How to develop mathematical thinking? How to cultivate mathematical thinking

Don't say those obscure words, mathematical thinking is logical thinking, as you said for a long time without thinking about the problem caused by the dullness of thinking is a matter of course, I used to be because of my good mathematics, I feel that I don't need to study anymore, the college entrance examination has a period of time to study other subjects and abandon mathematics, and the results of the monthly exam are not very satisfactory.

This tells you that you must usually do the questions, maybe sometimes you will feel that the questions are very boring, you don't need to do a lot of questions, as long as you do different types of questions, it will be almost the same, so that after a long time, the effect will be long;

Maybe one day you will find that after taking a new class, you have a higher correct rate of homework questions left by the teacher than other students, then you will have a sense of accomplishment, so that you can cultivate an interest in learning mathematics, and you will not feel bored when you do the problems again, but do not do a math problem for a day as if you have a shortcoming.

After cultivating your interest, through the consolidation and practice of question types, your logical thinking ability will naturally improve.

The most important thing is to have the spirit of facing difficulties, encountering problems is not terrible, as long as you overcome the psychological obstacles, those problems are sometimes a paper tiger, do not put the problem that does not do, even if you think about it for a long time or a day do not come up, but also think when you go to bed at night, really can't think of it and don't ask the teacher, to cultivate their independent thinking ability, I believe that if it is a difficult problem the teacher will not wait for you to ask, most of the students have not made the should.

If your mathematics is particularly poor, you have to make more body and turn more books, and when you don't understand it, you can turn the book to find the nature of the theorem, and the book will turn more and remember those theorems, and make flexible use of the purpose of knowledge, there are many questions on the side of the change of question, some people will not, there is a problem with the learning method, know how the nature of the theorem is obtained, the general theorems are deduced with the theorems that you have learned before, just like the theorems in front of the pyramid will be able to prove the theorems in the back, That way, even if you forget it in the exam room, you can prove it again.

I hope you can persevere, and don't back down when you encounter difficulties!

Comprehend it independently, no one can teach this.

Let's usually do more questions, which is largely the interest of the city's individuals.

I don't know, I saw it at the time, but I will have a lot of questions, I like it.

Here's how to develop mathematical thinking:1. Cultivate mathematical thinking ability, pay attention to understanding concepts and lay a good foundation. You find that students who have just entered the school are very proficient in counting, but they are completely unclear about the concept of number, so many elementary school teachers have to put a lot of effort into preparing for the understanding of numbers within 10 in the lesson in the teaching of overweight.

There are many conceptual meanings in the textbooks, and teachers should guide students to understand and grasp the meaning in simple terms. When teaching, students can count according to the actual situation, from the real thing (such as pencils, sticks, pictures), to the use of numbers or abacus beads instead of numbers, and finally the empty concept abstracted to concrete numbers. The formation of the concept of number is a gradual abstract process, and teachers should start with the life knowledge that students are familiar with, and gradually guide them to understand that number represents the number of things.

2. Cultivate mathematical thinking ability, pay attention to practice, and improve active thinking. It is necessary to cultivate mathematical thinking ability according to the characteristics of different age groups, especially the thinking of first-grade students is inseparable from action, and it is visual thinking. Through practice, it has been proved that the teacher will vividly display the abstract mathematical knowledge through the intuitive teaching of posing and drawing, so that students can form a perceptual to rational cognitive process, so that the knowledge obtained is firm, thus effectively promoting the activity of thinking.

Through hands-on operation, perceiving phenomena and experiencing practical operations, students can profoundly develop the understanding of abstract thinking, and finally form mathematical thinking ability. Therefore, we must start from the age characteristics and thinking characteristics of students, strengthen intuitive teaching, learn through various senses, and give students as many opportunities as possible to operate. Cultivating children's mathematical thinking ability is to cultivate students' ability to conduct preliminary analysis, synthesis, abstraction, judgment, reasoning, etc., and learn to think about problems, which requires teachers to pay attention to the connection between knowledge when teaching.

3. Cultivate mathematical thinking ability, strengthen language training, and promote divergent thinking. To cultivate mathematical thinking ability, it is necessary to think in an organized and evidence-based manner, and to describe the thinking process in a relatively complete manner. Through the description of language to test whether students want to think about mathematical thinking is organized and grounded, it is necessary to rely on language to test, so our teachers or parents should pay attention to training students to speak to promote thinking from the first grade, which is conducive to the development of students' thinking.

Through the form of one question and one answer, consciously train your child to speak. Only by posing, looking, and talking, can students' operational observation, thinking and language be organically combined to lay a solid foundation for cultivating mathematical thinking ability.

The first is to let students explain their problem-solving ideas to others.

Appropriately show weakness and inspire the child's sympathy, the mother does not understand, ask the child to help me explain the idea of the problem to others. Because speech is the best mode of thinking training. In the process of explanation, the child can once again sort out the idea of answering this question, parents should find out in time, which step of the idea is not very clear, the child does not know why, then guide the child to find the answer, improve the idea of solving the problem, so that the next time you encounter a similar problem, the speed of solving the problem will be improved.

The second is to train some graphical reasoning frequently. Geometric figures can be very intuitive and vivid for students to generate ideas, ideas, skills and other thinking, because this kind of topic requires children to have strong observation and logical reasoning ability. Therefore, training more graphical reasoning is very helpful for thinking skills.

In addition, we should encourage children to form habits, if the topic is difficult and complicated, and the thinking is very confusing, we can use the drawing method to help understand, so that the conditions given by the topic will be clearly displayed on the diagram, so that the idea is clearer.

The third is to improve children's ability to use mathematics in life. Life and mathematics are closely related, parents should encourage their children to use the mathematics knowledge learned in the classroom to solve the difficulties encountered in life, and use the mathematics in our lives to exercise their thinking skills. For example, shopping, do you have enough money to buy everything on your wish list?

How to buy and how to match the best deal? For example, when you are traveling, how to judge how long it will take to reach your destination by the number of kilometers on the street sign and the number on the speedometer?

The fourth is to correctly use some auxiliary teaching aids, such as some books or apps for mathematical thinking training, [Number Sense Planet] is a good helper. An innovative gamified mathematical thinking training app, following the Singapore CPA teaching method, integrates mathematical knowledge points into the game, so that various mathematical principles can be visualized in children's familiar life scenes or novel virtual worlds. Children see fun games, and parents see the growth of math ability.

Mathematical thinking refers to a way of thinking that people have when solving mathematical problems, and is one of the key thinking abilities to solve mathematical problems and practical problems. In order to develop mathematical thinking in junior high school students, we need to develop some specific strategies for cultivating mathematical thinking.

First of all, we should pay attention to cultivating students' logical thinking ability in mathematics teaching. Logical thinking ability is the foundation, and only when students have good logical thinking ability can they better cultivate mathematical thinking. In teaching, we can focus on cultivating students' ability to classify, induct, reason and judge, and then improve students' logical thinking level.

At the same time, we can also guide students to better understand and apply logical thinking skills by setting up meaningful classroom cases.

Secondly, we need to pay attention to the cultivation of students' innovative thinking ability. To cultivate innovative thinking, students need to be inspired in the classroom and continuously summarize and improve through practice. We can use an entertaining way in teaching, through games, competitions and other ways to stimulate students' interest, so that students can cultivate their innovation ability in a relaxed atmosphere.

In addition, in the process of cultivating junior high school students' mathematical thinking, we should pay attention to the improvement and improvement of teachers themselves, and the teaching methods and educational concepts are the key to the cultivation of students' mathematical thinking. Therefore, we can exchange teaching experience in teacher training and seminars, and continuously summarize and improve the professional level of teachers, so as to better assist students in achieving the goal of mathematical thinking training.

Through the comprehensive implementation of the above measures, we can better provide junior high school students with mathematical thinking ability, not only help them better enjoy the mathematics learning process, but also lay a solid foundation for their future study and work.

Extraction code: DSFF's strongest brain king Yang Yi personally taught the industry's exclusive mathematical thinking training camp. Yang Yi has excellent imagination and creativity, has a thirst for knowledge about what he is interested in, and has a serious attitude, he likes accurate results, and does not like to get improvised, vague results and hasty things.

In the first brain test, Yang Yi was very good at the part he was good at, and he also completed the spinning Sudoku project that he had never been exposed to after a little try, showing amazing brain power, and Yang Yi was very optimistic about many people.

Course Catalog: Finding Patterns.

Advanced chapter on discovering the law.

Associative memory encoding.

Cross-fill game.

Puzzle chart.

Nine-house Sudoku algorithm preliminary.

Mathematical ability is not the ability to calculate or memorize formulas, nor is it the ability to brush questions, mathematical ability includes derivation, logic, calculus, operation, induction, summary, analysis and generalization, classification and discussion and so on. One of the most critical is the ability to derive logic, which is manifested in the ability to derive the results we need step by step from known conditions and formulas, and this ability is ...... because a, so b......This process is very clear, and this way of thinking that knows what it is and why it is is is mathematical thinking. Now I will list three thoughts for you, so that everyone can continue to cultivate this kind of mathematical knowledge.

The first step, when writing homework, don't focus on whether the question is answered correctly or wrongly, it doesn't matter, it just lies in the logic behind the question and how to find the answer.

The second step, in class, should focus on finding how formulas and theorems are derived step by step, instead of memorizing them as a mechanical cold thing, we need to know what he got because of what, and let it become the theorems and formulas that we internalize.

The third step, in life, is to look at the surface of a thing and find its essence downwards, rather than just looking at its surface.

The cultivation of mathematical thinking ability should be combined with children's learning ability at different stages. Children generally go through these stages when learning mathematics:

Shallow stage (before the age of 3): Thinks that numbers are just one word.

Beginner stage (3-6 years old): The amount of items, e.g. "I ate 4 blueberries".

Intermediate stage (6-9 years old): the relationship of things, such as 4 o'clock always comes before 5 o'clock.

Advanced stage (9-12 years): These quantities can be compared not only with each other, but also with manipulation.

Deep stage (after the age of 12): Numbers are symbols of quantities that can represent anything, and anything can be quantified by numbers. Therefore, parents do not need to deliberately let their children learn to count and calculate, but only need to teach their children the "mathematics" in life by playing games, overcome the limitations of visual perception, and have a certain understanding of quantity.

In the preschool stage, the baby can be about three years old, and gradually establish the concept of mathematics naturally and smoothly in life and games. At this stage, it is recommended to combine the L1-L3 stage of the [Number Sense Academy] of the Number Sense Planet to enlighten children's mathematical thinking.

In the early transition stage, children are 5-6 years old in the early school mathematics learning stage, the real mathematical thinking training begins, at this time the child's brain through the pre-operation stage, has a certain understanding of the relationship between things, at this time, as long as the parents choose the right way of enlightenment, not only within 10 addition and subtraction or simple multiplication and division, children can also do it gradually. At this stage, it is recommended to combine the L3-L4 module of the [Number Sense Academy] of the Number Sense Planet for children's mathematical thinking training.

In the school-age stage, children have entered the primary school mathematics learning stage, in addition to the school's fixed curriculum to learn knowledge, the main purpose is to stimulate children's interest and improve children's ability to actively explore and learn. It is suggested that you can combine the [Synchronous Practice] module of the Number Sense Planet with the primary school textbook for review, and use the [Number Sense Academy] L5-L6 module for preview and mathematics interest stimulation.