The quality of teachers' teaching mathematical concepts directly affects the quality of students' learning mathematics. Students' logical thinking ability, spatial imagination ability, operational drawing ability, flexible problem-solving ability and innovative inquiry ability are all based on clear concepts. These abilities are closely related to the clarity of the corresponding concepts and the depth and breadth of understanding. Practice has proved that strengthening concept teaching is an effective strategy to improve the quality of mathematics teaching in primary schools. Then, under the background of actively studying the effectiveness of classroom teaching, how should we effectively carry out the teaching of mathematical concepts in primary and high schools?

First, create an effective life situation and introduce concepts.

Situational creation is the eye of a class, which can be expected. The concept of mathematics is abstract and boring. It is necessary to introduce the concept into rich, typical and natural real life situations in teaching, so as to stand on the psychological needs of students. In every math class, we should try our best to catch the math problems in life and introduce concepts from the students' real life.

For example, letters represent numbers.

Teacher: "Students, do you like playing cards?"

The teacher took out four playing cards, 10, J, Q, K, and asked, "Who is the biggest of these four cards? Why? " Health: "K is the largest, because K stands for 13."

Teacher: "What does Q mean? What about J? "

After the students answered, the teacher concluded: "In other words, these letters all represent a number. Today we will learn to use letters to represent numbers. "

In this link, students' favorite and familiar playing cards are linked with mathematics, which not only combines students' real life and introduces new lessons from vivid life situations, but also stimulates students' interest in learning, so that students can devote themselves to the classroom and stimulate their enthusiasm for learning.

Second, a lot of perception, in-depth understanding of concepts.

The formation of concept is a process of accumulation and gradual progress, and concept teaching should follow the principles from concrete to abstract, from perceptual knowledge to rational knowledge. The thinking characteristics of primary school students are gradually changing from concrete thinking to abstract thinking. This transition still depends on rich perceptual materials to a great extent, from which mathematical concepts are summarized and abstracted. Math concepts are not taught by teachers, but by students themselves.

For example, the understanding of percentage.

After students know the percentage, they initially perceive the meaning and function of the percentage. Then through a lot of information, such as "Yao Ming joined the NBA League in the first year, shooting 49.8%; The forest coverage rate in Japan is as high as 65%, while that in China is only 14%. 6 1 class mid-term examination qualified rate is 99.6%, excellent rate is 72.2%. The turnover of foreign fast food is 220% of that of Chinese fast food. Through these, students can deeply understand the practical significance of percentage in real situations. After students have accumulated a lot of perceptual materials, let them summarize the meaning of percentage in their own words, and it will come naturally.

Third, guide students to understand concepts through comparison and practice.

Ushinski, a famous educator, said: "Comparison is the basis of all understanding and thinking. It is through comparison that we understand everything in the world. " In concept teaching, there will be many similar or similar concepts that are easily confused. In this case, the similarities and differences between concepts are found by comparison, and their differences and connections are clarified. This can not only deepen the understanding of concepts, but also strengthen new knowledge.

Many confusing concepts, such as number and number, time and moment, simplification and comparison, can be distinguished through comparative analysis. Contrast exercises can best reflect the connection and difference of mathematical knowledge. Cultivating students' knowledge transfer is often reflected in comparative exercises. For example, show 12: 8, let students calculate the simplified ratio and the ratio, and put the simplified ratio and the ratio together for students to answer. Generally, there are no mistakes, and students can easily know the difference between 3: 2 and 2/3. If we simply change it to 12: 8, for another example, if the ratio is a fraction or a decimal, the error rate is higher. Through more comparative exercises, students naturally find that there are still many rules to be found, (simplified proportion is the proportion in the form of fractions we require) and so on.

Fourth, deepen the understanding of concepts in asking questions and posing difficult problems.

Some important features of the concept, if we only rely on the teacher's emphasis or superficial revelation, may not receive good teaching results, but if we leave some room for students to question and deepen their understanding in solving problems, the concept will be more perfect. "Thinking because of doubt", people's thinking activities begin with doubt, and without doubt, there is no thinking. Therefore, in the process of concept formation, teachers consciously let students ask questions, which can promote students' understanding of concepts.

For example, the teaching fragment of the law of constant quotient

1. Observation shows that after observing and comparing a set of formulas, students find that the dividend and divisor are multiplied by the same number at the same time, and the result remains unchanged.

2. Guide the students to summarize: Who can summarize the law we just discovered in a complete sentence? After reporting and summarizing, show that the dividend and divisor are multiplied by the same number at the same time, and the quotient remains unchanged.

3. Question: Does the quotient remain the same when the dividend and divisor are multiplied by 0 at the same time?

4. Guide the students to conclude again: the divisor and divisor are divided by the same number at the same time (except zero), and the quotient remains unchanged.

5. Give it a try and verify the law.

Is there such an example in real life? Verifying the law of quotient invariance with examples.

Fifth, gradually build the concept into a network and make it systematic.

Students always learn from specific isolated concepts, even if they pay attention to some connections between concepts in teaching, it is often for the need of learning new concepts. Therefore, in the eyes of primary school students, concepts are often isolated and unrelated. In teaching, we must guide students to put the concepts they have learned together, find the vertical or horizontal connection between concepts, form a concept system, and transform the mathematical knowledge in textbooks into the cognitive structure in students' minds. The cognitive structure of this system not only helps to consolidate the understanding of concepts, but also promotes the transfer of knowledge and develops students' mathematical ability.

For example, the understanding of the ratio

After teaching comparison, let students sort out the connections and differences between comparison, division and division, and communicate their internal connections. It lays a foundation for the diversification of problem-solving algorithms for teaching scores in the future. Comparing ratio, fraction and division, following the internal relationship of knowledge, is helpful to guide students to establish a good cognitive structure. Students are not only aware of the relationship between concepts, but also a process of establishing a complete knowledge network. When learning specific isolated concepts, we will not deeply understand the essence of these concepts. Only starting from the whole knowledge system can we understand them more deeply and know their position and role in the whole system.

Sixth, pay attention to the emotional experience in concept teaching.

It is clearly pointed out in the new curriculum standard that "students should take part in specific mathematics activities and learn mathematics through personal experience". In the teaching of concept class, we should also attach importance to students' emotional experience. When introducing concepts from real life, students can experience the life of mathematical knowledge; When exploring knowledge in a large number of computing activities, students can experience the formation process of concepts; In the teacher-student interaction, students can experience the joy of success; When applying concepts to life, students can experience the application value of mathematics.

Mathematical concepts are the reflection of the essential attributes of quantitative relations and spatial forms in the objective world in the human brain. All mathematical knowledge is based on a series of mathematical concepts. The basic knowledge of calculation, geometry and algebra, and the ability to solve simple practical problems with mathematical knowledge are all based on the mastery of mathematical concepts. Only by carrying out concept teaching effectively can students acquire mathematical knowledge, further cultivate various mathematical abilities and develop their thinking.