Mathematical concept is the reflection of the quantitative relationship and the essential attribute of spatial form in objective reality in the human brain. The research object of mathematics is the quantitative relationship and spatial form of objective things. In mathematics, the color, material, smell and other attributes of objective things are regarded as non-essential attributes and discarded, leaving only their common attributes in shape, size, position and quantity. In mathematical science, the meaning of mathematical concepts should be precisely defined, so mathematical concepts are more accurate than general concepts.

There are many concepts in primary school mathematics, including the concepts of number, operation, quantity and measurement, geometric shape, ratio and proportion, equation and related concepts of preliminary statistical knowledge. These concepts are important contents of elementary school mathematics basic knowledge, and they are interrelated. Only by grasping the concept of number clearly and firmly can we understand the concept of operation, and mastering the concept of operation can promote the formation of the concept of divisibility of numbers.

Second, the expression of mathematical concepts in primary schools

Concepts in primary school mathematics textbooks have different forms of expression according to the acceptance of primary school students, among which descriptive expression and defined expression are the most important two.

1. Define formula

Definition is a method to reveal the connotation or extension of a concept in concise and complete language. The specific method is to explain the new concept to be defined with the original concept. These defined concepts grasp the essential characteristics of a class of things and reveal the essential attributes of a class of things. Such a concept, in the analysis, synthesis, comparison and classification of a large number of inquiry materials, has changed from intuition to representation and then to rational understanding. For example, "a triangle with two equal sides is called an isosceles triangle"; "An equation with unknowns is called an equation" and so on. The concepts, conditions and conclusions defined in this way are very obvious, which is convenient for students to grasp the essence of mathematical concepts at once.

2. Descriptive expression

Describing concepts in some vivid and concrete language is called descriptive. This method is different from definition. Descriptive concepts are generally established by students' perception of representations and choosing representative special cases as reference objects. For example: "When we count objects, 1, 2, 3, 4, 5 ... are called natural numbers"; "Things like 1.25, 0.726 and 0.005 are decimals" and so on. This concept will improve with the increase of children's knowledge and understanding, and it is generally used in the following two situations in primary school mathematics textbooks.

One is to describe the original concepts such as point, line, body and set in mathematics. For example, the concept of "straight line" in textbooks is described as follows: take a straight line and tighten it, and it becomes a straight line. Plane is explained by class desktop, blackboard surface and lake surface.

The other is that for some difficult-to-understand concepts, if it is difficult for primary school students to understand with simple and general definitions, they will use descriptive expressions instead. For example, the understanding of a straight cylinder and a straight cone can't be defined by a rotating body like middle school students, because primary school students still lack the viewpoint of movement, and they can only describe their characteristics vividly through physical objects, but can't reveal their essential attributes in the form of definitions. In the process of observation and spelling, students realize that the characteristics of a cylinder are that the upper and lower bottom surfaces are equal circles and the side surfaces are rectangular.

Generally speaking, in mathematics textbooks, the concept of lower grades in primary schools is more descriptive. With the gradual development of primary school students' thinking ability, definitions are gradually adopted in middle school, but some definitions are only preliminary and need to be developed. In the whole primary school stage, because of the contradiction between the abstraction of mathematical concepts and the visualization of students' thinking, most concepts are not strictly defined; Instead, starting from the actual cases that students know or the existing knowledge and experience, we should try our best to help students understand the essential attributes of concepts through intuitive and concrete images. For the concepts that are not easy to understand, we will not give a definition for the time being or adopt the method of gradual infiltration in stages to solve them. Therefore, the concept of mathematics in primary schools presents two characteristics: first, the intuition of mathematical concepts; The second is the stage of mathematical concept. When teaching mathematical concepts, we must pay attention to fully understand these two characteristics of the textbook.

Third, the significance of primary school mathematics concept teaching

First of all, mathematical concepts are an important part of basic mathematical knowledge.

Basic knowledge of primary school mathematics includes: concepts, laws, properties, laws, formulas, etc. Among them, mathematical concept is not only an important part of basic mathematical knowledge, but also the basis for learning other mathematical knowledge. The process of students mastering basic knowledge is actually the process of mastering concepts and using them to judge and reason. Laws in mathematics are based on a series of concepts. Facts have proved that if students have correct, clear and complete mathematical concepts, it will help them master basic knowledge and improve their ability to operate and solve problems. On the contrary, if students have unclear concepts, they will not be able to master laws, rules and formulas. For example, the rule of pen addition within integer 100 is: "The same numbers are aligned, starting with one digit, and when each digit is full of ten, it will enter one into ten digits." In order to make students understand and master this law, they must know the meanings of "digit", "unit", "ten digits" and "one digit is full of ten" in advance. If they don't understand these concepts clearly, they can't learn this law. For another example, the formula of circular area S=πr2 should be based on the concepts of circle, radius, square and pi. In short, some concepts in primary school mathematics are the basis and basic knowledge for future study. Primary school mathematics is a highly conceptual subject, that is to say, the teaching of any part of the content can not be separated from conceptual teaching.

Secondly, mathematical concepts are the basis of developing thinking and cultivating mathematical ability.

Concept is one of the thinking forms and the starting point of judgment and reasoning, so concept teaching can play an important role in cultivating students' thinking ability. Without a correct concept, there can be no correct judgment and reasoning, let alone the cultivation of logical thinking ability. For example, "an equation with an unknown number is called an equation", which is a judgment. In this judgment, students must be very clear about the concepts of "unknown" and "equation" in order to form this judgment, and thus infer the following six questions, which are equations.

( 1)56+23 = 79(2)23-x = 67(3)x÷5 = 4.5

(4)44×2 = 88(5)75÷x = 4(6)9+x = 123

In the process of concept teaching, in order to make students acquire related concepts smoothly, it is often necessary to provide students with rich perceptual materials for observation. On the basis of observation, through the inspiration and guidance of teachers, the perceptual materials are compared, analyzed and synthesized, and finally the essential attributes of the concept are abstracted. Through a series of judgments and reasoning, the concept has been consolidated and applied. So as to gradually improve students' initial logical thinking ability.

6. 1.3 General requirements for the teaching of mathematical concepts

1. Let students understand the concept accurately.

To understand a concept, one must be able to cite the realistic prototype reflected by the concept, the other must be clear about the connotation and extension of the concept, that is, the common essential attributes of a class of things reflected by the concept and all objects reflected by the concept, and the third must master the words or symbols representing the concept.

2. Make students grasp the concept firmly.

Mastering concepts means memorizing concepts on the basis of understanding them, and correctly distinguishing positive examples and counterexamples of concepts. Can classify concepts and form a certain concept system.

3. Enable students to use concepts correctly.

The application of concepts is mainly manifested in that students can identify the essential attributes of concepts in different specific situations, and make judgments and inferences by using the related attributes of concepts.

Fourthly, the process and method of mathematics concept teaching in primary schools.

According to the psychological process and characteristics of mathematical concept learning, the teaching of mathematical concepts is generally divided into three stages: ① introducing concepts to make students perceive concepts and form representations; ② Through analysis, abstraction and generalization, students can understand and clarify the concepts; ③ Make students consolidate and apply concepts through examples and exercises.

(A) the introduction of mathematical concepts

The introduction of mathematical concepts is the first and very important link in the teaching of mathematical concepts. If the concept is introduced properly, it can closely focus on the theme, fully stimulate students' interest and learning motivation, and lay the foundation for students to master the concept smoothly.

The process of introducing new concepts is to reveal the occurrence and formation process of concepts. The occurrence and formation process of each mathematical concept is different, and some are direct reflections of realistic models. Some are obtained after one or more abstractions on the basis of existing concepts; Some come from the needs of the development of mathematical theory; Some are produced to solve practical problems; Some idealize the object of thinking and get it through reasoning; Others arise from theoretical existence or the structure of mathematical objects. Therefore, in teaching, we must choose different ways to introduce concepts according to the background of various concepts and the specific situation of students. Generally speaking, the introduction of mathematical concepts can adopt the following methods.

1. Introduce a new concept based on perceptual materials.

Use the things that students come into contact with in daily life or the practical problems in textbooks, as well as models, graphs and charts as perceptual materials to guide students to acquire concepts through observation, analysis, comparison, induction and generalization.

For example, when learning the concept of "parallel lines", students can identify some familiar examples, such as rails, the upper and lower edges of doorframes, and the upper and lower edges of blackboards, and then analyze the attributes of each example to find out the common essential attributes. Rails have properties: they are made of iron and can be regarded as two straight lines. On a plane, the two sides can extend indefinitely and never intersect. You can also analyze the properties of the upper and lower sides of the door frame and blackboard. Through comparison, we can find that their common attributes are: they can be regarded as two straight lines abstractly; Two straight lines are on the same plane; The distance between them is equal everywhere; Two straight lines have nothing in common, etc. Finally, the essential attributes are abstracted and the definition of parallel lines is obtained.

The introduction of new concepts based on perceptual materials is taught by the way of concept formation. Therefore, in teaching, we should choose those cases that can fully show the characteristics of the introduced concepts and correctly guide students to observe and analyze. Only in this way can students sum up the common essential attributes from cases and form concepts.

2. Introduce new concepts with the relationship between old and new concepts.

If there is a certain relationship between the old and new concepts, such as compatibility and incompatibility, then the introduction of new concepts can make full use of this relationship.

For example, when learning the meaning of multiplication, we can introduce it from the meaning of addition. For another example, when learning the concept of "divisibility", it can be introduced from "division". For another example, learning "prime factor" can be introduced from the concepts of "factor" and "prime number". For another example, when learning the concepts of prime numbers and composite numbers, the concept of divisor can be introduced: "Please write down all divisors of the numbers 1, 2, 6, 7, 8, 12,1,15. How many divisors do they have? Can you give a classification standard to classify these figures? Can you find a variety of classification methods? Of all the classification methods you have found, which is the latest? "

3. Introduce new concepts in the form of "problems".

Introducing new concepts in the form of "questions" is also a common method in concept teaching. Generally speaking, there are two ways to introduce concepts with "problems": ① to introduce mathematical concepts from real life problems; ② Introduce concepts from the development of mathematical problems or theories themselves.

4. Introduce new concepts from the process of concept occurrence.

Some concepts in mathematics are defined by occurrence. In the teaching of this kind of concept, we can use the visual teaching AIDS of demonstration activities or the method of demonstration drawing to reveal the happening process of things. Concepts such as decimals and fractions can be introduced in this way. This method is intuitive and reflects the viewpoint and thought of movement change. At the same time, the introduction process naturally and irrefutably clarified the objective existence of this concept.

(B) the formation of mathematical concepts

Introducing concepts is only the first step in concept teaching. In order to get the concept, students must be guided to understand the concept accurately, to make clear the connotation and extension of the concept, and to correctly express the essential attributes of the concept. Therefore, some targeted methods can be adopted in teaching.

1, comparative analogy.

By comparing concepts, we can find out the differences between concepts, and by analogy, we can find out the similarities or similarities between concepts. For example, when learning the concept of division, we can compare it with the concept of division and find the difference between them. To talk about a new concept by comparison or analogy, we must highlight the difference between the old and new concepts, clarify the connotation of the new concept, and prevent the old concept from having a negative transfer effect on learning the new concept.

2. Use counterexamples appropriately.

In concept teaching, besides revealing the connotation of the concept from the front, we should also consider using appropriate counterexamples to highlight the essential attributes of the concept, especially by comparing the differences between positive examples and counterexamples, so that students can reflect on their mistakes, which is more conducive to strengthening their understanding of the essential attributes of the concept.

Using counterexamples to highlight the essential attributes of concepts, its essence is to let students know the extension of concepts and deepen their understanding of the connotation of concepts. Any object with the essential attributes reflected by a concept must belong to the extension set of the concept, and the construction of counterexample is to let students find out the objects that do not belong to the extension set of the concept. Obviously, this is an important means in concept teaching. However, it must be noted that the counterexample should be appropriate to prevent students from being too difficult, too biased, distracting and unable to highlight the essential attributes of the concept.

3. Rational use of variants.

Understanding concepts by relying on perceptual materials is often because the perceptual materials provided are one-sided and limited, or the non-essential attributes of perceptual materials have obvious outstanding characteristics, which is easy to form interference information, thus weakening students' correct understanding of the essential attributes of concepts. Therefore, we should pay attention to the use of variants in teaching to reflect and describe the essential attributes of concepts from different angles and aspects. Generally speaking, variants include graphic variants, formula variants and letter variants.

For example, when teaching the concept of "isosceles triangle", teachers should use variant graphics to strengthen this concept in addition to commonly used graphics, because when using the nature of isosceles triangle to solve problems, the graphics they encounter are often the latter.

(C) the consolidation of mathematical concepts

In order for students to master the concepts they have learned, there must be a process of concept consolidation and application. Attention should be paid to the following aspects in teaching.

1, pay attention to review in time.

The consolidation of concepts is completed and realized in the understanding and application of concepts, and at the same time, it should be reviewed in time. Consolidation cannot be separated from necessary review. The way to review can be to repeat individual concepts, to review concepts by solving problems, and more to review concepts in the concept system. When concept teaching reaches a certain stage, especially at the end of chapter review, final review and graduation review, we should pay attention to sorting out and systematizing the concepts we have learned, find out the vertical and horizontal relations between concepts, and form a concept system.

2. Pay attention to application

In concept teaching, we should not only guide students to form concepts from concrete to abstract, but also let them use concepts from abstract to concrete. Whether students grasp a concept firmly depends not only on whether they can say the name of the concept, but also on whether they can use the concept correctly and flexibly. Through application, they can deepen their understanding, enhance their memory and improve their awareness of mathematics application.

The application of concept can be carried out from the connotation and extension of concept.

Application of the concept of (1)

① Retell the definition of the concept or fill in the blanks according to the definition.

(2) According to the definition, judge right or wrong or correct mistakes.

③ Reasoning according to the definition.

④ Calculated according to the definition.

Example 4( 1) What is a prime number? This is a prime number.

(2) True or false:

27 and 20 are prime numbers ()

34 and 85 are prime numbers ()

Two numbers with common divisor 1 are prime numbers ()

Two composite numbers cannot be prime numbers ()

(3) One angle of an obtuse triangle is 82o, and the degrees of the other two angles are prime numbers. How many degrees can these two angles be?

(4) If P is a prime number, then all natural numbers less than P are coprime with P ... Is this correct? Please explain why?

2. Application of concept extension

(1) example

(2) Identify positive or negative examples. And explain why.

(3) Select cases from the extension of the concept according to the specified conditions.

(4) Classify concepts according to different standards.

Example 5( 1) lists the cylindrical objects you have seen.

(2) Which shaded parts in the picture below are fan-shaped? (Figure 6-2)

(3) The simplest true fraction with denominator of 9 has a false fraction with numerator of 9, and the smallest is

(4) Natural numbers 2- 19 are divided into two categories according to different standards (at least three different classification methods are proposed).

The application of concepts can be divided into simple application and comprehensive application. After a new concept is initially formed, simple application can promote the understanding of the new concept. Comprehensive application is generally after learning a series of concepts, combining these concepts can cultivate students' comprehensive application ability.

Fifth, the problems that should be paid attention to in the teaching of mathematical concepts in primary schools.

1. Grasp the goal of concept teaching and handle the contradiction between the development and stages of concept teaching.

The concept itself has its strict logical system. Under certain conditions, the connotation and extension of a concept are fixed, which is the certainty of the concept. Due to the continuous development and change of objective things and the deepening of people's understanding, the concept of reflecting the essential attributes of objective things is also constantly developing and changing. The concept teaching in primary school is often carried out in stages, taking into account the acceptance ability of primary school students. For example, the concept of "number" has different requirements at different stages. At first I only knew 1, 2, 3, ..., and then I gradually knew zero. With the growth of students' age, I introduced fractions (decimals), and then gradually introduced positive numbers and negative numbers, rational numbers and irrational numbers, extending numbers to the range of real numbers and complex numbers. Another example is the understanding of "0". At first, we only knew that it meant no, and later we knew that it could mean no unit in digits, and we also knew that "0" could mean a boundary.

Therefore, the systematicness and development of mathematical concepts and the stages of concept teaching have become a pair of contradictions to be solved in teaching. The key to solve this contradiction is to grasp the phased goal of concept teaching.

In order to strengthen concept teaching, teachers must carefully study textbooks, master the system of primary school mathematics concepts, and understand the context of concept development. Concepts are developing step by step, and they are interrelated. Different concepts have different specific requirements, even the same concept has different requirements at different learning stages.

The meanings of many concepts are gradually developed, which are generally given by description and then defined. For example, three leaps in understanding the meaning of fractions. For the first time, before learning decimals, let students have a preliminary understanding of fractions. "As mentioned above,,,,, and so on are all fractions." Through a lot of perceptual and intuitive understanding, combined with specific things to describe what a fraction is, we can initially understand that a fraction is an average score and understand who is who's score. The second leap is from concrete to abstract, and the unit "1" is divided into several parts on average, indicating that one or more of them can be expressed by fractions. Abstractfrom concrete things. Then the definition of score is summarized, but the concept of score is given descriptively. This is a leap of sensibility. The third leap is the understanding and expansion of the unit "1". The unit "1" can not only represent an object, a graph, a unit of measurement, but also a group. Finally, it is abstracted that whoever divides is the unit "1", so that the three levels of units "1" and "1" cannot be achieved overnight. It is necessary to show the development process of knowledge and guide students to understand scores in the process of knowledge development.

Another example is the understanding of cuboids and cubes. Many textbooks are divided into two stages. In the lower grades, the initial understanding of cuboids and cubes first appeared. Students can observe some physical objects and physical drawings, such as cartons containing ink bottles and Rubik's cubes. Accumulate some perceptual knowledge about cuboids and cubes, know what shapes they are and know the names of these shapes. Then through operation and observation, we can know how many faces a cuboid and a cube have and what shape each face is, so as to further deepen our perceptual understanding of cuboid and cube. Then abstract the figures (not perspective views) of cuboids and cubes from the objects. However, in this teaching stage, students are required to know the names of cuboids and cubes, and to be able to identify and distinguish these shapes. Just stay at the level of perceptual knowledge. The second stage is in the senior grade. Teaching should be introduced from examples. When teaching the knowledge of cuboids, let students collect the objects of cuboids first. The teacher first explains what are the faces, edges and vertices of a cuboid. Ask students to count the number of faces, edges and vertices respectively, measure the length of edges, calculate the size of each face, and compare the relationship and difference between up and down, left and right, front and back edges and faces. Then the characteristics of cuboids are summarized. Then abstract the geometry of the cuboid from the instance of the cuboid. Then, students can observe the figure by comparing it with the real thing, and find out how many faces and edges they can see at most without changing the observation direction. What is invisible and how to show it in the picture. Students can also think about it and have a look, gradually understand the geometric shape of a cuboid and form a correct representation.

When grasping the phased objectives, we should pay attention to the following points:

(1) At every teaching stage, the concept should be clear, so as not to cause conceptual confusion. Some concepts are not strictly defined, but according to students' acceptance ability, they should either replace definitions with descriptions or reveal the essential characteristics of concepts in plain language. At the same time, pay attention to strict definition in the future.

(2) When a teaching stage is completed, it should be pointed out that the concept develops and changes according to the specific situation. For example, after a student knows the cuboid, he thinks that any piece of paper in the textbook is also a cuboid. It shows that students have a further understanding of the concept of cuboid, and teachers should affirm it.

(3) When developing concepts, teachers should not only point out the connections and differences between original concepts and development concepts, so that students can master them, but also guide students to learn related concepts and pay attention to their development and changes. For example, the concept of "multiple" usually means that if the quantity of A is regarded as 1 and there are so many quantities of B, then the quantity of B is several times that of A. After the introduction of fraction, the concept of "multiple" has been developed, which includes the original concept of "multiple". If the quantity of A is regarded as L, the quantity of B can also be a fraction of the quantity of A. ..

Therefore, in the teaching of mathematical concepts, it is necessary to clarify the order of concepts and understand the internal relations between concepts. With the development and change of objective things and the deepening of research, mathematical concepts are constantly evolving. Students' understanding of mathematical concepts also needs to be gradually deepened with the improvement of mathematics learning. When teaching, we should not only pay attention to the teaching stage, but also mention the later requirements to the front, which is beyond the students' cognitive ability; We should also pay attention to the continuity of teaching, leave room for the teaching of the previous concepts, and lay the groundwork for the later teaching. So as to deal with the relationship between the stages and continuity of mastering concepts.

2. Strengthen intuitive teaching and handle the contradiction between concrete and abstract.

Although most of the concepts in the textbook are not strictly defined, they are all based on the actual cases or existing knowledge and experience that students know, and try to help students understand the essential attributes of concepts through intuitive and concrete images. For the concepts that are not easy to understand, we will not give a definition for the time being or adopt the method of gradual infiltration in stages to solve them. But for primary school students, mathematical concepts are abstract. When they form mathematical concepts, they generally need to have corresponding perceptual experience as the basis. It takes some time to put perceptual materials back and forth in their minds, from vague to gradually clear, and from many related materials, through their own operations and thinking activities, they gradually establish the general appearance of things and separate the main essential characteristics or attributes of things, which is the basis for forming concepts. Therefore, in teaching, we must strengthen intuition and solve the contradiction between the abstraction of mathematical concepts and the visualization of students' thinking.

(1) Transform concreteness and abstraction through demonstration and operation.

In teaching, we should try our best to transform some relatively abstract contents into concrete contents through appropriate demonstrations or operations, and then abstract the essential attributes of concepts.

The basic knowledge of geometry, whether it is the concept of line, surface and body, or the concept of characteristics and properties of graphics, is very abstract. Therefore, we should strengthen demonstration and operation in teaching, so that students can understand these concepts through testing, touching, swinging and spelling, and thus abstract them.

For example, the concept of "pi" is very abstract. Some teachers arrange for each student to make a circle with a self-defined radius before class. In class, let each student write three contents in the classroom exercise book: (1) Write the diameter of the circle he made; (2) Roll the circle by yourself, measure the length of the circle once, and write it in the exercise book; (3) Calculate that the circumference of a circle is several times the diameter. After class, each student is required to report his own calculation results.

Then guide the students to analyze and find that no matter the size of a circle, its circumference is always a little more than three times its diameter. At this time, it is revealed that this multiple is a fixed number, which is mathematically called pi. Then ask the students to draw a circle at will and measure the diameter and circumference to verify. In this way, students are guided to analyze, synthesize, abstract and summarize a large number of perceptual materials, and abandon the non-essential attributes of things (such as the size of a circle and the units used in measurement). ), grasp the essential characteristics of things (the circumference is always a little more than three times the diameter), and form a concept.

In this way, with the help of intuitive teaching, teachers make use of students' original basic knowledge, and gradually become abstract, closely linked and clear-cut. Through physical demonstration, students can establish representations, thus solving the contradiction between the abstraction of mathematical knowledge and the visualization of children's thinking.

(2) Combining with the actual life of students, the concrete and abstract transformation is carried out.

Many quantitative relations in teaching are abstracted from concrete life contents. Therefore, in teaching, we should make full use of students' real life and adopt appropriate methods to transform concrete and abstract, that is, to transform abstract content into students' specific life knowledge, and then abstract students' life knowledge into teaching content.

For example, in the teaching of multiplication and method of substitution, students are often asked to answer such exercises first: How much does it cost to buy two boxes of pens for a box of 10 pens and a 3 yuan? Students find that there are two ways to solve this problem. One way is to find out "how much is a box" first, and then find out "how much is two boxes". The formula is (3× 10 )× 2 = 60 yuan; The other is to find out "how many" first, and then "how much are two boxes". The formula is 3× (2× 10) = 60 yuan. The teaching of Multiplication and Distribution Law also allows students to answer similar questions, such as: a coat, 50 yuan, a pair of pants, 30 yuan. How much does it cost to buy five suits like this? In this way, with the help of students' familiar life scenes, abstract problems become concrete.

The relationship between unit price, total price and quantity in the same common quantity relationship; The relationship between distance, speed and time, workload, work efficiency and working time should be abstracted through specific topics in combination with students' life experience, and then these relationships should be used to analyze and solve problems. This kind of training is conducive to the gradual transition of students' thinking to abstract thinking, and gradually relieves the contradiction between the abstraction of knowledge and the concrete image of students' thinking.

However, using intuition is not an end, it is just a means to arouse students' positive thinking. So concept teaching can't just stay in perceptual knowledge. After students acquire rich perceptual knowledge, they should abstract and summarize the observed things, reveal the essential attributes of concepts, make knowledge leap from perceptual to rational, and form concepts.

3. Follow the characteristics of primary school students' learning concept and organize a reasonable and orderly teaching process.

Although primary school students acquire concepts in two basic forms: concept formation and concept assimilation, and the formation of each concept has its own characteristics, however, how to acquire concepts generally follows the concept formation path of "introduction, understanding, consolidation and deepening". The following is a description of the teaching strategies and problems that should be paid attention to in all aspects of concept teaching.

The introduction of the concept of (1) should pay attention to providing rich and typical perceptual materials.

In the process of introducing concepts, we should pay attention to let students establish clear representations. Because the establishment of clear typical representations that can highlight the commonness of things is an important basis for the formation of concepts, no matter how to introduce concepts in the concept teaching of primary school mathematics, we should consider how to let primary school students establish clear representations in their minds. At the beginning of concept teaching, we should provide students with rich and typical perceptual materials by intuitive means, such as objects, models, wall charts or demonstrations, etc., to guide students to observe, and let students operate by themselves in combination with experiments, so that students can get in touch with related objects and enrich their perceptual knowledge.

For example, in a class about the meaning of teaching scores, a teacher provided students with various operating materials in advance in order to break through the teaching difficulties of unit "L": a rope, four apples, six pandas, a rectangular piece of paper, a line segment with a length of L meters, etc. Through comparison, it is concluded that an object, a unit of measurement and a whole can use the unit "1".