Designing exercises well plays an important role in improving students' thinking ability.
To sum up, in primary school mathematics teaching, carrying out purposeful and planned thinking training for students is conducive to improving the quality of mathematics teaching and developing students' thinking ability, thus comprehensively improving students' quality.
How to cultivate students' mathematical thinking ability in grade three: First, start with specific perceptual knowledge and actively promote students' thinking.
In the teaching of basic knowledge of mathematics, we should strengthen the teaching of forming concepts, rules and laws, which is also an important means to cultivate students' initial logical thinking ability. However, the teaching in this area is abstract, and the students are young, lack of life experience, poor abstract thinking ability and difficult to learn. Students' learning of abstract knowledge is a leap on the basis of a lot of perceptual knowledge. Perceptual knowledge is the basis for students to understand knowledge, and intuition is the way and source of information for mathematical abstract thinking. When teaching, I pay attention to the transformation from intuition to abstraction, and gradually cultivate students' abstract thinking ability. In teaching the knowledge of "angle", in order to make students get the correct concept of angle, I first guide students to observe the angles formed by objects and models, such as triangles, pentagrams, open scissors and fans, and abstract the angles from these objects. Then through physical demonstration, nail one end of two thin wooden strips together and rotate one of them, which intuitively shows that a ray can get different angles by rotating around its endpoint. Students can demonstrate by themselves with prepared learning tools, and clarify the concept of angle from the perspective of movement, so as to prepare for introducing the concepts of straight angle and rounded corner.
Second, actively develop students' thinking from the connection between old and new knowledge.
Mathematical knowledge has a strict logical system. As far as students' learning process is concerned, some old knowledge is the basis of new knowledge, and new knowledge is the extension and development of old knowledge. Students' cognitive activities are always based on existing old knowledge and experience. Every time I teach a little new knowledge, I review the old knowledge as much as possible, make full use of the existing knowledge to pave the way, and guide students to use the law of knowledge transfer and develop their thinking in the process of acquiring new knowledge. For example, when teaching the relationship between the parts of addition and subtraction, I first reviewed the names of the parts of addition, and then guided the students to draw from 35+25 = 60: 60-25 = 35; 60-35=25。 By comparison, we can see that the figures in the latter two formulas are actually addends in the former formula. Through observation and comparison, let the students sum up the formula for finding addend: one addend = and- another addend. In this way, students are guided to learn new knowledge by reviewing the past, and new knowledge is brought into the original knowledge system, which enriches knowledge, broadens their horizons and develops their thinking.
Third, carefully design questions to guide students' thinking
Pupils have poor independence, are not good at organizing their own thinking activities, and often think of what they see. Cultivating students' logical thinking ability is mainly through the demonstration, guidance and guidance of teachers in the teaching process, so that students can acquire some thinking methods in a subtle way. Teachers carefully design questions in the teaching process, put forward some enlightening questions, stimulate thinking, and mobilize students' enthusiasm and initiative to the maximum extent. Students' thinking ability can be effectively developed only when they are active in thinking. In the teaching process, teachers should ask questions with moderate depth and rich thoughts according to the key points of the textbook and students' reality, so that each student's thinking activities can be activated and new knowledge can be mastered through correct thinking methods.
Fourth, carry out reasoning training to promote students' thinking.
Language is the tool and shell of thinking. Strengthening language training in mathematics classroom, especially oral reasoning training, is a good way to develop students' thinking. When studying the chapter "Decimals and Composite Numbers", because decimals and composite numbers are rewritten, more knowledge needs to be comprehensively applied, which is exactly where students are prone to make mistakes. How to break through the difficulties and let students master this part of knowledge? I pay attention to strengthening reasoning training in classroom teaching. After the students learn the examples, inspire them to summarize the rewriting methods of decimal and composite numbers, and then let the students tell the process of doing the problems according to the methods. Through such repeated reasoning training, good results have been achieved, which not only deepens students' understanding of knowledge, but also promotes the development of thinking ability.
How to train junior three students' mathematical mind map for mathematics is actually to analyze the conditions given by mathematical problems layer by layer, then assist knowledge points and finally achieve the effect of solving problems. If you review, you can draw the knowledge point formula of the articles of association into a mind map, which will be clear at a glance when reviewing, and sometimes you can even add your own mistakes.
How to cultivate middle school students' mathematical thinking training should first interest students.
Then you have to have good questions to guide your thinking.
Draw inferences from others.
This is my ideal, I am just a student.
How to cultivate the mathematical thinking of first-year students and Mao? Remember addition and subtraction.
The key is to cultivate learning attitude.
Let the children be spoiled, willful and arbitrary. In the back.
First, the use of intuitive demonstrations to inspire students' thinking
The thinking of junior students is in the stage of concrete image thinking, and mathematics is highly abstract, so
How to promote the transition from students' thinking in images to abstract thinking in the teaching process? In my opinion, teachers should pay attention to using rich perceptual materials to draw out mathematical problems from things familiar to students. Through intuitive teaching, students' logical thinking ability can be cultivated.
For example, when teaching "understanding of addition", I first show the picture of "two children jumping rubber bands", and then demonstrate "another child is coming" and ask, "How many children are jumping rubber bands?" Then draw a big circle. Then, ask the students to demonstrate their gestures and dictate their meanings. In this way, students intuitively perceive that the sum of "two children and one child" is "three children" and should be calculated by addition. At this point, the students initially made it clear that "the two parts are combined to get the sum, and the addition calculation is applied". Then let the students talk about the meaning of "2+ 1=3" and let them analyze the information they get, that is, "3 consists of two parts, one of which is 2, which means the original two children; The other part is 1, which means another child has come. 2 is part of 3, and 1 is another part of 3. " In this way, students not only solve the quantitative relationship of addition, but also lay the foundation for the next step of learning subtraction.
Second, through practical operation, stimulate students' thinking
Hands-on operation is an effective means to develop pupils' thinking. Therefore, through intuitive operation, make
Students' multiple senses participate in teaching practice, so that students can think in operation and operate in thinking.
For example, when teaching "carry addition within 20", I asked students to prepare a digital cylinder in advance.
Put small sticks in it. First, put 9 sticks in each bucket and take 2 sticks in your hand. Then ask the question: "How many sticks can you take out of your hand to make 9 sticks 10?" Students will think, "1 and 9 make up 10, take 1 stick from your hand and put it in a bit tube." Then he asked, "When the number of digital cylinders is 10, which one should be put into the digital cylinder?" 2 pieces, take out 1 and 9 pieces to make 10 pieces. How many sticks are left? Which one should be put in the digital cylinder? " In this way, students can use their hands and brains to think and master how to calculate the carry addition within 20 by the method of "adding ten". Finally, I also ask students to describe the thinking process in language to promote the internalization of new knowledge. In this way, by mobilizing the enthusiasm of students' thinking activities, guiding them to use their brains, talk and use their brains, and actively acquire knowledge, it is conducive to cultivating students' thinking ability.
Third, train language expression and develop students' thinking.
Let students think methodically and reasonably, and describe the thinking process, which can not only exercise students' ability.
Oral expression ability is more important to the development of students' logical thinking ability. Therefore, in the teaching process, in addition to using intuitive demonstrations and organizing students' operations, it is also necessary to pay attention to the training of students' thinking order, so that students can tell the thinking process of using intuition and operation in their own language.
Is the third-grade mathematical thinking training in New Oriental related to school mathematics? Mathematical thinking training in the third grade of primary school should be carried out. After entering the third grade of primary school, students should be trained in abstract thinking regularly, otherwise they will not be able to react in junior high school.
How to cultivate sixth-grade students' mathematical thinking is to do more questions in this respect. Can't draw line segments, can't set equations, can't origami, and it's clear at a glance. If you can't do it again, ask the teacher or someone else.
How to cultivate the mathematical thinking ability of grade three 1 and students' logical thinking ability is an important task in primary school mathematics teaching, and the content of thinking is very extensive. According to psychological research, there are all kinds of thinking. What kind of thinking ability should be cultivated in primary school mathematics teaching? It is clearly stipulated in the "Mathematics Teaching Syllabus for Primary Schools" that "students should have preliminary logical thinking ability." This rule is very correct. Below I try to do some analysis from two aspects:
(1) First look at the characteristics of mathematics. Mathematics itself is a definite system composed of many judgments, which are represented by mathematical terms, logical terms and mathematical statements represented by corresponding symbols. And some new judgments are formed by some judgments with the help of logical reasoning. And the sum of these judgments constitutes the science of mathematics. Although the content of primary school mathematics is simple and there is no strict reasoning, it is inseparable from judgment and reasoning, which provides a very favorable condition for cultivating students' logical thinking ability.
(2) Let's look at the thinking characteristics of primary school students. Grade three students are in the transition stage from concrete image thinking to abstract logical thinking. The abstract logical thinking mentioned here mainly refers to formal logical thinking. Therefore, it can be said that the primary school stage is a favorable period for developing students' abstract logical thinking, especially in middle and high grades. It can be seen that it is in line with the subject characteristics of mathematics and the thinking characteristics of primary school students to cultivate the initial logical thinking ability as the purpose of mathematics teaching in the primary school mathematics syllabus. It is worth noting that the provisions in the outline have not received enough attention. There was a time when people talked a lot about creative thinking, but little about logical thinking. As we all know, in a sense, logical thinking is the basis of creative thinking, and creative thinking is often the abbreviation of logical thinking. As far as most students are concerned, it is difficult to develop creative thinking without good logical thinking training. Therefore, how to implement the objective requirements of "Primary Mathematics Teaching Syllabus" and cultivate students' logical thinking ability in a planned and step-by-step manner is still a problem worthy of attention and serious study. The emphasis on cultivating the initial logical thinking ability in the syllabus only shows that this is the main idea, which does not mean excluding the development of other thinking abilities. For example, although students are transitioning to abstract logical thinking in primary school, thinking in images has not disappeared. In the senior grade of primary school, some mathematical contents, such as the teaching of concepts such as prime number and composite number, are easier for students to understand and master through practical operation or demonstration of teaching AIDS; At the same time, cultivate students' thinking in images.
Wei will continue to develop. For another example, although the cultivation of creative thinking ability cannot be the main task of primary school mathematics teaching, it can promote the creativity of students' thinking when teaching new knowledge closely related to old knowledge and solving some thoughtful exercises. We should pay attention to it consciously in teaching. As for dialectical thinking, theoretically speaking, it belongs to the advanced stage of abstract logical thinking;
From the development process of individual thinking, it is later than the development of formal logical thinking. According to preliminary research, primary school students began to sprout dialectical thinking at the age of ten. Therefore, it is not appropriate to take the development of dialectical thinking as the teaching purpose in primary school prematurely, but to combine the teaching of some mathematical contents with some dialectical viewpoint factors to accumulate some perceptual materials for the development of dialectical thinking. For example, the appearance of the first volume of the general textbook can let students intuitively know that the second addend has changed and the gain number has also changed. There are also some tables in middle school textbooks to let students tell how the multiplicand (or dividend) changes and how the product (or quotient) changes. This has accumulated some perceptual materials for the view that things are interrelated and constantly changing in the future.
How to cultivate and improve the mathematical thinking ability of first-year students? One of the characteristics of the new curriculum standard is to embody "people-oriented development". As a math teacher in the first grade of primary school, according to the psychological characteristics of the first grade students, we should design the classroom teaching in a planned and purposeful way, create a pleasant classroom environment, teach the methods of learning mathematics, cultivate students' interest in learning mathematics, highlight students' dominant position, and let students actively participate in learning activities, so that students' thinking ability can be initially developed and gradually improved while actively acquiring knowledge. One of the characteristics of the new curriculum standard is to embody "people-oriented development". As a math teacher in the first grade of primary school, according to the psychological characteristics of the first grade students, we should design the classroom teaching in a planned and purposeful way, create a pleasant classroom environment, teach the methods of learning mathematics, cultivate students' interest in learning mathematics, highlight students' dominant position, and let students actively participate in learning activities, so that students' thinking ability can be initially developed and gradually improved while actively acquiring knowledge. When observing things, first-year students only pay attention to obvious external phenomena and ignore hidden and essential things. Therefore, we should pay attention to guiding students to focus on key parts and granting observation methods, so that they can find laws in observation and find better ways to solve problems. For example, when looking at the problem of matching pictures in teaching, most students can only get the addition of 2+4=6 or 4+2=6 by observing the appearance, while ignoring the formula of implicit subtraction. At this time, the teacher should guide the students to observe first, then look at the whole picture and think: How many apples are there? Cover the left side again and ask: How many apples are there on the right? Then cover your right and ask: How many apples are there on the left? Let the students understand vividly that the formula obtained by subtraction is 6-2=4 or 6-4=2 if one part is removed from the total and the other part is left. Students understand that this observation method is from the whole to the part, and then look back to let students see that the observation method of addition formula is from the part to the whole, and know that the meaning of addition is to combine the two parts to get the sum. It is particularly important to cultivate students' mathematical thinking ability from grade one. As math teachers, we should raise this awareness in future math teaching, so that children can develop good math thinking ability from an early age and lay a foundation for further study.