students can master the knowledge and skills they have learned more firmly; Through the comparison of various solutions, students can have a deeper understanding of what they have learned and experience the beauty of simplicity in mathematics.

(2) Cultivate students' creative thinking.

Creative thinking is a way of thinking with initiative and originality. This kind of thinking breaks through the shackles of habitual thinking. In the process of solving problems, either put forward new ideas or solve the unsolved problems of predecessors. Innovation is its essential feature. For example, when answering "What you know is round", some students replied: Water drops are round, nostrils are round, and mouse holes are round. These answers are imaginative, unique and creative.

In practical teaching, teachers should first create a democratic, relaxed and harmonious teaching environment and learning atmosphere for students. Secondly, in teaching, teachers should not rush to judge or evaluate students' answers or suggestions, let alone give comments rashly, especially for some seemingly absurd answers that are inconsistent with teachers' original intentions, they should also be allowed to make further explanations. Third, as a teacher, we should respect every question raised by students, encourage students' sense of accomplishment and enterprising spirit through language and rewards, and encourage students to express different opinions and creative behaviors in time, thus cultivating students' creativity.

* * * will affect the spatial imagination? Hello * * * will cause memory loss and lead to various physical and mental diseases. * * * must give up once!

Baidu jiese bar

Can spatial imagination be exercised the day after tomorrow? Of course, the so-called "asking questions in sequence", some abilities and skills are relatively simple to learn, while others are relatively difficult to learn, but good results can be achieved through hard work.

Look at some simple space graphics, think more, find the feeling, and gradually increase the complexity. This is how I learned engineering drawing and mechanical drawing in my university. As long as the technology is good.

Also, guess, did you study solid geometry in high school? After that, solid geometry simply has a vector.

How to exercise spatial imagination? 1. First look at the three-dimensional animation of various basic geometric figures, and generate the first impression of three-dimensional space from the rolling geometric figures, and establish the concepts of space and three-dimensional space in your mind.

2. Then watch the physical object of basic geometry, carefully observe its shape, close your eyes, imagine its appearance in your mind, and practice it repeatedly with different geometric figures.

Step 3: Pick up the basic geometry, put it in a fixed position, and then observe its shape from six directions. Then close your eyes and imagine the different shapes of geometric figures in your mind when you look in all directions, that is, imagine the shape of each face and practice with different geometric figures, from simple to complex.

4. Step 4, put the basic geometry in the projection space (the projection space model can be made of waste paper boxes), close your eyes and imagine it with the projection space and parallel light. What does the plane figure look like when parallel light is projected from front to back, from top to bottom and from left to right? Practice repeatedly from simple to complex, and draw a sketch on the draft after imagination.

5. Step 5, imagine the three-dimensional shape of the basic geometry from the three views. The front view is projected from front to back, the top view is projected from top to bottom, and the left view is projected from left to right. Together, the three-dimensional shape of geometry can be imagined.

Using the above methods, you will quickly develop a strong space imagination from simple three-dimensional to complex three-dimensional (you can also use various objects or mechanical parts around you).

How to cultivate spatial imagination? Read more stereoscopic pictures, think about painting if you have nothing to do, and you will get used to it.

How to practice your spatial imagination? Watch more movies, especially science fiction movies. I recommend several masters, Hitchcock, Kurosawa, Celciolione, and they all handle the space quite well.

How to cultivate the ability of spatial imagination? 1. Supplementing students with basic mathematical knowledge about spatial forms, such as geometric knowledge, coordinate method and geometric quantity, is the fundamental guarantee for cultivating students' spatial imagination. We can deepen our understanding of geometric figures through quantitative analysis, which is conducive to cultivating students' spatial imagination ability. 2. Cultivating students' observation and imagination ability by using teaching model is the basis of the formation and development of spatial imagination. By observing and analyzing models and objects in class, students can establish spatial perceptual knowledge in their minds, form the overall image of space, establish spatial skeleton, and then abstract it into a plane figure of spatial form. When looking at a painting, we should think of the surface from the painting and the body from the surface, thus forming the concept of "one painting is one". In this way, the more three-dimensional information stored in students' thinking, the more three-dimensional images they can extract when using, and the stronger their spatial thinking ability. This not only enriches perceptual knowledge, enhances students' spatial thinking ability, but also stimulates students' interest in learning. 3. Learning, practicing and drawing stereograms are helpful to the cultivation of spatial imagination. Stereograph is the key to develop spatial imagination and a bridge from perceptual knowledge to rational knowledge. The biggest advantage of stereogram is intuition, which can reflect three-dimensional shapes on two-dimensional plane and help students enhance their thinking ability. For beginners, because of the gap in knowledge structure, there is almost no concept of space, but they can know some simple three-dimensional diagrams by their own intuition, such as cuboids, cubes, cylinders and so on. In view of this feature, lead students to draw a three-dimensional diagram of the basic body, and then draw basic bodies such as prisms and cones. In this way, through the change of lines, we can understand the outlines of various basic geometric figures and initially establish the concept of space. On this basis, gradually guide students to draw some complex graphics. Through the guidance of students' intuitive feelings, students' interest in learning is greatly stimulated, the obscurity of pure theoretical knowledge is avoided, and the fear of painting is eliminated. Fourth, let students do experiments, let abstract knowledge images pick out abstract and difficult contents in teaching, and let students draw conclusions through experiments themselves. For example, "the projection characteristics of straight lines" is one of the theoretical bases of the whole mechanical drawing teaching, and it is also one of the key points of the textbook, but this part is abstract and it is difficult for students to really understand it thoroughly. When teaching this part, let the students prepare two pencils in pairs (the new one is for straight line and the other is for drawing), a piece of paper and a triangle. A student randomly draws a "straight line" (that is, a pencil) on a piece of white paper (but it is not vertical). Another student projected every point on the pencil one by one according to the projection knowledge of points, and came to the conclusion that the projection of a straight line is a straight line. Then we can know that we can only take the projection connection of two points on the straight line. Then, the projections of the "straight line" parallel to the projection plane, perpendicular to the projection plane and inclined to the projection plane are made respectively, and their lengths are measured and compared with the actual lengths of the "straight line" (pencil) respectively. It is concluded that the projection parallel to the projection plane is equal to the actual length, the projection perpendicular to the projection plane has only one point, and the projection inclined to the projection plane is shorter than the actual length. Then realize the projection characteristics of the straight line, that is, authenticity, accumulation and contraction, which is natural. This can not only make students have a very intuitive understanding of the projection of straight lines, but also have a deeper understanding of the characteristics of the projection of straight lines. In a word, it is impossible to cultivate spatial imagination overnight. In the teaching process, the combination of lecture and practice and gradual training can make each student build a "spatial skeleton" in his mind and gradually enhance his spatial imagination ability.

Does cosmology need a strong spatial imagination? Of course.

LS, why is it 1 1 dimension?

The universe actually has infinite dimensions.

But multi-dimensional space does not need specific imagination.

Because nobody can do it.

Including Einstein

Einstein's multidimensional calculation is also derived by mathematical methods.

Studying linear algebra in college can help you understand the meaning of multidimensional.

Imagine

So cosmology is actually mainly mathematics.

The whole universe is a very mathematical model.

You need strong math skills.