1. Solve application problems to make them clear their goals and clear their minds.
Through mathematics learning in compulsory education, students can acquire important mathematics knowledge, basic mathematical thinking methods and necessary application skills necessary to adapt to future social life and further development; Initially learn to use mathematical thinking to observe and analyze the real society, solve problems in daily life and other disciplines, and enhance the awareness of applied mathematics; Understand the close relationship between mathematics and nature and human society, understand the value of mathematics, and enhance the understanding of mathematics and confidence in learning mathematics well; Have a preliminary spirit of innovation and practical ability, and can be fully developed in emotional attitude and general ability.
2. Solving application problems can stimulate their interest and form habits.
Interest is the motive force of seeking knowledge, the source of learning initiative and enthusiasm, and plays an important role in intellectual development. Mathematics is a highly abstract subject, and how to arouse interest is a problem that mathematics teachers should attach great importance to in the teaching process. In primary school mathematics teaching, teachers should make more efforts on the issue of "attracting interest". Excavate interesting factors, interesting knowledge and interesting stories in the textbook to arouse students' interest. Especially in the lower grades, children are more willing to guess riddles and listen to stories. If we can closely combine the teaching materials and organize teaching in the form of riddles and stories, it will play a very good role in stimulating interest. Let students experience the happiness of learning success through interest and develop good study habits.
3. Apply problem solving to let them explore independently and improve their ability to solve problems.
In the process of solving problems, teachers should guide students to participate in learning and inquiry activities, so that students can think clearly in images on the basis of independent thinking, which is helpful to analyze quantitative relations and improve their ability to solve applied problems. Teachers should use training methods suitable for solving application problems for students of different grades, so as to receive better teaching results. In the lower grades, physical pictures are the main teaching method. Because the thinking and understanding of junior students can't be separated from the activities they act on the object, in junior teaching, each student is equipped with a set of mathematics learning tools, and students are organized to practice with their brains in a planned way, which closely combines independent inquiry with cooperative communication. For example, when teaching the application problem of "Find a number more than one number", students put △ and ○ together with safflower and yellow flower, and find that the number of flowers of safflower is the same as that of yellow flower, and more than that of yellow flower. Through the teaching of object diagram, students can cooperate and communicate, which provides the basis of thinking in images for the teaching of this kind of application problems, so that they can better grasp the relationship between quantity and solution on the basis of understanding and improve their creative problem-solving ability.
4. To solve practical problems, we should carefully examine the questions and attach importance to the analysis of quantitative relations.
Correctly analyzing the quantitative relationship is the key to correctly answering application questions and the central link in the teaching process of application questions. In the teaching of application problems, we should pay special attention to training students to analyze the dependence between known quantities and unknown quantities in application problems, and abstract the quantitative relationship from application problems. For example, a professional breeding household raises 800 white rabbits, and the number of black rabbits is 3 times more than that of white rabbits 10. How many rabbits does this breeding professional keep? There are two quantitative relations in this problem: ① Professional households raise rabbits = white rabbits+black rabbits; ② Black rabbit = white rabbit× 3+10. Make clear these two quantitative relations, and the problem will be solved. Comments: In order to prevent students from making mistakes when they encounter slightly changed topics, students' divergent thinking ability should be brought into play in teaching, and students should be guided to analyze quantitative relations from multiple angles, sides and directions.
5. To solve practical problems, we should pay attention to the internal relationship between knowledge and guide the flexible use of problem-solving strategies.
Teachers encourage and advocate the diversification of problem-solving strategies and respect students' different levels of problem solving. The difficulty in solving problems is due to the lack of appropriate problem-solving strategies, which requires teachers to be good at studying and summarizing problem-solving strategies for different types of questions, and give appropriate guidance and guidance. ① The reason why students are confused about some application problems lies in the influence of fixed thinking. At this time, the teacher should guide the students to change their thinking angle and make their thinking clear. For example, Xiaohong scored an average of 86 points in Chinese, English and mathematics in the final exam. After the music score was published, his average score increased by 1 point. How is Xiaohong's music performance? According to the conventional solution, it can be seen that Xiaohong took four courses at the end of the term and asked to take the score. You can subtract the total score of three courses from the total score of four courses. Because the average score of the four courses is higher than that of the three courses 1 min, the average score of the four courses is 86+ 1=87 (min), the total score of the four courses is 87×4=348 (min), and the total score of the three courses of Chinese, English and Mathematics is 86×3=258 (min). If you look at it from another angle: Xiaohong Music also scored 86 points, and the average score of the four courses was 86 points. However, the average score of the actual four subjects is higher than that of three of them, which is just distributed to all subjects, making each subject increase by 1 point. This * * * is 1×4=4 (points) more. Clear thinking and problem solving. We can quickly calculate that Xiaohong's score is 86+ 1×4=90 (points). (2) Some topics are complicated, and it is impossible to start thinking with conventional methods. At this time, teachers should guide students to think from the overall situation, grasp the whole, comprehensively observe the relationship between quantity and quantity, and find the key to the problem, so that the effect of solving problems is particularly good. For example, the average value of four numbers is16; If one of the numbers is changed to 20, the average of these four numbers is 18. What was the initial number of changes? After reading the topic, most students may want to know what these four numbers are and are busy looking for them. This is obviously impossible and unnecessary. The answer to this question should be grasped from the overall perspective. Don't just look at a certain number, simply consider these four numbers separately. First of all, we should know that the sum of the four numbers after the change is 18×4=72, and the sum of the four numbers before the change is 16×4=64, which is 72-64 = 8 more than before the change. So, what number becomes 20 after adding 8? This simplifies the problem. (3) Solving the application problem of finding the average is inseparable from the quantitative relationship of "total amount ÷ total number of copies = average". However, if we can think carefully about the meaning of the word "average" and solve those flexible problems, we can often think of simpler methods. In the word "average", "flat" means "leveling", that is, moving more makes up less, and "average" means equality. The meaning of the word "average", in layman's terms, is to use the method of "shifting more to make up less" to make each copy equal. (4) When solving application problems, we should prevent and correct the fixed pattern of examination and problem-solving methods. After meeting the basic teaching requirements or learning new knowledge, we should demonstrate and encourage students to broaden their thinking, flexibly shift their thinking angles, optimize their thinking and solve problems skillfully. For example, it takes Party A 30 days and Party B 60 days to process 600 parts. Now Party A and Party B are cooperating. How many days will it take to complete the task? According to the conventional solution, first calculate the number of parts processed by Party A and Party B every day, and then calculate the number of parts processed by Party A and Party B every day when they cooperate. According to the meaning, the formula is: 600 ÷ (600 ÷ 30+600 ÷ 60) = 20.
(day). After learning engineering problems, students can be inspired to answer by solving engineering problems: If the total number of parts to be processed is "1", the work efficiency of Party A and Party B is 1/30 and 1/60 respectively, and the formula is:1÷ (1). Therefore, the cooperation between Party A and Party B is 1 day, which is equivalent to Party B working alone (1+2) days. If Party B works alone for 60 days, when Party A and Party B work together, it only needs 60 ÷ (1+2) = 20 (days). Comments: In teaching, teachers should pay attention to guiding students to use what they have learned flexibly to solve application problems and understand their different ideas and methods of solving problems.
To sum up, teachers should understand the problem-solving design in applied teaching, make the old and new knowledge closely linked and develop students' thinking. Make different students get different mathematics in different activities, meet different students' learning needs, demand quality from the classroom, fully mobilize learning interest, develop learning potential, and improve the ability to analyze and solve problems, thus improving the quality of mathematics education and teaching.