Let's pay attention to the subject characteristics of mathematics first. One of the characteristics of primary school mathematics is very systematic. Every new knowledge is often closely linked with old knowledge. New knowledge is the extension and development of old knowledge, and old knowledge is the foundation and growing point of new knowledge. Sometimes new knowledge can migrate from old knowledge, but at the same time it becomes the basis of subsequent knowledge. Therefore, the knowledge of mathematics is like a chain, interlocking.

It can be seen that it is not difficult for teachers to make a breakthrough in teaching if they are good at capturing the connection points between mathematical knowledge, consciously taking "transfer" as a method to help students learn, bringing forth the old and accumulating the new from the old, and the organization is moving.

Case 1: Basic Properties of Fractions

The basic nature of a fraction is described as follows: the numerator and denominator of a fraction are multiplied or divided by the same number at the same time (except 0), and the size of the fraction remains unchanged.

In teaching, if we regard it as an isolated knowledge point, observe the change of 1/2=2/4=6/ 12 one by one from left to right, and describe the change process from who to whom over and over again, the teacher's purpose is to make students realize the existence of this law and learn to express it in the same way, but in the end,

If we analyze the knowledge base of the basic nature of fractions before teaching, we will find the "constant nature of quotient" and "the relationship between fractions and division" which are very similar to their descriptions. At this time, in order to break through the teaching difficulty of "guiding students to summarize the basic nature of fractions", we can arrange the narration of "the constant nature of quotient" and the practice of "the relationship between fractions and division" in the review session before class.

There are many knowledge points that can be taught by transfer method. For example, a divisor is the division of two digits. It transfers learning based on the written calculation of division with divisor of single digits, but it only increases trial quotient and quotient adjustment, which makes it more difficult and the method more flexible. For example, the multiplier is a multi-digit multiplication, which is migrated on the basis of learning one-digit multiplication, and the operation method is the same.

It can be seen that in the process of mathematics teaching, we should pay attention to revealing and establishing the internal relationship between old and new knowledge, and start from the existing knowledge and experience, and use the method of transfer to break through the difficulties. The key to implementing this method is that students should master old knowledge skillfully, and his previous knowledge is solid. Therefore, it is emphasized that teachers should regard themselves as "gatekeepers" every year, so that students can "walk steadily every step".

2. Grasp the connection between knowledge, adopt the strategy of transformation, and break through the key and difficult points.

Transformation-it means that it is often difficult to solve some problems directly when solving mathematical problems. Through observation, analysis, analogy, association and other thinking processes, we choose to use appropriate mathematical methods to transform the original problem into a new one (which is relatively familiar to us), and through the solution of the new problem, we can achieve the purpose of solving the original problem. This kind of thinking method is called "transformation thinking method". In teaching, if teachers can "change the new into the old", grasp the "vertical and horizontal connection" between knowledge, help students form a knowledge network, and gradually teach students some transformation thinking methods, so that they can learn new knowledge and analyze new problems from the perspective of transformation, so that their understanding of knowledge can be deepened and finally achieve mastery.

For example, the formulas of triangular area, trapezoidal area and circular area are deduced.

3. Strengthen perceptual participation and use intuitive methods to break through teaching difficulties.

Intuition-refers to making full use of teaching tools such as objects, models and multimedia computers in the teaching process, helping students understand and master mathematical knowledge and promoting the development of thinking through practical operation, observation and thinking activities. Intuitive teaching is one of the most commonly used and independent teaching methods in primary school mathematics teaching activities.

(1) hands-on operation to solve key and difficult problems.

For example, the derivative of the circular area.

(2) Solve key and difficult problems by drawing.

You can use charts to help solve problems, such as (

(3) Visual demonstration to solve key and difficult problems.

For example, use courseware to demonstrate the translation and rotation of an object and the rotation of the clock in a day, so that students can understand the meaning of 24-hour timing. When learning the volume calculation of a long cube, if the courseware is used to help students realize that the volume is actually the unit number of the volume of an object, they will not waste time in communication and reporting.

(4) Formulating songs to help students remember intuitively.

For example, remember the songs of the day. There are five factors and multiple units in teaching, and the concepts are numerous and confusing. Teachers can guide students to write their own songs to help them remember. If it is very difficult for students to memorize the prime number table within 100, they can be guided to compose these numbers into songs to memorize: two, three, five, seven, eleven, thirteen is followed by seventeen, nineteen, two, three, twenty-nine, three, seven, forty-one, four, three, four, seven, fifty-three, five and sixty-one.

If you want to find the greatest common factor and the smallest common multiple, you can also remember them with the following ballads:

The coprime of two numbers should be remembered that the greatest common factor is 1 and the least common multiple is the product;

When the relationship between two numbers is multiple, the maximum common factor is smaller and the minimum common multiple is larger;

If the relationship between two numbers is not obvious, try to find the quotient by short division. Multiply the greatest common factor by half and the least common multiple by a circle.

The key to using intuitive methods well is to turn abstract into concrete, stimulate students' interest in learning, promote students' understanding of knowledge and develop their thinking ability.

There are many ways to break through the teaching difficulties. The methods introduced above are aimed at the situation that some knowledge points are used alone in teaching, and of course these methods can also be used in combination. In short, in order to effectively improve classroom efficiency in teaching, we must go deep into it.