The poor mathematical ability of American students is mainly due to the disorder of mathematical education theory. There are serious problems in the teaching methods of teachers in normal universities when training prospective teachers, which leads to teachers being at a loss in teaching. For a long time, American mathematics teaching has been roughly divided into two theories: traditional school and new mathematics school. The former emphasizes basic mathematical calculus ability, such as reciting multiplication tables, skilled mental arithmetic and basic calculation ability. The latter, also known as discovery teaching, was later combined with constructivism theory, which advocated strengthening students' understanding ability of mathematics, establishing students' mathematical concepts, and then teaching students basic mathematical operation ability.
Traditionalists believe that mathematics is a step-by-step discipline, and every new concept at each level must have a solid mathematical foundation at the previous level. They think that the new mathematics school only pays attention to making students spend a lot of time learning something that looks fancy, ignoring the cultivation of basics.
The new school of mathematics thinks that the traditional school has separated the connection between mathematical knowledge. In teaching, students should not be told the ins and outs of mathematical concepts and the methods of solving problems, but should be allowed to discover and discover by themselves. Teachers should encourage any problem-solving method that is contrary to tradition but correct in concept. If students find the laws and formulas of mathematics by themselves, they don't need to do a lot of problem-solving exercises at all. At the same time, the new mathematics school thinks that traditional mathematics education is divorced from reality and calculates with a pen and a piece of paper in class all day. Students know nothing about the application of mathematics in society. Therefore, we advocate opening schools, allowing students to participate in practice and learn mathematics in society.
The two schools of mathematics education have their own supporters and the support of the government, and they are equally matched. The focus of the debate between the two factions is how to teach mathematics, so that students can have the ability of basic mathematics, so as to smoothly connect the mathematics courses at all stages.
Due to the public recommendation of NCTM (National Association of Mathematics Teachers) and the establishment of new courses and evaluation standards based on the theory of New Mathematics School, public primary and secondary schools in most parts of the United States have already adopted the method of New Mathematics School to teach mathematics. However, the ruthless reality tells us that there is no doubt that American students' mathematical ability continues to decline. Recently, the American government and related experts believe that the current debate between the two schools of mathematics education is a waste of resources and time, and students are victims. It is hoped that the two schools can cooperate with each other to find the knowledge to teach basic mathematical theories and concepts.
According to the data, in some places where traditional mathematics education is quite successful, if we learn the mathematics education theory of the new mathematics school that has failed in the United States (such as 1993), it will lead to the crisis of mathematics education. Students who are educated by the curriculum and teaching methods similar to those of the New American Mathematics School have greatly reduced their ability to calculate and solve problems, and their mathematical concepts are vague, which can not meet the requirements of middle school mathematics. It can be seen that the wrong theory of public mathematics education in the United States not only hurts domestic students, but also begins to hurt overseas students who blindly study its teaching theory. Colleagues in the domestic mathematics education field should learn lessons.
(The distant mountains were arranged in June 2005 1. 10. Fang Fan, Why American Mathematics Education lags behind, Teachers' Way, No.1 12, 2004)
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