At present, many primary school students are not enthusiastic about learning mathematics and lack interest in learning. They think mathematics is particularly difficult to learn. As long as it is carefully analyzed, it is not difficult to find that the main reason is that students have not made some mathematical concepts clear. For example, the maximum approximate number 12 is equal to the minimum multiple. The students' judgment is wrong. The factors involved in this problem are "limited", the smallest is 1, and the largest is itself. "Multiply", the multiple of natural number is "infinite", the smallest is itself, and the largest is not. However, "equal sex" students make mistakes, which shows that students have not understood and mastered mathematical concepts well. Mathematical concept is the core content of "two basics" (namely basic knowledge and basic skills) teaching; It is the starting point of basic knowledge; Is the basis of logical reasoning; It is the guarantee of correct, reasonable and fast operation. Students' correct, clear and complete mastery of mathematical concepts is the basis of mastering mathematical knowledge. If students are not clear about the concept, it will also affect students' learning interest and learning effect. If you don't know what "fraction" and "fraction unit" are, then the arithmetic of the four fractions will be difficult to understand, which will directly affect the improvement of the calculation ability of the four fractions. Correct, rapid, reasonable and flexible computing ability can only be formed on the basis of clear concept, mastery of computing rules and proper practice. Only when students have a clear concept can they analyze and reason; Logical thinking ability and problem-solving ability can be continuously improved. Therefore, it is extremely important for students to form concepts and master and use them correctly in teaching. The process of mathematics teaching is "concept teaching". A math teacher should put concept teaching in a prominent position. Some concepts in primary school mathematics are difficult for primary school students to understand because of their young age, little knowledge, little life experience and poor abstract thinking ability. Therefore, in the process of teaching related concepts, teachers must proceed from the actual age of primary school students, so as to receive good teaching results.
First, let students understand mathematical concepts in teaching
1. Introduce the concept intuitively and vividly.
The concept of mathematics is abstract, but primary school students, especially those in lower grades, are in the stage of thinking mainly in images due to the limitations of age, knowledge and life. Knowing a thing and understanding a mathematical truth mainly depends on the specific image of the thing. Therefore, in the process of teaching mathematical concepts, teachers must be careful and patient, and try to introduce familiar contents in students' daily life. In this way, students' interest in learning will be high and their enthusiasm for thinking will be high. For example, when teaching average application problems, I use pencils as teaching AIDS to review the concept of "average score". I use nine small wooden blocks of the same size to make three piles, the first pile 1, the second pile 2 and the third pile 6. I asked, "Is there the same amount in each pile?" Which pile is more? Which pile is less? "Students can answer correctly. At this time, I mixed these three piles of wood together and divided them into three pieces, each of which was three pieces. I told the students that the new number "3" is the "average" of these three piles of wood blocks. I'll show you again. Let the students look carefully and think carefully: How did the "average" come from? The students saw me combine the original three piles into one pile, and then divide the pile of wood into three parts, each pile is exactly three pieces. This demonstration process not only reveals the concept of "average", but also consciously permeates the calculation method of "total quantity/total number of copies = average". Then arrange 1, 2, 6 pieces of wood according to the original appearance for students to observe. The average "3" is larger than the original figure. The students said that the average of 3 is smaller than the original number and larger than the original number. In this way, students understand the essential characteristics of the concept of "seeking average" vividly.
2. Use old knowledge to introduce new concepts
Some concepts in mathematics are often difficult to express intuitively. Such as scale, cyclic decimal, etc. But they are all intrinsically related to old knowledge. I will make full use of old knowledge to introduce new concepts. When preparing lessons, we should analyze what old knowledge of this new concept is internally related to it. It is easy for students to use their old knowledge to teach new concepts. Suhomlinski said: "Teaching students to acquire knowledge with existing knowledge is the highest teaching skill." Psychologically, students are easy to be active and fearless; Fearless and difficult, easy to inspire thinking; Old knowledge is memorable and easy to be encouraged; Therefore, the teaching effect of introducing new concepts by using old knowledge is good. For example, the concepts of "common multiple" and "minimum common multiple" are all obtained by finding the respective "multiples" of several numbers. In short, taking the existing knowledge as the basis for learning new knowledge, taking the old with the new, changing the new into the old, and so on, not only let students know the concept clearly, but also master the relationship between the old and new concepts.
3. Understand the essence of things through practice and form concepts.
As the saying goes, practice makes true knowledge, and the hand is the teacher of the brain. By demonstrating learning tools, students can understand some concepts that are difficult to explain. For example, the comparison of the number of students in the first grade of primary school. Is to use chickens and ducklings to learn tools and compare them one by one. For example, a chick versus a duckling, a second chick versus a second duckling, … until the sixth chick has no duckling to compare with, it is called that there are more chicks than ducklings 1. Another example is that the second-grade primary school students learn the concept of "as much" with the learning tools of red flowers and yellow flowers. The students put five red flowers first, and then five yellow flowers as many as red flowers. In this way, "as many" mathematical concepts are formed through demonstration (hands) and thinking (brains), which conforms to the law of practice, cognition, practice and re-cognition. This is better than the teacher demonstrating, the students watching, the teacher explaining and the students listening. Impressive and unforgettable.
4. From concrete to abstract, reveal the essence of the concept.
In teaching, we should not only adapt to the characteristics of students' thinking in images, but also cultivate their abstract thinking ability. In concept teaching, we should be good at creating conditions for students, guiding students to master concepts through observation, thinking and exploring the meaning of concepts, and follow the cognitive process from perceptual knowledge to rational knowledge. Only in this way can students' logical thinking ability be cultivated. For example, the concept of pi is abstract. Generally, teachers let students know the relationship between the circumference and diameter of a circle through hands-on operation. Through observation, thinking and analysis, students will soon find that no matter the size of a circle, the circumference of each circle is a little more than three times the diameter. The teacher pointed out: "This multiple is a fixed number, which is mathematically called" pi ". In this way, students are guided to analyze and synthesize a large number of perceptual materials, and abstract and summarize non-essential things (such as the size of the circle, the color of the cardboard, the unit used for measurement, etc.). ) and grasp the essential characteristics of things (no matter the size of a circle, the circumference is always a little more than three times the diameter). Formed a concept.
5. Use "variant" to guide students to understand the essence of the concept
After students have mastered the concept, I often change the narrative method of the concept, so that students can understand the concept from all sides. Concepts can be expressed in various ways. For example, a prime number can be said to be "a natural number has no other factors except 1 and itself." This number is called a prime number. " Sometimes it is said that "it is just a number that is a multiple of two factors 1 and itself". Students can understand all kinds of narratives, which shows that the understanding of concepts is thorough and flexible, not rote learning. Sometimes you can change the non-essential characteristics of the concept, let students analyze it and deepen their understanding of the essential characteristics.
6. A more approximate concept.
In primary school mathematics, some concepts have similar meanings, but their essential attributes are different. For example, there are many similarities and internal relations between the concepts of number and number, quantity and quantity, reduction and reduction. Students often get confused about such concepts, so they must compare them to avoid mutual interference. Comparison is mainly to find out their similarities and differences, which requires an analysis of the two concepts to see what their essential characteristics are. Then find out their similarities and differences respectively, so that students can see the internal relations of the objects to be compared and their differences. In this way, the concept of learning will be clearer. Often guiding students to compare and distinguish similar concepts can not only cultivate students' habit of consciously confusing concepts, but also improve their ability to understand concepts. Years of teaching experience: attaching importance to cultivating students' comparative thinking has several advantages: (1) It is conducive to cultivating students' logical thinking. (2) It helps to improve students' ability to analyze problems. (3) It is beneficial to cultivate students' systematic way of thinking.
Teachers should help students sum up the meaning of concepts.
The dominant position of students in teaching is necessary, but the dominant position of teachers in the whole teaching process can not be ignored. Teachers should play a leading role. Under certain conditions, the subject and object status of teachers and students are interdependent and mutually transformed. In concept teaching, teachers should be good at creating conditions for students to master concepts along the process of observation, thinking, understanding, expression, from perceptual to rational, from concrete to abstract. This can easily arouse students' enthusiasm and initiative, and can also teach students to discover the truth. For example, I teach the concepts of prime numbers and composite numbers. I'll write a few numbers on the blackboard first: 1, 2, 3, 4, 5, 6, 8, 9, 1 1 2. Let the students write the factors of each number separately. In order to facilitate students' observation, consciously make the following arrangements, and students write the following answers:
1—— 1 2—— 1、2 6—— 1、2、3、6
3—— 1、3 4—— 1、2、4
5—— 1、5 8—— 1、2、4、8
1 1—— 1、 1 1 9—— 1、3、9
12—— 1、2、3、4、6、 12
After the revision, let the students observe carefully and find out the factorial law of natural numbers. After observation, the students found a rule. Some people say that there are three laws, while others think that there are four situations. I commend my classmates for their good observation and analytical skills. Are the three laws. So I inspired them to see which three? ① A natural number has only one factor; ② A natural number has two factors; ③ A natural number has more than three factors. In this case, I was inspired again: what is the number of a factor? How do two people feel? What kind of factor is greater than three? Students found that only one is1; Two people have 1 and themselves; Sanduoyou 1, yourself, and other factors. Finally, the teacher affirmed that the students summed up the concepts of prime number and composite number after reading the book. At this time, the students were very encouraged and thought they had discovered the truth. The concepts of prime number and composite number left a deep impression on me and will never be forgotten. I consciously ask students to study what "1" looks like. The students were silent. I said, "Look at the book." ? Tell me if you know. "In the mouth of students, saying" 1 "is neither a prime number nor a composite number. I asked, "Why"? Students answer: Because there is only one factor of "1", the calculation itself does not have "1", which is better than the teacher directly telling or urging them to take the initiative. With the help of teachers, let students analyze, synthesize and abstract a large number of perceptual materials. Abandon the non-essential things of things and phenomena, and grasp the essential characteristics of things and phenomena to form concepts. Because it is obtained by students' mental work, it is easy to understand and has a solid memory.
Second, consolidate the concept.
In teaching, students are required not only to understand concepts, but also to remember and use them flexibly. I think the memory and application of concepts complement each other. Therefore, it is of special significance to strengthen practice and review and summarize in time in teaching.
1, the concepts learned must be summarized to be systematically consolidated.
After a period of study, students are guided to sort out the concepts they have learned, and the connections and differences between concepts are clear, so that students can master a complete concept system. For example, after students learn all the knowledge of "comparison", I help them sum up what is comparison; The relationship between ratio, division and score; The basic nature of ratio, which can simplify the ratio; After reviewing this series of knowledge clearly, we can solve the practical problem of finding three kinds of scale problems and proportional distribution. Only by clearly understanding the meaning of proportion can we continue to learn proportion. Two expressions with equal ratios are called proportions. In this way, a conceptual system is formed, which is easy to understand and remember. Only by studying concepts in a down-to-earth manner can we apply concepts to solve practical problems smoothly.
2. Consolidate the concept through practical application.
The purpose of learning is to solve practical problems. By solving practical problems, it is bound to deepen the understanding of basic concepts. If the students learn the meaning of decimals, I will let them go to the store to find out the prices of several commodities in their spare time, write them down in exercise books, and let them report to you in class the next day. Through the process of understanding, it is very natural to understand the meaning, reading and writing of decimals. For another example, after learning all kinds of plane graphics, I asked the students to go home and observe where there are these plane graphics at home. Through this form of homework, students feel fresh and interesting. This not only consolidates the concepts learned, but also improves students' ability to use mathematical concepts to solve practical problems.
3. The comprehensive application of concepts not only consolidates concepts, but also tests the understanding of concepts.
After students form correct mathematical concepts, they should further design various concept exercises, so that students can use them comprehensively and think flexibly to consolidate their concepts. This is also a good practice form to cultivate and test students' judgment ability. This kind of topic is flexible and can examine many aspects of mathematical knowledge. Consolidating mathematical concepts is a good practice in recent years.
The purpose of practicing concept exercises is to make students comprehensively use, distinguish and compare, and deepen their understanding of concepts. The assigned exercises should have a certain gradient and level, and the order of exercises should be considered according to the order of concepts and students' understanding. According to the actual needs of students and teaching, we should adopt various forms and methods to design, stimulate students' interest in learning and achieve the purpose of consolidating concepts. In particular, it is necessary to organize the teaching of conceptual exercises and guide students to analyze and judge together.
Years of teaching practice have made me deeply realize that it is very important for teachers to explain concepts carefully to improve teaching quality, which is not only the premise of implementing "two basics", but also the key to enable students to develop their intelligence and cultivate their ability. But this is only the beginning of learning mathematics. More importantly, after students form concepts, they should be good at creating conditions for them to use concepts frequently, so that they can make a greater leap. Only when students use the concepts they have mastered can they understand the concepts more deeply and master new mathematical knowledge better. Only in this way can we cultivate our ability and develop our intelligence.