Let's walk into the classroom in Holland first.
At the beginning of class in a middle school in the Netherlands, the teacher showed a Muslim prayer carpet with a compass on it. The teacher asked the children to think about the relationship between the angle and the arc with a map and calculate the shortest distance from the local area to Mecca, the holy place of Islam. In this class, you can see 15-and 16-year-old children, discussing noisily around the map and calculating according to various data provided by the teacher.
In particular, although the atmosphere of running a school in the Netherlands is very free, the mathematics teaching method in this school is not a special case. As early as the late 1960s, the Netherlands began to reform mathematics education. This is not only a change in form, but a real reform in mathematics teaching in connotation. At that time, Dutch mathematics educators put forward a new point of view, saying: "The only correct way to learn mathematics is' re-creation', that is, students discover or create this concept by themselves; The task of mathematics teachers is to guide and help students to do this kind of re-creation work, rather than instilling ready-made knowledge into students. "
Under this new thinking direction, the Dutch believe that mathematics education should be realistic and proceed from real life. The so-called "reality" and "practicality" means that students discover mathematical concepts from their familiar lives and then apply the learned mathematical concepts to real life.
As children grow older, they can gradually step into more abstract mathematical symbol calculation. When teaching each unit, Dutch math teachers will still pay attention to the connection between mathematics and nature or real life. The purpose of this kind of teaching is to let children feel mathematics and connect mathematical thinking with life. Dutch mathematics educator said: "There is a deep gap between algebra and boiled potatoes, between workplace problems and geometry, and the task of mathematics education is to fill these gaps."
Bridging the gap between mathematics and life here is not to simplify or vulgarize mathematics, on the contrary, it is to establish the relationship between mathematical thinking and life. The Dutch believe that the past mathematics textbooks were based on the subject system and presented mathematical knowledge in concise language. Although the knowledge structure of mathematics exists, the thinking process is compressed. Students often see the result of thinking, but they can't see the process of thinking activities and don't understand the relationship between mathematical logic and the world.
Therefore, teachers should guide students to actively participate in the formation and development of knowledge in classroom teaching. For example, when teaching the calculation of "the area of the side of a cylinder", students are not immediately told to expand the side into a rectangle to calculate, but are given space to think and explore and try various algorithms. Just like this, mathematics education in the Netherlands brings nonstandard algorithms and mathematics language invented by students into the learning process, emphasizing the openness of mathematics learning, hoping to stimulate the learning style of coexistence of diversity and independent thinking through this process.
The goal of mathematics teaching set by the Dutch government is simple and clear, and each "goal" has great freedom.
For example, the syllabus of Dutch primary schools says that the general objectives of mathematics courses include: thinking about their own mathematical activities and testing the correctness of the results of these activities; Understand and explore simple relationships, rules, models and structures; You can describe the process of inquiry, reason in your own language and apply it.
The teaching objectives of mathematics curriculum in Dutch middle schools are: to cultivate a correct attitude towards mathematics; Develop the ability of mathematics appreciation; Understand the application of mathematics in other disciplines.
Under the basic outline, teachers can decide mathematics textbooks and teaching methods. Interestingly, most Dutch teachers now choose new mathematics teaching methods instead of traditional and indoctrinating mathematics learning methods. The syllabus planned by the Dutch government has left enough flexible space for the development and research of mathematics courses and teachers' practical teaching activities. This flexible space is helpful to the exploration of mathematics courses, and also helps teachers to adjust teaching according to the actual situation. Because in the classroom, mathematics teachers can fully explore and create, which plays a positive role in the whole mathematics education system and is full of vitality. Under the same idea, every teacher can take his children to explore and discover mathematics in different ways and establish the relationship between himself and mathematical thinking.
From the beginning of mathematics teaching reform to the present, a new generation of mathematics teachers has become the main body of the Dutch mathematics teaching team, and the new mathematics teaching ideas have been recognized by the Dutch government, society and the public. At present, 80% of primary school textbooks and 100% of middle school textbooks (including junior high school and senior high school) are all textbooks based on the new concept of mathematics education. The flexible application of these new mathematics textbooks and teaching methods has not only failed to reduce the Dutch mathematics ability, on the contrary, the Dutch children's mathematics achievements are excellent.