Mathematical concept is the "cell" of mathematical knowledge and the first element of logical thinking. The research, expression and application of all mathematical laws are inseparable from mathematical concepts. Concept is an important part of elementary school mathematics basic knowledge. They are interrelated and are the basis of learning other mathematical knowledge. Therefore, a good concept class is of great significance to the follow-up study of primary school students and the cultivation of mathematical quality development.
First, the concept of teaching strategies
There is a preparation process for children to learn mathematical concepts, which is called "concept introduction". Good and effective concept introduction is helpful for students to actively understand and master concepts.
The basic strategy of concept introduction is:
1, introduction of life examples
Mathematics comes from life. Introducing concepts with life examples is an effective way to teach mathematical concepts. It can change mathematics from "unfamiliar" to "familiar" and from "serious" to "cordial", thus making students willing to approach mathematics. For example, the teaching of "straight lines and line segments". Four sets of shots can be presented for students to observe. Scene 1: Mother knits a sweater, highlighting the winding wool scattered on the ground. Lens 2: Stay cables on cable-stayed bridges. Scene 3: A girl is talking on the phone, with her fingers around the winding telephone line. Lens 4: The picture of lifting a heavy object with a rope on the construction site highlights the straight wire rope. Then ask, "What did you see on the screen just now? Can you classify these lines? Is there any way to straighten these lines? " These familiar life phenomena not only arouse students' memories of life, but also stimulate students' desire to explore and provide students with the opportunity to "do math".
2, from the introduction of intuitive operation
Organizing students' hands-on operation can enable students to gain distinct perception with the help of action thinking. For example, teaching the concept of "average score" can guide students to operate first and give two monkeys eight peaches to see how many different scores there are. Then make a comparison and tell me which division you think is the fairest. Let students realize that one of the many points is different, that is, everyone's points are the same, thus forming the appearance of "average points"
3. Transfer and introduction of old knowledge
The relationship between mathematical concepts is very close. In the middle and senior grades, many concepts can be introduced directly by contacting related old concepts. For example, the teaching of "prime numbers and numbers". Because prime numbers and sums are divisible by divisors, we can review the concept of divisors in teaching, but students can find all the divisors of 1, 2, 6, 7, 8, 1 1, 12, 15. How many divisors do students have in guiding them to observe and compare? Can you give a classification standard to classify these scores? Thus paving the way for the derivation of prime numbers and sums. For another example, the concept of multiplication can be introduced from addition and the concept of division can be introduced from division.
4, from the introduction of situational questions.
Rich scenes can not only stimulate students' desire for learning, but also help students to actively observe and think, and cultivate students' ability to find and ask questions through observation. For example, in the teaching of the concept of "volume", you can first fill two identical glass containers with water, then take out two stones with obviously different sizes and put them in two glass containers respectively, so that students can observe what happened and think about why water overflowed after the stones were put in the containers. Why put more water into the container with bigger stones? Make students have a perceptual knowledge of the space occupied by stones and prepare for the introduction of "volume".
5. Start with hands-on calculation.
Some mathematical concepts are difficult for students to observe or operate, but students can be organized to calculate and gain perceptual knowledge. For example, the teaching of the concept of "circulating decimal". Students can be required to calculate the fractional division first,10/3,58.6/11. In the process of calculation, students will find that they are divisible, and notice that when the remainder appears repeatedly, the quotient also appears repeatedly, so as to perceive the cyclic decimal.
There are many ways to introduce mathematical concepts, and sometimes several methods need to be used together to achieve good teaching results.
Second, the concept of teaching strategies
The establishment of concept is the central link of concept teaching. There are two basic forms for pupils to establish mathematical concepts: one is the formation of concepts, and the other is the assimilation of concepts. Because the thinking characteristics of primary school students are in the transition stage from image thinking to abstract logical thinking, primary school students learn mathematical concepts in the form of "concept formation". The formation of mathematical concepts generally goes through three processes: intuitive perception-establishing representation-explaining essential attributes.
1, enhance perception
Perception is the beginning for people to know things. Without perception, it is impossible to understand the nature and laws of things. Therefore, in concept teaching, we should first provide students with rich perceptual materials purposefully and systematically according to the teaching content, guide students to observe, and combine students' own hands-on operation to enrich perceptual knowledge and prepare for the formation of concepts. When organizing students' perception activities, we should consciously highlight the perceived objects from the background so that students can clearly perceive them. At the same time, change from static to dynamic, leaving a clear and profound impression on students.
Step 2 pay attention to your appearance
Representation is the image left by the human brain after its perception of objective things, and it is the result of multi-level perception. Representation is close to perception, which has certain concreteness, and at the same time it is close to concept, which has certain abstraction and plays a bridge role from perception to concept. The establishment of representation can help students get rid of the dependence on intuitive materials, overcome the limitations of perception, and lay the foundation for revealing the essential attributes of concepts. So after the demonstration or operation, don't rush to generalize, let the students leave the intuitive examples, think back silently and arouse the images in their minds. Through the guidance of teachers, the representation changes from vague to clear, from scattered to concentrated, and then to abstract generalization. For example, on the basis of intuitively perceiving that the blackboard surface, the desk surface and the textbook surface are rectangular, geometric figures are abstracted.
3. Reveal essential attributes
After students fully perceive and form appearances, teachers should seize the opportunity to guide students to analyze, compare and synthesize, summarize the essential attributes of things, and extend these essential attributes to all similar things, thus forming concepts.
Such as "triangle understanding" teaching. First, let the students say the triangle objects that are common in daily life. Then show pictures of pennants, red scarves and triangles on the screen and ask what shapes these objects are. Then the teacher removed the color from the picture, leaving only the outer frames of three objects. Let the students talk about the similarities and differences of these three figures. Discard the non-essential things such as color, size and material of these three objects, and abstract the characteristics of triangles: they are all composed of three lines. Then the teacher showed three line segments and slowly circled a triangle on the screen, vividly highlighting the characteristics of "circle", which is the students' accurate understanding: "The figure surrounded by three line segments is called a triangle".
4. Deeply understand the connotation and extension of the concept.
When the essential attributes of the concept are revealed by definition, students' understanding of the concept is still superficial. Therefore, teachers should take all means to help students gradually understand the connotation and extension of concepts, so that students can master concepts on the basis of understanding. Generally, the following methods can be adopted.
(1) Key words of analysis concept. After summarizing the concept of score, we can further analyze: ① What does the unit "1" mean? ② Why do you want to quote "1"? ③ What does "average score" mean? (4) What do you mean by "indicating this copy or copies"? Only by clarifying the meanings of these conceptual words can we have a profound understanding of the concept of score.
(2) Positive examples and counterexamples of applying concepts. Positive examples are conducive to the generalization of concepts, and counterexamples are conducive to the identification of concepts. Therefore, teachers should not only make full use of positive examples to help students understand the connotation of concepts positively, but also use negative examples to promote students' discrimination of concepts in time. For example, after learning the concept of "cyclic decimal", we can give some positive and negative examples.
(3) Use variants to highlight the connotation and extension of concepts. "Variant" means that the essential attribute remains unchanged rather than changed. For example, when teaching "the height of triangle", students can display variant graphics when making heights in standard graphics, but students make heights according to concepts. In this way, even if the connotation of "the height of the triangle" is strengthened, the extension is completely exposed. If only standard graphics are provided, students will only be higher on the standard graphics, but not on the variant graphics, which narrows the extension of the concept of "height of triangle".
Third, the teaching strategy of concept consolidation
It is impossible for students to master concepts at once, but from concrete to abstract, and then from abstract to concrete many times. When students initially establish concepts, they need to use various methods to promote the maintenance of concepts in students' cognitive structure, deepen their understanding and memory of concepts through continuous use, and consolidate the newly established concepts.
1, promoting memory
In order to consolidate the new concept, we need to remember it first. In teaching, we must follow the law of memory and guide students to remember concepts. Memory includes mechanical memory and understanding memory. The mechanical memory of the concept is to remember it according to the expression of the concept in the textbook. Pupils' mechanical memory ability is generally strong, but if this memory does not rise to understanding memory in time, it will be easy to forget, and even if it is remembered, it will be difficult to use. The understanding and memory of the concept is the memory after the connotation and extension of the concept are clarified and the new concept is linked with the students' original knowledge and experience.
2. Boot example
Bootstrap example is to let students simply apply the obtained concepts to practice, explain the concepts through examples, and deepen their understanding of the concepts. Experienced teachers, according to the specific characteristics of primary school students, always let students give examples to concretize their concepts after analysis, synthesis and abstract summary. For example, students can find out which problems in life can be solved by multiplication after learning a preliminary understanding of multiplication.
3. Strengthen the application
Whether students grasp a concept firmly depends not only on whether the concept can be named and defined, but also on whether it can be applied correctly. Through application, students can understand, 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. The application of concept connotation includes: ① retelling the definition or filling in the blanks according to the definition; (2) judging right or wrong according to the definition; ③ Reasoning according to the definition; ④ Calculated according to the definition. The applications of concept extension are as follows: ① Examples; (2) Find positive or negative examples and explain the reasons; ③ Select cases from the extension of the concept according to the specified conditions; ④ Classify concepts according to different standards.
Step 4 pay attention to discrimination
With the deepening of learning, students have more and more concepts, some of which are expressed in the same words, and some of which have similar connotations, which are easy to confuse students, such as prime numbers and prime numbers, divisible and divisible, sum numbers and even numbers. Therefore, in the consolidation stage of concepts, we should pay attention to guiding students to use comparative methods to understand the connections and differences of confusing concepts, so as to promote the accurate distinction of concepts.
In a word, elementary school mathematics concept teaching is an important part of elementary school mathematics teaching. In concept class, teachers must adopt scientific teaching strategies according to students' cognitive rules and specific characteristics of concepts to ensure the quality of mathematics concept teaching. In primary school mathematics teaching, it is an important task of classroom teaching to help students gradually form correct mathematical concepts.