Squat down and talk to the students. Squat as high as a student.

Teachers in China all appreciate Mr. Yu Yongzheng, and students also like his classes. Why? Professor Yang Zaisui made a wonderful summary in the preface written for Yu Yongzheng's Teaching the Sea: "Teacher Yu Yongzheng knows children and understands them. He often puts himself in the shoes: if I were a child of six or seven years old. " The reason is clear, that is, Teacher Yu Yongzheng squatted down to talk to the students! Similarly, math teachers can only squat down and be as tall as students, just as thinking scientist Zhang Guangjian said, "Only when there is a similar harmonious vibration between teachers and students' hearts can students and their studies produce * * * sounds".

Squatting down as high as a student is not only a teaching idea, but also a little teaching wisdom.

First, look at mathematics with the same thinking height as students.

In mathematics teaching, in order to find the contact point and vibration point between students and mathematics knowledge and grasp the opportunity of education, we should first pay attention to treating mathematics with students' thinking. If we always treat children from the perspective of an adult, then all the words and deeds of children are childish, and those novel and eccentric thinking and behaviors may be denied, which will stifle children's nature and creativity. Guzman, former chairman of the International Commission on Mathematics Education, once pointed out: "In the early years of primary school, all the factors of traditional education inhibited children's innate creativity. After nearly four years of efforts to bring his thinking into the adult track, by the age of ten, the spontaneity of thinking, flashing ideas and interest in unknown things have disappeared in many children ... This is very sad. "

An article was published in China Education News. The author tells a real case: when judging whether the areas of two parallelograms with the same base and height are equal, most students either calculate, cut or shift, and deduce that they are equal. Only chenchen's classmates were surprised: "I don't need anything. I can see at a glance that the two figures in the picture are equal in area. " Because of the shadow of the picture on the lower image, it is equal. "The teacher also smiled kindly in the laughter of the students. She quickly woke up from Chen Chen's embarrassment and tactfully added, "The teacher appreciates Chen Chen's ability to put forward such a unique reason. Out of curiosity, how did Chen Chen come up with it? "Chen Chen told the teacher that a person's shadow is as long as a person's height. Judging from his expression, he is somewhat proud. If the teacher realizes, "Yes, sometimes it's the same length." Other students echoed, saying that sometimes it was long and sometimes it was short. The teacher gestured to everyone with his eyes, and then asked Chen Chen, "Do you think it is possible to directly judge that the figure and its shadow area are equal? "Chen Chen shook his head without embarrassment or depression." Students in Chen Chen can come up with a reason that no one has ever thought of, and this idea is half right. We should be proud of having such students! " The teacher lost no time in encouraging Chen Chen. The students applauded and Chen Chen sat down gracefully.

In this case, the teacher once again clearly realized that the students' thinking is in the primary stage, and the idea of mathematics is imaginative and one-sided. This is how Chen Chen catches the shadow, and sometimes he thinks as long as he really does. Mathematics Curriculum Standard for Compulsory Education puts forward "respecting students' unique feelings". Teachers should let students finish their opinions, listen to their real voices and look at the problem from their standpoint.

Second, express mathematics in the same language as students.

Touched the * * * vibration point, but also be good at childlike innocence. Language is the shell and tool of thinking. Children, especially children in lower grades, not only have different thinking forms from adults, but also are easily overlooked. The language is not rich and accurate, and the logic and accuracy of expression are still lacking. Suhomlinski said: "A teacher who doesn't know educational science is like a cardiologist who doesn't know the structure of the heart and an ophthalmologist who doesn't know the most subtle neural connection mechanism between the eyes and the cerebral hemisphere cortex." Only by mastering students' language can a math teacher easily lead students to the kingdom of mathematics.

When I teach Positioning, I take it for granted that preparing lessons is very simple: students learn the four directions of east, south, west and north, as long as they learn the four directions of southeast, southwest, northeast and northwest, and then identify them. According to the presentation order of the textbooks, when the reference object becomes the Children's Palace, the students' error rate is very high. After careful analysis, I think that although we adults think it is easy to decompose, students' thinking language still stays in a "relative position", that is, what is the center and what is the observation point. For the orientation change caused by the change of reference object, teachers don't use children's language to express it, and students are stuck in their own language, resulting in slow thinking adjustment and inevitable mistakes.

For such language barriers, it is necessary for teachers to give students a crutch and a step to help them by going up a flight of stairs. After the redesign, with the help of the directional board, let the students talk about which side of the school is Ren Minqiao, which side of the school is Ren Minqiao, which side of the school is Ren Minqiao. When the students are prompted to determine the position, the directional board will follow people to that place. When students are asked to talk about methods, they say that "the center of the direction board is ourselves", which is the way students think about the position of reference objects, indicating that their thinking has reached a new height with the help of language. In other words, they established the identity of reference, orienteering board and self. Sure enough, teachers and students then use the directional board to verify the harmony between the plan and the spatial direction. By the end of class, many students can get rid of the tangible crutch of the orienteering board and establish an invisible reference in their hearts. "I stand at the observation point and I am the center of the orienteering board."

I made a small survey and found that students' mastery and understanding of language and characters directly affect their math scores. To express mathematics in students' language, on the one hand, we should build a bridge between students' life experience and mathematical thinking with the help of situations and operations, on the other hand, we should help students break down their mathematical thinking into several steps that can be expressed in their own language, so that they can reach a new height according to the steps.

Third, show the same high interest in mathematics as students.

Judging from students' age and psychological characteristics, in order to obtain real subjective learning, their learning activities will always start with questions and interests. Students are active and curious, and paying attention to their own lives and interesting issues will always be their motivation for active learning. Dr. Hill, a famous psychologist, said that there are only small differences between people, but this difference often leads to huge differences. Small differences between people mean whether they are interested in things. Only by showing mathematics in a way that students are interested in can students be interested in the learning content itself.

In the teaching of "cognitive circle", I created a shooting scene from the perspective of students' interest. First, let the students talk about whether it is fair to throw more balls into the middle basket in a rectangle or a square, and guide the students to say that it should be round. Then ask the students to consider where the basket should be put. Students are keenly aware that it should be placed in the center of a circle. Then let the students say where everyone should stand. The students think that we should lose money in the circle, not in the circle, outside the circle, so that everyone can throw the ball into the basket at exactly the same distance and the game is fair. Finally, let the students simulate on paper to prove their judgment and show their new findings: each circle has countless radii, and each radius is equal and within the same circle.

The situation of pitching competition comes from students' life and is close to their experiences, which is rich in many exploratory contents related to the understanding of the circle. Showing mathematics with students' interests and language has triggered students' cognitive conflicts. As explorers, students naturally take an active part, think actively and construct mathematical knowledge from beginning to end.

Fourth, look at mathematics with the same high desire as students.

The classroom should be a torch to ignite students' wisdom, and it is challenging to give the torch and fire. Let students enter mathematics with questions and curiosity, and then look at mathematics with new question marks, so as to truly enter the kingdom of mathematics.

For the lesson of "Derivation of Circular Area", students often think that the circular area is only related to the radius, which easily leads to the illusion that the circular area can only be calculated by the radius, and they are helpless to solve the problem of areas with circles, semicircles and sectors in some combination drawings. When I was teaching "circle area", I started with students' curiosity and asked them to guess what the circle area was related to. Without formulas and concepts, students relate the measurement of area units to the square area tangent to the circle, which is d2 or (2r)2. Then ask the students to guess boldly what the area of the circle might be, d2 or r2. According to the relationship that the circumference and diameter of a circle are π times, students guess whether it is πr2 or πd2. Then the formula of circular area is deduced by cutting method to confirm their conjecture.

The original boring process of regional derivation, because it allows students to guess, satisfies their curiosity, activates students' thinking and becomes interesting. At the same time, this kind of questions makes students feel that the area of a circle is not only related to the square of the radius, but also related to the square around it; The semicircle area is also related to the rectangular area (half of that square); The area of circle (sector) is related to the area of small square (square), which opens up a new idea of solving problems by using circle area.

Being the same height as students means that teachers should use their wisdom, adjust their sight and keep the same height as students; When teaching, we should not only have the course objectives in mind, but also squat down to the height of a class student. Smart teachers are always so good at thinking about their problems, answering their doubts, sharing their happiness, feeling their experiences and discovering their progress from the same height as students.

(Editor Chen Jianping)