Story 1: interviewer's exam questions

A company wants to recruit some excellent employees. The human resources department selected several resumes from many college students and entered the second round of interview. A question raised by the interviewer stumped many candidates. The question is this: How many golf balls can China consume a year? Some people say they don't know, some people turn a blind eye to a very high number, and the examiner is not satisfied. Finally, the interviewer is waiting for a different answer. He said he didn't know the answer either, but he could find it. The internet is very developed, and Du Niang can't answer this question. I search how many golf courses there are in China, and then sample how many customers play in a golf course, and then sample how many golf balls a customer can consume in a year. Then we can know how many golf balls China can consume a year. The child was admitted.

The moral of the story is that when you don't know the answer to a question, how can you know the answer? The ability to solve problems is more useful than knowing how many ready-made answers.

The enlightenment to education is not to let students remember how many answers and master how many skills, but to let students learn to think.

What kind of value orientation should mathematics education adhere to? The key point is to develop thinking.

Double Basis-Three-dimensional Goal-Core Literacy

If teachers let students master more knowledge and skills in class, then they are good teachers. Later, look at knowledge, skills and study habits. We not only learned, but also learned. It depends on what kind of emotional experience students get, whether they like learning more and more or whether they are more and more tired of learning. In recent years, we have entered the era of core literacy. What are the differences and connections between core literacy and three-dimensional goals? This is worthy of teachers' thinking. Mainly from taking knowledge as the main body to promoting people's all-round development.

Mathematics education can't just let students remember some formula concepts and master problem-solving skills; On the contrary, we should teach for understanding, for promoting development and for the formation and development of core literacy.

Example: distance, time, speed, you can tell the students the formula first, and then do a lot of exercises, which is also a math class.

Teacher Niu has three highlights in teaching the course "Distance, Time and Speed".

1, pay attention to the cultivation of logical reasoning literacy.

The comparison of speed and speed in a class took nearly 30 minutes. How to compare? Pleasant Goat and Pleasant Goat spend the same time, but the distance is different. Pleasant Goat's home is far from school, so Pleasant Goat is faster than Pleasant Goat. At the same time, whoever is farther away will walk faster. The home of Meiyangyang and Lazy Sheep is as far from school, but it takes 6 minutes for Meiyangyang and 4 minutes for Lazy Sheep. At the same time, whoever is far away will walk fast. In this way, it is found that Meiyangyang is the slowest. Then who is the fastest!

The distance and time between lazy sheep and pleasant sheep are different. Speed naturally comes from how many meters you walk per minute, and you need speed at this time. This requires a process of logical reasoning. He is faster than him, he is faster than him, so he is the slowest; Fastest than anyone, how many meters per minute, that is, speed, will be solved! Guide students to review and reflect on how we compare who is the fastest. Taking knowledge and skills as the carrier and cultivating students' logical thinking literacy as the main goal.

2. Really understand the meaning of "speed"

On the one hand, the abstract concept of "speed" is closely related to the familiar life experience of "specific speed and specific speed", which raises students' superficial and vague understanding of speed to the height of mathematics; On the other hand, "cognitive conflict" is carefully set up to let students feel the relationship between distance, time and speed from the calculation of speed.

3. Experience the "re-creation" process of speed units.

Speed unit is also a brand-new concept. Setting the conflict, Shenzhou I is also 8 kilometers, and Uncle Zhang is also 8 kilometers. How to distinguish two 8 kilometers? Add time, followed by a unit, and you can distinguish two 8 kilometers.

Case 2: The Mystery of Triangle

How to teach for the development of thinking and core literacy?

In the mathematics textbook of Beijing Normal University, there is a unit to measure angles and compare them. How many angles of different degrees can be drawn with a triangular ruler? A set of triangles has a 30-degree, a 60-degree, two 90-degrees and two 45-degrees, which were treated as exercises in previous teaching to let students know which angles are in a set of triangles. Under the background of core literacy orientation, how to develop students' thinking ability and how to make core literacy fall! Let this topic be a lesson.

First of all, review the angles in a set of triangles, what triangles are generally used for, and how to draw 30 angles. The children draw 30 angles in a set of triangles. This is knowledge preparation.

An open question, how many angles can be drawn with a set of triangles? Mark the degree next to each angle, and mark which two angles it consists of. Arrange all the corners you draw in order from small to large. What did you find?

It took the students ten minutes to finish the task. Most students will draw 10 angle, 30 45 60 75 90105120135150180. Some students asked if it could be reduced. The teacher asked the students to find a pattern, and the students found that the difference between two adjacent corners was 15. Careful observation shows that 165 is missing. The teacher asked the students to try to draw an angle of 165. In order to make the law more complete, the students went to textual research. A student said that a straight angle can be subtracted from 15. How to draw the angle of 15? Draw an angle 15 and extend an edge to form a right angle, and you get 165.

Which corner is the hardest to find and how to find it? Let the students review the process of looking for just now, let the students precipitate their experience and become literate. The student said that he guessed that he had missed a corner from the corner he found. This conjecture is called reasoning. Reasoning comes out before verification. This is a very important way of thinking.

The teacher listed the discovery process of Neptune. 1846 On September 28th, Dr. Galle of Berlin Observatory in Germany received a letter. This letter was written to him by a young French mathematician, Le Ye Wei, asking him to aim his telescope at a specific sky at night. Le Ye Wei predicted that a new planet would be found there-the eighth planet in the solar system. Dr. Galle immediately picked up the accurate star map and started searching that night. After only half an hour's observation, he found a faint star in the sky, indicated by Le Ye Wei. After 24 hours of observation, it is confirmed that this star is constantly moving and is indeed an undiscovered planet. Revelle's prediction came true-the new planet was later named Neptune.

It is irresponsible for a teacher to ignore the exam when teaching, but it is also sad to just stare at the exam. Therefore, teachers should really teach for the development of students' thinking and core literacy.

Story 2: Bees and Butterflies

When a little girl and her mother were playing in the park, they found that bees buzzed while flying, while butterflies flew silently. If the mother has scientific literacy, there may be two answers, one is to tell the child the answer directly, and the other is to take the child to study together. Mother took out a piece of paper and showed it to the child, so that the child could discover the mystery. This is experiential learning. In order to implement the development of mathematics core literacy, experiential learning is needed. After teaching and learning, the knowledge is not made clear by the teacher, but by the students. Learning ≠ learning ≠ learning ≠ learning, with high efficiency ≠ large capacity and great difficulty.

The formation and development of students' core literacy is essentially not "taught" by teachers, but "experienced" by students; Not by memory and imitation, but by students' participation in activities, in which they form understanding and sentiment. It is necessary to provide students with time and space for enlightenment, so that students can experience thinking and discovery in the process of knowledge creation, experience twists and turns and wisdom in the process of knowledge formation, and gradually form and develop core literacy through exploration and experience.

Case: the meaning of decimals

This is a very abstract class. The basic goal of this course is to make students understand that one decimal represents a few tenths, two decimals represent a few percent and three decimals represent a few thousandths. How to make students understand these are all difficult points.

The teacher showed a square. If the square is 1, how can it be expressed by 0. 1? Students divide the square into ten parts, each part is 0. 1, and then guide the students to recall what they have learned before. Students naturally think of scores, one tenth of which is 0. 1. Two copies are 0.2, which is two tenths. To sum up in one sentence, a fraction of a point represents a few tenths, and a decimal place represents a few tenths. Which decimal place is the most important, 0. 1 is the most important, and 0. 1 is a counting unit of decimal places. 101 is one. Ten into one.

Ask the students to guess the area of the shadow. Most students guessed 0. 1, with 0. 1 on the left, and the second place after the decimal point was uncertain. How to determine the second place after the decimal point and guide students to subdivide the shaded part? With the help of intuitive graphics, the understanding is more thorough.

Engineering problems: Team A needs 10 days and Team B needs 15 days to build a 420-meter-long road. If two teams cooperate, how many days will it take to complete?

Examples of the first volume of the sixth grade of People's Education Press. This question is also very abstract.

Let the children do it themselves, calculate the work efficiency, and divide the total amount by the sum of the work efficiency to solve it. Then change the known conditions and build a 2 10 meter road. It takes 65,438+00 days for Team A to maintain independently, and 65,438+05 days for Team B to maintain independently. For example, how many days will it take for two teams to cooperate?

Let the students guess first. The students said that it would be finished in three days. The teacher asked why. The total amount of work has been reduced by half, and other conditions remain unchanged, the working hours must be reduced by half. Make a guess first, then verify it. After the calculation, the result is still 6 days, so there is a cognitive conflict. Obviously, the total workload has been reduced by half.

Discussing the existing problems, the students found that no matter how far it is, it can be completed in 6 days. The journey is short and the repair is slow, and it will be completed in 6 days. As long as the following conditions remain unchanged, the number of completion days remains unchanged. Ask the students to verify whether the result is correct. Then the teacher guided and removed the condition of the total length of the road, okay?

Then show a real example: it takes 15 days for Team A and 15 days for Team B to repair a section of road. For example, how many days will it take for two teams to cooperate?

After discussion, the students think that the total length of the road should be taken as the unit, and then the work efficiency of both parties should be calculated, and then the number of days to be completed should be calculated.

Exercise 1. A batch of goods were transported by cart alone, 10 times, and transported by trolley alone, 15 times. If the cart and the car are combined, how many days can it be delivered?

Health:1÷ (1:10+1÷15) = 6 (times)

Exercise 2. The distance between a and b is 300 kilometers. The express train can complete the journey in 3 hours, and the local train can complete the journey in 6 hours. The express train and the local train leave from A and B at the same time. How many hours can they meet?

Health: 300 ÷ (300 ÷ 3+300: 6) = 2 (hours)

Health:1÷ (1/3+1/6) = 2 (hours)

Teacher: The problems of road construction, freight transportation and encounter here can all be attributed to the same kind of problems and can all be solved according to the methods of engineering problems.

This is a mathematical modeling process.

Teachers should not only pay attention to knowledge and skills, but also take knowledge and skills as the carrier to promote the development of students' mathematical thinking ability and let the core literacy really land. This is the direction of our teaching. Students will not only learn, but also learn and enjoy learning. The more they learn, the more they love math!

Classroom is a place where teachers and students meet, their hearts attract and their emotions connect. Our children should be happy and happy in class.