(A) the definition and research of current mathematical thinking
In the process of learning western mathematics and learning western mathematics education in modern China, more attention was paid to the study of mathematical ability. The long-term popular expression of mathematical ability in China is "three abilities", namely, mathematical operation ability, spatial imagination ability and logical thinking ability.
With the development of mathematics application, on the basis of emphasizing the wide application of mathematics in social practice, mathematics education began to pay attention to the ability to solve practical problems. 1996, the "logical thinking ability" is changed to "thinking ability" on the grounds that mathematical thinking is not just logical thinking; In addition to the three abilities, it also puts forward the idea of "gradually cultivating the ability to analyze and solve practical problems"
The Mathematics Teaching Syllabus for Full-time Senior High Schools issued in 2002 gives a more detailed description of mathematics ability, which not only refers to general mathematics ability, but also defines the "mathematical thinking ability" that only mathematics subjects have. It includes: spatial imagination, intuitive conjecture, inductive abstraction, symbolic representation, operational solution, deductive proof, system construction and many other aspects.
High school mathematics curriculum should focus on improving students' mathematical thinking ability, which is one of the basic goals of mathematics education. In the process of learning mathematics and solving problems by using mathematics, people constantly go through such thinking processes as intuitive feeling, observation and discovery, inductive analogy, spatial imagination, abstract generalization, symbolic representation, operational solution, data processing, deductive proof and reflective construction. These processes are the concrete embodiment of mathematical thinking ability, which helps students to think and judge the mathematical model contained in objective things. Mathematical thinking ability plays a unique role in the formation of rational thinking.
(B) Research and application of foreign mathematical ability and mathematical thinking
Western countries are the leaders of modern mathematics education, and they are the "authentic" successors of ancient Greek mathematics. The requirements of these countries for mathematics education can give us some reference.
In 2000, the American Association of Mathematics Teachers issued the Mathematics Curriculum Standard, which mentioned six abilities:
(1) Mathematical operation ability
(2) the ability to solve problems
(3) the ability of logical reasoning
(4) Mathematical contact ability
(5) Mathematical communication ability
(6) Mathematical expression ability
1989, Golfes, a mathematician and mathematics educator from Southampton University in England, gave a lecture on mathematics education at Northwest Normal University at the invitation of the State Education Commission of China. He also put forward ten aspects of mathematical ability in college mathematics education:
From the above comparison, we can see that whether it is today's mathematics education in the west or 20 years ago, mathematics ability, mathematics thinking and mathematics education in the west all require the combination with other social activities. In other words, in western mathematics education or western mathematics thought, the application of mathematics in practice has received special attention.