Mathematics is a very widely used subject. Hua, a great mathematician, once said: "The universe is big, the particles are tiny, the speed of rockets, the cleverness of chemical industry, the change of the earth, the mystery of life, and the complexity of the sun and the moon are everywhere." This should be a perfect exposition of the relationship between mathematics and life! The new curriculum attaches great importance to the connection between mathematics and real life. It not only requires mathematics teaching to start from familiar life scenes and interesting things, but also provides students with opportunities for observation and operation, so that students have more opportunities to learn and understand mathematics from familiar things around them, realize that mathematics is around them and feel the interest of mathematics, and also stimulate students' interest in solving practical problems by using mathematics, cultivate students' exploration spirit, application consciousness and practical ability, apply what they have learned and further understand the role and value of mathematics.
First, create life scenes, cultivate strong interest and stimulate the desire to explore
Interest is the best teacher. A strong interest in learning can make people's brains in the most active state and receive teaching information best. A strong interest in learning can effectively induce learning motivation and urge students to consciously concentrate and devote themselves to learning activities. For example, when I was teaching Understanding Circle, I found many pictures from ancient big carriages, chariots in Qin Terracotta Warriors, modern wooden carts, modern trains, vans and even luxury cars, so that students could feel the progress of human beings and the development of culture from the appearance. But no matter which dynasty, function and shape of the car, the wheels are always round. Why? As soon as the question was raised, the students expressed their opinions in combination with their own life experiences, and the atmosphere suddenly became active. So that students have a strong interest in the circle, but also inspired students to actively explore the nature of the circle psychological tendency, so the effect is very good. Since mathematics comes from life, it is necessary to closely connect with life, be close to life, reasonably organize teaching materials, fully tap potential life materials, find out the "meeting point" between each section and students' life reality, create certain situations for students, mobilize students' experience in life, let them feel beauty and cultivate strong interest, thus stimulating students' learning motivation and enthusiasm for participation, stimulating students' thirst for knowledge and enhancing their initiative in learning mathematics.
Second, let students use mathematical knowledge to solve practical problems and cultivate students' ability to apply mathematics.
Mathematics is a language and an indispensable way to know the world. The ability to use mathematics is one of the most basic qualities that future citizens should have. The new curriculum standard points out: "It is necessary to cultivate students to abstract practical problems into mathematical problems and form the consciousness of using mathematics." In my opinion, we should start from the following five aspects in teaching to cultivate students' mathematical application ability.
1. Attach importance to the process of knowledge formation and cultivate students' awareness of using mathematics.
Mathematical concepts and laws are mostly abstracted from practical problems. Therefore, in the teaching of mathematical concepts and laws, we should not simply impart these mathematical knowledge to students, but gradually guide students to analyze, abstract and summarize prototypes from actual examples or students' existing knowledge, understand the abstract process of knowledge, and understand its use and scope of application, so that students can form an understanding of the ways that must be followed in learning and applying mathematics. For example, when teaching the concept of "plane mosaic", I asked students to express their views according to the problems of "tile laying" they saw in their lives. The students scrambled to distinguish the floor tiles at home, the colored tiles on the street and the wall tiles in the bathroom ... I then asked the students, "Do you know what rules the foreman follows when laying eggs?" Therefore, naturally introducing the concept of "plane mosaic" can not only deepen students' understanding and memory of knowledge, but also stimulate students' interest in mathematics and enhance their awareness of using mathematics.
2. Carefully design exercises and apply mathematical knowledge to real life.
Mathematician Paulia once said: "The responsibility of a math teacher is to develop students' problem-solving ability as much as possible. "It can be seen that it is not our ultimate goal to understand the meaning and value of mathematics and to understand and master knowledge in connection with real life. The ultimate goal is to apply what you have learned to find, analyze and solve problems in life. Mathematics comes from life and should also be applied to life. For example, in the teaching of "the positional relationship between a point and a circle", in order to consolidate new knowledge, we have carefully designed the following exercises: A point on a straight line L, a point on a straight line L, and a road M intersects with the straight line L at a distance of A180m. It is known that the circular area around 100 meters will be affected by noise when the tractor is driving on the road. (1) Will schools be affected by tractor noise? And explain why. What would you think if you were a student in this school? In this way, new knowledge can be closely combined with real life, which can promote students to further understand and master the positional relationship between points and circles, improve their ability to analyze problems, and experience the success and happiness of applying mathematical knowledge to solve practical problems. At the same time, let students feel the harm of tractor noise to people, arouse environmental awareness and receive unexpected results.
3. Strengthen modeling training and cultivate the ability to establish mathematical models.
Establishing a suitable mathematical model is the premise of solving practical problems with mathematics. Mathematical modeling ability is a key step in the application of mathematical ability. For example, there is an example in The Application of Linear Function: A city has 200 tons of chemical fertilizer, and B city has 300 tons of chemical fertilizer. Now we have to transport all these fertilizers to C and D townships. The cost of transporting chemical fertilizer from city A to townships C and D is 20 yuan/ton and 25 yuan/ton respectively, and the cost of transporting chemical fertilizer from city B to townships C and D is 15 yuan/ton and 24 yuan/ton respectively. Now, township C needs 240 tons of chemical fertilizer, and township D needs 260 tons of chemical fertilizer. What's the lowest total freight? In teaching, I first designed several questions: (1) What are the variables that affect the total freight? (2) What is the amount of chemical fertilizer transported from City A and City B to Township C and Township D respectively? (3) What is the relationship between these quantities? After solving these three problems, guide students to establish a functional relationship model between total freight and fertilizer delivery on one of the transportation routes, and use the maximum value of the function to solve the problem. In fact, when solving practical problems, especially the process of solving comprehensive practical problems, it is actually the process of building mathematical models. In teaching, students can be guided to observe, analyze, abstract and summarize some practical problems (such as interest, stock, profit, insurance, etc. ) as a mathematical model to cultivate students' modeling ability. Through modeling training, students can recognize definitions, concepts, theorems, formulas and so on. Mathematics is a mathematical model gradually abstracted from the real world, which is inextricably linked with the real world.
4. Expand life practice and create a platform for students to use mathematical knowledge.
In the teaching practice of the new curriculum, we should insist that mathematics comes from life, takes root in life, and in turn applies it to and serves life, so as to make the process of students' application of mathematics interesting and life-oriented, and provide a broad space for students to apply mathematical knowledge and improve their mathematical ability in life. Let students return what they have learned in class to life, and make up for what they can't learn in class with what they have learned in life practice, which naturally satisfies students' curiosity, produces a strong voice of teaching and learning, and learns to solve problems in life practice. For example, when teaching "axisymmetric graphics", I carried out such practical activities-to see who found many examples of axisymmetric graphics in life. In this way, it is meaningless to report for class robbery. For another example, when I was teaching "Describing data with a fan chart", I assigned such a "practical" assignment: please collect the data of China's economic census in 2006 as much as possible after class, make a fan-shaped statistical chart, and read the chart to analyze what achievements China has made in economic development in the new period. This greatly enriches students' mathematics knowledge, enhances students' practical operation ability, and makes them truly experience that mathematics is in our lives, thus stimulating their feelings of loving mathematics, learning mathematics and using mathematics, and cultivating their initiative of carefully observing mathematics and consciously applying mathematics knowledge to real life.
5. Encourage students to pay attention to mathematics in their lives.
In our life, mathematical knowledge is everywhere. As long as you pay attention, you will find that, for example, the growth rate, the accounting of enterprise costs and profits, market research and analysis, and the arrangement of competition times can make students feel the universality of mathematics application. Defining mathematics can help them better understand nature and human society, better adapt to life, and express and communicate more effectively. As a teacher, students should be encouraged to make bold discoveries in life and be good at asking questions. Over time, students will feel the joy of knowledge, want to discover and create, and have an urgent desire to learn knowledge.
In a word, the basic quality of mathematics application is the basic quality that people at any level must have in the future. As a student, paying attention to the application ability of mathematics will have a great influence on his life. Therefore, in the experiment of the new curriculum reform, we should always insist on putting the learning of mathematics knowledge in the big classroom of students' life, which should be closely combined with real life before, during and even after class, so that students can learn, understand and use mathematics in familiar situations and realize the intrinsic value of mathematics. Let all students learn mathematics happily, learn mathematics, and let different students have different development in mathematics.
How to improve math scores?
1. Make a mistake, usually read more and ask more questions.
2. Go back to the textbook and look at theorems or examples, which may get twice the result with half the effort.
Ever-changing, theorems or examples in textbooks are very important, and many college entrance examination questions have evolved from this. Candidates have done a lot of questions in the review some time ago, which may alienate them. They must review it again before the exam.
3. Be familiar with all kinds of questions and the rhythm of answering questions, and keep in good condition. In the difficulty selection of test questions, we should choose ones that are simpler than usual and conducive to restoring confidence.
As for the review points, trigonometric function, probability statistics and solid geometry are the easiest to give intermediate questions, and candidates can focus on practicing these questions in the final sprint stage.
Many students often get stuck in a math exam because of one question, which will affect the answers to other questions. Therefore, it is best to make an on-the-spot psychological plan for yourself, think about the measures to deal with the bad situations that may be encountered in the examination room, and make full psychological preparations.
Which is better, Canadian BC course or Alevel 10 course?
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BC curriculum refers to the high school curriculum in Brithsh Columbia, Canada, and BC is the abbrev