There is a universal connection between things, and they can be transformed into each other. Reduction is one of the most commonly used and basic thinking methods in mathematics. The so-called transformation means that in the process of solving problems, we can explore the essence of problems from different angles of thinking and different analytical aspects by transforming the direction of solving problems and find the best answer. Transformation means that for some difficult problems that need to be solved directly, through observation, analysis, analogy, association and other thinking processes, appropriate mathematical methods are selected to transform the original problems into easy problems that have been mastered, and the original problems are solved by solving the transformed problems. Conversion is an effective way of thinking, the core and essence of mathematical thought and the soul of mathematical thought. Therefore, teachers should embody this way of thinking in every link of teaching, so that students can learn more easily and efficiently.

First, pay attention to the infiltration and transformation of ideas in the teaching process.

Contradictions are universal and can be transformed into each other. In specific teaching activities, teachers should let students know that a lot of new knowledge is based on old knowledge, which is an extension and expansion of old knowledge. Therefore, when introducing new knowledge, teachers should pay attention to the connection with old and new knowledge. On the one hand, they should review and consolidate their old knowledge and look for the shadow of the old knowledge in the new knowledge, on the other hand, they should use the old knowledge to solve the new knowledge indirectly, so as to transform new difficult problems from the old knowledge and achieve the purpose of answering new problems. Through the introduction and infiltration of teachers in the teaching process, the transformed thinking method gradually takes root in students' minds, and the students form a thinking mode of solving doubts and answering difficulties with transformed thinking method over time.

For example, when teaching the area calculation method of parallelogram, students can transform the area calculation method of parallelogram into the area calculation method of rectangle through the guidance of transformation thought; Later, when calculating the area of triangle and trapezoid, it was transformed into parallelogram, thus forming a fixed transformation thinking. When learning to calculate the area of a circle and its volume, it is easy for students to think of a transformed way of thinking to learn new knowledge, thus greatly improving the learning efficiency.

Second, the transformation methods commonly used in primary school mathematics teaching

1. Transform in calculation, simplify the complex and optimize the problem-solving strategy.

When dealing with and solving some mathematical problems, we often encounter some complicated operations or problems with very chaotic quantitative relations. At this time, teachers need to change their problem-solving strategies and use various algorithms, laws and properties to simplify the complex, which is often called simplification.

For example: (267+123× 894) ÷ (894×124-627) Because there is the same factor 894 in the formula, we can convert it into: (267+123× 894) ÷.

For another example, when teaching the division of decimals, it is calculated by converting primary schools into integers; When teaching the division of fractions, we operate by converting division into multiplication. As long as we can find a breakthrough and do some mutual transformation between problems of the same nature, we will simplify complex problems, so as to achieve twice the result with half the effort and make ourselves suddenly enlightened.

2. Transformation between quantity and shape

The conversion between quantity and number is widely used. There is a thinking method of combining numbers and shapes in middle schools. In primary school, when we teach new knowledge or solve mathematical problems, in order to be intuitive, we express the relationship between quantities in pictures, and use the division and transformation law of the relationship between quantities on the pictures to solve problems. For example, the calculation methods and formulas of various graphic areas are all based on students' hands-on experiments. First, transform the graph into the graph you have learned, and observe and explore the relationship between the transformed graph and the original graph on the map. For example, the derivation of parallelogram area is to convert parallelogram into rectangle on the map, so the calculation of parallelogram area is the same as that of rectangle area.

For example, for the formula of junior high school 9, students can be organized to color on the square paper of 10 multiplied by l0. 1 9s, line 9, l01; Two nines, two lines drawn, 20 MINUS 2 ... and so on, concise and intuitive, clear at a glance. This combines abstract mathematical knowledge with concrete graphics, which is convenient for young students to understand, so that every child can actively participate in teaching activities and improve learning efficiency.

3. Equivalent transformation

Equivalent transformation is to change the known data into the unknown quantity to be solved through the equal or consistent values between quantities. For example, Xiaoming spent 52 yuan to buy 4 kilograms of oranges and 5 kilograms of apples. As we all know, the price per kilogram of oranges is twice that of apples. How much are two kinds of fruits per kilogram?

This problem gives the quantity and total price of two kinds of fruits, and finds their unit price. When solving a problem, students feel that the known conditions in the problem are not sufficient and it is difficult to start. At this point, teachers should be good at guiding students to think: if you ask the unit price of a fruit, you must know the total price of the fruit and its quantity. Can you convert two kinds of fruits into one kind of fruit according to their quantitative relationship? Can the price of 4 kilograms of oranges be converted into the price of 8 kilograms of apples according to "the price of 1 kg of oranges is twice that of 1 kg of apples"? This problem is converted into (8+5), which is13kg 52 yuan of apple blossom. What is the unit price of apples? With the price of apples, we can work out the price of oranges. In this way, through equivalent transformation, hidden conditions will naturally appear.

Third, strengthen the role of transformational thinking in practice and cultivate students' awareness of transformational thinking.

For intermediate and advanced students, the design of exercises is no longer simply limited to the scope of example exercises. The exercises of senior students are more flexible and challenging, and many students are often confused when they encounter complex and changeable exercises. This requires teachers to strengthen the practice of transformation exercises in their usual teaching, so that students can strengthen the formation of transformation ideas in their consciousness through practice and guide their actions when necessary.

For example, when teaching the least common multiple, students often encounter some distribution problems, which are difficult for students to solve. If there is such a question: "There are a batch of bricks, each of which is 45 cm long and 30 cm wide. How many bricks can you use to lay a square? "

To solve this problem, students must first understand the conditions for paving squares, that is, the sides must be equal. Then, they have to think about how to put the rectangle into a square. Considering that several are equal in length and width, this requires a common multiple of 45 and 30, in which "at least several" is to find their least common multiple. In this way, an exercise that looks like a geometric figure is transformed into algebraic knowledge to solve. The solution is simple and easy for teachers to understand.

The thought of conversion is ubiquitous and runs through the whole mathematics teaching and learning, which is the essence of mathematics. In the specific teaching process, teachers should be good at guiding students to form transformed thinking methods, teaching better and serving students better.