As a very important mathematical thinking method, conversion can help students discover the essence through phenomena, so as to apply mathematical knowledge to solve practical problems and truly apply what they have learned.

Abstract: With the continuous advancement of the new curriculum standard of Shanghai Science Edition, the idea of transformation occupies an increasing proportion in mathematical thought. Applying the idea of reduction can deal with abstract and complex problems concretely and simply, which is the key to cultivate students' mathematical thinking. Based on the significance of conversion thought to junior high school mathematics teaching, this paper analyzes the practice of conversion thought in junior high school mathematics teaching with specific cases.

Keywords: changing thinking; Junior high school mathematics; practice

At present, mathematics teaching emphasizes that teachers should not only impart basic knowledge to students, but also infiltrate mathematics thoughts into mathematics knowledge. Mathematical thoughts are people's understanding of the essence of mathematics summed up through practice, which is also the essence of mathematics and plays a positive role in cultivating students' problem-solving ability. The thought of conversion is a part of mathematics thought, and it can simplify complex problems by infiltrating it into junior high school mathematics teaching. Shanghai science edition mathematics textbook actively introduces the idea of mathematical transformation, which makes it possible for teachers to introduce and infiltrate the idea of mathematical transformation to students.

First, the significance of transforming ideas to junior high school mathematics teaching

Junior high school mathematics involves many mathematical principles and connotations, and the thought of reduction, as an important mathematical thought, can help students understand the mathematical principles and connotations in depth. Students master the transformation method, which will greatly improve their mathematics literacy. In addition, transforming ideas can further improve the knowledge system of mathematics teachers and guide them to develop towards teaching specialization. The significance of conversion thought in practice is also very prominent.

Second, the practice of applying the thought of conversion to junior high school mathematics teaching

Familiar with unfamiliar problems

The learning of mathematical knowledge is a process from unfamiliarity to familiarity. Junior high school students can calculate the answers to familiar questions in the fastest way. But for unfamiliar topics, it takes more time and energy. For example, in the mathematics teaching of Shanghai Science Edition? What is the relationship between the angles of a triangle? The problem is shown in figure 1. The isosceles triangle ABC moves in a straight line at a speed of 2m/s until AB and CD coincide. If it moves for x seconds, the overlapping part of triangle and square is the area ym2. Finally, find the relationship between x and y. For this problem, teachers can use the static problems that students have learned and mastered, that is, use graphics and known conditions to solve unknown problems. The infiltration of transformation ideas inspires students to find out the line segment related to the moving point, express it with the formula containing X, and finally find out the relationship between X and Y. Using this method, unfamiliar dynamic problems can be turned into simple static problems, thus helping students solve problems.

The concretization of abstract problems

The concretization of abstract problems is the concrete embodiment of reduction thought. As a function problem that junior high school students first come into contact with, linear function will make students feel very abstract. Therefore, teachers can set up teaching situations and ask questions to students before teaching begins. Do students know how to charge mobile phones? This problem is a common problem in students' daily life, which can fully mobilize students' enthusiasm and students will actively speak. Then, the teacher summed up two different payment methods and asked:? Which of the two payment methods is more cost-effective when you formally enter the teaching process?

(3) Transforming axioms and formulas into known conditions

As we all know, the application of textbook knowledge, especially the formulas and axioms summarized by mathematicians, provides great convenience for solving mathematical problems. For example, how to turn axioms into known conditions, and select specific mathematical problems as cases. As shown in Figure 2, in the triangle ABC, AD is the height on the side of BC, and AE is equally divided. BAC，？ B, is it? C is 75 respectively? 、45? , for a corner? DAE and? The degree of AEC. Judging from the topic, this topic mainly applies the external angle theorem. Although the topic is not clear, it can be used as a theorem to solve problems. After mastering the external angle theorem, students can find a solution to this kind of problem faster in their later study.

(D) the principle of harmony and unity

The principle of harmony and unity means that the problems to be solved should be coordinated in expression, especially in quantity and form, and the conditions and conclusions of the problems should be more reasonable and appropriate. For example, this method can be used to solve problems in the teaching of circles, especially in the solution of irregular areas of circles. In junior high school mathematics teaching, although the thought of reduction is not listed as a separate chapter, this way of thinking runs through the whole course.

Third, the conclusion

As a very important mathematical thinking method, conversion can help students discover the essence through phenomena, so as to apply mathematical knowledge to solve practical problems and truly apply what they have learned. Therefore, in teaching, teachers should correctly understand the idea of cultural transformation, combine teaching content with students' characteristics, convey the idea of cultural transformation to students, simplify and concretize complex and abstract problems, reduce the difficulty of mathematics problems, and make students gradually interested in mathematics.

References:

[1] Wang, Han Longshu, Qu Jun. Teaching design of mathematical thought based on heuristic teaching: using? Turn to thought? For example [J]. Teaching and Management, 20 15( 1):57-59.

[2] Li Yanni. How to infiltrate mathematical thinking methods into junior high school mathematics teaching [J]. Chizi (Middle School), 20 15( 12):286.

[3] Jin Shengyang. Research on Teaching Strategies of Infiltrating Mathematical Thinking Methods in Junior Middle School Mathematics Teaching [J]. China Off-campus Education, 2015 (33):114.

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