How to train students to discover math problems from life

1. You can use multiplication to calculate how much it costs to buy a few catties of vegetables.

2. The straight line between two points is the shortest, so you know how to walk closely.

3. Judge the time according to the length of the shadow.

4. Identify the direction according to the Big Dipper.

5. Sweating in the water tank means that it is going to rain.

Mathematics and everyday life are two intertwined threads, a statement made by the 45-year-old Indian mathematician Gautam Mukherjee at the recent International Congress of Mathematicians. Around 3,500 experts attended the congress to discuss the current state and prospects of mathematics and explain how mathematics affects people's daily lives.

From thermostats to Internet search engines. If the thermostatic index of the heater is determined to be 20 degrees Celsius, the machine bend should first heat up the room temperature to more than 20 degrees Celsius, then stop working until the room temperature drops below 20 degrees Celsius, and then start heating again. Enrique Suasua, a professor at the Autonomous University of Madrid, noted

When to open and close the heating and when to stop heating is not arbitrary, but needs to be accurately calculated using mathematical equations. "These equations are used to maintain the speed of the disc or to determine when to add water to the underground cistern.

"People are used to thinking that things work alone, but in fact there are other factors behind them that make them work," Suyasuya said. "For example, a search engine on the Internet to search for a word does not result by chance.

"In the eyes of mathematicians, a network is like an infinite number of glass balls on a plane, and you have to find the balls you need and sort them, and this process is done by calculating the equations of all the variables," he said. ”

Bicycle helmets and energy-efficient cars. In recent years, the front half of a bicycle helmet has become more rounded, and the back half is more like a bird's beak. This change is not based on aesthetic considerations, but according to aerodynamic principles designed to allow athletes to achieve better results.

Engineers use different equations to simulate the movement of solids in the air until the best design data is obtained. Airplanes, automobiles, and ships all need to use equations in their designs to be faster, more durable, and more fuel-efficient.

Decision-making and management levels. Angel Sánchez, a professor at the Carlos III University of Madrid, said that in companies, mathematics can be used to understand the interpersonal relationships of employees, such as which employees have the best interpersonal relationships and who has the most comprehensive information. Mathematicians come to a conclusion by performing calculations on an employee's email records through mathematical theorems.

The application of mathematics in sociology is also very widespread, and even more so in statistics. It can even be used to avert epidemics or mitigate their impact. When we can't immunize the entire population, math can help us determine who must be vaccinated to reduce the risk.

In the arts, mathematics is still everywhere. **, painting, sculpture, ......All disciplines of art are aided by mathematics in one way or another. Japanese sculptor Keizo Shio likes to use geometry and topology to create his own works, using mathematical calculations to divide the granite used in sculptures.

Chao Huisan said: "Mathematics is the language of the universe. ”

The Mathematics Curriculum Standards emphasize that mathematics teaching should reflect life.

It is necessary to start from the students' existing life experience and knowledge, and let the students experience the process of explaining and applying the actual type. As the saying goes, life is inseparable from mathematics, and mathematics is inseparable from life. Therefore, in mathematics teaching, teachers should actively create an environment for students to experience, so that students can feel the close connection between mathematics and real life, integrate the "mathematical world" into the "living world", and guide students to use the mathematical knowledge and methods they have learned to solve practical problems in life.

I was always thinking about how to answer this question with math.

Cultivating students' ability to ask questions is an important part of the excellent mathematics curriculum, which has attracted great attention from teachers. So, how do you develop students' ability to ask questions?

We know that teachers should control the speaking time in the process of instruction, generally no more than 15 minutes, so that students can be given 30 minutes of activity time, during this time, the ability to cultivate students' ability to ask questions will greatly improve the efficiency of the classroom.

In order to cultivate students' ability to ask questions, it is necessary to strengthen students' awareness of problems. First, students are required to ask their classmates and teachers about what they do not understand in class, what they will not do in homework, and what they cannot understand in books. Second, students are required to ask questions in each lesson according to the teacher's instructions.

One or two questions; Third, students are encouraged to observe problems with a critical eye in the process of learning, dare to question textbooks and authorities, and be able to put forward different opinions.

Teachers should take a positive, enthusiastic and rigorous attitude towards students' questions, respect and seriously think about students' questions, and when students' questions are too simple and ridiculous, they can give guidance and explanations instead of ridicule and sarcasm; When the teacher cannot answer the student's question for a while, it is necessary to be flexible and not perfunctory; When students ask good questions, they should be given full affirmation and praise, so that they can experience the joy of success and enhance their awareness and interest in asking questions. In this way, the students' enthusiasm for asking questions is greatly improved, and the questions they ask are more powerful.

Albert Einstein once said, "Asking a problem is often more important than solving a problem, because solving a problem may be a mere mathematical or experimental skill, while asking new questions, new possibilities, looking at old problems from a new perspective requires creative imagination and marks a real advance in science." ”

Also in daily teaching, it is often more important for students to ask a good question than to solve a problem! Because it not only marks that students are actively learning, but also that students' knowledge and abilities are developing in harmony. There are two main reasons for this;

First. The process by which students ask questions about what they have learned is the process of understanding the knowledge of the book deeply. On the basis of their own knowledge and comprehension level, students put forward personalized doubts, which is helpful to truly understand the new knowledge and help to truly construct the new knowledge into the architecture of their old knowledge.

Only in this way can students avoid reading books and reading books, master truly useful knowledge, and truly understand the connotation and extension of knowledge.

Didn't Confucius say: "If you learn without thinking, you will be reckless, and if you think without learning, you will die"? This sentence is a method of reading and learning advocated by Confucius.

It means that if you blindly read a book without thinking, you will not be able to make reasonable and effective use of the knowledge of the book because you cannot deeply understand the meaning of the book, and eventually fall into a confused situation. If students only read books and don't think, they won't ask many valuable questions. Based on the questions asked by the students, the teacher can understand the level of thinking and understanding of the students, so as to achieve the individualized teaching.

Second. The process by which students question their knowledge is the process of developing their various abilities. "Asking a problem is half the way a problem is solved" is not false at all. A good question often has to go through a more complex thinking process.

A child's ability to walk can only be acquired through walking training when he constantly falls down and gets up again; A person's running ability can only be exercised in the process of continuous running; Jumping ability can only be improved through the practice of constantly jumping high ......

Similarly, the improvement of students' thinking skills such as independent thinking, divergent thinking, imagination, and logical reasoning can only rely on the corresponding thinking practice activities that they regularly carry out.

You can pique their interest by making games and get them to ask questions, trying not to be too strict with them.

This can be used to stimulate students' interest through some fun math problems.

Use the wrong questions to test the students, and use some math stories to enlighten the students!!