This article is reproduced from the official account of WeChat: Tongxing College (ID:tong ng plan).
Wen, Black, Pu, Bian, Travis
This paper talks about how to stimulate children's interest in mathematics. Even parents who don't like mathematics can actually cultivate children who love mathematics.
Psychologists have found that whether a person likes, hates or is afraid of mathematics is mostly formed in early childhood.
Italian child educator Montessori also pointed out that 2-6 years old is the most important "mathematical sensitive period" in children's life.
During this time, children will have great interest and thirst for knowledge in quantitative relations, arrangement order and graphic space. The most intuitive thing is that when children see something on the table, they will count: "Eat three in the morning and four at night."
This marks the arrival of children's mathematical sensitive period.
Montessori thought:
1 year 10 months is the key period for children to master the concept of elementary numbers;
Two-and-a-half-year-old is a critical period for the development of children's counting ability;
Three and a half years old is the beginning of simple operation;
5-6 years old is a critical period for children to master mathematical concepts, perform abstract operations and form comprehensive mathematical abilities.
At this stage, if parents can guide them in place, children will be more likely to like abstract thinking of mathematics, thus cultivating logical reasoning ability. "
Everyone knows the truth, but practice is the only criterion to test the truth. How to seize the precious sensitive period of mathematics? What methods are used to cultivate children's mathematical potential?
Educational methods in different periods
18-22 months, you can master the primary concept of quantity. It is suggested to teach your baby to sing "digital songs" and sing the numbers out loud. Most children can learn verbal arithmetic, and gifted children can learn numbers above 10.
2-3 years old, with the concept of primary counting, you can count by pointing to items. You can distinguish the obvious features of objects, such as shape, color, name and the concept of classification. Through the demonstration of adults, you can put the same type of things together. Some difficult ones, such as deer and horses, fathers and orangutans, may not be clear.
4 years old, with clear counting ability, can count things and tell the total amount, and has obvious classification ability. Adults can tell children to classify by color, shape or nature. There are obvious concepts of weights and measures, such as being able to distinguish height, thinness, length and weight. For example, you will say, mom, you have gained weight recently.
5 years old, able to perform simple mathematical operations; Can look at the clock and tell the time; Know money, value and use. You can calculate the money for buying things with the help of adults, or you can make simple measurements.
For example, use a cup to measure the subtle difference between a medium cup and a large cup, and use a rope to measure the farthest distance in the world. At the birthday party, children can share the cake with everyone and learn the concept of score.
How to distinguish arithmetic from mathematics?
After discovering that children have the ability to calculate, many parents are addicted to letting their children calculate. I suggest you pull back from the brink and distinguish between two concepts, namely arithmetic and mathematics.
"Children count slowly, will it limit their math development?" This is the most frequently asked question by parents.
Many friends may be misled into thinking that mathematical ability is the ability to calculate and solve application problems quickly. In fact, there is still a big gap between "arithmetic" and "mathematics", which is equivalent to "Dong Shi" and "Xi Shi".
Directly speaking, arithmetic is a subject to hone "correct and fast" answers, while mathematics is a subject to cultivate your ability to solve unknown problems.
Professor Qiu Chengtong, a tenured professor at Harvard University and a mathematician of Chinese descent, was stumped by a complicated calculation question put forward by the audience when he was a guest on the CCTV program Let's Talk. Professor Qiu bluntly said that he was really not good at calculation.
In fact, most mathematicians spend their whole lives guessing and proving. Come up with solutions to various problems, which is the real mathematical ability. Mathematics is not a competition with calculators, but with vendors.
So I don't think parents need to worry about their children's arithmetic speed. It is far more important to train their children's way of thinking than to acquire knowledge.
For children over 5 years old, the most important thing is to let them see the fun of mathematics. The so-called fun of mathematics is actually the fun of games. You can solve puzzles and complete tasks with your own brain.
Game scene is the most suitable way to cultivate children's interest in mathematics, because games can comprehensively exercise children's awareness of rules, execution ability and strategies.
I use a picture on the Internet to illustrate that playing simple guessing games with children is not boring, but also really exercises logical thinking.
How to find an even number between 15 and 20 that is not equal to 18? From the picture, we can clearly see the child's thinking track. How does the brain make a judgment after receiving every message?
Mathematics provides a kind of logical thinking, which is called algorithm in computer science.
Thinking can be trained slowly from simple to complex. However, if children have been learning to calculate since childhood, it will lead to poor ability to deal with problems, easy to have an aversion to mathematics, and affect the development of logical thinking.
So, how can we teach today's children mathematics well without being obsessed with teaching calculation?
I think we can talk about the probability with our children. For example, the children of mermaids and centaurs have a quarter chance of becoming human, and a quarter of them are seahorses.
You can also try to bring your children together to think about interesting math games, taking the famous prisoner's dilemma in game theory as an example:
The story tells that the little monkey and the little bear were caught stealing fruit by the police, and were locked in different rooms for interrogation, so they could not communicate with each other.
The police told everyone: if both people don't admit it, they will be locked up for one day; If both of them confess, they are grounded for ten days each; If one of them confesses and the other denies it, he will be released and denied imprisonment for one month.
Therefore, both the little monkey and the little bear are faced with two choices: either confession or denial.
You can ask children what they think of this problem. What does he think will be the final result?
At this time, children may feel at a loss because it is difficult to guess what they are doing at the same time.
Fortunately, we found that this is a symmetrical problem, that is, the situation faced by the little monkey and the little bear is exactly the same. The idea at this time is to bring yourself into it. Please think about it: What would I do if I were a bear?
If I were a bear, this bear thinks there are only two possible situations:
In the first case, if the little monkey doesn't admit it, then I will put it home frankly, and if I don't admit it, I will be confined for one day. Confession is better than denial.
In the second case, the little monkey confesses, so I will be locked up for ten days if I confess, and for one month if I deny it. Confession is better than denial.
So, although I don't know what my other half will choose, my best choice is always honesty. The same is true of little monkeys.
As a result, both suspects chose to confess and were locked up for ten days. Isn't it interesting?
Compared with the four operations, thinking in these games is the real exercise of mathematical ability. No matter numbers, graphs, functions, equations, vectors, sequences, etc. They are just tools to cultivate logical thinking.
There are also good and bad ways of thinking. Good methods can make people progress faster, and bad methods can imprison people. Mysterious and mysterious, the gate of Wan Qi.
Where does the fun of thinking about games come from?
There are many excellent educational children's books on the market that contain these math games. I recommend several books, such as Montessori Children's Mathematical Ability Training in Sensitive Period, Thinking Training for 365 Days, Gifted Preparation, and American Classic Mathematics Enlightenment Picture Book.
You can play thinking games with your children. Competition comes first, friendship comes second.
If the child is over six years old, will he lose the chance to become true love with mathematics?
That was not the case. Children in the lower grades of primary school can still have a strong interest in mathematics under the correct guidance of their parents and teachers.
Many math teachers have more say in how to improve their math scores. I just want to share my personal experience here. Personally, I think that besides listening to the teacher in class, a lot of practice is essential.
We all have the experience of going to a strange place now. If you have tried to find it again, whether you have reached the finish line or not, whether you have detoured many times. At this time, as long as people give a hint, in fact, just turn right in the small park, and it will react immediately.
However, if you don't walk in person and only know the theoretical way, "turn left at the second crossing for 200 meters, then turn right for 400 meters and then turn left", you may not be able to reflect that you want to turn right next time you walk to the small park.
I learned in math class that I don't know where to start when I encounter problems in the exam, just because I haven't walked through the small park myself.
Mathematics needs repeated practice and application. Only by solving the problem in a down-to-earth way can two birds in the forest become a bird in their hands.
Today, I have talked about so many opportunities and methods for children to learn mathematics, but there is still a big question unanswered. Namely: what is the use of mathematics (after the college entrance examination)?
Wang Xiaobo wrote this passage in the book The Joy of Thinking:
"When I was in college, my math professor once said in class: You may not need my math all your life, but I still want to teach, because this knowledge is good, you should know. I admire this teacher's lofty mind all my life. I would also like to say that such a mind is rare among China humanistic intellectuals. "
Actually, it's right What is the sum of squares of sin and cos? There is not much impact on life. However, although the knowledge points have been eroded by time, the thinking logic and problem-solving ability left by mathematics have benefited people from all walks of life.
Mathematics, like Delighting in Rain on a Spring Night, sneaked into the night with the wind and moistened things silently. Thinking is a more intangible force than foreign languages and technology. But many people don't believe in the function of mathematics because they can't see or touch it.
When I was in college, I decided to be a math teacher with both ability and political integrity.
I heard that some teachers are loved by students because of their skills of drawing circles by hand. In order to be a beloved math teacher, I try to draw circles in the dormitory every day.
Unfortunately, the painting was not round in the end, and I didn't become a math teacher, leaving only a warm old time.