On how to cultivate primary school students' consciousness of mathematical innovation

First, change traditional ideas and believe that students have innovative potential.

For a long time, influenced by old ideas, when it comes to innovation, people are used to equating it with great inventions, thus inhibiting many people's innovation ability. Creationism holds that everyone has creativity and creative potential, and primary school students are no exception. Never think that primary school students can only accept but not create. Despise their creative potential. As far as primary school students are concerned, as long as they observe, think, explore and summarize themselves, they can all be understood as innovation. Innovative consciousness must be cultivated from an early age. As teachers, we should be sure that ordinary students have different levels of creative potential. How to tap this ability? For example, when I teach "triangle area", I first review the area calculation of rectangles, squares and parallelograms I have learned, and then give students several pieces of paper with equal and unequal areas. Then ask: "How to calculate the area of one of the triangles? What do you think? " Students get five different deduction and calculation methods through cutting and spelling. Finally, everyone reported the discussion and summarized the calculation formula of triangle area. I found that those students who are usually considered as "students with learning difficulties" have also found solutions. This is the "innovation" and "invention" of students.

Second, create a democratic and equal teaching atmosphere and induce innovative consciousness.

The great educator Tao Xingzhi pointed out that "democracy is the best condition for creation". A democratic, equal, relaxed, harmonious and pleasant teaching atmosphere can make students have the desire to participate consciously. Rogers said: "The general conditions conducive to creative activities are psychological security and freedom". In traditional education, the position of teachers in teaching is the first. Teachers think that they are the center and director of teaching, so they consciously or unconsciously maintain their authority in front of students. This practice inhibits the development of students, especially the development of creative behavior characterized by originality and bold questioning. Only in a democratic and pleasant learning atmosphere can students' enthusiasm for learning soar and be conducive to the germination of students' innovative consciousness. Without a democratic atmosphere, many students may not dare to think and guess, even if they think of something, they may not dare to say anything. Being criticized by the teacher for being afraid of making mistakes. Teachers should respect students' findings and take seriously all kinds of questions raised by students. Even if these questions seem very childish and ridiculous, they will never seek perfection, let alone criticize and satirize, or suppress or obliterate students' findings. Instead, we should try our best to find out their bright spots, give them affirmation, let them dare to think, speak and do, and induce their sense of innovation.

For example, when teaching "Finding the perimeter of a rectangle", I demonstrated with a computer courseware: "A basketball court is 28 meters long and 15 meters wide. What is the circumference of the basketball court? After students think independently, they come up with three different methods to find the circumference. Method 1: 28+ 15+28+ 15=86 (m); Method 2, 28+28+ 15+ 15=86 (m); Method 3: 28×2=56 (m), 15×2=30 (m), 56+30=86 (m). I have given a positive affirmation. Then, I asked: Is there any other solution to this problem? At this time, a student stood up and said, "teacher, I have another idea." The formula is 28+ 15=43 (m) and 43×2=86 (m). After this classmate finished speaking, I immediately said; "You speak very well. This method is unique. " Among these four methods, let students choose the best one, and students have a heated debate about it. Finally, they all agree that method 4 is the best. Only in this relaxed and pleasant atmosphere can we arouse students' initiative to learn and make them happy to learn, and only in this atmosphere can students' potential be fully brought into play and their highest level be fully displayed.

Third, set aside time and space for thinking and induce innovative inspiration.

The cultivation and formation of students' innovative consciousness must have their own time and space. Without the time and space for students to think, there will be no thinking, and of course there will be no sense of innovation. Therefore, in teaching, teachers must provide students with enough time and space for thinking. In the teaching process, the questions raised by teachers should not be too simple and direct, and students can answer them without thinking, but they should have a certain thinking space. Teachers should give students enough time to think about all the problems worth thinking about. If students are asked to answer questions as soon as they are asked, only a few students with quick thinking may respond, and most students have no time to think. In a word, only by providing students with enough time and space to think, can their innovative consciousness develop gradually. For example, after teaching "perimeter and area of rectangle and square", I showed a question: how many ways can a rectangle or square with a length of 20 cm be enclosed? What is the circumference of these figures? What else did you find? After independent thinking, group cooperation, discussion and communication, the students came up with five different enclosing methods, and found that the perimeters of these figures were all equal. After further thinking and exploration, the students also found that when the length and width of a rectangle or square with equal circumference are closer, the larger the area, the largest the square area. This greatly increases the space for students to explore, and also helps to guide students' thinking to develop in depth.

Fourth, encourage questioning and raising difficult questions, and cultivate innovative consciousness.

"Inventing tens of millions, the starting point is a problem". Asking questions and asking difficult questions is the beginning for students to explore knowledge and discover problems. To develop intelligence and cultivate innovative consciousness, it is very important to cultivate students' good habits of questioning and asking difficult questions, and to encourage students to think more and ask more questions. Einstein once said, "It is more important to ask a question than to solve it". Educators in our country also attach great importance to questioning and asking difficult questions. They put forward: "learning needs doubt, big doubt makes great progress, and small doubt makes little progress." Dr. Li Zhengdao told the students in the junior class of science and technology: "If you don't ask questions, you will never make world-class works, and in the end you can only imitate and copy." All these show the importance of questioning and asking difficult questions. Therefore, teachers should encourage students to be good at asking questions from the characteristics of students' strong curiosity, studiousness, activeness and thirst for knowledge. Mathematics classroom teaching should encourage students to think whimsically and transfer the right of teachers to ask more questions to students. Even if students ask childish and inappropriate questions, they should not be ignored, but should be given positive evaluation to protect students' self-esteem and self-confidence. Only in this way can students gradually develop the good habit of "being good at finding problems, daring to ask questions and being brave in arguing about problems". For example, when teaching the calculation method of "division with zero at the middle and the end of quotient", the textbook States: "0 is divided by any non-zero number to get 0". Some students asked: Why can 0 be a dividend but not a divisor? For another example, when teaching the understanding of "year, month and day", some students asked: Why is a year 12 months instead of 13 months? For another example, when teaching "Classification of angles", some students asked: What is an angle greater than180 and less than 360? This kind of independent thinking and questioning contains the learning spirit of students' courage to explore and create.

5. Encourage students to guess boldly and develop creative thinking ability.

Newton said; "Without bold speculation, there can be no great discovery." Mathematical conjecture is the intermediary of mathematical creation from recessive to dominant. The process of putting forward mathematical conjecture is essentially the process of mathematical exploration and creation. Gpolia, an advocate of mathematical method theory, once said that in the field of mathematics, conjecture is reasonable, worthy of respect and a responsible attitude. Mathematical conjecture can shorten the time of solving problems; You can get the opportunity of mathematical discovery and exercise your mathematical thinking. Many important discoveries in history were made by this illogical means of reasonable speculation. The famous Goldbach conjecture is a typical example. In teaching, students should be encouraged to guess boldly. Never throw cold water on a wrong classmate. You can ask them how they guessed and lead them to find out. If they guess wrong, sometimes it will lead to another discovery, perhaps a better one. For example, when teaching "Calculation of Rectangular Area", I took out a piece of rectangular paper with a length of 5 cm and a width of 3 cm and asked the students: How to calculate the rectangular area quickly? What is the relationship between the area and the length and width of a rectangle? Let students think independently and try boldly. Student A said: Find the rectangular area of length × width. Student B said: Find the area of a rectangle with length+width. Obviously, student A's guess is right and student B's guess is wrong. I don't directly deny this, but let students speak their own thinking process boldly. Give affirmation to student A's guess and encourage student B's guess. It is commendable for me to further guide students to dare to guess boldly, but can you verify whether the result of your guess is correct? After students substitute numbers, they find that the results are not consistent with the pendulum of 1 square decimeter. Let students correct their mistakes, protect their enthusiasm for learning, enhance their confidence and give them guidance in exploring new knowledge.

Sixth, improve teaching methods and cultivate innovative consciousness.

Because teachers' teaching time and content are limited, and students' development is infinite, teachers must constantly improve teaching methods in classroom teaching, and pay attention to infiltration method while guiding students to master basic knowledge, so as to cultivate students' learning ability and improve their innovative consciousness.

1. Infiltrate learning methods and enrich innovative content. "

Darwin famously said, "The most valuable knowledge is the knowledge about methods." Learning methods can ensure a person to acquire knowledge continuously and improve his learning and innovation ability. In teaching, teachers should gradually infiltrate learning methods such as reading, observation and hands-on operation and thinking methods such as deductive reasoning and inductive reasoning with a purpose and plan.

First of all, we should provide students with a demonstration of learning the law, which will have a long-term subtle influence on students. For example, to guide students to read math textbooks, we should draw up an outline of reading guidance according to the contents of textbooks and students' reality before class to arrange reading before class and cultivate students' habit of reading independently. Combine knowledge teaching with classroom reading, set questions from existing knowledge, real life and specific practical operation, and guide students to find answers from textbooks with questions. Read it again after class, summarize the main knowledge points of this lesson or this unit, make it systematic and form learning ability. Secondly, combine teaching practice to guide specific learning methods, such as carefully examining questions with students and analyzing the meaning of questions when analyzing examples. Make students learn to think about the synthesis method of knowable problems according to relevant conditions, and think about the analysis method of knowable conditions according to problems, and summarize these methods into general problem-solving ideas from the specific answers of various application problems. In order to cultivate students' ability and enrich innovative content.

2. Pay attention to hands-on operation and cultivate innovative ability.

At present, with the rapid development of science and technology, there is an urgent need for people who can think and do things. Practice has proved that it is difficult for people who can only use their brains but not their hands to make scientific and technological inventions. Those who can use their hands can encourage them to use their brains and promote each other with their hands. Modern teaching theory emphasizes: "Let students do science with their hands, not with their ears." At present, the poor hands-on ability of primary school students is a prominent problem. The key point is that teachers don't provide enough hands-on and practical opportunities for students in most cases. Therefore, we must attach importance to the cultivation of students' practical ability in teaching. For example, when teaching "Understanding Trapezoids", after guiding students to understand trapezoids, let students take out a rectangle, a triangle and a parallelogram prepared before class, and ask students to cut each figure at will to make it a trapezoid. After I put forward my request, the students actively began to use their brains to find ways to cut out the trapezoid in different ways. In the process of cutting, the students gave full play to their creative talents. Finally, I also designed a trapezoid-like figure with two curved sides, so that students can make it into a trapezoid with only one cut. At this time, some students were puzzled and frowned. Some students were creative and cut the graphics in half before cutting them. Through brain and hands-on operation, students have stimulated their potential creativity and gradually formed a sense of innovation.

3. Use open teaching methods to cultivate innovative consciousness.

The essence of open teaching is to let students actively participate in the learning process and exploration process. Only when students actively participate can "human development" be truly realized. If mathematics knowledge is effectively taught to students, there will inevitably be spoon-feeding, indoctrination and rote learning teaching methods. From the teaching itself, the purpose of students' learning mathematics is not only to remember some knowledge, but more importantly, to improve their interest in learning mathematics through mathematics activities, gain the experience of emotional attitudes and values in mathematics learning, and improve their scientific literacy. Therefore, teachers should "teach with textbooks", trust students, emancipate their minds and hands, explore independently, cooperate and communicate, and actively explore "mathematics" under the guidance of teachers. Constructing open teaching and cultivating students' innovative consciousness.

For example, in a math class, I showed a topic for students to think about: students should make a rectangular card with a length of 15cm and a width of 10cm. Now there is only a large rectangular paper with a length of 45cm and a width of 35cm. How many cards can I make at most? Some students said they could make nine, some students said they could make eight, and some students said they could make 10. I ask students not to jump to conclusions so quickly. Through drawing, cutting, calculation and discussion, it is finally concluded that 10 sheet can be cut. Pupils often want to be a discoverer and explorer. Designing such open questions for students to answer creates an "exploratory" feeling artistic conception for them, thus cultivating their innovative consciousness and practical ability.

In a word, it is a long-term and arduous task to cultivate students' innovative consciousness in primary school mathematics teaching. As mathematics teachers, we must stand at the height of 2 1 century, renew our teaching concepts, change students' adaptive development into creative development, and really lay a solid foundation for cultivating creative talents.