First, study mathematics and expand students' intelligent structure
Intelligent structure is one of the main components of human quality cultivated and formed by mathematics education. Students plan and optimize their studies in various fields through number and calculation, space and graphics, quantity and measurement, statistics and probability, equations and relationships, etc., and observe, discover and understand the real world, so that students can fully realize that mathematics has emerged and developed from human practical activities and has been widely used in practice. Students learn and master the basic methods of scientific research by participating in mathematical activities, such as carefully observing experiments, boldly trying to guess, carefully reasoning and strictly demonstrating. Establish and strengthen mathematical consciousness, such as reduction consciousness, abstraction consciousness, reasoning consciousness, symbol consciousness, quantification consciousness, etc.
Thinking quality is the core of intellectual quality. The basic components of mathematical thinking can be divided into four basic types: concrete thinking, abstract thinking, intuitive thinking and functional thinking.
These qualities comprehensively reflect the main characteristics of logical thinking, image thinking, intuitive thinking and dialectical thinking. Students' thinking quality can be improved by regular mathematical thinking training. Excellent thinking quality has the characteristics of flexibility, rigor, criticism, extensiveness and creativity. The flexibility of thinking is characterized by not being greatly influenced by the mindset, being able to accurately adjust the direction of thinking, being good at jumping out of the old mode or traditional thinking track, and being able to find another way with a winding path. We advocate multiple solutions to one problem in mathematics education, which is an effective way to cultivate the flexibility of thinking. The rigor of thinking is manifested in careful consideration of problems. In mathematics, intuitive methods are allowed to solve problems, but students should be encouraged not to stay at the level of intuitive understanding, and reasonable reasoning can be used, but accurate calculation and logical argumentation should be carried out. Correctly using concepts and answering questions completely reflect the rigor of thinking. Critical thinking means to dare to put forward your own views on existing mathematical expressions or arguments, rather than blindly following them. The broadness of thinking means that a mathematical case can have many explanations, a mathematical problem can have many forms of expression, and a problem can have many different solutions. The creativity of thinking refers to the degree of innovation of thinking activities, which is manifested in the novelty and uniqueness of the ways, methods and results of analyzing and solving problems. Being good at finding, solving and extending problems is the performance of innovative thinking.
The formation of these good thinking qualities will gradually be promoted to innovative consciousness and creative consciousness. And these qualities and abilities are exactly the goals pursued by our educators.
Second, learning mathematics to improve students' psychological quality
The key to a person's success or failure actually does not depend on his absolute IQ, but on his psychological quality to a greater extent. In other words, whether a person's psychological quality adapts to the environment is a necessary condition for winning study and life and plays a balanced role in the formation of people's quality.
Problems are the motive force for the emergence, origin and development of mathematics, and problems often stem from curiosity. From Watt's observation of boiling water to some complex scientific discoveries, it all stems from curiosity. The curiosity of teenagers is the most prominent. With the growth of age, people gradually lost this precious nature. Mathematics is a subject full of mystery and interest, such as the famous "four-color problem" and "seven-bridge problem", which aroused the curiosity of many naive children and activated the wisdom of many mathematical geniuses.
The abstraction of mathematics makes the solution of mathematical problems often accompanied by difficulties, which makes students experience setbacks and failures. And this is an excellent opportunity to sharpen your will and polish your psychological quality. The more frustrated and brave you are, the less you will form a better psychological quality in the greenhouse. A famous math educator once said: "If students don't have the opportunity to taste all the ups and downs of the struggle for solving in school, then his math education will fail in the most important place."
Third, the perception of mathematics, enhance students' aesthetic awareness
The beauty of mathematics has attracted people's attention since ancient times. Mathematical beauty is different from natural beauty and artistic beauty. Mathematical beauty is a kind of rational beauty and abstract beauty. People who don't have a certain mathematical literacy can't feel the beauty of mathematics, let alone discover it. The beauty of mathematics lies in simplicity, symmetry, harmony, unity and strangeness. Pythagorean theorem expresses the relationship between the side lengths of all right-angled triangles in a simple and neat form, and its conciseness and generalization give people a beautiful enjoyment. Some seemingly dazzling objects, once analyzed mathematically, appear orderly, thus arousing rational aesthetic feeling. For example, the golden section embodies the beauty of proportion and is pleasing to the eye. The symmetry of mathematical figures and expressions gives people visual pleasure, such as the coefficients of binomial expansion and the images of inverse functions. Symmetry in the structure of mathematical propositions gives people the best inspiration, which leads to innovation and infinite association.
Fourth, experience mathematics and improve students' personality.
Mathematics professors are honest and upright. British lawyers have to learn a lot of mathematics in universities so far, and American masters in linguistics are more willing to recruit students of science and engineering. This is not because lawyers' work or language research is directly related to mathematics, but because they can develop an independent, objective and fair work style and rigorous academic character after strict mathematics training. Mathematics education is one of the main channels to cultivate students' concept of honesty, and the concept of honesty formed in mathematics classroom is lasting and deeply rooted.
People who have received a good mathematics education will have a positive impact on their future work because of their quality formed in mathematics learning and training. The accuracy and rigor of mathematics will reduce the arbitrariness of students in their future work; The abstract analysis of mathematics makes them good at understanding the essence of things through phenomena. The incisive arguments and concise expressions in mathematics make them concise and to the point. In a word, we should not unilaterally understand mathematics education in compulsory education stage as imparting knowledge and training skills. The ultimate value of mathematics lies in that students may rarely have the opportunity to directly use a theorem and formula in mathematics when they step into society, but the ideas, methods and spirit of mathematics will certainly accompany them all their lives. As a math educator, we should focus on improving people's quality. As the new curriculum standard advocates, "everyone learns valuable mathematics;" Everyone can get the necessary mathematics; Different people have different developments in mathematics. "