"A cabin is only 6 square meters. If you live in it, how will you decorate it?"
On December 25th, 2023, in the "Research and Practice Class of China Mathematicians Entering the Primary School Classroom" taught by Hua Yinglong, Vice President of Beijing No.2 Experimental Primary School, interesting questions deeply attracted the sixth graders.
The Mathematics Curriculum Standard for Compulsory Education (2022 Edition) points out: "The content design should reflect the application of mathematics in nature and society, show the great mathematicians in the history of mathematics development, especially the famous mathematicians in ancient and modern China, and the role of their mathematical achievements in the development of human civilization, and enhance students’ patriotic feelings and national pride."
It coincides with the 90th anniversary of the birth of Chen Jingrun, a famous mathematician in China. Hua Yinglong can’t help but think about the requirements of the curriculum standard: What kind of collision will happen when the world-famous China mathematician enters the primary school classroom? I want to chase the "brightest" star with my children!
Plant the seeds of curiosity
This class begins with the sharing of reading experience before class. Before class, the students previewed the reportage Goldbach conjecture in advance. In class, the students scrambled to share their feelings.
"Although some people discriminated against him, he didn’t waver in his love for mathematics. He was always calm, and his tolerant spirit was worth learning."
"I want to say to Chen Jingrun that you are really amazing. You were born in a family with no math environment, but you have made such achievements through hard work."
"What impressed me most was that Chen Jingrun studied hard in a 6-square-meter hut despite the difficult conditions."
…………
Students talked about being moved by Chen Jingrun’s spirit of studying and studying, and began to notice the mathematical element of "6 square meters" under the guidance of the teacher.
Hua Yinglong asked, "What kind of math topic do you think you can make up about the 6-square-meter hut?"
"Chen Jingrun’s room is 6 square meters, and their chimneys account for one-sixth of the room. How big is the living area?"
"The room is 6 square meters in total, and a chimney has cut the room into a corner, which is one-sixth of the room area. How big is this corner plus the total room area?"
…………
According to Hua Yinglong’s questions, the students expressed their opinions and collected five different proposition ideas. Hua Yinglong immediately gave his own examples. The students called "simplicity" and "logic", and an ordinary application problem set off a hearty "brainstorming" between teachers and students.
The reading method with "questioning" as the main guidance makes students experience the fun brought by mathematics reading, and guides students to think deeply and be eager to try after thinking.
After mastering more clues, students are more curious about the "6 square meter cabin". Hua Yinglong continued to ask: "What is a 6-square-meter cabin like?" He asked the students to draw a plan of the hut. With the help of students’ work sharing, Hua Yinglong has drawn out one enlightening question after another.
Through mathematics to restore the hut, children’s eyes look at the hut in a variety of ways: some are trapezoidal, some are square, some are marked with the position of the door and bed, and careful students mark the size of each layout …
"Teachers’ teaching design should read the world from a mathematical perspective, which is fascinating," Hua Yinglong said. "As a guide for students’ mathematics learning, we should plant a seed for them, hoping that one day, this seed will blossom a flower of’ everything counts’."
Bold trial and error in exploration
Around the "hut", Hua Yinglong took the students to solve the side length, and the "mathematical flavor" became stronger and stronger. At this time, a quick student confused the area and perimeter, and the students corrected his algorithm one after another. Hua Yinglong praised the student’s quick response and bold speech: "Children, in reading, not only reading, but also thinking. Every mistake is a reminder. We want to thank this classmate for reminding us." There was applause at the scene.
When calculating the side length of the hut, the students encountered a difficult problem-they had not touched the square root and could not continue to calculate.
"Children, we can’t make a square, can we still count?" Hua Yinglong asked. He didn’t impart knowledge beyond the outline, but left time for students to think. When a student tried repeatedly on the toilet paper and found the answer by reverse deduction, Hua Yinglong showed it to everyone with surprise and led them to summarize this valuable thinking process:
"Children, did this classmate try it right just once? No, he also found the answer by mistake, right? " Hua Yinglong once again guides students to correctly look at mistakes in learning. In such a class, students’ frustration tolerance is strong.
"Making mistakes is something everyone has to experience, including teachers." Hua Yinglong said, "We have to tell students that mistakes are often reminders, reminding us to calm down and think: Where is the problem? Why is it wrong? What new possibilities will there be? What new problems can you think about? "
"Where is the 6-square-meter hut and what is it really like?"
In order to give the child an accurate answer, Hua Yinglong shared his "journey to find the truth" after reading relevant books and materials, and went to the address of his former residence "No.88 Zhongguancun Street" in the materials to find out, but found that this was not the location of his mathematics institute. When I went to Fujian, I learned that there was a "Chen Jingrun Experimental Primary School" in the local area. I went there quickly, but I didn’t get the answer … Despite the twists and turns, with the help of Song Li, Chen Jingrun’s nephew, the real hut emerged a little bit: the room was square, and it became a "knife handle" shape after being occupied by the garbage passage. Because the space was narrow, people had to close the door before they could barely stand open …
Hua Yinglong’s exploration process of constantly trying to find a "real cabin" inadvertently set the best example for students.
Give students a bigger world.
"Students, suppose you enter Chen Jingrun’s cabin now, what do you want to say to him?"
As the class draws to a close, Hua Yinglong throws out the last question of this class. As early as in the open space next to the podium, he outlined the spatial structure of the hut with tape, suggesting that students take a walk in the "hut" and feel the living space of 6 square meters.
Some children bluntly said, "I love this mathematician very much, and I hope he will pay attention to his health and live in a big house." Some children felt "the sense of accomplishment gained by tireless knowledge" through repeated thinking, and some children called "Mr. Chen Jingrun is so great that in a difficult environment, he has confirmed the" Goldbach conjecture "that even the great mathematician Euler has not confirmed …
At this point, students’ feelings are not only the absorption after reading, but also the spiritual baptism after the classroom and teachers jointly verify and explore.
The students read the ten characters written by Hua Yinglong on the blackboard in unison-"A humble room grows into a superstar, and hardships make a great man". At that moment, the little boy seemed to have crossed time and space, ignorant and firmly paying tribute to the mathematician.
What can mathematics leave for students?
"A good math reading class is to give students reading energy and spiritual nourishment." Hua Yinglong replied in class, "I always think that education is humanized, which is the highest realm pursued by education." I am a primary school math teacher, but I don’t teach math. I use math to teach children. "
China Education News, January 5, 2024, 9th edition.