Concept teaching is not the same as concept class teaching. The learning of a concept can be completed by multiple concepts. Understanding and mastering concepts is a step-by-step process, which needs to be applied repeatedly in the subsequent courses of concept class to deepen understanding. For example, after learning the function, compare the size by the nature of the function:-x+5 >; 2x2-3x+ 1, the students can do it right, but they can't say why. Students know to use equations, inequalities and other properties, but did not expect to use-x+5 >; As two functions, 2x2-3x+ 1 shows that students need to understand the concept, value and problem of function from the perspective of function again. Therefore, teachers should guide students to re-understand concepts such as function and treat these two numbers from the perspective of function. They are the comparison of two functions. We can analyze the value of the comparison function from the image and solve it by studying the monotonicity of the function. Every concept is not learned overnight, and it is very important to understand the original concept in the subsequent courses of concept class.

Concept is the reflection of the essential attributes and characteristics of objective things in people's minds. Mathematical concept is a form of thinking that reflects the essential attributes of spatial form and quantitative relationship in the real world. In junior high school mathematics teaching, strengthening the teaching of concepts and correctly understanding mathematical concepts are the premise of mastering the basic knowledge of mathematics, the basis of learning theorems, formulas, laws and mathematical ideas well, and clarifying concepts is the key to improving the ability to solve problems. Under the guidance of the new round of curriculum reform concept, combined with my teaching practice, I will discuss some related problems of mathematics concept teaching with you.

Mathematics is natural, mathematics is clear. Any mathematical concept has its background, and its rationality can be found by examining its context. In order for students to understand the concept, we must first understand its background, analyze the essential attributes of the concept through a large number of examples, and let students summarize the concept, improve the concept and further consolidate and apply the concept. Talent is students' initial mastery of concepts.

The following are some teaching cases of concepts and laws.

1, Algebra Concept Teaching

The concept of algebra (letters represent numbers) has always been a difficult point for students to learn algebra, and there are many students.

After learning, I can only remember the formal characteristics of algebra, but I can't understand the meaning of letters representing numbers. The essence of algebraic expression is that knowledge numbers and numbers can be operated like numbers. To understand this, we need the following four levels.

(1) Understand specific algebraic expressions through operational activities.

Question 1: Let the students build a square with matchsticks in the following ways, and please fill in the following table:

Question 2: There are some rectangles whose length is three times the width. Please fill in the following form:

Through the above two questions, let students have a preliminary understanding of the various relationships represented by numbers with the same meaning.

(2) In the inquiry stage, experience the process in algebraic expressions.

According to the situation in the activity stage, some questions can be put forward for students to discuss and explore:

① What is the relationship between 3n+1 in question1and specific figures?

(2) What are the characteristics and significance of taking the formula expressed by specific letters as a whole? (need

Algebraic characteristics after repeated experience, reflection and abstraction: an operational relationship; Letters represent a class of numbers, etc. ).

This stage also includes the evaluation of column algebra and algebra. The following questions can be designed to give students a better understanding of algebra.

Characteristics of quantity:

(1) each Bao Shu has 12 copies, and n Bao Shu has _ _ _ _ _ _ _.

(2) The temperature drops from t℃ to 2℃, which is _ _ _ _ _ _ _ _ _ _.

(3) The side length of a square is x, so its area is _ _ _ _ _ _.

(4) If you buy X square meters of carpet (A yuan per square meter) and pay Y cubic meters of tap water fee (B yuan per cubic meter), * * * will spend _ _ _ _ _ _ _ _ _ _?

(3) In the object stage, algebraic expressions are formalized.

This stage includes establishing the formal definition of algebraic expression, simplifying algebraic expression, merging similar terms and factorization.

Solve and solve equations and other operations. Students realize that the object of operation is a formal algebra, not a number, and algebra itself embodies the structural relationship of an operation, not just the operation process. At this stage, students must understand the meaning of letters and identify algebraic expressions.

(4) In the schema stage, establish a comprehensive psychological schema.

Through the above three stages of teaching, students should establish the following algebraic psychological table in their minds.

Symbol: concrete examples, operation process, the mathematical idea that letters represent a number, and the definition of algebraic expressions can be used.

2, rational number addition rule

(1) operation: various possible results of calculating the victory or defeat of a football team in a football match.

Different situations:

(+3)+(+2)——+5 (-2)+(- 1)——-3

(+3)+(-2)——+ 1 (-3)+(+2)——- 1

(+3)+ 0——+3 …………

(where the two rational numbers in each summation formula are fractions of the first half and the second half).

(2) Explore the law: comprehensively analyze the characteristics of the above formula as a whole: summarize the law and understand the operational significance by comparing the process and results of addition of the same sign, addition of different signs and addition of one number and zero.

(3) Forming an object: integrating various laws into a complete rational number addition rule to generate a rational number sum model;

Rational number+rational number = ① sign ② value

This stage also includes the operation of arbitrary sum of rational numbers and algebraic evaluation according to the mode and specific operation law of rational sum.

(4) Forming a schema: The rational number addition rule is established in students' minds with a comprehensive psychological schema, including concrete examples of football matches, abstract operation processes, complete operation rules and formation modes. And through the later study, we can get the difference and connection with other concepts and laws.

Therefore, the link of concept teaching should include the introduction of concepts-the formation of concepts-the generalization of concepts-the definition of concepts-the application of concepts-the formation of cognition. Compared with the concept of new curriculum reform, students' learning in traditional teaching mode lacks "activity" stage and has not fully experienced the formation process of concepts. The establishment of students' mathematical concepts depends on teachers, not quick experience and quick abstraction. Reflect the situation are:

(1) The rapid abstraction process makes it difficult for a few students to learn meaningfully, and it is also difficult to trigger all students' learning activities. Most students can't understand mathematical concepts, so they have to learn by rote. For example, students learn rational number operation for a long time and often make mistakes in symbolic operation, which is caused by students' ignorance of rational number operation.

(2) Teachers quickly experience and abstract mathematical concepts instead of students. Even students who can learn meaningfully with their teachers are incoherent in their learning activities, and the concept constructed lacks integrity. For example, when students study algebra concepts, they often make mistakes such as a+a+a×2=3a×2, 25x-4=2 1x, 5yz-5z=y, which is caused by students' failure to carry out necessary "activities", making the "inquiry" experience incomplete and unnecessary. Another example is that the error (x+2) 2 =1= x2+4x+4 =1= ... when solving the equation, it shows that students still stay at the level of the operation process and do not understand the structural characteristics of the equation object.

(3) The schema level of students' concept construction is the highest stage of learning, which is difficult for many students to achieve under the existing teaching environment. For example, why learn to solve equations? What is the essence of solving equations?

Mathematics concept teaching under the new curriculum reform concept is a learning process from students' activities, inquiry objects and schema, which embodies the regularity of the formation of mathematics knowledge. To this end, I combine my own teaching practice and adopt the following strategies to teach mathematical concepts:

(1) Teachers should base "teaching" on students' "learning" activities.

In order for students to construct complete mathematical knowledge, we must first design students' learning activities. This requires teachers to create problem situations, and the following aspects should be paid attention to when designing: ① It can reveal the realistic background and formation process of mathematical knowledge; (2) Suitable for students' learning level, so that learning activities can be carried out smoothly; ③ Appropriate number of questions, so that students can have full activity experience; (4) Pay attention to fun, and the activities can be varied to stimulate all students' interest in learning.

(2) Reflect the mathematical thinking method in the formation of mathematical knowledge.

Mathematical thinking method is the soul of knowledge generation. Mastering the mathematical thinking method in the formation of mathematical knowledge is the main line for students to develop their thinking and construct their concepts. Students should give tips and suggestions in their study and summarize them in the summary. In addition, design questions that can arouse students' reflection, such as "What is your result?" "How did you get it?" "Why did you do that?" ..... let students successfully complete the transition from "activity" to "inquiry" and from "inquiry" to "object".

(3) The establishment of mathematical objects needs to be repeated many times.

The establishment of a mathematical concept from "inquiry" to "object" is sometimes difficult and long (such as the concept of function). The compression and abstraction from "inquiry" to "object" need to be repeated many times, step by step, and spiral up until students really understand. The establishment of "object" should pay attention to concise text form and symbol representation, so that students can establish an intuitive structural image of mathematical knowledge in their minds. Strengthen the connection and application of knowledge to help students establish a complete psychological schema of mathematical knowledge in their minds.

To sum up, mathematics concept teaching should try to cultivate students' dialectical materialism, improve their cognitive structure and develop their thinking ability by revealing the process of concept formation, development and application. It is not difficult to improve the quality of mathematics teaching as long as we follow the cognitive law and attach importance to the research and practice of concept teaching.