A modern person must first have independent spirit and ability. Independence is an essential quality of modern people, an important component of a sound personality, and the basis for people to stand on the society and give full play to their potential. Einstein said: "Without creative people who think and criticize independently, the upward development of society is unimaginable." Primary education is the foundation of education. Mathematics education for Chinese children in primary school is to lay the foundation for the study of junior high school mathematics, senior high school mathematics and college mathematics in the future, and at the same time to cultivate Chinese children's thinking logic ability. Therefore, primary school mathematics teaching plays an extremely important role in primary education. In mathematics learning, it is the key to cultivate primary school students' ability to think and solve problems independently. So, how to cultivate students' independent ability? Let's talk about some opinions on cultivating students' independent thinking ability.

First of all, as a teacher, we should teach students how to think and guide them to consciously form the habit of independent thinking. In the usual teaching process, lectures should not be too detailed, giving students room to think, and not letting students develop dependence. When students are tired from the excitement of independent thinking, rather than from pure memory, when education is successful, because the advent of the information age means that processing information is more important than memorizing information. Not because we don't need to remember information, but because we only have very limited brain "memory" space. Instead of using limited mental resources to remember irrelevant facts, it is better to give full play to the thinking function of the brain and think about problems coherently.

Secondly, it is to create a good thinking atmosphere for students. Psychologist Rogers believes that a person's creativity can only be expressed and developed to the maximum extent under the conditions of "psychological security" and "psychological freedom". Isn't thinking like this? It is difficult for people to think calmly and innovate under the psychological state of depression, fear and tension. Therefore, it is particularly important to create a good atmosphere conducive to students' independent learning and active participation, and to give students "psychological safety". In a democratic and harmonious classroom atmosphere, teachers and students can talk on an equal footing, students can think quietly and deeply, and non-intellectual factors such as emotion, motivation, belief and will can also be cultivated imperceptibly. Especially when students' thinking is difficult or stuck, we should encourage them to think again boldly instead of interrupting, scolding or laughing at them stiffly. In this way, students will gradually summon up courage in a tolerant atmosphere, open the floodgate of thinking, and gradually develop a good habit of being willing to think and thinking deeply.

Furthermore, guide students to think correctly. Only when teachers teach students the correct thinking methods and train their thinking well can they improve their ability to find, analyze and solve problems. Make students "think well and process orderly", and students' initial logical thinking ability can be formed continuously. Guide orderly thinking. The important task of mathematics teaching is to cultivate students' ability of observation and analysis and orderly thinking from the outside to the inside. In the exploration of new knowledge, teachers should take the process of problem discovery and thinking as an important teaching link, not only to let students know how to think about this problem, but also to let students know why they think like this. When teaching backward method to solve problems, I introduced Li Bai's poem of buying wine, and used operational experiments to help students understand clearly what they got in each step backwards, and then encouraged students to express their thinking process in an orderly way. With this kind of teaching, students not only master the final result, but also learn how to think about mathematics in an orderly way, thus solving problems.

Finally, guide students to learn to reflect in the process of thinking. Friedenthal, a famous Dutch mathematics educator, pointed out: "Reflection is the core and motivation of mathematical thinking activities." Learning is a systematic project, and learning to reflect is an indispensable factor in students' development. The process of students' reflection on mathematics thinking is to monitor and adjust their own mathematics learning, and then guide, dominate, decide and monitor their mathematical cognitive activities. Teachers should pay attention to guiding students to form reflective consciousness and master reflective methods in teaching.

In short, in order for students to learn to learn, teachers should have a correct understanding, adopt correct methods and persist for a long time, so as to achieve good achievements in this respect.

Home Education Teaching School-based teaching and research cultivates students' independent thinking ability, allowing them to develop independently

Cultivating students' independent thinking ability, allowing students to develop independently

In the classroom, we implement an autonomous mutual learning classroom teaching mode, which requires students' own quality and ability. Although the autonomous mutual learning classroom requires group cooperative learning, However, students' cooperative ability must be based on their independent thinking ability, which is one of the abilities that students must have to implement the self-help learning classroom model. However, there are still many students who are not good at thinking with their heads and are highly dependent, and fish in troubled waters when working in groups. Personally, I think it is very important to cultivate primary school students' independent thinking ability and get rid of their mental dependence, so I summarize the following methods.

first, enlightening questions: let students have questions to think about and create independent thinking situations for them

enlightening questions are one of the main means to arouse students' enthusiasm and guide them to think independently. Teachers can create opportunities and situations for students to think independently by asking questions, point out the direction of thinking for students, and let students explore new knowledge and exercise their thinking ability through active independent thinking. The purpose of enlightening questions is not to answer, but to ask students questions and inspire them to find answers through independent thinking. A class involves a lot of knowledge, and there are many questions to be asked. Teachers should be good at grasping the key points, difficulties and doubts of knowledge and carefully designing questions, so as to stimulate students' interest in independent thinking and promote the harmony and unity of knowledge and ability.

1. Ask questions in time when students are exposed to the key and essence of new knowledge

This can not only guide and inspire students to correctly grasp the essence of what they have learned, so as to successfully master what they have learned or form skills, but also bring students into a positive learning situation, prompting them to think positively, so as to enlighten their thinking and exercise ability. What is important here is to contact the old knowledge to grasp the "breakthrough point" of the problem.

(1) Grasping the transition point between old and new knowledge

New knowledge is often extended and developed on the basis of old knowledge. When guiding students to transition from old knowledge to new knowledge, students can be inspired to think, communicate the connection between old and new knowledge, and smoothly realize the connection between old and new knowledge through appropriate questions. For example, when teaching the area calculation of a rectangle, the teacher immediately asked, "Can you measure the size of the water surface of a swimming pool with the area unit?" This makes students feel that it is too inconvenient to use the method of mathematical area unit, so as to stimulate students' psychology of finding simple methods, so as to consciously open their minds, carefully observe and think, and finally find the formula of "rectangular area = length × width".

(2) Grasping the transformation point of old and new knowledge

Many new knowledge is only added with new content on the basis of old knowledge, or is transformed from old knowledge by recombination. Therefore, it is an important and effective way to learn new knowledge and solve new problems by transforming or decomposing the new knowledge and problems into the old knowledge that has been mastered. In teaching, clever questioning at the transformation point of old and new knowledge is bound to inspire students to think independently and make them feel suddenly enlightened later. For example. When learning "area calculation of cylinder", the following questions are designed: "What kind of graphics will be obtained after the side of cylinder is unfolded? The length and width of this figure are equal to which part of the cylinder? Who can propose the calculation method of lateral area of a cylinder through demonstration, observation and thinking? " Through this group of questions, guide the students to think independently, transform the new knowledge into the old knowledge they have learned, and thus get the calculation formula of measuring area by themselves.

(3) Grasping the contradiction between old and new knowledge

In the process of learning new knowledge, students often feel the contradiction between new knowledge and existing knowledge structure

and then they have curiosity and interest in independent thinking. At this time, teachers' proper questioning can inspire students to think independently, find ways and methods to solve "contradictions" and master new knowledge. For example, when learning the law of decimal addition and subtraction, the vertical calculation of decimal addition and subtraction requires "decimal point alignment", which conflicts with the vertical calculation of integer addition and subtraction that students have mastered. At this point, ask: what method can we use to align the digits with the same decimal? Students are thinking about the alignment of hundreds, tens, units, tens and percentiles one by one. So, what is the easiest way to express it? This leads students to say that decimal addition and subtraction should be "decimal point alignment" when writing vertical.

2. Ask questions in time when students' independent thinking is blocked

Teachers ask questions not only to impart knowledge to students, but more importantly, to stimulate students' interest in independent thinking, enlighten their wisdom, guide students to master the correct thinking methods and cultivate their independent thinking ability. When students encounter difficulties in independent thinking, teachers promptly induce them to ask further questions, which will not only enable students to think deeply, but also enable them to deeply understand knowledge. For example, when teaching "addition and subtraction of fractions with different denominators", two oral arithmetic problems of addition and subtraction of fractions with different denominators, 1/2+1/3, 1/2-1/4, are finally given, requiring students to accept new knowledge through independent thinking. The teacher has put forward the following three questions for students to think about: Can we add and subtract directly? Why can't we just add and subtract? Who can use the learned knowledge to transform first, and then add and subtract? After some thinking, students learned that they should use the knowledge of general points, first convert different denominators into the same denominators, and then add and subtract. After the teacher gave affirmation and the students succeeded in the trial calculation, they asked such a question: "Why can't the scores be added and subtracted directly with different units?" The students were lost in thought again. At this time, the teacher demonstrated that the shadow representing 1/2 circle and the shadow representing 1/3 circle were put together, and the result was that it could not be represented by half or three. This demonstration reinforces the truth that different fractional units cannot be added directly. Then the teacher demonstrated that the shadow representing 3/6 circle and the shadow representing 2/6 circle were put together, and the truth that "only the fractional units are the same, the result can be expressed by a fraction" was verified from the front.

3. Ask questions in time when students are disturbed by fixed thinking patterns

At this time, the purpose of asking questions is to guide students to change their thinking angles and directions and seek new ways and methods to solve problems. If there is such a calculation question, "The square area is 4 square centimeters. What is the area of the circle to be cut into the largest circle?" When students answer questions, because there is no direct condition for the area of a circle in the questions, they are disturbed by the thinking method that the area of a circle must know the radius, and feel at a loss for a moment. At this time, the teacher asked in time: "If you can't find the radius, can you find the square of the radius?" What is the relationship between the square of radius and square? " Show pictures to inspire students to think. Through comparative observation, students find that the square of radius is 1/4 of the square area, thus solving the problem quickly. After teachers' questioning and instruction, once students break through the interference of fixed thinking, they can find out different conventional ideas and problem-solving methods, and feel the joy of success. Over time, they like to think for themselves and broaden their thinking to find answers.

Second, practical operation: Starting from sensibility, inspire students to think independently

When primary school students think about problems, the components of concrete images play a major role and their abstract ability is weak. Intuitive teaching with perceptual materials, especially for students to operate by themselves, can obviously help them think independently, enhance their spatial concept and exercise their abstract thinking ability.

for example, "a rectangular iron plate, 3 cm long and 25 cm wide, cut squares with sides of 5 cm from the four corners as shown on the right, and then make a box without a cover. How many milliliters does this box have? " When students have difficulty in answering independently, they are taught to do the following: each person takes a rectangular piece of paper, draws a small square with the same size at the four corners, then cuts it off, and then folds it into a box with reference to the dotted line on the picture. At this time, the teacher asked: What shape is the box in the question? What are its length, width and height? Students observe carefully, think actively, gain real understanding knowledge and know that hands-on operation can help them think, analyze and solve problems.

3. Encourage questioning and asking difficult questions: Encourage students to find problems through independent thinking and ask questions actively.

A student who has no doubt is not a student who can think independently. In teaching, teachers should encourage students to constantly "discover new problems" and "ask new questions". For example, when talking about "the meaning of comparison", point out that the latter term of comparison cannot be zero and ask students why. Any questions? Some students ask: Why is there a 3: score in sports competitions? At this time, we might as well guide the students to discuss this issue, so that they can understand in the process of arguing that the meaning of a few scores in a sports competition is a record of the achievements of two contestants, and it does not mean that the two scores are divided. Another example is a math problem: there are 3 colored papers in the school. It takes 11 pieces to make paper flowers and 9 pieces to make flags. How many pieces are left? On the basis of the analysis of line drawing, the students use the newly learned two-step subtraction calculation to get the result. Then ask who can come up with different solutions? After a while of thinking, a student asked, Teacher, can you add up the 11 pieces used for making paper flowers and the 9 pieces used for making flags first? The teacher immediately praised the student's good idea, which not only affirmed the student, but also encouraged all the students to question and ask questions. After independent thinking, students are bound to have questions and are eager to solve problems, which forms the best state of learning. Students consciously arouse the enthusiasm of independent thinking, which will inevitably produce the best learning effect.

Fourth, provide thinking topics: let students practice alone, and urge them to solve more difficult problems alone

After each unit, write several thinking questions that are difficult and can sublimate students' thinking, let students take them home to think, and then explain them in math activity class, which is very beneficial to improve students' independent thinking ability. For example, after learning the knowledge of "circumference and area of a circle", I once wrote a thinking question: "There is a grassy field near a straight canal. Tie a sheep to the canal with a three-meter rope and ask what is the circumference of the place where the sheep can eat grass?" Let several students work out this problem on the blackboard first, and the students will quickly list the formula: 2×3.14×3. The teacher denied it on the spot, and the students were puzzled and needed to be pointed out. At this time, I deliberately said, "I won't talk about this problem today, so take it back and think about it." I believe that students can answer it independently. " Sure enough, the students reported their answers to the teacher one after another the next day. Some drawings and some operation demonstrations can write the formula of 2×3.14×3÷2. Teachers consciously put forward thinking questions, deliberately fail to answer difficult questions in time, and encourage students to think for themselves after class, which can effectively promote the improvement of students' independent thinking ability.

five, vary from person to person: make all students think independently.