First, teachers strive to create teaching situations and cultivate students' awareness of applying mathematics.
Learning mathematics is to explain and solve problems in life. Therefore, in order to cultivate students' application consciousness, we must insist on emphasizing the practical application situation of mathematical problems in teaching. In teaching, more problem situations can be designed to let students experience the process of knowledge formation, and students can connect mathematics with real life and realize that life contains mathematical information, thus realizing the application value of mathematics. For example, in the teaching of "Polynomial Multiplying Polynomial", teachers can design the following situations: during the period of returning farmland to forest in a certain area, a rectangular forest area with an original length of m meters and a width of a meter will be increased by n meters and widened by b meters. Please indicate the current area of this forest area. Question: (1) How to express the expanded forest area; (2) Why are the equations expressed in different ways equal? (Students discuss in groups and communicate with each other to get the answer) Students get two different representations, one is (m+n) (a+n) m 2; The other is (ma+mb+na+nb) m 2. The above two results are correct, so the polynomial multiplication formula can be obtained. In teaching materials, teachers should replace some examples that rural students are unfamiliar with, or appropriately supplement some interesting questions that are close to rural students' lives, especially some abstract math problems in teaching materials, and teachers should appropriately select some examples that are suitable for rural students' lives to teach. In this way, students not only intuitively grasp the knowledge of teaching materials, but also enhance their interest in applying mathematics knowledge. For another example, when teaching the exploration of "the condition of triangle congruence-ASA", teachers can introduce such practical problems: a triangular glass was broken into three pieces, and now it is necessary to go to a glass shop to match an identical glass. Do I need to bring all three pieces to match the original glass? If you bring one, which one should you bring? This makes students unconsciously enter the learning situation of exploring the triangle congruence condition law of new knowledge "Angle and Angle".
Second, through the teaching of practical exercises, cultivate students' modeling ability.
In teaching, teachers should, according to teaching practice, create questions that are closely related to teaching materials, pay attention to situations, are novel and have a strong sense of the times. As examples and exercises, teachers should guide students to turn practical problems into mathematical problems, let students know the methods of establishing mathematical models, cultivate their ability to establish mathematical problems, feel the relationship between mathematical knowledge and life practice, abstract mathematical knowledge and mathematical laws, establish mathematical models, and use mathematical knowledge scientifically and reasonably to carry out correct operations and reasoning. For example, when teaching the content of "profit and loss in sales" in Practical Problems and One-dimensional Equation, in order to let students further understand the related problems in sales, the author added an exercise: Boss Wang sold two pieces of jewelry that day, each of which was worth 600 yuan and priced at 800 yuan. The first one is sold at a 20% discount. Afterwards, Boss Wang always felt that it was sold out, and the second piece was based on the selling price of the first piece. Still not losing money or making money? When solving this application problem, the mathematical model of the equation can be established to solve it. For another example, when solving the problem of pulley length between two wheels, through transformation, a mathematical model can be established to find the length of the common tangent and arc outside two circles. In teaching, we can also select some application problems according to the teaching content to train students to model, and we can also combine some practical problems that students are familiar with in life, production, science and technology and current commodity economy (such as interest, stock, profit, population, etc.) to guide students to transform them into mathematical models through observation, analysis, abstraction and generalization, so as to cultivate students' modeling ability.
Third, pay attention to the connection with other disciplines and reflect the application of mathematics.
Mathematics is the basis of learning other subjects well, and it is also an indispensable tool for people to participate in social activities, engage in productive labor, study various subjects and study modern science and technology. Therefore, it is one of the effective methods for teachers to contact other disciplines to cultivate students' awareness of applied mathematics. For example, the application of vectors in physics, the relationship between distance and time and speed, the calculation in chemistry, the balance of equations, and the genetic problems in biology mentioned in textbooks are all practical applications of mathematical knowledge, involving algebra, equations, functions, lines, surfaces, vectors and other related knowledge in geometry. The creation of these situations makes students realize the close relationship between mathematics and other disciplines, and fully embodies the important role of mathematical knowledge in various fields, so that students can feel the application value of mathematics. For another example, the problem of sewage treatment is often based on the knowledge of biology and chemistry, but it involves the statistical theory of mathematics, environmental simulation of process design and so on. Therefore, teachers are required to establish the teaching concept of lifelong learning, pay attention to the specialty of the subject, constantly "recharge", broaden their knowledge fields, make themselves have extensive cultural and scientific literacy, and build a new knowledge system.
Fourthly, through developing mathematical activities, students' practical ability is cultivated.
In teaching, some teachers, afraid of trouble, regard the math activities in the new textbook as extracurricular reading materials, whether they are casual students or simply talk in class. In fact, in teaching, teachers should often organize and let students participate in mathematical practice activities, so that students can practice in person, find mathematical factors from reality and find solutions. For example, in the teaching of "coordinates of points on the plane", students can freely draw the plane distribution map of simple school or village landmark buildings. After studying "data collection and arrangement", students can investigate the yield, selling price and production cost of local rice varieties, and then give reasonable suggestions to farmers by calculating and comparing the yield per mu. Students have accumulated practical experience in solving practical problems through hands-on operation, thus further cultivating their application ability.
In a word, cultivating students' awareness of mathematics application plays an important role in mathematics education and is the key to improve students' interest in learning mathematics. In mathematics teaching practice, teachers should be good at integrating theory with practice, collect examples of mathematics application around them, pay attention to the connection with other disciplines, provide students with more mathematics application background, let students realize that mathematics is in life from life practice, let students experience the process of mathematics application personally, and then cultivate students' application consciousness and problem-solving ability, and promote students' all-round sustainable development.
(Editor: Zhang Huawei)