Aesthetic education in mathematics should be carried out, because beautiful flowers are blooming everywhere in the garden of mathematics. The following is about the beauty of mathematics and its characteristics, as well as the role of beauty of mathematics in mathematics teaching.

First, the beauty of mathematics and its characteristics

Marx said: human social production activities are carried out in accordance with the "aesthetic principle". Of course, mathematical knowledge as a spiritual product is also in line with the aesthetic principle. Mathematics has the characteristics of literature and art, that is, mathematics also has its own beauty in content, structure and method, which is called mathematical beauty. Specifically, the essence of mathematical beauty is the integration of mathematical relationship structure system and human intention as aesthetic subject. That is to say, after the existence and struggle between the internal structure method of mathematics and human intention, it will inevitably merge into a new category, which is the beauty of mathematics.

Everything and phenomena have their unique characteristics, and the beauty of mathematics is no exception. The content and characteristics of mathematical beauty can be summarized as harmony and singularity, and the characteristics of harmony are unity, simplicity, symmetry, regularity, invariance and appropriateness.

1. Unity. The so-called unity is the harmony of parts, parts and the whole. The objective world has unity, and mathematics, as a language to describe the objective world, must also have unity.

2. simple. The objective world is not only unified, but also unified in a simple law, summing up a simple and clear law in complexity, giving people a sense of beauty.

3. Symmetry. In the objective world, there are many forms of symmetry. In geometric figures, there are axial symmetry, central symmetry and mirror symmetry, all of which give people beautiful enjoyment.

4. Neat. The so-called neat beauty of mathematics refers to the consistent repetition of all mathematical symbols in the same way and in the same shape.

5. Invariance. Invariance is also a kind of beauty. In a mathematical relationship structure system, those changing invariants and unchanging relationships often show the charm of beauty.

6. appropriateness. Appropriateness also presents a mathematical beauty. In daily life, some things show moderation in quantity, that is, we often say that no more, no less, just right, often give people beautiful enjoyment.

7. A new and unusual relational structure has appeared in singularity mathematics, which can induce a kind of pleasure in people's imagination and produce a kind of surprise in people's hearts. This is the singularity of mathematical beauty.

Second, the role of aesthetic education in middle school mathematics teaching

Xu Lizhi, a famous mathematician in China, once expounded the beauty of mathematics. As a scientific principle, mathematics has the characteristics of general language, literature and art, and he also thinks: "One of the purposes of mathematics teaching is to enable students to acquire mathematical aesthetic ability. That is, it can enhance students' subjective perception of mathematical beauty. Therefore, mathematics aesthetic education plays an important role in middle school mathematics teaching. Specific performance in the following aspects:

1. Aesthetic education in mathematics can cultivate students' interest in learning mathematics. Einstein said, "Interest is the best teacher." Therefore, as long as students are interested in mathematics, they will think more diligently about mathematical problems and are willing to study them. As long as teachers fully tap the mathematical beauty contained in some numbers, formulas, theorems and laws in teaching activities, students will certainly enjoy this beauty and fall in love with mathematics. As long as students are interested in mathematics, they will naturally study mathematics actively rather than passively.

2. Aesthetic education in mathematics is conducive to cultivating students' divergent thinking ability. Divergent thinking is mainly manifested in the intuitive imagination between numbers and shapes, rational reasoning in the process of exploration, formal simulation from finite to infinite, and speculation on the relationship between mathematical structures. In many cases, we can look at an algebraic expression from different angles. In particular, the perfect unity of number and shape in mathematics-the combination of number and shape in middle school mathematics teaching activities is very useful for cultivating students' mathematical aesthetic feeling, cultivating students' divergent thinking ability, broadening students' knowledge horizons, allowing students to jump out of the traditional thinking mode and give play to their subjective initiative in thinking.

3. Mathematical aesthetic education can cultivate a person's perfect personality to a certain extent and help him form a good world outlook, outlook on life and values. Qin Xin, a math educator, said, "According to my years of experience, studying math science will gradually cultivate the characteristics of young people with obvious moral colors, which can then become their main moral factors." (1), mathematics teaching is honest and upright. As long as a proposition is not proved, it can not be included in the treasure house of truth for the time being, and people have reason to doubt it, regardless of the qualifications and reputation of the person who put forward this proposition. If the proposition is proved, then its truth will be recognized, generally adopted and implemented, and there is no phenomenon of people downplaying it. (2) People who have received a good math education will have a positive impact on their work because of their qualities formed in math learning and training. The accuracy and rigor of mathematics make them less vague and general in their work. The abstract analysis of mathematics makes them good at understanding the essence of things through phenomena. The incisive argumentation and concise expression in mathematics make their conversation and writing concise. We should not simply understand mathematics education as imparting knowledge and training skills. Mathematics education needs to cultivate people's quality.

4. Mathematical aesthetic education can train mathematicians, artists, philosophers and other disciplines. Recent research shows that Picasso and Einstein are of the same ancestry. It sounds incredible at first. One is a painter, the other is a scientist. How can they be homologous? 1905, Einstein published his special theory of relativity; 19 16, he published his general theory of relativity; 1907, Picasso completed the oil painting "The Maiden of avignon", officially announcing the birth of cubism. It turned out that as early as 1902, their group had read the book Science and Conjecture written by the French mathematician Henri Poincare at the same time, and was deeply influenced by it. This book aims to explain the relationship between geometric language and physical motion. It inspired Einstein's research on four-dimensional space, and at the same time introduced time as the fourth dimension into Picasso's picture, depicting the whole movement process in a single picture. In fact, mathematician Klein said: "Mathematics is the highest intellectual achievement of human beings and the most unique creation of human mind. Music can inspire or soothe feelings, painting can make people pleasing to the eye, poetry can touch people's hearts, philosophers can gain wisdom, science can improve material life, but mathematics can give all of the above. "