First, grasp the word "complement" and initially cultivate students' analytical ability and comprehensive ability.
"Complement" is to supplement the conditions and problems of incomplete questions, making them become one-step or two-step calculation application questions. The practice of supplementary conditions and questions can help students further master the structure and quantitative relationship of application questions, and initially cultivate their comprehensive analytical thinking ability from the conditions and questions. Xiao Ming has 18 chickens and 9 big chickens. Let the students analyze the quantitative relationship according to the conditions and fill in the blanks. Some students said, "Chicken 18 is just a partial number, and Chicken 9 is just another partial number, which can add up to a total." At this time, the teacher asked again, "What questions can you add?" Some students said: "Compared with the number of big chickens, the number of chickens is a large number, and the number of big chickens is a decimal number, which can make up the difference." Others said: "Compared with the number of big chickens, the number of big chickens is multiple, and the number of chickens is multiple, so we can make up the problem of multiple." This process of supplementing problems with conditions is a comprehensive process. Another example: there are three black rabbits. How many are there in white rabbits and black rabbits? What are the conditions for this question? How many white rabbits and black rabbits do you need? What two conditions must be known? (the number of white rabbits and the number of black rabbits), the number of black rabbits is already known, and the number of white rabbits must be supplemented. This process of thinking about conditions from problems is a process of analysis. Teachers often consciously train students to supplement questions by conditions and conditions by questions, which not only makes students have a clear understanding of the structure of application problems, but also cultivates students' comprehensive analytical thinking ability.
Second, grasp the word "comparison" and initially cultivate students' ability to observe and compare.
"Comparison" is comparison. Educator ushinski said: "Comparison is the basis of all understanding and thinking. It is through comparison that we understand everything in the world." Through comparison, we can distinguish similar and similar knowledge in application problems and find out their differences, thus deepening students' understanding of what they have learned. In teaching, I make full use of teaching materials to guide students to observe and compare and find out the similarities and differences between the two questions. For example, on page 88 of Book 2, Example 7: ① There are 9 red flowers and 6 yellow flowers. How much less yellow flowers are than red flowers? ② There are 9 red flowers and 3 fewer yellow flowers. How many yellow flowers are there? First, guide the students to observe and compare the questions and answer: one of the two questions has the same condition, that is, 9 red flowers, and the other condition is different from the question. Then let the students observe the similarities and differences between the two problems with direct vision: ① The second condition in the problem is the problem in the problem; The question in the first question becomes the condition in the second question. Therefore, when solving a problem, we should establish a problem-solving method according to the conditions and problems. Finally, two problems are compared from the structure: from the conditions, we know that there are more safflower and fewer yellow flowers, and safflower can be divided into two parts: one part is as much as yellow flowers, and the other part is more than yellow flowers. From this, it can be concluded that the problem 1 requires that the number of yellow flowers is less than that of safflower, and that as many parts as yellow flowers are removed from safflower, and the rest is the part with more red flowers than yellow flowers, that is, the part with less yellow flowers than red flowers, that is, "9-6 = 3 (flowers)". Question 2 is to find out the number of yellow flowers, and remove the part with more red flowers than yellow flowers from the part with red flowers, that is, the part with as many red flowers as yellow flowers, that is, the number of yellow flowers, that is, "9-3 = 6 (flowers)" Such observation and comparison make students more aware of the structure and quantitative relationship between the two types of application problems and cultivate their ability of observation and comparison.
Third, grasp the word "painting" and initially cultivate students' abstract generalization ability.
"Painting" is to express the conditions and problems of application problems with intuitive graphics. In order to make students get enough perceptual materials and rich representations, teachers should abstract and summarize them, and students' knowledge will rise from perceptual knowledge to rational knowledge, thus cultivating students' ability of abstract generalization. For example, the question in the first grade application teaching is "There are 8 red flowers on the left, 3 yellow flowers on the right, one * * *, how many flowers are there?" Draw eight red flowers with red chalk on the left side of the blackboard for students to observe, and draw three yellow flowers with yellow chalk on the right side of the blackboard. Guide students to say "eight red flowers on the left and three yellow flowers on the right" while looking at the blackboard, so that students can obtain perceptual materials first. Then lead the students to ask questions: "A * * *, how many flowers are there?" Naturally, the problem of "drawing" has become a mathematical problem, that is, an application problem. Students can easily grasp the structure of application questions, make students analyze the quantitative relationship according to the meaning of the questions and the established representation, and easily say the meaning of "how many flowers does a * * * need", that is, add 8 and 3 to calculate, which cultivates students' abstract generalization ability.
Fourth, grasp the word "problem" and initially cultivate students' judgment and reasoning ability.
"Ask" means that the teacher asks questions and lets the students answer them.
1. Grasp the key sentences and conduct judgment and reasoning training: ① There are five more apples than pears. Who has more? (There are many apples) What two parts can apples be divided into? (Some of them are as many as pears, while others are more than pears.) There are three fewer winter melons than pumpkins. Who has more? (There are many pumpkins) What are the two parts of a pumpkin? In the above two cases, the first question is to guide students to make direct judgments based on the knowledge of "greater than" and "less than" application questions. The second problem is to infer which two parts can be divided according to the judgment. This practice not only strengthens the key and difficult points of application problems in lower grades, but also develops students' judgment and reasoning ability.
2. Put forward the problem of continuity, and conduct judgment and reasoning training. For example, there are 28 students in Grade Two who want to carry out extracurricular activities. They are divided into four groups on average. How many people are in each group? What does this question say? Tell me what the terms are. What's the problem? (2) What are the actual requirements for finding the number of people in each group? Divide the total number of people into several parts on average, and how much is each part; (3) divide the total into several parts? How to find it? Division); (4) How to form it? (28÷4)。 These four small questions are designed to reveal the origin of the formula "28÷4". The process of students' answering questions is a process of judgment and reasoning. In this process, they not only solved the problem (listed formula 28÷4), but also received the training of judgment and reasoning. In the teaching process, teachers should carefully design questions, guide students' thinking and show the reasoning process. Let students master judgment and reasoning methods in routine training, and gradually be able to think and solve problems independently.
Fifth, grasp the word "say" and initially cultivate students' orderly and systematic thinking.
"Say" refers to the meaning, ideas and strategies of the problem. In the teaching of application problems in lower grades, students are not only required to know how to calculate correctly, but more importantly, they should be guided to fully "explain" the meaning, ideas and strategies of the problems, and their thinking should be organized and systematic. For example, there are 250 apple trees in the orchard, and there are 50 fewer pear trees than apple trees. How many pear trees and apple trees are there?
1, first guide the students to explain the meaning of the question: one condition told in the question is that there are 250 apple trees, and the other condition is that there are 50 fewer pear trees than apple trees. The question is how many pear trees and apple trees are there?
2. Guide students to think: How many apple trees and pear trees do you need? You must know the number of pear trees and apple trees. The number of apple trees is known. You must first find out the number of pear trees. This kind of thinking is clear, and the problem-solving strategy appears.
3. Demonstration: The number of pear trees is 250-50 = 200 (plants), and the number of apple trees and pear trees is 250+200 = 450 (plants). Language is the shell of thinking. It shows that thinking determines the expression of language, and language in turn promotes the development of thinking and makes thinking more organized. In the teaching of application problems in lower grades, it is helpful for students to understand the structure of application problems and cultivate the systematic and orderly thinking of students by guiding students to tell the meaning, ideas and strategies of the problems.
Sixth, grasp the word "change" and initially cultivate the flexibility and agility of students' thinking.
"Change" is the condition and problem of transformation. It can train students to think from multiple angles and directions, explain the essence of problems, and make students think more flexibly and quickly. For example, "6 red balloons, 24 yellow balloons, * * * How many balloons are there? It can be changed to: ① The red balloon (Le Ballon Rouge) has 6 balloons, which is 18 more than the red balloon. * * How many balloons are there? ② There are 24 yellow balloons, less than red balloons 18. * * How many balloons are there? ③ Six red balloons, less than yellow balloons 18. * * How many balloons are there? ④ There are 24 yellow balloons, more than red balloons 18. * * How many balloons are there? There are six red balloons, and the number of yellow balloons is four times that of red balloons. How many balloons are there in the box? ⑥ There are 24 yellow balloons, four times as many as red balloons. How many balloons are there in the box? Although the form of conditional narrative has changed, the quantitative relationship between Yellow Balloon and Red Balloon is the same. This transformation training makes students' thinking not fixed on the structure and solution of a problem, thus cultivating students' good habit of carefully understanding the meaning of the problem and analyzing the quantitative relationship, developing students' multi-directional thinking ability and adaptability, and improving the flexibility and agility of thinking. In short, in the teaching of application problems in lower grades, teachers should consciously take various forms and gradually cultivate students' logical thinking ability in order to achieve better teaching results.