Arithmetic and mathematics are two different things

Every time I go to dinner with a few friends, someone will always ask me: “Yong Ye, how much is everyone sharing?” At this moment I will feel guilty. My friends asked me this way because they thought I was a math teacher and my mental arithmetic must be very good. Actually, I’m not good at mental arithmetic at all. To be more precise, I am not good at arithmetic originally.

Although it sounds like an excuse, mathematical ability is not equal to computing ability. As long as you have the voice recognition function of your smartphone, you can know the result of the calculation with just one mouth.

Does “the ability to quickly solve practical problems” represent mathematical ability? In fact, this is not enough to show that a person has mathematical ability. As long as you have more contact with various problem types, and understand how to classify the problems into categories, and then apply the established solutions, you can quickly solve the application problems.

Mathematics is not a science of speed. For example, the famous Fermat’s theorem was finally proved after about 350 years. Moreover, classifying and analyzing known question types is one of the tasks that computers are good at. The ability that we humans need is to propose solutions to unknown problems that have not yet established an algorithm, and to find the direction of the solution even if they cannot. This is true mathematical ability.

After standing on the front line of teaching, I found that children are always asked for speed when they answer questions, so they are less and less used to thinking. This is a very serious matter. I think thoughtfulness is more encouraged than quick response.

My friend T Jun and I met at the University of Tokyo Opera Troupe. He was really “considered” when performing community work. For example, when I want to send postcards to various universities to inform them of the concert, I directly propose: “Anyway, as long as it is possible, can all be sent?” But he will think carefully about each school. Is the postage of postcards really effective? “Although this university has an opera society, it actually plays musicals …”

Therefore, what I thought could be solved in 5 minutes took almost an hour to complete, but the final result was of course quite good results. Decisive conclusions and mathematical abilities are exactly opposite. Taking time to think patiently when necessary is an important way to cultivate mathematical logical thinking.

A well-known Japanese mathematics teacher, Mr. Yasuda Yasushi, mentioned in “The Method of One More Point in Mathematics at the University of Tokyo: Science”: “The capacity of the mind to put in mathematical facts is one of the important factors that determine whether mathematics is good or not. Excellent people have ‘drawers’ in their brains, which can be arranged neatly, even if the situation is slightly complicated, and it will not cause confusion. People who are not good at mathematics usually have a small capacity, so they are used to blindly turning things in front of them into formulas, ignoring them. Overall, only the problem at hand. ”

Generally speaking, people who are good at mathematics have an excellent ability called “logical courage”. Even standing at the entrance where the end point is not visible, there is courage to move in the direction that you think is right. Conversely, as long as people who are not good at mathematics stand at the entrance of the invisible end, they can easily think timidly that “I’m afraid I can’t do it” and choose to give up.

What we really need is not the ability to find the answer one step ahead of others, but the ability to find the correct answer logically step by step no matter how difficult a problem is. I think that the continuity of dripping through stones is the real mathematical ability. Arithmetic is a subject that trains you on how to “quickly and correctly answer known problems.” Mathematics is a subject that “cultivates your ability to answer unknown problems.”