After years of classroom teaching practice, I deeply understand that the fundamental task of mathematics education is to teach students how to learn and how to apply knowledge to solve practical problems. As a math teacher, I should educate students to learn to turn practical problems into math problems, that is, to build math models. Perhaps many teachers will ask, "Why are their students so stupid and have poor ability to solve practical problems?" In fact, these problems have a lot to do with our usual teaching. It is precisely because we have not systematically trained students to build mathematical models and cultivated their modeling consciousness. Therefore, students' ability to solve problems has not been improved, which has affected their academic performance. So I think one of the key points of our mathematics teaching is to cultivate students' modeling consciousness and train students' modeling ability. It is a difficult problem for most junior middle school students to turn practical problems into mathematical problems. Only by consciously cultivating students' modeling ideas in teaching can students overcome this problem and release the powerful motivation to learn and solve practical problems. So how to build a mathematical model?

First, the cognition of mathematical modeling

In classroom teaching, in order to cultivate students' awareness of using mathematical models to solve practical application problems and successfully establish mathematical models, students should first know mathematical models. Mathematical model is a model that simulates reality with mathematical language, that is, abstracting the main characteristics and relations of some things in practical problems into mathematical language, which approximately reflects the internal relations and changing process of objective things. All mathematical concepts, formulas, equations and functional relationships are called mathematical models.

The method of establishing a mathematical model is to construct a corresponding mathematical model for the actual problem. Through the study of the mathematical model, the mathematical method to solve the problem is usually divided into the following three steps.

Firstly, the characteristics of practical problems are abstracted mathematically and an appropriate mathematical model is constructed.

Second, the common types of mathematical models

In classroom teaching, I divide the common mathematical models in junior high school into four categories: ① trigonometric function and functional model; ② Equation and inequality model; ③ Geometric model; ④ Statistical model. The following is the classification of classroom teaching cases.

Third, clear the obstacles of students' mathematical modeling and find solutions.

First, in the practical application of junior high school mathematics, there are often many terms in other knowledge fields. Because students have little contact with the outside world, they are unfamiliar with these terms and don't know their meanings, so they can't read the questions and correctly understand their meanings, let alone solve problems. For example, students don't understand the concepts of direction angle, slope angle, lighting, interest rate, interest, profit and discount in real life, which affects students to build mathematical models. In view of students' obstacles in this respect, I asked students to use the network platform and teachers to explain the meanings of these nouns, and then the teachers analyzed and explained them, thus successfully establishing a mathematical model to solve practical problems.

Secondly, mathematical modeling method is a kind of mental work to solve practical problems by using mathematical knowledge and methods. Many students, especially rural middle school students, have poor psychological quality, so they lack confidence in solving practical problems. In view of this modeling obstacle, we should pay attention to the cultivation of mathematical application consciousness and the training of students' mathematical abilities such as mathematical language and reading comprehension. Specifically, we should do a good job in the following aspects of teaching.

1. Let students experience mathematics, taste the joy of success, and pay attention to cultivating students' self-confidence.

In the usual teaching, we should strengthen the teaching of practical problems, so that students can discover, create and use mathematics from their lives and gain enough confidence in the process. For example, when teaching the calculation method of savings deposit interest, students can be organized to go to the bank for field visits and ask students questions: how to choose the term of savings deposit and how to set the interest rate? Suppose you deposit 5000 yuan in the bank, try to calculate the amount of interest you can get after three years. The deposit methods are: ① 65,438+0 years, and the principal and interest will be transferred after the expiration of each year; (2) Deposit for 2 years, and transfer the principal and interest at maturity; ③ Three-year fixed term, lump-sum deposit and lump-sum withdrawal. Which of the above deposit methods earns the most interest? Please use your math knowledge to discuss the conclusion. This survey enables students to break through the psychological fear of deposit interest rate and interest calculation, and calculate the way to get the maximum interest from deposits according to the survey data, and most students can explain and explain it with mathematical principles. As can be seen from the above examples, we should pay attention to connecting with things around us in teaching and create opportunities for students to experience mathematics, which can enhance students' confidence in mathematical modeling.

2. Cultivate students' reading comprehension ability

Reading helps to cultivate students' inquiry ability and self-study ability. Influenced by their reading and analysis ability, the mastery of basic mathematical knowledge and the ability of mathematical language conversion, many students can't relate practical problems with corresponding mathematical models. For example, after the loss of Malaysia Airlines MH370, the China government actively participated in the search and rescue. On a certain day, two professional rescue boats A and B in China received information about suspicious floating objects at the same time. Suspected floating object P is 53.5 northeast of rescue ship A, northwest of rescue ship B, and due east of rescue ship A 140 nautical mile: ① Find the distance from suspected floating object P to the straight line where two ships A and B are located; ② If rescue ship A and rescue ship B set out at the same time at the speed of 40 knots and 30 knots respectively, and went to search and rescue in a straight line at a constant speed, try to determine which ship arrived at P first by calculation. According to the classroom investigation, after reading the above questions, ask the students what mathematical knowledge they think and what mathematical model to build to solve the problems. Many students can't answer. In my opinion, the reason is that students have conversion obstacles when converting their main language into mathematical language, and they can't establish mathematical models for practical problems. Therefore, mathematics teaching must attach importance to mathematics reading. As a math teacher, we should not only cultivate students' reading ability, but also give them scientific and effective reading methods to make them realize the importance of math reading.

In a word, cultivating students' ability to solve practical problems is to cultivate students' modeling ability, which plays an important role in improving students' interest in learning and cultivating innovative consciousness. We should attach importance to it in teaching and give students correct guidance.