Primary school mathematics is an abstract logic subject. Primary school students, especially those in lower grades, mainly think figuratively. Thinking often begins with action. The following small series has sorted out how to train children's mathematical thinking. Welcome to read!

1 how to cultivate children's mathematical thinking

The goal is interesting.

Mathematics is characterized by strict logic and wide applicability. We should make full use of the characteristics of the subject, combine the teaching content, reveal the learning objectives, and pay attention to combining specific objectives with lofty ideals, so as to turn interest into interest and become the eternal driving force for learning.

For example, when teaching the knowledge of "divisibility of numbers", students are introduced to such knowledge: mathematics is the queen of natural science, number theory is the crown on the queen's head, and Goldbach conjecture is the jewel in the crown. Learning this part of knowledge well can lay a foundation for everyone to learn other mathematics knowledge well. When I grow up, I will try my best to conquer Goldbach's conjecture and show the wisdom of China people to the people of the world, just like Chen Jingrun, a famous mathematician in China. When learning abacus, firstly, I quote the legendary example of China's psychic calculation to introduce the calculation function of electronic computer. But after the game, our ancestors invented abacus to do addition and subtraction, sometimes faster than computers. Abacus is not only a good calculation tool, but also a learning tool that can develop children's intelligence. Learning abacus can improve oral and written calculation ability. Now primary school students all over the world are learning abacus. So as to stimulate students' interest in learning abacus.

Operation promotes thinking.

Primary school mathematics is an abstract logic subject. Primary school students, especially those in lower grades, mainly think figuratively. Thinking often begins with action. In teaching, I pay attention to designing the links of students' operation or teachers' demonstration, so that students can move their hands, eyes, brain and mouth during operation observation. Mobilize students' positive thinking, so that students can become masters of exploring knowledge and discovering knowledge laws.

For example, when teaching "division with remainder", let students begin to explore learning tools, using a small disk of 10 as an apple and two round disks as plates. First place: put 10 apples on two plates on average. The students quickly sorted them out and put five on each plate. Rearrange: put 9 apples evenly on 2 plates. The students are in trouble. Small hands were raised one by one, and some said, "Teacher, I put five on each plate, which is not enough." Some said, "Teacher, I put four on each plate, and there is none left!" " "On the basis of students' learning tools, the teacher pointed out that in daily life, something is often divided equally and finally left, further revealing that the content of this lesson is' division with remainder'. Students' hands-on practice and full perception of division results will lay a good foundation for establishing the concept of division with remainder and mastering the thinking mode of division with remainder.

2 the specific application of mind mapping

The use of mind map by primary school mathematics teachers

Primary school math teachers can use mind maps to prepare lessons before reviewing their lessons. For example, when reviewing the knowledge points of "triangle", the teacher should list all the relevant knowledge points of triangle before class, sort them out by means of mind map, and inform the students of the central review point of this review class, so that they can draw their own mind map. In classroom teaching, teachers can let students show their mind maps drawn before class, explain the themes and related concepts of students' mind maps, and guide students to clarify the relationship between different levels. Finally, guide students to analyze the shortcomings of the existing mind map and further improve it. In this process, students should be guided to recall and understand the related concepts in the pictures and correct their mistakes.

You can use group cooperation to review, and let students improve their group's mind map through group cooperation. For example, taking triangle as the central word, teachers can first write the word "triangle" in the middle of the blackboard, then draw two lines on both sides of it, and then write "classification by angle" and "classification by edge" at the back of the lines, asking students to improve this mind map until it is completed.

Students' Use of Mind Map

Pupils are often interested in new things, and if traditional teaching methods are used in review classes, their interest in learning can often not be stimulated. From the students' point of view, the use of mind map can achieve the purpose of connecting knowledge points in series and improving the efficiency of listening to lectures.

Before class, students can use mind map to preview, thus improving the efficiency of class. Students can draw a mind map through group cooperation according to the central words given by the teacher in advance. Take the triangle as an example. Students can draw mind maps in several different colors. For example, triangles classified by angle are written in red, triangles classified by edges are written in green, and the corresponding triangles are drawn next to the text. Because the mind map is illustrated, primary and secondary school students can not only sort out and connect the triangle knowledge points in this process, but also get the happiness of the game and learn in the game.

3 How to cultivate students' mathematical thinking

Principles to be followed in mastering mathematical thinking methods

1, the infiltration principle of quantitative change to qualitative change because the surface knowledge and deep knowledge of mathematics are an organic whole, they are interrelated, interdependent and synergistic. Mathematical thinking method always takes surface knowledge as the carrier, and realizes deep knowledge in surface knowledge. Because the mathematical thinking method is the reflection of the essence and internal relations of superficial knowledge, it is more abstract and generalized. If there is some form of mathematical thinking method, it is difficult to find a fixed mathematical thinking form and embody it as a consciousness or concept. Therefore, its teaching can not be achieved overnight, but should be infiltrated for a long time; Only by repeated infiltration can it spiral up; After a long time, it will come naturally.

2, the principle of inspiration The so-called inspiration is used to guide others to understand. Teachers should be persuasive, pay attention to explaining the formation process of concepts to students, consciously use heuristic principles, and purposefully guide students to participate in the teaching process with a developmental perspective, proceeding from the reality of students, from simple to complex, and achieving the same goal. Inspire students to form scientific thinking methods, stimulate students' exploration spirit, and master the methods of self-absorption of knowledge. Use metaphors. Appropriate and vivid metaphors can make the content to be expounded easy to understand, persuasive and infectious. The key of heuristic education is to encourage students to ask questions and think about them. Heuristic education can stimulate and cultivate first-class talents. More than two thousand years ago, Confucius (55 1 ~ 479 BC), a great educator in China, said: "Don't be angry, don't be unhappy, don't get rich", which is the embodiment of heuristic teaching.

Teachers should fully encourage students to discover, ask, discuss and solve problems.

Teachers use profound language, create situations, encourage students to break their own thinking mode and ask questions from a unique angle. Encourage students to ask questions critically. Critical questioning is the concentrated expression of innovative thinking. It is through critical questioning that scientific invention and creation begin, which makes students dare to question the contents of textbooks and teachers' explanations, especially students' views. Because there is a lot of room for discussion, they dare to question even more. Being able to break away from convention, raise critical questions, and be brave in practice, verification and solution are essential qualities for students with innovative consciousness.

In the process of classroom teaching, teachers should make all kinds of summaries in each class, and also consciously let students summarize. Generalization ability is a reflection of comprehensive quality. Cultivating students' summing-up ability, that is, cultivating students' ability to concentrate on thinking, is complementary to cultivating students' thinking of seeking differences. Concentrated thinking enables students to master all kinds of knowledge accurately and flexibly, sum up and refine their own opinions, which is the basis of thinking differently, ensuring the breadth, novelty and scientificity of thinking differently. Cultivate the ability to summarize, and give students as many opportunities to summarize as possible in classroom teaching, such as summarizing a problem; Summarize the content of a lesson; Summarize the results of the discussion; Summarize the pros and cons of the debate. In each conclusion, select a number of students to speak and ask them to express their unique understanding and not agree with each other. After summing up, let the students ask the deeper questions they found in order to further extend and expand their thinking.

4 the cultivation of mathematical thinking ability

Multimedia teaching to cultivate mathematical thinking ability

As an auxiliary means of conventional teaching, multimedia has been paid more and more attention by primary school mathematics teachers, which is inseparable from its positive role. One of the characteristics of slide show and projection is that the image is concrete, vivid and intuitive, which can provide students with vivid, vivid and clear visual images, stimulate students' interest and curiosity, and mobilize students' enthusiasm for learning. For example, if the section "Understanding and using protractor" is explained according to book illustrations or model teaching AIDS, the visibility is too low, which will affect students' learning enthusiasm. If the transparent protractor is placed on the projector stage and explained by projection, it can meet the visual and intuitive needs of students and make them concentrate on their learning activities with interest.

Thinking ability is the core of intelligence. Thinking originates from observation, and observation provides information for thinking. Slides and projections can provide students with rich perceptual materials in a short time, and make students' senses and thinking active. For example, the derivation of parallelogram area formula, using vivid and colorful slides, supplemented by simple and clear expressions, is easy to attract students' attention, thus stimulating students' interest in parallelogram cutting and splicing methods, helping students understand parallelogram area formula, and clarifying the internal relationship between parallelogram and rectangle, laying a good foundation for learning the derivation of triangle and trapezoid area formulas in the future. Observation is the antenna of thinking and an important ability for students to know the world and increase their knowledge. Slide and projection not only provide students with things or phenomena that have never been involved, but also create conditions for students to directly perceive and observe these things or phenomena, making indirect knowledge and abstract concepts concrete and visual. It not only highlights the key points and essential characteristics of things, but also facilitates students' observation, forms appearances and enhances students' observation ability in practice. For example, when talking about "the surface area of a cylinder", students can clearly understand that the surface area of a cylinder is composed of "two identical upper and lower circular areas and a lateral area" by projecting a composite slide of a cylinder and a cylindrical surface. When the side is unfolded, it happens to be a rectangle. The length of this rectangle is the circumference of the upper (or lower) bottom surface, and the width is the height of the cylinder.

Consolidate exercises and cultivate students' critical thinking

Mathematics syllabus clearly points out: "Practice is an integral part of mathematics teaching and indispensable for mastering knowledge and skills." Through practice, we can know students' learning results in time and feed back classroom teaching information, master and understand students' thinking process, and adjust teaching in a targeted manner. Students often lack a correct understanding of concepts, formulas, rules and theorems. In practice, so there are some mistakes in practice. Students should be guided to read textbooks. Find out problems, correct mistakes, and guide students to use their critical and thinking abilities, instead of becoming slaves to books just for learning knowledge.

Through this kind of teaching, let students realize that textbooks also have shortcomings, don't be superstitious about textbooks, and have their own unique opinions. This is very effective in cultivating students' critical thinking.