1. Exquisite graphics can always bring people beautiful enjoyment.
For example, the sixth question on page 1 13 of Mathematics in Grade 1 of East China Normal University Edition: Please take a given figure (two circles, two triangles and two parallel lines) as the component, conceive a unique and meaningful figure, and write one or two humorous comments. In teaching, I ask students to design, use their imagination, communicate with each other, and then show and reward the outstanding works of the whole class. Such as Chariot, Kite, Sunset in the Mountain, Reflection in the Stream and many other ingenious and meaningful graphics with humorous explanations, let the students experience the fun of success. I am surprised that simple geometric figures can also form beautiful patterns, which greatly improves students' interest in learning mathematics.
2. Symmetrical and balanced mathematical pattern design has greatly improved students' aesthetic level and creativity.
By studying symmetrical graphics, students not only gain knowledge, but also enjoy beauty and improve their ability to analyze problems. There are many symmetrical figures in the objective world, which makes us feel the beauty of the mathematical world. Many symmetrical figures are created by people, the best of which can be said to be the crystallization of human wisdom. These graphics decorate every aspect of our life, which not only improves our aesthetic level and creativity, but also gives us an extra way to solve problems. For some topics, thinking from a symmetrical perspective can give ingenious answers to the questions.
Second, by discovering the beauty of harmony in mathematics, students feel that learning mathematics is "interesting"
From the definition, theorem, axiom, nature, formula, mathematical method, mathematical thought and so on. There is an inevitable connection between seemingly independent and unrelated knowledge. In particular, the harmony shown by the symmetry and unity of mathematics is a real beauty, which not only helps to reduce the learning burden of students, but also makes students feel the fun of learning mathematics. For example, when teaching people the property of "the three lines of an isosceles triangle are integrated" in the section of the isosceles triangle in the first year of mathematics (Volume II), we only need to know one of the three lines of an isosceles triangle (the bisector of the vertex, the middle line on the bottom and the high line on the bottom) to explain the other two lines. It is much easier for students to master this theory. For example, in the chapter of parallelogram, there are both differences and inevitable connections between several quadrangles. It is very important for students to understand the changing process from a general quadrangle to a parallelogram to a rectangle, a diamond and a square, and to reduce the learning burden. At the same time, students discover the changing process of all parallelograms, master the differences and connections between these figures, and feel the fun of learning.
Third, discover the incomplete beauty in mathematics, improve students' ability to analyze problems, make students feel confused about learning mathematics, and stimulate students' desire to learn.
The "incomplete" mathematics textbooks in contemporary primary and secondary schools provide students with opportunities to exercise their thinking. Of course, the "incompleteness" here refers to the incompleteness of mathematical knowledge caused by the lack of cognitive ability. In our textbooks, mathematics has been developing in self-contradiction. It also means that the disharmony in mathematics is everywhere, which also constitutes the incomplete beauty of mathematics and makes an indelible contribution to enriching the connotation of mathematics and cultivating students' mathematical ability. For example, when teaching the use of average, median and mode, a teacher gave students such a question: A city sports commission selected an athlete from two athletes, A and B, to participate in the National Games, and each shot five times, and the number of rings hit was: A: 7 rings, 8 rings, 9 rings, 8 rings and 8 rings; B: 5 ring, 10 ring, 6 ring, 9 ring, 10 ring. According to the above data, who do you think is more suitable for the National Games? So the students analyzed the results of A and B: (1) average: 8 rings; (2) Median: A is 8 rings and B is 9 rings; (3) Mode: A is 8 rings, and B is 10 rings. Obviously, from the two indicators of median and mode, B is superior to A, but the leaders of the Municipal Sports Commission have selected A athletes to participate in the National Games. Do you think this is fair? Tell me why. The students are in high spirits. Yes, everyone thinks that B should take part in the National Games, because the main indicator of athletes' performance is the average level. In the case of the same average level, why not let B's athletes go, because B's performance is extremely unstable. The stability of the grade should be expressed by another quantity. Therefore, students are eager to continue to study the quantity that can show the stability of grades-variance. The teacher is not in a hurry to explain, but only tells the students that they will learn in the future textbooks, thus leaving an imperfect ending for students to discuss and solve doubts, thus stimulating students' desire to learn and improving their interest in learning.
In short, mathematics is always beautiful, mathematics is a science of beauty, and the pursuit of mathematical beauty is one of the driving forces for the development of mathematics and the driving force for students to learn mathematics. Mathematics itself is full of beauty from form to content. Teachers should fully explore and show the beauty of mathematics in teaching, so that students can study happily in a beautiful environment, thus improving their interest in learning.