How to cultivate students' innovative spirit in primary school mathematics teaching

Nowadays, with the rapid development of science and technology, the standards of social evaluation of talents have also changed, which requires talents in 2 1 century not only to have knowledge, but also to have innovative consciousness and creativity. How many innovative talents a country has will determine the speed of economic development and the size of scientific and technological progress. The core of quality education is innovative education, which refers to education that focuses on cultivating students' innovative consciousness and practical ability. Innovative education is related to the rise and fall of the Chinese nation. Education shoulders a special mission in cultivating national innovative spirit and innovative talents.

General Secretary Jiang pointed out: "Innovation is the soul of a nation and an inexhaustible motive force for a country's prosperity." It also instructed the Third Plenary Session of "Establishing the Innovative Spirit of the Whole Nation" to emphasize the cultivation of students' creative spirit and innovative ability. Therefore, cultivating students' innovative consciousness is an important content of the current primary education and teaching reform, and it is also an inevitable need of human development. In primary school mathematics teaching, we should focus on students' life experience and social background, broaden students' horizons, expand students' learning space and time, create a harmonious and natural classroom atmosphere by establishing a democratic and equal relationship between teachers and students, optimize the teaching process, reform exercises and homework design, promote learning with happiness, and cultivate students' innovative consciousness.

First, contact the reality of life, establish innovative ideas

Students come to school not only to acquire knowledge, but also to become smarter. But for a long time, under the bondage of traditional ideas and the pressure of entrance examination, many teachers have become teaching machines. When preparing lessons, they are often superstitious about textbooks, mainly textbooks, teaching reference books and teaching plans, and dare not deal with textbooks boldly. In class, students are often afraid to take the initiative to explore. Students are bound in the circle of teachers and classrooms, passively instilled by teachers, and their creative personality is suppressed. This kind of closed teaching emphasizes the accumulation of knowledge and cultivates knowledge-based and scholar-oriented talents. Innovative education emphasizes teaching students to actively explore and create knowledge, and cultivating creative and pioneering talents. Therefore, in order to implement innovative education and cultivate students' innovative ability, teachers must change their concepts, establish innovative education concepts and enhance the awareness of openness in classroom teaching.

Mathematics is everywhere in real life, and students' learning content can be learned from teaching and life practice. When designing the teaching content, teachers should consciously connect the theoretical knowledge they want to learn with the students' existing life experience, so that abstract mathematical knowledge can be carried by intuitive and rich objective things, and students can experience that mathematical knowledge is around and life is full of mathematics. Make full use of people and things in students' living environment, start with things that students can see and touch in their daily life, actively create active and operable teaching contents that students can do, and urge students to invest in learning with a positive attitude, understand and master knowledge in practical activities, and change "learning by doing" into "learning by doing". At the same time, students experience the value of knowledge in this integrated activity of learning, doing and using, which further stimulates their desire to learn knowledge and explore the world. Teachers should actively organize students to go out of the classroom and campus to learn about the world, enrich their experience, enrich the teaching content, and activate the teaching content, so that the acquisition, application and innovation of knowledge can be integrated with each other, and all aspects of their abilities can develop simultaneously. For example, when teaching orientation and counting, the teacher observes the seats in the class to guide students to talk about themselves and which group the students around them are sitting in. Guide students to realize that two conditions are needed to determine the position of an object, and initially penetrate coordinate knowledge. Or organize students to use what they have learned to find seats in the "cinema" to see who can find them quickly and accurately, so that students can apply what they have learned and think with interest. Explore the problems encountered, enrich and develop the knowledge learned, and stimulate the sense of innovation.

Second, create a teaching atmosphere and cultivate students' innovative consciousness

Classroom atmosphere will affect students' learning mood. A relaxed, lively and lively learning atmosphere can make emotions have positive motivation and perception. It organizes, maintains and guides behavior. Creating a lively learning atmosphere is the premise of cultivating students' innovative consciousness.

1. Establish a democratic, equal and harmonious relationship between teachers and students.

Psychological research shows that good emotions can stimulate students' spirit, while bad emotions will inhibit students' intellectual activities. Teachers should respect every student and let every student have the opportunity to show himself and enjoy the happiness of success. We should bring smiles into the classroom to encourage students, so as to protect their self-esteem and cultivate their self-confidence. Only when students study in a democratic and harmonious atmosphere can their thinking always be active, and they dare to think, speak, ask questions and innovate. In the process of teaching, teachers can talk to students in a consultative tone, such as "Who wants to talk …" "Who wants to talk …" and so on. After listening to the students' different opinions, he said, "I'm really honored. I agree with him. " Although the words are simple, it is enough to show that the teacher has regarded himself as a member of the students, thus establishing a more equal and harmonious relationship between teachers and students. This can not only improve the efficiency of classroom teaching, but also eliminate students' alert psychology. Students' thinking is active and creative, which is especially needed in mathematics learning and the key to cultivate students' innovative consciousness.

2. Protect curiosity, stimulate curiosity and encourage students to question boldly.

Curiosity and thirst for knowledge are not only the incentives to stimulate students' creative activities, but also the driving force of students' creative thinking. On some issues, students will put forward some bizarre and even absurd views. As teachers, we should respect all kinds of questions raised by students, treat students as masters of learning sincerely, and let students light the flame of knowledge and creation. At the same time, we should be good at asking some questions that students are familiar with and need to solve with their brains, and guide students to find and find answers by themselves. We should be good at using inspiring and expectant language to cultivate students' self-confidence and enterprising spirit. For example, "What a great idea you have!" "You set an example for your classmates!" "Who has more and better solutions?" Wait, these passionate languages can greatly arouse students' enthusiasm and creativity.

Encouraging students to question and ask difficult questions is the starting point of cultivating students' innovative consciousness. Einstein, a famous scientist, once said, "It is often more important to ask a question than to solve it." Because there is no nervous thinking activity of students, there is no question. Therefore, in teaching, teachers should leave time and space for students to ask questions, pay attention to guiding students to find and ask questions, ignite the sparks of students' thinking and stimulate students' desire to explore. For example, when learning the derivation of trapezoid area formula, students propose that in addition to splicing two identical trapezoids into parallelograms, the derivation can be made. When deriving the lateral area formula of a cylinder, some students asked whether it was possible to cut the edge along a diagonal line and expand it to get a parallelogram to derive the lateral area formula. I encourage these questions and opinions, whether correct or not, to guide students to think positively. Over time, students' curiosity, thirst for knowledge and creativity will be organically combined and gradually form a sense of innovation.

Thirdly, optimize the teaching process and cultivate students' innovative consciousness.

1, optimize the introduction of new courses, stimulate students' interest in learning, and cultivate students' innovative consciousness.

Lead-in is a prelude to a class, and the quality of lead-in directly affects students' interest and enthusiasm in learning. As we all know, interest is the best teacher for students to learn. Interest can stimulate students to explore actively and persistently, which is the starting point of cultivating students' innovative consciousness. For example, when teaching the feature that numbers can be divisible by 3, teachers can ask students to divide any natural number by 3 first, and then ask students to quote any number, and teachers will immediately judge whether this number can be divisible by 3. In this way, students will be impressed by the teacher's ability to foresee things, such as God's help, thus generating the desire to explore mysteries, cultivating students' interest in learning mathematics and stimulating students' innovative consciousness.

2. Optimize the exploration of new knowledge and cultivate students' innovative consciousness in the process of solving problems.

It is necessary to change the situation that teachers tell students to listen and teachers passively accept students, and strive to turn the teaching process into a process in which students explore independently and actively participate in acquiring knowledge under the guidance of teachers. In this process, teachers should convey teaching information to students in a certain order and level around teaching objectives, and ask "What do you think?" In the process of guiding students' thinking. "Why do you think so?" "Is there any other way?" And so on, try to find the bright spot of students' thinking, give affirmation and encouragement in time, and protect and cultivate students' innovative consciousness.

(1) Pay attention to the actual operation.

Practical operation is an important means for students to experience the process of knowledge formation, and it is very important in the teaching of preliminary geometry knowledge. For example, when learning the "understanding of the circle", students can find the position, radius and diameter of the center of the circle by folding and measuring. For another example, when learning "the side area of a cylinder", students can find the relationship between the side surface of the cylinder and the development diagram by cutting the side surface of the cylinder and spreading it evenly along a height of the cylinder, and then deduce the calculation formula of the side area of the cylinder. You can also guide students to cut edges along the diagonal and expand them into parallelograms. Or tear the edge directly and transform it into a rectangle through cutting and repairing. All these methods can derive the formula for calculating the side area of the cylinder, and it is in these practical operations that students' practical ability and innovative consciousness are cultivated.

(2) Pay attention to trying.

In mathematics teaching, teachers should create conditions for students to try and make them dare to try and be good at trying. When learning division with remainder, you can design the following topics: () ⊙()= 8...5. Let students further consolidate the relationship between divisor and remainder after trying to fill in. Furthermore, in division with remainder, if the divisor is 9, what is the possible remainder? Let the students guess boldly. If you want to try and guess, you should allow mistakes. Teachers should pay attention to protecting students' self-esteem and sense of participation, and cultivate students' innovative consciousness.

(3) Pay attention to independent thinking

The development of cognition is inseparable from students' original mathematical reality, and the development of potential is inseparable from independent thinking and active exploration of practical activities. In classroom teaching, students should try to explore new knowledge before thinking independently, learn to think independently, and cultivate students' interest in solving problems. For example, in the teaching of "reciprocal", after students understand the meaning of reciprocal, let students write their own questions. The first student gives 2/5, and the students quickly say its reciprocal. I asked: can you come up with a new topic? This "challenging" question breaks the students' mindset and encourages them to concentrate their cognitive attention and find another way. At this time, the students actively used their brains, and the topics were false scores, fractions, decimals and special numbers "1" and "0", which greatly mobilized the enthusiasm of all students for countdown. Thus, the innovative consciousness is transformed into concrete innovative behavior, and good teaching effect is achieved.

Fourthly, deal with teaching materials flexibly and cultivate students' innovative consciousness.

Mathematics textbooks are the embodiment of mathematics knowledge, but book-based teaching is not conducive to the cultivation of students' innovative consciousness. Although the compilers can follow the principles of compiling textbooks, they should try their best to be simple and easy to understand, which is in line with students' cognitive characteristics. For most of them, it is impossible to describe all the contents in detail and show the process of knowledge discovery one by one. So it still shows that it can provide materials for students to learn actively. If the teacher's teaching only stays at the level of light as water, students' thinking will be hindered by the lack of new information in specific life. Ye Shengtao once said: "Teaching materials can only be used as the basis for teaching. To teach well and benefit students, teachers should be good at using it. " Therefore, in actual teaching, teachers should establish a holistic concept, read through the textbooks from the systematic perspective, understand the arrangement intention of the textbooks, find out the position and role of each part of the textbooks in the whole textbook system, and analyze and deal with the textbooks from the perspective of connection and development. According to the students' situation and teaching content, we should enrich, reorganize and deal with the hidden factors in the teaching materials, creatively use the teaching materials, and optimize the combination of teaching objectives such as knowledge points and moral education content in the teaching materials, so as to make students interested in the knowledge itself and stimulate their inner motivation to learn.

For example, in the teaching of "Preliminary Understanding of Division", the example is as follows: "Divide the 10 button into two parts, each part is □." I said, "Who wants to show you what they think?" I created a good teaching situation, and then let the students talk about how to divide it. After I affirmed the students' ideas, I changed the question slightly and changed it to: "Divide the 10 button into □ blocks, each block is □." Then guide students to observe and think, and stand up and express their opinions freely. In the teaching of this link, I changed the single question in the book into a flexible question, which not only permeated the dialectical materialism view that things are the development and change of sports, but also made the teaching content more problematic, interesting, open, different and practical.

Fifth, optimize exercises and homework to cultivate students' innovative consciousness.

1, optimize the exercise design

Almost all the exercises in the old textbooks have complete conditions and questions, and the task of solving problems is to find the only answer. Such exercises are easy for students to be satisfied with getting correct answers, and lack of further research and discussion on the diversity of problem-solving ideas and the internal factors of problems. In the long run, students will become single-minded, rigid and narrow-minded. The germination of innovation was restrained, and the sense of innovation was not cultivated. Therefore, teachers are required to creatively design independent thinking, divergent and open exercises with certain difficulties when preparing lessons.

① Conditions are open.

For example, when teaching "Cognition of Multiplicity", design an exercise: there are 6 monkeys, 2 pandas, 8 sika deer, 3 swans and 1 elephant in the zoo, and ask students to talk about the multiple relationship between the two animals with what they have learned. This design is convenient for students to actively think and explore when both quantities change, and obtain a way of thinking that they (or classmates) have never had before.

② Openness of the problem

In other words, the questions it raises are often uncertain, and the subject must collect other necessary information before he can start to solve the problems. For example, when reviewing, you can design such a topic: "There are 36 chickens in Abby Mallard, 18 chickens, and 7 chickens are less than geese. What questions can I ask?

③ Concept and openness

In other words, there is no ready-made problem-solving model for the topic, and we can think and explore the problem from multiple angles with different knowledge and different strategies.

If there is subject teaching, I have designed such a topic: "Class 24 students take part in the broadcast gymnastics competition in a certain year (1). Please help me design it. How should I queue up?" Students can make different answers according to different ways of thinking, thus cultivating students' creative consciousness.

Because the conditions are comprehensive, multi-directional, novel and redundant, students are naturally in an active position in the process of solving problems, and their active thinking, exploration and thinking abilities are fully trained, and their thinking is more profound, flexible, meticulous, creative and critical. In the long run, students can be encouraged to constantly seek differences, dare to challenge problems and cultivate their innovative consciousness.

2. Reform the homework design

The design and arrangement of homework is the deepening and continuation of classroom teaching. At present, the disadvantages of mathematics teaching are that students have a solid grasp of written knowledge and high test scores. However, in order to really let students solve practical problems in life, many students are often at a loss and become real "bookworms". We should change the way of homework arrangement that only focused on knowledge consolidation in the past, but design some thoughtful, practical and open topics based on the principle of "jumping and picking fruits" and pay attention to connecting with students' real life. Or let students design their own homework, so that students of different levels can play the main role and improve their innovation ability.

For example, after learning the "understanding of cylinders", students can be arranged to make a satisfactory cylinder model and cultivate their hands-on operation ability. After learning the "quantitative relationship between unit price, mathematical quantity and total price", students should be arranged to do a survey in the vegetable market to find out how many melons 5 yuan money can buy and cultivate their practical ability.

In a word, cultivating students' innovative consciousness is the sacred duty entrusted to every educator by the times. Teachers should base the teaching content on what students like every day, flexibly control the teaching materials, strive to design exploratory and open classroom teaching content, and design exercises with thinking ability, which are all important links to stimulate students' interest in learning and cultivate their exploration ability and innovative spirit. Only exploratory teaching content can conform to the current trend of teaching reform, and also make students' ability develop harmoniously, so that our mathematics classroom not only focuses on the growth of students' knowledge, but also pays more attention to students' lifelong sustainable development. Only in this way can we finally realize the cultivation and improvement of students' innovative consciousness and cultivate innovative talents from generation to generation!