First, the understanding of the importance of chart analysis is the premise.
Mathematical application problems are difficult for primary school students who are in the transition stage from image thinking to abstract thinking, because the text description is abstract and the quantitative relationship is complicated. If we don't master an intuitive and scientific analysis method, constantly explore ideas and improve the ability to solve problems, it will greatly dampen the enthusiasm of students in the long run. Therefore, as a practical mathematical thinking method, chart method can help students learn to solve complex application problems easily and happily, which can not only cultivate students' understanding ability, improve their thinking ability, but also arouse their enthusiasm and initiative in solving application problems.
(A) with the help of charts to solve problems, can be abstracted into concrete.
Pupils are young, and the limitations of cognitive ability, knowledge structure and understanding ability affect students' understanding of known conditions and unknown problems to some extent. Teachers guide students to express the quantitative relationship in the topic in the form of charts, which is more in line with the cognitive law of primary school students and makes profound mathematical problems intuitive, vivid and concrete.
(2) Using charts to solve problems can simplify the complex.
Travel problems and engineering problems involve a large number and complex relationships, which often make it difficult for students to clarify their relationships. With the help of line segment representation in the chart, we can accurately find out the one-to-one correspondence between quantity and quantity, so as to sort out the mess and easily solve the required problems.
With the help of charts, we can turn knowledge into ability.
The premise of solving application problems by chart method is to learn to examine problems. Through reading, we can clarify the relationship between known conditions and unknown conditions, and cultivate students' understanding ability and logical thinking ability over time. At the same time, it can also stimulate students' inspiration, turn abstract into concrete and improve students' association ability.
Second, the accurate analysis of quantitative relations in mathematics is the key.
Quantitative relationship refers to the relationship between known quantity and unknown quantity in application problems. Only when the quantitative relationship is clear, can we choose the appropriate algorithm according to the meaning of the four operations, transform mathematical problems into mathematical formulas and solve them through calculation. The quantitative relationship analysis method is divided into three steps: the first step is to find the quantity in the problem; The second step is to clarify the relationship between quantity and quantity; The third step is to solve all the problems that arise. Let's talk about the application of quantitative relationship analysis from the following aspects with examples.
For example, "the school held a calligraphy contest, with 35 participants in the third grade, and the number of participants in the third grade was three times that of the third grade." The number of participants in grade five is more than the total number of students in grades three and four 12. How many people are in the fifth grade? " Teacher: How many quantities are there in the question? Health: three. Teacher: Which two quantities are directly related? Student: There are 35 participants in Grade Three, and the number of participants in Grade Four is three times that of Grade Three. Teacher: What problem does the relationship between these two quantities cause in our minds? Student: How many people took part in the competition in the fourth grade? Teacher: How to solve this problem in a formulaic way? Student: Multiply by 35 ×3= 105 (person). Teacher: Now there is another number: there are 105 students in the fourth grade, so which two numbers are related? What kind of problems will arise according to their relationship? Students: 35 students in grade three and 0/05 students in grade four. The question is: how many people are in the third and fourth grades? Teacher: So how to formulate the second step? Health: 105+35= 140 (person). Teacher: According to the quantity produced now, what are the two quantities? Students: Grade 3 and 4 140, and the number of students in Grade 5 is more than the total number of students in Grade 3 and 4 12. Teacher: What problems can the relationship between these two quantities help us solve? Student: How many people took part in the competition in Grade Five? Teacher: Then how to work out the formula for the last question? Health:140+12 =152 (person)
Third, it is the basis of cultivating students' skilled chart ability.
Chart method has great advantages in solving mathematical application problems because of its intuition and practicality. For primary school students, especially junior three students, it will be very difficult to transform abstract language into concrete and intuitive pictures and complete the abstract process from words to charts. This requires teachers to carry out training in related fields from the beginning of students' contact with application problems, and gradually improve students' ability to examine problems and drawing. Generally speaking, through scientific training in three aspects, we can accurately and skillfully realize the transformation from words to pictures.
(1) Teachers should demonstrate by themselves and set a good example.
Teachers are required to form the habit of using charts in solving problems, starting with the most basic "1". For example, 1 apple can be represented by a circle, a person can be represented by a vertical line, and a distance can be represented by a horizontal line. Teach students to draw a gourd ladle by hand, imitate it step by step, and find out the quantitative relationship, so don't rush for success.
(2) Teachers should teach students in accordance with their aptitude.
As students understand the concept of "1", they can extrapolate to a large number. For example, the length of 20 meters, if it is really drawn with 20 meters, it will be very difficult. Teachers can instruct students to use 1 cm or 3 cm or 4 cm to indicate the length, and how many centimeters and fractions are represented by 1 can be clearly expressed by drawing. In the concrete process, reading, dictation and drawing should be organically combined to realize the organic unity of quantitative relationship and drawing.
(3) Teachers should let go and do a good job of counseling in time.
After students have mastered certain skills, teachers can let students draw by themselves, express according to what teachers usually say, or draw creatively according to their own understanding and preferences, as long as the quantitative relationship is reflected scientifically, reasonably and intuitively, and the principle of simplicity is followed. Teachers can give timely guidance, and constantly cultivate students' initiative and consciousness in solving problems by using charts. At the same time, students can cooperate and communicate in groups, choose the best scheme and make continuous improvement.
Practice has proved that the chart method has the advantages of intuition, image and practicality, which fully conforms to the age characteristics of middle and low school students who mainly think in concrete images. If students have mastered the method of solving problems with the help of charts since childhood, their ability to analyze and solve problems will be greatly improved, which will be of great help to their future study and life.