How should teachers guide students to form a preliminary concept of "area" in mathematics teaching in primary schools? Write an article about your experience.
The cultivation of innovation ability is a systematic project, which must be started from an early age. Mathematics is one of the most suitable subjects to cultivate students' creative thinking, because mathematics is highly abstract, strict logic and extensive. It can provide students with a wide range of thinking materials and cultivate students' profundity, flexibility and originality in the process of learning mathematics knowledge. At the same time, adopting flexible and diverse solutions can also help students form the good habit of independent thinking and hard study at a very young age, which is conducive to the development of thinking flexibility and agility. Therefore, for primary school students, we must first start from the sense of innovation. Classroom teaching is the main position of teachers' teaching and students' learning, and it is naturally the main channel to cultivate students' innovative consciousness. How to cultivate students' innovative consciousness in primary school mathematics classroom teaching, I have made some attempts. First, promote teaching democracy, encourage students to participate, ignite the spark of students' wisdom, and tap students' innovative potential. Teachers should establish a scientific educational concept and a correct view of students, fully develop teaching democracy, and mobilize students' enthusiasm and initiative in learning. In teaching practice, we should guide students to think independently, encourage students to express their opinions and treat them equally. The curiosity, self-esteem and innovative consciousness of primary school students are closely related. As teachers, we must treat students with a democratic and equal attitude and be the guide for students to explore true knowledge. 2. Establish the prestige of teachers in the eyes of students and encourage students not to be superstitious about teachers. Teachers should update their educational concepts, firmly establish students' subjective view and "service consciousness": treat students as independent people, developing people and potential people; I love every student and believe that every student can develop on the original basis through his own efforts. Teachers should be good at encouraging students to express their opinions, which is an important aspect of developing teaching democracy and an important prerequisite for cultivating students' innovative consciousness. Therefore, in teaching, students should be given more opportunities to express their independent opinions, students with original opinions should be encouraged and praised, wrong opinions should be guided in time, and imperfect opinions should be supplemented to promote the development of students' innovative consciousness. There are often many ways to solve mathematical problems, such as some application problems, one or two of which are obvious. After students list this formula, teachers should expand it from multiple angles and directions, encourage and induce students to think about whether there are other ways to do it. Through such thinking, we can often find many ways to solve problems. In this process, students' intelligence is developed, their thinking ability and innovative consciousness are cultivated, especially the teaching democracy is fully developed, so that teachers can get in touch with students, study and discuss with students and inspire students to think. For those students who have strong personality and love to ask "new" and "strange" questions, their creative potential has been explored without thorough persuasion and giving up, thus stimulating and developing students' innovative consciousness. Second, teachers should be good at guiding students to explore new knowledge. Students' innovative consciousness is gradually formed in the process of students exploring new knowledge. Therefore, primary school mathematics teaching should study learning methods, and guide students to ask, analyze and solve problems in their own learning. 1. Create situations, encourage questions and cultivate students' ability to ask questions. Einstein once said, "It is often more important to ask a question than to solve it." Therefore, teachers should pay attention to creating situations to inspire students to ask questions constantly. Teachers should provide incentives for students, set suspense, open the floodgates of students' thinking and stimulate the motivation to explore new knowledge; Intense debate and discussion is also an effective way to arouse students' enthusiasm and active thinking, so that students can taste the pleasure of acquiring knowledge in discussion. 2, timely inspiration, guide students to carry out creative activities, cultivate students' innovative consciousness. Freudenthal, a Dutch mathematician, said: "The teaching method of explaining and analyzing mathematics as an activity is called the re-creation method." That is, students discover or create the mathematics knowledge they want to learn by themselves. The teacher's task is to help and guide students in this re-creation work, rather than instilling ready-made knowledge into students. According to the characteristics of mathematics and primary school students' thinking, with the help of teaching methods such as practical activities and teaching forms such as group interaction, mathematical conclusions can be better reduced to a lively knowledge generation process, thus guiding students to become discoverers in the process of exploring problems. (1) Focus on practical activities. Paulia said: "It is a good way to learn mathematics to be good at retreating, retreating enough, and retreating to the most primitive point without losing its importance." For the teaching of introducing new knowledge from real life, we should try our best to provide a prototype, so that students can explore and discover new knowledge through their own practical activities, such as teaching the perimeter of rectangles and squares. After students understand the meaning of the perimeter of triangles, rectangles and other graphics through intuitive images, give everyone a rectangle (of different sizes) and let them try to calculate its perimeter. At this time, we can find that students use a ruler to measure, but some measure the length of four sides, and some only measure the length and width. Although these two measurement methods reflect the difference of students' intelligence level, all students actively participate in this activity. In the column type, some columns are (length+width) ×2, others are: length ×2- width ×2, and more often, the four sides are added in turn. At this time, let students speak their own thinking process boldly, and choose the most appropriate method in mutual communication, discussion, analysis and comparison, so as to raise the low-level mathematics knowledge to the advanced mathematics knowledge, and let students experience the formation process of knowledge and learn mathematics in mathematics activities. (2) Pay attention to group interactive teaching. Teachers should organize students to discuss in groups in time, create a new learning atmosphere of equality, harmony and humanity, fully mobilize students' enthusiasm and initiative in learning, overcome thinking obstacles in mutual inspiration and help, open up ideas and promote the development of innovative consciousness. When solving the unknown number of the high base in a triangle by solving the sequence equation, the idea of solving the problem is based on the same triangle, and the areas obtained by the corresponding base and height are equal. After learning, the teacher asked to discuss in groups. What other problems can this problem-solving idea solve? The group had a heated discussion. Some people say that we can find the unknown base and unknown height of two triangles with equal areas (that is, we can extend the equivalence relationship in one triangle to two triangles). The results also inspired other students' thinking. Someone immediately said: you can find the unknown length, width or bottom and height in rectangles and quadrangles with equal areas; Find the unknown length, width or bottom of rectangle and triangle with equal area. High; Some students connect this with another, find the length, width or side length of a rectangle with equal circumference, and find the unknown efficiency or working time when the total amount of work is equal ... Students are very happy to find that they can solve so many problems with the same idea and see the results of their own thinking. Group discussion stimulates students' innovative spirit, cultivates students' innovative emotion, enhances students' innovative consciousness and further improves students' innovative ability. Third, optimize the exercise design, set up thinking obstacles, and let students "jump up and pick fruits". The answer to a question is often different from others'. There are always new ideas and designs, which are unique and belong to the basic performance of innovative consciousness. This different thinking is the starting point and foundation of creative thinking. In the design of classroom practice, we should constantly set up thinking obstacles and constantly trigger students' cognitive conflicts. Within the scope of students' ability, let students jump up and pick fruits, cultivate their innovative consciousness, and experience the joy of success in this process. In order to cultivate students' innovative consciousness, some creative homework should be arranged according to the characteristics of teaching materials, so as to open students' thinking and activate their innovative consciousness. For example, after learning the area of parallelogram, triangle and trapezoid, the teacher broke away from convention and led the students out of the classroom to an open space in the school, and then arranged a question: "How many design schemes can we design on this open space?" Students are exposed to this problem and are very enthusiastic. They use their basic knowledge and rich imagination to present various original design schemes to others. At this time, students' innovative consciousness has been fully brought into play.