First, guide students to "ask"
"Question" is the beginning and main line of "inquiry". In order to enable students to "ask", teachers should create problem situations suitable for students' actual and cognitive level, so that students can find the necessary mathematical information and problems to be solved. Therefore, problem situation is the starting point, beginning and main line of "doing" mathematics. Whether to create challenging and attractive problem situations is the key for students to learn mathematics well.
For example, there are two teachers teaching "circumference" and there are two different ways of thinking, so there are two different ways of doing it. Method 1: Teachers provide students with CDs made of different sizes of cardboard. Ask them to measure the diameter of the circle first, then roll on the ruler one by one and record its circumference, and then guide the students to discover the relationship between circumference and diameter. Method 2: Teachers first create scenes through multimedia, and then provide materials, CDs made of various materials and circles on paper, so that students can explore the relationship between the circumference and diameter of circles. Obviously, the first method is to let students verify the relationship between the circumference and diameter of a circle under the guidance of the teacher, which is a mathematical activity of "remembering" the conclusion. The second method is to "do" mathematical activities with the clue of problem consciousness under certain circumstances. The reason why question scenarios are created here is because students constantly have cognitive conflicts in the process of exploring questions: "The application of circles is everywhere. The circles made of hard paper can be measured by rolling or string, but the circles made of soft cloth cannot be measured like this. What should I do? " The contradiction between solving problems and the limitations of methods and knowledge is constantly activated, which induces students' desire and enthusiasm for exploration. In group cooperative learning, through mutual inspiration and exploration, folding method can be used. But this method of drawing circles on paper has been challenged again. Students will naturally turn to careful exploration. In this way, the whole activity process is the process of students asking questions and putting forward difficult problems, which embodies the process of finding problems, putting forward problems and solving problems.
Second, guide students to "play"
Children's nature is to "play", and the new mathematics curriculum should also change the old-fashioned face and let students "play" well!
"Playing" mathematics means that students perceive things through idiosyncrasies or materialized activities under positive emotional experience. With the game of problem consciousness, "play" has a direction. If "asking" is the starting point and main line of learning, then "playing" is the way to explore the main line. "Playing" mathematics is not only a cognitive process of students, but also a hunger process of teacher-student activities and emotional communication. Emotional activities belong to the dynamic system, which can promote the active participation of the subject. The uniqueness of "playing" mathematics lies in that the learning subject is in a happy and positive psychological state and actively and consciously "does". Compared with passive "memorizing" mathematics, it changes "asking me to learn" into "I want to learn". "I want to learn" is based on students' internal learning needs, while "I want to learn" is based on external motivation and compulsion. The inherent needs of students in learning mathematics are mainly manifested in their interest in learning. There are direct interests and indirect interests. Direct interest points directly to the activity itself, and indirect interest points to the result of the activity. With students' interest in learning, learning activities are no longer a burden, but a kind of enjoyment and a quick experience, which makes students want to learn more, more willing to learn and more fond of learning.
"Play" must be based on independent exploration and group cooperation. The "game" in this situation can make the classroom of mathematics learning a place for mathematics research and cooperation and communication between people, and can improve students' adaptability, cooperation and communication qualities necessary for adapting to the future society.
Third, guide students to "realize"
Enlightenment is an important stage of mathematics and any other learning. "Enlightenment" is generally a kind of comprehension or sentiment based on feeling and perception, and it is the most important form of human wisdom and quality development. If "play" is the external movement of hands and eyes, "enlightenment" is the internal movement of the brain. Games can provide external information for enlightenment, and enlightenment can sublimate games. If you just play and stay at the level of perception, the process of interaction between play and enlightenment is the best way to "do" mathematics.
"Enlightenment" is not only a process, but also an important result of mathematics learning. When students have "enlightenment", they really gain something. And "enlightenment" cannot be said or replaced by others, but must be an experience and epiphany under subjective efforts. Teachers can only guide themselves to experience the process of knowledge discovery and method formation through reasonable scenario creation and reasonable prototype inspiration, rather than simply telling. Nor is it a simple hint or temptation. We should take measures to fully mobilize students' thinking to "realize".
Fourth, guide students to "use"
"Mathematics Curriculum Standard" points out that students should learn to observe and analyze the real society by using mathematical thinking mode, solve problems in daily life and other disciplines, and enhance their awareness of applied mathematics. Students should be encouraged to "actively try to use the knowledge and methods they have learned to find strategies to solve problems from the perspective of mathematics." It can be seen that the application of mathematics is the primary and basic goal of mathematics teaching, and it is also one of the focuses of current mathematics curriculum reform.
Mathematics will show its value and charm only when it returns to life. Only when students return to life and use mathematics can "everyone learn valuable mathematics" be truly realized. In mathematics teaching, teachers should be good at collecting teaching examples in real life and introducing themes from social life into mathematics classroom teaching, so that students can establish the consciousness of "using mathematics", cultivate their ability and experience the fun of "using mathematics" in the process of discovering problems, solving problems and practicing activities. It is also necessary to guide students to find mathematical problems from real life and establish the consciousness of "using mathematics". Mathematics comes from life, and there is mathematics everywhere in life. "Mathematics Curriculum Standards" points out: "In teaching, we should create learning scenes that are closely related to students' living environment and knowledge background and are of interest to students, so that students can gradually understand the process of the generation, formation and development of mathematical knowledge in activities such as observation, operation, speculation, exchange and reflection, gain positive emotional experience, feel the power of mathematics and master the necessary basic knowledge and skills. "Let students participate in some practical activities with math problems, and experience the fun of' using math' while improving their ability. In mathematics teaching, teachers organize students to participate in mathematics practice activities with real life background purposefully and in a planned way, and solve some simple practical problems by using the mathematics knowledge they have learned, which can not only consolidate the mathematics knowledge they have learned, but also broaden students' mathematical horizons.
The idea of new curriculum reform of basic education in China and effective classroom teaching should not only grasp the characteristics of teaching materials, cultivate students' exploratory thinking and strengthen the guidance of learning methods, but also effectively combine teaching materials with real life. In the teaching process, teachers must play their positive role, correctly guide and give full play to their subjective initiative, so as to improve students' mathematics learning ability and ultimately improve their comprehensive quality.