After entering the new century, we are faced with many problems, the most crucial of which is how to upgrade the industry, and talents play an important role in this respect. What kind of talents are needed? Experts pointed out that talents with the following four qualities are needed: first, new ideas; Second, it can continue to engage in technological innovation; Third, be good at managing and opening up markets; Fourth, there is team spirit. Therefore, we should strengthen the cultivation of students' abilities in these four aspects in mathematics teaching.

First, cultivate students' new ideas and concepts in mathematics teaching.

New ideas include not only new understanding and new ideas about things, but also a process of continuous learning. Therefore, as a new talent, we must learn to learn. Only by continuous learning can we acquire new knowledge, renew our concepts and form new understandings. In the history of mathematics, Descartes, a great French mathematician, liked reading extensively when he was a student and realized the disadvantages of the separation of algebra and geometry. He studied the drawing problem of geometry by algebraic method, and pointed out the relationship between drawing problem and equation solution. Through specific problems, he put forward the coordinate method, expressed geometric curves as algebraic equations, asserted that the number of curve equations had nothing to do with the choice of coordinate axes, and classified curves by the number of equations, thus realizing the relationship between the intersection points of curves and the solutions of equations. It advocates a new viewpoint of combining algebra with geometry and applying quantitative methods to geometry research, thus creating analytic geometry. As a math teacher, we should not only teach students to learn, but also teach them to learn. In the teaching of inequality proof, I mainly teach students how to analyze problems, flexibly use three basic proof methods: comparison method, analysis method and synthesis method, and guide students to learn and prove inequalities with new methods such as triangle, complex number and geometry.

For example, it is known that A > = 0, B > = 0, a+b= 1, and verification (A+2) (A+2)+(B+2) > = 25/2.

There are many ways to prove this inequality. In addition to the basic proof, it can also be proved by finding the maximum of quadratic function, triangle substitution and constructing right triangle. If A+B = 1 (A > = 0, B > = 0) is taken as a line segment in the plane rectangular coordinate system, it can also be verified by analytic geometry knowledge. The proof is as follows: take the straight line segment x+y= 1, (0 = < X > = 1), (A+2) (A+2)+(B+2) (B+2) as the point (-2, -2), and the straight line segment X+in the plane rectangular coordinate system. Because the distance from a point to a straight line is the minimum of the distance from this point to any point on the straight line. And d * d = (-2-2- 1 |)/2 = 25/2, so (a+2) (a+2)+(b+2) > = 25/2. It is better to teach people to fish than to teach them to fish. Only by mastering methods and forming ideas can students benefit for life.

Second, cultivate students' innovative ability in mathematics teaching

Innovative ability is mainly manifested in seeking new methods to solve problems in mathematics teaching. "Learning begins with thinking, and thinking begins with doubt". Students' thinking process of exploring knowledge always starts with problems, and develops and innovates in solving problems. In the teaching process, students can operate, think and express, explore the unknown, seek objective truth and become discoverers under the situation created by teachers. Students should participate in this exploration process from beginning to end and cultivate their innovative ability. For example, in the teaching of ball volume, I divided the students into three groups in my spare time and asked everyone in the first group to make a hemisphere with a radius of 10 cm; In the second group, each person made a cone with a radius of 10 cm and a height of 10 cm; In the third group, each person made a cylinder with a radius of 10 cm and a height of 10 cm. One person in each group forms multiple groups. Each group puts the cone into the cylinder, and then fills the cylinder with soil in the hemisphere. The students found the relationship between them. The volume of a hemisphere is equal to the difference between the volumes of a cylinder and a cone. The derivation of the volume formula of a sphere is a perfect example of the flexible application of these thinking methods, which integrates axiomatic thinking, reduction thinking, equal product analogy thinking and cut-and-complement transformation method. Thirdly, through the analysis of the thinking of solving the volume problem in teaching, a systematic and coherent deduction clue of the volume formula is formed, and these thinking methods are clearly presented to students. Students can understand the creative thinking process of mathematicians and stimulate their creative thinking and innovation ability.

Third, cultivate students' ability to manage and develop the market in mathematics teaching.

All mathematical knowledge comes from real life, and many problems in real life need to be solved by mathematical knowledge and mathematical thinking methods. For example, according to what program the washing machine runs, it is beneficial to save water; How to manage fishermen can not only achieve the highest yield, but also achieve sustainable development; How can a good product design be quickly recognized by the market and produce good economic benefits? Therefore, we should consciously cultivate students' ability to manage and develop the market in mathematics teaching. The ability to manage and develop the market is mainly reflected in how to design the best solution or model for a mathematical problem or practical problem in mathematics teaching. If the combinatorial identity CNM = CNM-1+CN-1m-1is proved, the general analysis can be completed by some appropriate calculation or simplification. But it can make students think about whether it can be proved by the meaning of combined numbers. That is, a combination model is constructed, and the left end of the original formula is the combination number of n elements in m. The right hand side of the original formula can be regarded as another algorithm for the same problem: the combinations that meet the conditions are divided into two categories, one is that there is a CNM- 1 method without taking an element; One is to force a 1, and there are CN- 1m- 1 methods. From the uniqueness of addition principle's reconciliation, we can know that the original formula is effective. For another example, when operating and developing the market, we often need to make some basic statistics on the market, and there are many examples of controlling and grasping the market by establishing mathematical models for analysis and research. The explanation of such problems can not only improve students' intelligence and ability to solve practical problems by applying mathematical knowledge, but also be of great benefit to improving students' ability to manage and open up markets.

Fourthly, cultivate students' team spirit in mathematics teaching.

Team spirit is a working spirit of mutual cooperation and collaboration. Mathematics teachers should design more problems that students can solve through cooperation in teaching, enhance students' sense of cooperation and cultivate students' team spirit. For example, when I was teaching the volume formula of the ball, before class, I asked 20 students to make cylinders with radii of 10, 9.5, 9 ... 0.5 cm and use 0.5 cm thick cardboard in turn to list the volume calculation formula of each cylinder and calculate the results. Another 40 students were asked to make cylinders with radii of 10, 9.75, 9.5 ... 0.5 and 0.25 cm, using cardboard with thickness of 0.25 cm, listing the volume calculation formula of each cylinder and calculating the results. In class, I first write the volume formula of the ball on the blackboard, and then let the students connect the two groups of cylinders from big to small with two thin iron wires through the central axis to get two approximate hemispherical geometric figures. Let's compare their volumes with those of a hemisphere with a radius of 10 cm. It is found that the volume of the second group is closer to the volume of the hemisphere than that of the first group. If the thickness of cardboard is reduced, the geometric volume will be closer to the volume of the hemisphere, which will help students find another proof of the volume formula of the ball. At the same time, it not only tells students why the experimental materials in the teaching process are prepared by everyone, but also lets students consciously destroy the connected geometry and their small cylinders. Through these, the students realize that only Qi Xin can work together to reach the other side of success. The advantage of mathematics teaching is not only to let students learn to know and do; But also make students understand the goals and tasks of common life and common development.

References:

/News/2005- 1 1/8424788397 1 146 1 . shtml