Chen Lin of Xinbeijiang Primary School in Qingyuan City

How to improve their math literacy and make their classes more interesting in math culture is always a concern of every math teacher. With these questions, I read the book Mathematical Culture by three professors, Zheng Yuxin, Wang Xianchang and Cai Zhong. Through reading, I really made clear the meaning and essence of mathematics education, and had a deeper understanding of the goal and realization way of mathematics education.

This book talks about the rapid development of mathematics today from the origin of ancient Greek mathematics. It shows me the long history of mathematics development, and the characters who once appeared in primary school mathematics textbooks are vividly on the paper. By comparing the history of mathematics development in the West and China, we can preliminarily understand the main contributions of famous mathematicians in past dynasties and the historical process of mathematics development. This book is more than just a historical narrative. The professor further expounded from his own point of view what mathematics is culture and the significance of taking mathematics as culture, which made my understanding of mathematics culture more profound.

What inspired me the most in the whole book was the content of "Looking at Mathematics Culture from the Angle of Education". The author emphasizes that attention should be paid to correcting such a tendency, and the role of mathematical tools should not be emphasized blindly. However, at present, the teaching goal of mathematics curriculum in primary and secondary schools in China is mainly to teach mathematics as a tool, and more attention should be paid to the training and cultivation of mathematical thinking in daily teaching. From the teaching point of view, the following questions are particularly important, that is, how to cultivate students' mathematical thinking through daily mathematics teaching, because "thinking activities do not appear after acquiring the knowledge of the course content, but an integral part of the successful learning process. Therefore, the course content must be able to inspire students' thinking, even in the most humble and basic classroom situation. "This passage made me clear that the training and cultivation of mathematical thinking is more important than the study of specific mathematical knowledge and skills. As a result, I deeply thought about my classroom. ...

"A nation without a developed mathematical culture is doomed to decline, and a nation without mathematics as a culture is doomed to decline. We should strive to establish a clear mathematical consciousness of a nation or country. " I think that the training of thinking methods should be infiltrated into the daily mathematics teaching activities, and the analysis of thinking methods should be used to drive and promote the teaching of specific mathematics content.

It is mentioned in the book that Mr. Xiaowenqiang borrowed the exposition of Yuan Mei, a writer in Qing Dynasty, on "learning, talent and knowledge" to illustrate the three purposes of mathematics education. He believes that mathematics education in a broad sense not only regards mathematics as a practical tool, but also realizes a wider educational function through mathematics teaching, including expanding mathematical thinking to general thinking, cultivating correct learning methods and attitudes, good style of study and moral cultivation, and also including learning pleasure and respect for knowledge brought by mathematics appreciation. We must clarify the relationship between the three. Compared with the study of specific mathematical knowledge, the cultural value of mathematics (including thinking training and cultural literacy) is more important.

Chapter two: Thinking about "foundation" and "height"

-Thoughts on Reading "A Series of Empirical Studies on Chinese and American Students' Mathematics Learning"

Chen Lin of Xinbeijiang Primary School, Qingyuan City, Guangdong Province

I have carefully read Professor Cai Jinfa's book "A Series of Empirical Studies on Chinese and American Students' Mathematics Learning", in which the metaphor of "foundation" and "height" caused me to think deeply. Professor Cai believes that students' mastery of basic knowledge and skills is equivalent to laying the "foundation" of a building, and their problem-solving ability is just like the ground part of a building. The higher the floor, the larger the building area, which means the higher the income. The achievements of "double basics" teaching in mathematics in China have attracted worldwide attention. According to common sense, children's ability to solve problems should also be amazing. Is this result common sense? On the contrary, the data studied by Professor Cai shows that China students are much better than American students in calculating problems, solving simple problems and solving complex problems with process constraints, but worse than American students in solving complex problems with open processes. Most problems in real life are complex problems with open process. Our students have laid a solid foundation with a lot of energy and sweat, but they may not be transformed into the ability to solve unconventional problems and open complex problems. The average score of students in China is far ahead by 35 percentage points. When solving simple problems, the gap narrowed to 10 percentage point. Speaking of complicated problems, our children are 2 percentage points behind. The children have laid a solid foundation, but they are slightly inferior in height. The children seem to have won at the starting line, but lost at the finish line ... Such a huge contrast should make math educators re-examine us.

First of all, let's take a look at how American children "get taller later". Looking at the strategies of Chinese and American students to solve complex problems, only a few American students use abstract methods to solve problems, and most students like to use intuitive methods to solve problems, such as drawing, listing and describing in words, which are diverse and interesting. Most children in China use algebra to solve problems, and their problem-solving strategies are highly unified. Few students solve problems by drawing or listing (I believe that children who draw pictures to solve problems may be classified as poor students in the eyes of our teachers). When there is no way to solve the problem, the attitudes of students in the two countries are also very different. Children in the United States always want to write something, while children in China choose to give up with blank space.

Phenomenon: American children have solved many complicated problems in ways that Mr. China thinks are not too mathematical and rigorous.

Thinking: Do we have a prejudice that we despise intuitive and graphic representations and prefer algebraic representations such as numbers, laws and programs to solve problems, and think that these methods are the simplest and most optimized methods? At present, in problem-solving teaching, teachers are aware of the necessity of diversification of methods, but whether the following algorithm optimization will obliterate the diversification of algorithms. Usually, intuitive rather than mathematical methods will be ignored by teachers, who will guide students to screen out problem-solving strategies. Usually, when teachers guide children to compare methods, they always tend to recommend them with strict reasoning logic and concise and clear problem-solving methods. Will this practice make children? As a result, as long as there is no formula to solve the problem, children think that the problem is too difficult to solve by themselves. Many children would rather give up looking for a solution to the problem than try other methods. Even though I have some ideas in my mind, I don't think my method is a good one, and I dare not express it boldly, so I finally chose to give up.

Such a clip in the class makes me more convinced that the teacher's attitude towards problem-solving strategies has a great influence on children. In the lesson "Trapezoidal area" in the fifth grade textbook of Beijing Normal University, a teacher did an exercise: Wang Jia surrounded a trapezoidal fence, which was 55 meters long, and one of the fences was 15 meters long, so as to find the trapezoidal area surrounded by the fence. As shown in the figure (omitted)

In class, the teacher first guides students to analyze the known conditions and problems in the problem, so that students can discuss how to solve the problem in groups, and then let students show their own methods.

Student 1: "The area of the trapezoid is equal to the sum of the upper bottom and the lower bottom multiplied by the height divided by 2. I use 55 meters to subtract the height 15 meters, which is exactly equal to the sum of the upper bottom and the lower bottom, and then multiply 15 by 2 to get an area of 225 ordinary meters. "

The analysis of student 1 is clear, the reasoning logic is strict, and the formula is concise and clear. The teacher also praised the students' methods.

Teacher: "Any different ideas?"

Student 2: "I guess the length of three sides is 55 meters, and one side is 15 meters. When I look at the picture, one side is almost as long as 15 meters, so I take it as 15 meters, and the other side is much longer. I guess the length is 25 meters, which adds up to just 55 meters. Then I use the formula to calculate the area of the trapezoid.

Sheng Eryi said with a happy face, I think he is complacent because he can think of a solution to this problem, waiting for the teacher to praise him. What a lovely child!

Teacher: "Which method do students like?"

Health; "The first one."

Teacher: "Why?"

Health; "Because the first one is simple enough."

Division; "Then we can solve this problem in this simple way."

I sat next to Health 2 and obviously saw that Health 2 bowed his head. I think this child must feel "optimized". Is there really no merit in the assumption of Health 2? Is his guess groundless?

Think carefully about how many effective strategies have been optimized in our wishful pursuit of "optimization" of methods. Drawing, listing, hypothesis, guessing and verification ... these methods, which are slightly naive in the eyes of teachers and often ignored by us, have powerful problem-solving effects. Don't let this effective problem-solving strategy slip away in our algorithm optimization program. I think what we should do is to help children sort out many methods, let our children understand that there is no difference between good and bad methods, and boldly adopt different methods to solve problems according to actual problems, so as to solve problems. Teachers' ideas have a subtle influence on students. Only when teachers change their ideas, infiltrate various problem-solving strategies in teaching and pay attention to the diversity of strategies, I believe that our children will be able to build magnificent buildings on a solid "foundation" and realize the continuous rise of "height".