1 how to combine numbers and shapes in mathematics teaching
Stimulate students' interest in learning by using "combination of numbers and shapes"
Mathematics originates from life and serves life. Mathematics can give people the enjoyment of the beauty of lines and fluency. This aesthetic feeling is perfect in quantity and shape. For example, the image with inverse proportional function y=6/x is a hyperbola (as shown in figure 1). The image of quadratic function y=x2 is a parabola (as shown in Figure 2). Teachers should make full use of these materials in mathematics teaching activities, guide students to understand the beauty of mathematics, make students have strong feelings, strong interests and desire to explore mathematics, and induce students to pursue the beauty of mathematics, thus eliminating monotony, boredom and fear of mathematics and generating interest and desire to actively pursue mathematics learning.
Einstein once said, "Interest is the best teacher". Cultivating interest in learning is the internal motivation to overcome the difficulties in mathematics learning, which can change students' learning psychology from "I want to learn" to "I want to learn", and thus it is possible to obtain the best teaching effect. Infiltrating aesthetic feeling into mathematics teaching can enlighten and promote students' mathematical thinking activities, stimulate students' aesthetic feeling and give full play to their intelligence.
Improving students' ability by using "combination of numbers and shapes"
The combination of numbers and shapes is helpful to the memory of mathematical knowledge. We know that "memory is the storehouse of wisdom". The accumulation of knowledge and experience, the formation of skills, the mastery of skills, the cultivation of thinking ability, creativity and career achievements are all inseparable from good memory ability. Middle school teaching knowledge is basic knowledge, which needs students to remember and master firmly and use flexibly. In the whole teaching process, memory is not only a means to master knowledge, but also a process of knowledge accumulation. It is helpful to deepen knowledge and improve level. Some students are helpless when they encounter some math problems, and they can't find the ideas and methods to solve them, which is related to their lack of math knowledge in their minds. Only by firmly remembering the basic knowledge of mathematics, reviewing the past and learning new things, and practice makes perfect, can we further develop mathematical thinking and improve our innovative ability and creative consciousness. Using the characteristics of image memory in teaching, abstract mathematics will be visualized as much as possible, and the mathematical information and images input by students will be more profound. Forming mathematical models in students' minds can help students understand and remember vividly.
For example, when learning quadratic functions, we can use function images to remember relevant knowledge. Such as the opening direction, symmetry axis and maximum value of the function. As shown in figure 4, the image of function y= 1/2(x- 1)2, in which the range of independent variable x is all real numbers and the image is parabolic. The opening is downward, and the axis of symmetry x= 1 has the maximum value. On the left side of the axis of symmetry, y increases with the increase of x, and on the right side, y decreases with the increase of x ... Let students remember this with intuitive graphics.
2 the effectiveness of mathematics classroom teaching
Be good at using modern teaching methods.
Under the background of new curriculum standards and new textbooks, it is particularly important and urgent for teachers to master modern multimedia teaching methods. The remarkable characteristics of modern teaching methods are: first, it can effectively increase the class capacity of each class; Second, it can reduce the workload of teachers writing on the blackboard, so that teachers can have the energy to explain the examples thoroughly and improve the efficiency of explanation; Third, it is intuitive, easy to stimulate students' interest in learning, and conducive to improving students' initiative in learning; Fourth, it is helpful to review and summarize what the whole class has learned. At the end of classroom teaching, the teacher guides the students to summarize the content of this lesson, the key points and difficulties of learning. At the same time, through the projector, the content will jump to the screen in an instant, so that students can further understand and master the content of this lesson.
In classroom teaching, there are a lot of contents, such as some geometric figures in solid geometry, some simple but large number of small questions and answers, application questions with a large number of words, summary of chapters in review class, training of multiple-choice questions, etc. Can be done with the help of a projector. If possible, we can make our own computer courseware for teaching, and use computers to show what we teach vividly. For example, the drawing of sine curve and cosine curve and the derivation of pyramid volume formula can all be demonstrated by computer.
Teach students in accordance with their aptitude and at different levels, and learn to appreciate their own students.
In the process of learning knowledge, students have non-intelligence factors besides intelligence factors. Therefore, teaching should be differentiated and targeted according to the individual differences of each student and the reality of students, so that students at different levels can be improved. In classroom teaching, the questions raised by students with higher IQ can generally grasp the key to the problem. For this kind of students, we can make them think about deeper problems and do extensive exercises to promote their thinking ability and by going up one flight of stairs.
For students with low IQ, let them master the basics and do basic exercises seriously. Today, with the comprehensive promotion of quality education, our teachers should not only pay attention to the cultivation of outstanding students, but also care about poor students. We should praise and affirm their little progress in class. Appropriate encouragement and praise from teachers can bring endless self-confidence to students, stimulate their enthusiasm for learning, make them feel the joy of success in the teaching process, and improve them to some extent.
3 to stimulate students' motivation to learn mathematics
First, create problem situations to stimulate students' interest in learning
In math class, teachers should pay attention to creating a harmonious atmosphere between teachers and students, grasp the opportunity and rhythm, and make them feel "surprise, strangeness and danger", attract students with the charm of math, stimulate their curiosity, and at the same time, grasp the psychological characteristics of teenagers' good performance, closely follow the teaching content, create problem situations, and enhance students' confidence in learning math with the teaching mode of "jumping and picking". Ask questions related to the content of this lesson before math class, so that students have suspense and are eager to know the result of the questions. So that students have a strong interest in learning new problems from the beginning, so although the contents behind this class are all complicated calculations, the students' enthusiasm and interest in learning are very high and they are greatly satisfied.
Second, use the rich history of mathematics to improve students' interest in learning.
The stories and interesting stories of mathematicians at home and abroad can stimulate students' interest and cultivate their curiosity in learning mathematics. Therefore, teachers should introduce some mathematical history to students in a timely and appropriate way, from land survey in ancient Egypt to the formation of mathematics. From pi to nine-chapter arithmetic, from Zu Chongzhi, who has been studious all his life, to Hua, who is brilliant, scenes of history will make students deeply immersed in the struggle of the ancients, and will inspire students to pursue truth and make progress. At the same time, students will also get a lot of inspiration from the success and failure of mathematicians, thus generating great enthusiasm for learning mathematics. To do this, teachers should read more about the history of mathematics.
Third, a multi-solution, a clever solution to cultivate students' interest
There are many solutions to mathematical problems, and proper use of multiple solutions to one problem is conducive to cultivating students' non-intelligence factors and intelligence factors. It can make students understand textbook knowledge more deeply, master quite a lot of problem-solving methods and skills skillfully, and then enlighten thinking, develop intelligence and develop ability. According to the different teaching objectives of each class, different teaching methods can be adopted. Such as guided trial method, hands-on operation method, inquiry method, etc. Flexible teaching methods can better mobilize students' learning enthusiasm and develop their mathematical ability. A good problem-solving method can not only get twice the result with half the effort, but also promote the mastery of the learned knowledge. With the joy of solving problems skillfully and successfully, it is bound to stimulate students to further overcome new mathematical difficulties and enhance their interest in mathematics in the virtuous circle of "seeking skills → interest → seeking skills".
4 Mathematics autonomous learning ability training
Building a harmonious relationship between teachers and students
In traditional teaching, both teachers and textbooks exist as authorities. Students are in a passive position in peace in class. What's more, some teachers are not good at dealing with the relationship with students, which leads to disharmony between teachers and students, and students hate teachers. All these are very unfavorable to students' willingness to learn independently. Students are unwilling to learn and do not take the initiative to learn. Without a relaxed and focused environment in the teacher's class, it is naturally impossible to cultivate students' autonomous learning ability. Therefore, teachers should pay attention to cultivate a harmonious relationship between teachers and students, reduce their authority while ensuring the rigor of knowledge, and encourage students to ask questions boldly.
Without affecting the teaching progress, it is more than students' communication and discussion. Encourage students to put forward opinions and answer questions boldly. Analyze students' different opinions rationally and tell them whether their opinions are correct or not. At the same time, we should encourage them and never be impatient and perfunctory. Some students have some unique opinions or opinions, and teachers should start from the perspective of students' thinking. If some students' questions don't conform to mathematical concepts or common sense, teachers shouldn't reprimand or criticize them. Students and teachers are not superior and subordinate, so they should have the concept of equal dialogue.
Cultivate students' study habits
Good study habits are the basis for students to have a high level of autonomous learning ability. For students, having good study habits helps them to understand the new content they have learned in class more easily, and it is more difficult to forget what they have learned before. At the same time, it also ensures that students can study mathematics in their own time. Good study habits will breed effective learning methods, and at the same time, developing good study habits will be of great benefit to students' study in other disciplines and even their future study life. And good study habits are mainly manifested in the following aspects.
First, good preview habits, preview does not mean that teachers need to master what they need to learn before teaching, but to understand what they will learn and sort out the framework so as to master knowledge more comprehensively in future learning. Teachers can remind students to preview before each teaching to improve classroom efficiency. Second: take notes in class. Listen carefully to the teacher in class, cooperate with the teacher, answer questions actively, and make a record of what the teacher explained in class for future review and mastery. It should be noted that you can't delay class because of taking notes, and put the cart before the horse. Teachers should encourage students to take notes, and they can also check the students' learning situation, but they should be careful not to become a rigid requirement and another form of students' homework.