1 Interpretation of Mathematics Application Consciousness under the New Curriculum Standard
1. 1 background of strengthening the cultivation of application consciousness
Influenced by traditional textbooks, teaching methods and baton, the application of mathematics and its connection with life are often ignored. Some people even think that mathematics is arithmetic, so it is easy to ignore the cultivation of application consciousness in normal teaching. In order to cope with the exam, students often have a fear of difficulties in solving problems, which seems to be helpless. In the long run, students will lack sensitivity to some mathematical phenomena in life. Of course, without the motivation to explore, the application consciousness of mathematics is easy to be weak or even rigid, which runs counter to the idea of cultivating students' practical ability and innovative spirit. In this case, the new curriculum standard clearly describes the application consciousness, and clearly points out that the cultivation of application consciousness should reflect the following two aspects.
(1) realize that there is a lot of mathematical information in real life, and mathematics has a wide range of applications in the real world;
In the face of practical problems, I can actively try to use the mathematical knowledge and methods I have learned to find strategies to solve problems.
1.2 the significance of cultivating mathematics application consciousness
The new curriculum standard points out that mathematics is a process in which people qualitatively grasp and quantitatively describe the objective world, gradually abstract and generalize, form methods and theories, and widely apply them. It is of great practical significance to help people solve problems and directly create value for society. Therefore, the cultivation of application consciousness should always run through the whole process of students' learning, and through the cultivation of application consciousness, students should be guided to start from the practical problems of their familiar life, production and other disciplines. By observing, guessing, summarizing and verifying the necessary reasoning, they can consciously mathematize practical problems, and finally use the mathematical knowledge and skills they have learned to solve problems, thus cultivating students' practical application ability. It can be seen that paying attention to the cultivation of application consciousness will have a far-reaching impact on comprehensively promoting quality education and cultivating useful talents in the new century.
2. Combining with my own teaching practice, talk about some attempts to cultivate the consciousness of mathematics application.
2. 1 Create problem situations and activate the application consciousness of mathematics.
The new curriculum standard clearly points out that mathematics teaching in compulsory education stage should combine specific teaching contents and adopt the mode of "problem situation-modeling-explanation, application and expansion", in which the creation of problem situation is put in the first place, which reflects its importance in knowledge transmission, while traditional teaching often overemphasizes the logic and rigor of knowledge, and the choice of content problems often ignores students' cognitive level, and students lack interest in these. Pure mathematical problems divorced from reality often form rejection psychology. Through the creation of question situation, boring questions can be animated, students' desire for knowledge can be stimulated, and a friendly and lively learning atmosphere can be formed, which is an important prerequisite for activating mathematics application consciousness. For example, students generally feel that the application of Pythagorean theorem just learned is monotonous and boring, except for calculating the side length. At this time, according to the natural phenomenon of frequent typhoons in our city, I wrote the following application questions with typhoons as the background.
The example 1 is shown in the figure 1. According to the forecast of the meteorological department, the typhoon O center is currently located on the ocean surface due west of City A 160 km, and it is expected that the typhoon center will move to the northeast 60 at a speed of 30 km per hour. It is known that the typhoon center 100km is the disaster area. Excuse me:
(1) Does the typhoon have an impact on City A?
(2) If it is affected, how long will it last?
When the students read this topic, they were enthusiastic and eager to discuss with each other. In this learning process, students' awareness of application is aroused unconsciously.
2.2 Strengthen the infiltration of mathematical modeling ideas in teaching
Mathematical modeling is to solve practical problems, mathematize prototype problems, establish mathematical models, and then use the learned mathematical knowledge and skills to deal with and solve problems. Therefore, the teaching of mathematical modeling is to cultivate students' ability to use knowledge to solve practical problems. As long as we actively explore the means of subsistence (such as profit, taxi fare, mortgage, mobile phone bill, etc.). ), paying attention to social hotspots, carefully planning and analyzing, and gradually infiltrating the idea of mathematical modeling, students can be enabled.
Example 2 (Guangzhou Senior High School Entrance Examination in 38+0, 2006) At the beginning of ticket checking at the station, a (a(a>0) passengers queued up to check in the waiting room. After the check-in began, passengers continued to queue up for the station. If passengers enter the station at a fixed speed, the ticket checking speed at the ticket gate is also fixed. If you open a ticket gate, it will take 30 minutes to check all the passengers in line. if
Analysis: This example is difficult for students to associate with the mathematical knowledge and methods they have learned. If you are a webmaster, how to make overall arrangements is a practical problem. According to the specific relationship in the problem, students are guided to establish two mathematical models of equation and inequality through practical thinking and exploration, and finally solve this seemingly impossible task. In addition, some practical problems such as decision-making and value maximization can be solved through this model. through
2.3 Select interdisciplinary application problems to improve students' comprehensive ability.
The ability to use mathematical knowledge to solve problems Mathematics is an important tool for learning other disciplines and a world language. With the development of modern science and technology, the application field of mathematics has got unprecedented development. Therefore, in the usual teaching, we should pay attention to the connection with other disciplines and select some typical problems of other disciplines for mathematical analysis. This is not only helpful to deepen the understanding of other disciplines and broaden the knowledge, but also an important way to cultivate students' awareness of mathematics application.
Example 3 There is a clay block made of a special material with a mass of 30 grams. Now, it is cut into two pieces: the big one and the small one. The larger clay block is placed in the left plate of the balance without arms and weighs 27 grams, while the smaller clay block is placed in the right plate of the balance and weighs 8 grams. If we consider the arm length of the balance and ignore other factors, we can calculate the mass of the larger mud block according to the principle of lever balance.
2.4 Actively carry out comprehensive practical activities to develop students' mathematical ability.
The practice and comprehensive application of applied consciousness is a brand-new highlight of the new curriculum standard. It will help students integrate their knowledge and experience and solve challenging problems closely related to life through independent exploration and cooperative communication. Under the joint planning of teachers and students, they will gain some methods and experiences to explore problems, which will not only develop their thinking ability, but also deepen their understanding of relevant mathematical knowledge in practice. This successful experience of overcoming difficulties will make students realize that mathematics is just around the corner.
Example 4 Investigate "How do you dispose of waste batteries?"
Analysis: This is a comprehensive practical subject, involving knowledge such as investigation, data processing and environmental protection. It is necessary to design a good plan in advance, divide the work reasonably and make careful arrangements, which not only mobilizes the enthusiasm of students, but also cultivates the spirit of cooperative inquiry. This teaching mode fully embodies the dialectical materialism view that mathematics comes from and acts on practice, and at the same time cultivates students' love for life and concern for hot spots. Pay attention to practice and actively apply mathematical knowledge to solve problems. Of course, the cultivation of mathematics application consciousness cannot be achieved overnight, but it is a long-term and arduous task. As long as we insist on developing every student in our usual teaching and integrate theory with practice, I believe that our students' mathematics literacy will definitely make great progress.
refer to
1 Ministry of Education. Mathematics curriculum standard (experimental draft). Beijing: Beijing Normal University Press, 200 1.
2. Xu. Mathematics curriculum and teaching theory. Zhejiang Education Press, 2003.
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