Life is the source of mathematics. "Mathematics Curriculum Standard" points out: "Starting from students' existing experience, let students experience the process of abstracting practical problems into mathematical models and explaining and applying them. "Because of the lack of life experience, primary school students have difficulty in learning some knowledge, which requires our teachers to create some life situations for students, capture some life information, organize some practical activities, guide students to participate in the whole process of knowledge acquisition, establish mathematical representations for students, and let each student learn mathematics through experience.
1, create a situation. The curriculum standard emphasizes: "Mathematics teaching activities must be based on students' cognitive development level and existing knowledge and experience. "Only when students establish correct and rich representations in their minds can their understanding of knowledge produce a leap from quantitative accumulation to qualitative development. In teaching, it is necessary to create situations related to students' real life and knowledge background, so that students can strengthen their perception and experience of objects in activities such as observation, operation, imagination, simulation, analysis and reasoning, form rich representations and develop the concept of space well. For example; When teaching "Identification of Numbers 1-5", let students talk about "How many people are there in your family" and "How many buildings are there in your school" according to the actual situation, exchange their understanding of the actual median in life with the knowledge of "Numbers and Numbers", and try to express some information with the numbers they have learned. This kind of communication activity plays a very important role in creating digital representation for students.
2. Experience it for yourself. Representation comes from experience, and the establishment of mathematical representation can not be separated from students' personal experience activities. Through their own experience activities, students' understanding of mathematical knowledge and concepts changes from intuitive to abstract. For example, before learning "understanding the number within 10,000", students can be arranged to do a social survey, go to big shopping malls to investigate the data about the price of electrical appliances, and make records. When students bring survey data into the classroom and communicate in groups, we find that the data they bring is very rich. For example, the price of a refrigerator is 2980 yuan; The price of a washing machine is 980 yuan; The price of a rice cooker is 235 yuan; The price of a large-screen color TV is 10080 yuan ... Go to the vegetable market, weigh all kinds of vegetables and fruits, and feel the actual weight 1 00g,1kg,10kg and so on. Students constantly enrich their understanding of logarithm in open information. Mathematics in students' eyes is real and kind, and it is no longer boring. Students' mathematical representation is based on interesting and dynamic mathematical communication. These activities are deeply loved by students, which can not only enlighten students' sense of numbers, but also cultivate students' "pro-mathematics" behavior and are full of fun in mathematics learning.
3. Hands-on operation. Hands-on operation allows students' various senses to participate in learning and observe things from many angles, which is conducive to establishing mathematical representations in students' brains. For example, when teaching "the number of 1 1-20", the process of number is a process of exploration, and the number is 12. Due to different ways of thinking, the ways of counting students may be different: some are 1, and some are 1. There are two plots of land, and there are two plots of land until 12 plots are counted; Some bundle 10 into a bundle, and it is easy to see that it is 12. Then, through communication, the students vividly felt the superiority of "bundling 10 into a bundle" and had a real understanding of "one of 10 is ten". Another example is to teach the concept of remainder, so that students can divide the sticks first: (1) How many sticks are left in every two of the nine sticks? (2) 13, distributed to 5 people on average. How many sticks can each student get? How much is left? After the operation, guide the students to express the operation process in words, talk about how to divide the sticks, thus forming the appearance, and then let the students close their eyes and think about how to divide the following questions. (1) There are 7 biscuits. Each biscuit is divided into 3 pieces, which can be distributed to several people. How many pieces are left? ② Pencils 12, distributed to five people on average. How many pencils can each person divide, and how many pencils are left? In this way, students can think in operation and operate in thinking, and understand that dividend is the total number, divisor and quotient are the number of shares to be divided and each share, and the remainder is not enough, and the remainder is less than divisor. Correct and clear representations are formed in the mind, and correct thinking has a solid foundation. Practice has proved that the combination of eyes, ears, mouth and hands and the participation of various senses help students to perceive and understand numbers correctly, comprehensively and profoundly. Junior high school students get a sense of numbers mainly through the perception and operation of physical objects and specific learning tools. Through practical operation, let students do and use mathematics instead of listening and remembering mathematics.
4. Observe and compare. Observation is a lasting perceptual activity with purpose, order and positive thinking, and it is a kind of "thinking perception". In teaching, teachers should let students find that mathematics is around them, and life is full of mathematics, so that students can observe and understand things around them with mathematical eyes and feel the interest and function of mathematics, thus establishing mathematical representations. For example, when studying hours within 10, when learning "1", students are required to observe the things represented by "1" in real life. Students cite: 1 book, 1 bird, 1 tree, 1 stick, 1 country, 1 grape, 1 string stick ... and then instruct students to count. How many are there in a bundle? Help students understand that "1" can represent 1 individual (1 branch) or 1 set of such individuals (1 branch); It can represent very large objects (1 country) or very small objects (1 grape). It is the idea of "1" and "1" that permeates many of them. Another example is: when knowing "0", inspire students to tell where they have seen "0" in their daily lives, and students' enthusiasm suddenly rises. "I have seen it in sports competitions; "It can be seen from the thermometer;" "There is 0 on the phone;" "There is a 0 on my ruler" ... so that students can intuitively understand that "0" not only means no, but also means the dividing point between thermometer and direction map; Mark the starting point on the ruler; Mark the date on the calendar and form a number with other numbers on the phone number and license plate. These are all things around students, and students can easily understand and accept them. Another example is: when teaching area units, guide students to compare 1 m2 with1m2 to estimate the classroom area. By comparing 10 square meter with 100 square meter and 1000 square meter, we can recognize the larger area, and then estimate the area of campus, community and square. This method of observation and comparison helps students to understand the meaning of numbers, deepen their understanding of logarithms and gradually establish the representation of numbers.
Second, the use of multimedia to build mathematical representation
Multimedia teaching is the application of modern educational technology in education and teaching. It integrates sound, image, video and text, and has the characteristics of visualization, diversity, novelty, interest, intuition and richness, which can make students feel at home, stimulate their curiosity and arouse their enthusiasm for learning. Using multimedia technology, images are constructed in people's minds through perception, and representations of objective things are formed. Compared with ordinary teaching, it has the characteristics of intuitive images. For example, when teaching the area of a circle, students can divide the circle into four parts, eight parts and sixteen parts by operation, so that the area of the circle is close to that of a rectangle. However, to make the circular area closer to the rectangular area, students do not have enough manual operation and waste time. At this time, if teachers use multimedia technology to divide the circle into 32, 64 or even more shares, students can realize that the more shares, the closer the circle area is to the rectangular area. Once this kind of extreme thinking is cultivated, students will benefit a lot.
Third, help students establish their representations through painting.
Psychological research shows that the thinking form of primary school students, especially junior students, is still in the stage of intuitive thinking. They know abstract mathematical concepts and laws, and generally understand what they have learned through intuitive perceptual activities. Therefore, drawing can help students establish mathematical representations and help them understand knowledge points. For example, when teaching "average score", students' understanding of "average score" is not a blank sheet of paper. They already know that "average score" means getting a fair share and getting as much as possible. However, the true meaning of "average score" is not fully understood, so it is far from enough to rely on an example in the textbook. I continue to ask the students to think: if the number of monkeys is not considered, how can these six peaches be divided equally? Guide students to draw symbols such as triangles, circles and squares. In addition to the above-mentioned average distribution of two people, each person has three (○ ○ ○); It can also be distributed to three people on average, two each (○○○○○○○○○○○○○○○○○○○○○○○○○○967 You can also assign it to six people on average, and use1(○○○○○○○○○○○○○○○○○○○○○○○○9675 What are the similarities between them? Let the students understand that whether it is divided into 2, 3 or 6 copies, as long as each copy is the same, it is the average score.
On this basis, I will show two more pictures:
Figure (1) ◎ ◎ ◎ ◎ ◎ ◎.
Figure (2) ◎◎◎◎
Let the students distinguish: which picture is the average score? Why is the graph (1) average? Why is Figure (2) not an average score? Can we get an average score? Then ask the students to observe the diagram (1) and the changed diagram (2) and say, "How many?" ? How many shares are divided equally? How many copies per book? "Through drawing, distinguishing and talking, I believe that students have a more comprehensive understanding of the meaning of' average score'. In the teaching of application problems, because the prototype of application problems is complex and abstract, it is difficult for students to form a clear representation after ingesting their brains. If we use the method of combining numbers and shapes to draw line segments, we can help students to establish a correct representation and make clear the hidden and complicated quantitative relationship. It can not only abandon the specific plot of application problems, but also vividly reveal the relationship between conditions and problems, transform numbers into shapes, clearly show the internal relationship between known and unknown, and activate students' problem-solving thinking.
Fourthly, by guiding students' imagination, mathematical representation is established.
Imagination is an advanced and complex psychological activity unique to human beings. People must have imagination if they want to recall what they have experienced and imagine what they have not experienced. Imagination and perception, memory and thinking are also cognitive activities of objective things. Teenagers cannot live and study without imagination. Therefore, teachers should be good at creating problem situations in classroom teaching, stimulate students' desire to participate in inquiry and give full play to students' rich imagination. For example, after teaching trapezoidal knowledge, students can be guided to imagine: "What shape will the trapezoid become when one base of the trapezoid is gradually shortened to 0?"? When the short base of the trapezoid is extended to be equal to the other base, what shape does it become? " With the help of representation, seemingly unrelated triangles, parallelograms and trapezoids can be organically combined, and the area formulas of triangles and parallelograms can also be memorized according to the trapezoid area formula.
In short, in primary school mathematics teaching, teachers should give full play to the role of mathematical representation and help students to establish mathematical representation through various possible methods, so as to deepen students' understanding of abstract mathematical knowledge and mathematical concepts. Of course, helping students to create mathematical representations is not the ultimate goal of learning mathematics. On the basis of establishing mathematical representation, teachers should actively guide students to further rational thinking, learn to summarize, learn to summarize and sort out, and cultivate students' interest in learning mathematics.