Note: What kind of math education do we need?

When I went shopping the other day, the elder sister who sold vegetables mistyped the unit price. As soon as I asked the question, my sister mumbled something and immediately said, "Then knock out the four corners." Just before my math teacher worked out the exact number, my sister had given the correct answer. The gentleman on the side began to laugh that I was not as good as a vegetable seller. It suddenly occurred to me that Professor Liang Guancheng from the School of Education of the University of Hong Kong called "popular mathematics". Yes, if this matter is turned into an application problem, maybe the elder sister who sells vegetables needs to think for a long time; And once it becomes the price of vegetables that she touches every day, she is so skilled. Perhaps, this is just because mathematics has become a very valuable thing for the vegetable seller to solve her livelihood.

The curriculum standard (experimental draft) once proposed that everyone should learn valuable mathematics. "Valuable" mathematics should be closely related to students' real life and past knowledge and experience, which is attractive and interesting to them. In a broader sense, "valuable mathematics" is mathematics that meets the requirements of quality education. It should help students develop a sound personality and form positive values, and help students cultivate self-confidence, responsibility, cooperation, innovation, realistic attitude and scientific spirit. Valuable Mathematics is not only useful for students to further study, but also useful for students to engage in any occupation. It is particularly worth mentioning that this kind of mathematics learning experience should greatly enrich students' real life, and students will feel the richness of life and the inherent charm of mathematics learning because of mathematics learning.

And how do we do it in actual teaching? Looking at mainland education from so many experts from Hong Kong and Taiwan, we can find that our teaching pays more attention to the implementation of knowledge and skills and ignores the cultivation of students' learning ability. Pay more attention to teaching students how to learn and ignore students' learning from exploration; Pay more attention to the improvement of students' overall level and ignore their individual differences. ...

What kind of math teaching do we need? From the training these days, I think of the following points.

First, construct meaningful learning content.

Professor Liang Guancheng mentioned in the lecture: "In the face of meaningless learning content, students can only imitate and guess;" With meaningful learning content, students can understand and learn well. "Indeed, it is a very important part of our mathematics teaching to let students realize the application value of mathematics and that mathematics is the abstract process of human beings' quantity and shape to the real world. Therefore, in the usual mathematics teaching, it is necessary to construct meaningful learning content and guide students to experience the process of abstracting mathematical models from daily life, explaining them and widely applying them, so as to realize the practical application value of mathematics.

Second, provide learning space for independent exploration.

Hands-on operation, independent exploration and cooperative communication are important ways of mathematics learning. To truly change "teacher-centered", students should have more learning space for independent exploration. Dr. Wu, director of the Education Leadership Research Center of the University of Hong Kong, once mentioned that although there are students' independent inquiry and group communication activities, they are more inclined to teach students how to learn effectively. Hong Kong pays more attention to let students learn through exploration. As teachers, we should believe that students can learn by doing and exploring and give them enough time and space. Students' activities should be the most important part of the classroom, and teachers only create learning environment and provide assistance. Only in this way can we truly realize the "students are the masters of learning, and teachers are the organizers, guides and collaborators of learning" mentioned in the curriculum standard (experimental draft).

Third, pay attention to students' personal learning experience.

"If we regard a class of students as a forest and each student as a tree, should we take the collective as the center or the individual as the center?" Dr. Wu's question aroused our thinking. Constructivist learning theory puts forward that because of the complexity and diversity of objects, the particularity of learning emotions and the uniqueness of personal experience, students' learning process is diversified, and students' construction of object meaning is multidimensional. Therefore, we should pay more attention to the personalized characteristics of students' learning, so that they can get reasonable personal experience in knowledge learning; Suhomlinski of the former Soviet Union also stressed that we should try our best to explore the talents of every student. He pointed out: "The most important thing is to find his strongest side in every child, and to find him as the fundamental' smart point' for personal development, so that children can achieve outstanding achievements at his age in things that he can fully display and give play to his natural qualities." Visible. Paying attention to students' personal learning experience is also an important part of mathematics teaching. When teaching, we should respect each student's individual and help explore its value; We should take care of individual differences and the needs of special students, provide enough opportunities to support them to explore themselves; Pay attention to personal experiences, experiences and feelings. Only when every tree grows sturdily can the forest become more lush.

Fourth, carry out diversified teaching evaluation.

Whether it's Hongkong, Taiwan Province or Singapore. They advocate the diversification of evaluation methods, oppose excessive standardization and simplification, and attach importance not only to knowledge but also to learning process and values. Although the theory of multiple intelligences has been in Chinese mainland for a long time, the evaluation of knowledge and skills is still the main thing in the concrete implementation process. Curriculum standard (experimental draft) puts forward that the evaluation of mathematics learning should pay attention to the result and process of mathematics learning; We should pay attention to the level of mathematics learning, and pay more attention to the emotions, attitudes and values expressed in the process of mathematics learning. Therefore, the evaluation of students' mathematics learning should be diversified, and the evaluation subjects and methods should be diversified. Teachers' evaluation, peer evaluation and parents' evaluation can be combined, and managers (such as club members) in practice areas can also be invited to participate in the evaluation. Besides testing, the evaluation method can also be combined with classroom observation, after-class interview, homework analysis, hands-on operation and practical activities. The evaluation results can be combined with qualitative evaluation and quantitative evaluation, focusing on qualitative evaluation and stimulating students' mathematics learning with vivid language.