Aesthetic education, referred to as aesthetic education for short, is an education that cultivates people's correct and healthy aesthetic concepts and tastes and improves people's ability to appreciate and create beauty in a certain way. Its purpose, like moral education, intellectual education and physical education, is an indispensable and important link in cultivating all-round talents. In mathematics teaching, there are always infinite magical aesthetic factors, both in content, method and form of expression. Therefore, mathematics teaching has high aesthetic value.
Middle school is a period when people's aesthetic temperament is more prominent. As mathematics teachers, we should use this time to reveal the beauty of mathematics to students and give full play to the aesthetic function of mathematics teaching. Aesthetic education in middle school mathematics teaching can not only make students better perceive and understand the beauty of mathematics, but also make students subtly cultivate their sentiments, enrich their spiritual world and stimulate their interest in learning in pleasant mathematical aesthetic activities. It can also improve their ability to appreciate the beauty of mathematics, thus cultivating their creative potential in mathematics.
However, for a long time, people have paid attention to the teaching and training of basic knowledge and skills in middle school mathematics teaching, but neglected the implementation of aesthetic education in teaching. So how to give full play to the aesthetic function of mathematics in mathematics teaching? This paper intends to make a preliminary discussion on this issue.
First, teachers should be good at digging the beauty in mathematics.
In the process of mathematics teaching, we pay more attention to imparting knowledge and cultivating ability, but often fail to complete the educational task of aesthetic education. It is often empty talk to cultivate students' ability to discover and appreciate beauty. Through the research and discussion on the beauty of mathematics, teachers can consciously cultivate students' aesthetic concept, interest, emotion and ability in the teaching process, so that students can enjoy the beauty of mathematics and feel relaxed and happy in the learning process. Relax muscles, eliminate the fatigue caused by intense study, adjust the circadian rhythm, let the brain rest actively, and truly complete the educational task of aesthetic education.
In fact, mathematics is a science that studies the quantitative relationship and spatial form of the objective world. The beauty of mathematics is the simplicity, harmony, preciseness and strangeness contained in its unique abstract concepts, formula symbols, propositional models, structural systems, reasoning and argumentation, and thinking methods. It is a free form of mathematical creation, which reveals the regularity and is the real beauty of science.
In the process of mathematics learning, students are first exposed to mathematical concepts, formulas, theorems and rules. Although they contain aesthetic factors, the beauty of mathematics is mainly reflected by mathematical language, so it has certain indirectness and fuzziness. Therefore, not all students can feel the beauty of mathematics. This requires teachers to consciously cultivate students' aesthetic feeling of mathematics in teaching and guide them to discover and appreciate beauty. For example, for any triangle, their three median lines always intersect at one point, so that students can see that all triangles are so rather than coincidences, showing an ingenious beauty. Similarly, three bisectors, three perpendicular bisector and three heights of a triangle also intersect at one point, which further makes students realize that even the simplest figure-triangle contains iron-like laws.
Starting from the external expression of mathematical beauty, it is the principle that mathematics teaching should follow to turn abstraction into intuition and fully reveal its connotation of beauty. The same is true for the cultivation of spatial aesthetic feeling (that is, the perception of spatial characteristics such as the shape, size and orientation of objects). The space surface discussed in analytic geometry is symmetrical, although symmetry looks boring. If we regard it as a kind of beauty, we will find what kind of harmonious and unified aesthetic feeling there is between these figures and their equations. Therefore,
Second, teachers should attach importance to students' mathematical aesthetic imagination.
Mathematical aesthetics is inseparable from imagination, which plays a very important role in mathematics. When it comes to mathematical aesthetic imagination, we can't help but mention the number "0.6 18". "0.6 18" is called the golden section number in mathematics. According to this ratio, the line segment is divided into imaging frames, giving people a sense of harmony. It can divide the circle into ten equal parts, make it into a regular decagon, and connect the diagonals to get a regular pentagram; In addition, medical research has found that there is an optimal coupling coefficient in human body, which fluctuates between 0.6 17-0.675, and the golden section value is 0.6 18. The important condition for human consciousness to reach the best state is the brain-heart coupling mechanism, that is, the heart and brain participate in thinking in the form of optimal frequency coupling. These are not coincidences, but because of mathematics itself.
For another example, when teaching how to find the area of a circle by using the limit of the inscribed polygon area of a circle, we combined the "tangent circle method" pioneered by Liu Hui, a mathematician in Wei and Jin Dynasties: "If you cut it carefully, you will lose less; So that it can't be cut and can be combined with a circle without losing anything. " This shows that Liu Hui thought of the infinite separability of things and realized that infinity can be transformed into finiteness under certain conditions. What a novel and wonderful mathematical idea it was at that time!
For another example, the study of logarithm is more mechanical and boring. If you ask a question before studying this chapter, "How thick is a piece of paper with a thickness of 0.0 1mm after being folded ten times?" Students can do the math. Here, let's ask another question. How to fold 100 times? Some students may be able to work out that it is estimated to be 2 100 sheets of paper. That is 2100 = (210)10 ≈ (103)10 =1030, that is1030× 0.0. The students were amazed. This figure is only an estimate, and the students find it very interesting and curious. Its novelty arouses happy and rich "aesthetic" imagination in students' minds. Furthermore, in order to solve this complicated and amazing calculation, the pursuit of "simplicity", one of the expressions of mathematical beauty, has led to the emergence of logarithmic calculation methods. Students start with interest, beauty and pursuit.
Third, teachers should cultivate students' creative ability with beauty and wisdom.
The perfection and pursuit of mathematical beauty is an important clue and powerful means to discover new theories and create new inventions. In fact, when a theory, a problem or an object, whether its ideological content or its formal methods are not perfect, it will always follow aesthetic standards and continue to create, develop and improve it according to the law of beauty. This is creative aesthetic thought.
Creative aesthetic thought is intuitive, unified and creative, which is reflected everywhere in mathematics teaching.
When n is a natural number, n! Represents the product of n natural numbers from 1 to n, when n=0, 0! Obviously meaningless, it destroys the overall harmonious beauty of factorial definition. Check the formula Cnm=m! /(n！ (m-n)！ ), where m and n are natural numbers, m >；; N, when m=n, Cnm= 1 is on the left and m is on the right! /(m！ 0! ), in order to make the formula still hold when m=n, it is necessary to supplement the provision of 0! = 1, thus satisfying the harmony.
As an inducement, mathematical beauty can often promote students' understanding and mastery of mathematical knowledge. Once students' learning activities are full of aesthetic interest, the learning process will leave a beautiful track in progress. Aesthetic interest will become a catalyst for students' psychological life and a positive force for students' self-improvement, so that students can compare knowledge before and after and understand its internal relations, thus forming an orderly knowledge structure and problem-solving method system, which not only reduces students' learning burden, but also improves learning efficiency.
For example, in order to introduce the geometric meaning of arithmetic progression's general term formula, the teacher asked students to convert the formula αn=α 1+(n- 1)d into αn=dn+(α 1-d), and saw that when d≠0, αn is a linear expression about n, if y = Students can easily and creatively use a straight line to pass through the slope formula k = (y2-y 1)/(x2-x 1) of two points (x1,y1) to solve the problem of finding the tolerance d from arithmetic progression's two terms αm and αn, that is, d.
There is beauty everywhere in mathematics. If teachers concentrate on excavating the factors of mathematical beauty in teaching and infiltrate into classroom teaching imperceptibly, and stimulate students' experience of mathematical beauty, we can achieve twice the result with half the effort.