Where is the beauty of mathematics?
The aesthetic education of mathematical knowledge mainly makes students feel the inherent beauty of mathematical knowledge through teaching, such as the beauty of numbers, symbols and composition, cultivates and improves students' aesthetic ability, cultivates students' love for the beauty of mathematical knowledge, and gradually migrates to the love and pursuit of mathematical knowledge through students' "internalization", thus stimulating students' interest in learning mathematics and developing students' intelligence, thus achieving the purpose of educating people. There are abundant aesthetic education factors in primary school mathematics curriculum. It is necessary to fully tap the aesthetic education factors in mathematics textbooks, so that children can feel the beauty of mathematics and then like mathematics. The aesthetic education factors contained in mathematics textbooks mainly include the following aspects:
(1) The beauty of simplicity and abstraction of mathematics: The beauty of simplicity of mathematics does not mean that the content of mathematics itself is simple, but that the expression form, proof method and theoretical system of mathematics are simple. The formula c = 2π r is one of them. The most perfect figure in geometry-a circle, has an unusually simple and harmonious relationship between its perimeter and radius, and a legendary number "π" connects them closely. Another example is that the number "1" is as small as an atom or particle; As big as the sun, a universe ... everything in the universe can be represented by "1". Various formulas for calculating the area and volume of geometric shapes are simple and practical, and are foolproof. As long as the relevant conditions are met and the calculation is not wrong, the correct result can be obtained. Careful people can also find the internal relationship between them. For another example, many simple solutions are also the embodiment of concise beauty of mathematics. Simple example: Calculate 1
+-+-+-+-+-In the face of this calculation problem, if we rashly use the general division method,
Solving it will bring complicated calculation. A careful study of the characteristics of this problem shows that the fractional numerator of each problem is 1, and the denominator can be divided into the product of two connected natural numbers, namely 1× 2, 2× 3, 3× 4, 4× 5, 5× 6, 6× 7, 7× 8, 8× 9 and 9×. In this way, although in the calculation process, the number of terms in the fraction has doubled, but there are two identical fractions with positive and negative phases, and the middle terms cancel each other out, leaving only the first two terms and the last two terms, thus quickly obtaining the result, namely
This simple solution gives people a beautiful enjoyment.
(2) The beauty of numbers and symbols. Beautiful figures: first, the beginning of everything, unifying the world, taking the lead, how magnificent; Second, even numbers, double happiness, fly with me, how beautiful and happy; The third is the homonym of rising, which means the majority, three religions and nine streams, three students are lucky, three transgressions and four times, and the fourth is the fully enclosed structure, which is slow and steady. Small quadrangles are unique, extending in all directions and making a fortune in four seasons; For cyclic decimals, we can use the notation of cyclic knots to express them concisely and accurately. There are many symbols involved in mathematics learning, such as "+,-,×, ⊙" in four operations, ",=" with relatively large numbers, brackets [], brackets [], braces {} and so on. These symbols pay attention to symmetry up and down. If you don't pay attention to their symmetry when writing, you will be ruined by spelling mistakes.
(3) The beauty of composition and combination in mathematics. The basic knowledge of geometry is an important content of primary school mathematics, including the understanding and drawing of straight line, line segment, ray, angle, rectangle, square, circle, parallelogram, trapezoid, cuboid, cube and sphere. No matter how simple or complex, these figures have their own unique beauty. For example, the rigidity of straight lines, the lightness and smoothness of curves, the beauty of variation contained in triangles, the symmetry of isosceles triangles, isosceles trapezoid, rectangles and circles, and the steadiness and squareness of squares. Teachers can use all kinds of graphics provided by textbooks in teaching to guide students to experience their beauty and achieve the feeling of beauty in the process of understanding and mastering all kinds of graphics. And you can use the relationship between graphics or some interesting laws to give full play to students' imagination, so that they can combine their favorite things with various graphics and experience the beauty of mathematical combination.
(4) The beauty of symmetry in mathematical knowledge. Symmetry in mathematical knowledge mainly includes axisymmetrical beauty, such as isosceles triangle and rectangle; The beauty of equilateral symmetry of parallelogram and circle; Formal beauty and symmetrical beauty, such as positive (+) and negative (-), addition, subtraction, multiplication and division, positive proportion and inverse proportion. In teaching, we can closely connect with the reality of life and the fact that biological structures such as clothes, trousers and human body are axisymmetric, reveal the beauty of symmetry, let students know the value of symmetrical beauty, deepen their understanding of the concept of mathematical symmetrical beauty through examples, deepen their thinking and cultivate their ability to feel and appreciate beauty.
(5) Beautiful mathematical methods. The number of natural numbers is infinite: 1, 2, 3, 4, ... the number of odd numbers is infinite; 1, 3, 5 ... People adopt the mathematical method of "one-to-one correspondence": magically, it is found that there are the following relationships between natural sequences and odd-numbered sequences: 1, 2, 3, 4, ...
1、3、5、7、……
32 copies, the same approximate triangles are put together, and the circle magically becomes an approximate rectangle. The more copies are divided, the closer the figure is to the rectangle. This kind of conversion between curve and straight can also be found in life. "Bricks used for building walls are rectangular, which can be used to build a chimney with a circular section." Disassemble a chimney with a circular cross section made of square bricks, and you can get square bricks with rectangular faces.
(6) The beauty of mathematical thinking. There are rich ideological and moral education materials in mathematics knowledge, and many short stories have been written in primary school mathematics textbooks, such as the origin of division symbols and the origin of equal signs. Chen Jingrun, a mathematician in China, lived in a humble room, but in order to break through Goldbach's conjecture, he kept calculating and finally took off the jewel in the crown of mathematics through his efforts. Mathematician Hua, who didn't get good grades in mathematics in middle school, didn't go to college, but through his own self-study, he became a famous mathematician in China, was invited to give lectures abroad, and died in a foreign forum. Mathematicians' noble ideology and morality, deep patriotic enthusiasm and extraordinary intelligence are all good materials to educate our students, stimulate their love and pursuit of mathematics, cultivate their spirit of overcoming difficulties and making progress, and cultivate their lofty aspirations.
(7) The singular beauty of mathematical knowledge. Singularity is another basic content of mathematical beauty. It means that the results obtained are novel and unexpected. Tangram puzzles are often used in primary school math classes. With seven boards, you can make simple squares or ever-changing complex patterns, such as human figures, birds and animals, flowers and plants, houses and so on. Through jigsaw puzzles, students feel that there are many patterns, which is unexpected; The beauty of graphics is full of fun.
Interesting mathematics knowledge can not only make students feel different beauty, but also use the wonder of mathematics to dress up people's lives. For example, if you are a fashion designer, you will feel comfortable with your own design if you have the knowledge of the golden section. Bach's music is full of the symmetrical beauty of mathematics, and how many mathematical images are condensed on the architectural lines of the Egyptian pyramids ... It can be said that where there is mathematics, there is beauty.