Mathematical thinking ability provides a powerful way for people to express their understanding of various phenomena. When people think and reason, they often pay attention to patterns, structures and laws, and express the corresponding situation with the help of mathematical language. Students often wonder whether these patterns are accidental or reasonable. They have the ability to guess and think. In addition, it is reasonable and understandable to show students mathematics in teaching. As a high school student, we should deepen our understanding of mathematical argumentation, have rigorous mathematical thinking ability and master flexible thinking skills.
Thinking ability is an important condition for understanding mathematics. Mathematical thinking ability plays a unique role in mastering mathematical concepts, exploring problem-solving methods, cultivating students' exploration and innovation ability, and even future scientific research and innovation. Nowadays, the field of education is advancing in an all-round way, aiming at cultivating students' innovative ability. However, for a long time, mathematics teaching in middle schools has attached great importance to the rigor of thinking ability, overemphasized the importance of logical thinking ability and neglected vivid and reasonable thinking ability, making people mistakenly think that mathematics is a purely deductive science. In fact, every important discovery in the history of mathematics development, besides deductive thinking ability, perceptual thinking ability also plays an important role, and perceptual thinking ability and deductive thinking ability complement each other. In teaching, we should develop thinking and explore phenomena. Using reasonable thinking ability to guess, using deductive thinking ability to judge the result, can understand and make mathematical proof, that is, starting from assumptions, through strict deductive thinking ability to draw conclusions. In addition, high school students should be able to think independently, judge whether the arguments in mathematics are reasonable and understand the value of such arguments.
Stimulate students' curiosity and interest in mathematical thinking ability
(1) Curiosity is a great driving force for scientific discovery and an explicit expression of innovative consciousness. Without curiosity and thirst for knowledge, it is impossible to produce inventions of great value to society and mankind. One of teachers' duties is to protect and develop students' curiosity. Students are very interested in improving teaching effect and cultivating innovative consciousness, and this process can further strengthen students' curiosity. For example, we can use interesting inspiring stories in mathematics, real-life phenomena and counter-intuitive phenomena to stimulate curiosity.
(2) Mathematical thinking ability is not a special activity at a specific time and on a specific topic. It should be a natural and inseparable activity in classroom teaching. In teaching, we should stimulate questions, promote thinking, clarify opinions and sow the seeds of mathematical thinking ability through appropriate situations. In all content fields and all grade levels of mathematics, it can be found that the ability of systematic thinking is an inherent feature of mathematics curriculum, although there are different requirements for the rigor of mathematics.
(3) Evaluation should not only pay attention to the results of students' mathematics learning, but also pay attention to their mathematics learning process; We should not only pay attention to students' mathematics learning level, but also pay attention to the changes of their emotional attitudes in mathematics activities and the development of students' personality and potential. In other words, we should pay attention to the evaluation of students' innovative spirit in the study of rational thinking ability and the study of continuous reflection ability in mathematics learning. For example, compare different personalities in the form of induction and analogy to understand the essence of * * * *. Of course, the appreciation of mathematical beauty, the exploration of laws and rules, and the thinking of some famous problems can stimulate students' interest in mathematical thinking ability. For example, Goldbach conjectures that an even number (greater than 4) can be written as the sum of two prime numbers.
Lay the foundation of mathematical thinking ability
Mathematical thinking ability is a thinking form that draws a new mathematical judgment according to one or several mathematical judgments. The basic knowledge of mathematics that students learn is often used as the basis of mathematical judgment, so mastering mathematical concepts, theorems, formulas and their relationships is the necessary foundation of digital thinking ability. If high school students want to think correctly, they should also master the knowledge of propositional structure and logical thinking ability, and understand and master the basic proof methods. Of course, rich imagination is also the basis of mathematical thinking ability.
The cultivation of students' thinking ability is organically integrated into the process of mathematics teaching
The formation of ability is a slow process with its own characteristics and laws. It is not that students "understand" or "know", but that students "comprehend" this truth, law and thinking method, and this "comprehension" can only be carried out in mathematics teaching. Therefore, teaching activities must provide space for students to explore and communicate, carefully organize and guide students to experience scientific activities such as observation, experiment, conjecture and proof, and organically integrate the cultivation of thinking ability in this process. Any attempt to impart ability to students cannot achieve good teaching results. In the usual teaching, whether it is concept teaching or problem-solving teaching, students should be given a place to observe and a space to think, so that they have the opportunity to find and ask questions. We should try our best to provide students with opportunities to find problems. In the classroom, teachers can sometimes deliberately leave some questions, dew point flaws, set misunderstandings in the process of explanation, arouse students' doubts, make students think, and use cognitive conflicts to cause discussion and even debate. This will not only promote students to listen carefully and make bold discoveries, but also help students to understand and master knowledge. In class, teachers should encourage students to guess, doubt and ask their own questions. Doing this for a long time can cultivate students' innovative consciousness of thinking ability.
Put the cultivation of thinking ability into practice and use it comprehensively.
The middle school stage is an important stage for students to transition from image thinking to abstract thinking. Teachers should pay attention to inspiring students' thinking in every teaching link, persist in training and gradually improve students' thinking quality. Mathematics teaching must change the simplification of cultivating students' thinking ability, provide students with time and space for independent exploration and cooperation, set realistic, meaningful and challenging questions, guide students to participate in the analysis process, properly organize and guide students' learning activities, and really encourage students to respect and cooperate with them. This can expand the space of students' thinking ability and make students' thinking ability develop effectively.
Expand the vision of students' mathematical thinking ability
Mathematical thinking ability is a natural psychological activity in digital classroom. In teaching, teachers should persistently cultivate students' mathematical thinking ability through a large number of clues. In order to develop mathematical thinking ability healthily, we should broaden our horizons and strengthen the training of thinking ability. The textbook requires students to combine the mathematical examples they have learned with real life examples, sum up their own rational thinking ability and deductive thinking ability, and experience the role of rational thinking ability and deductive thinking ability in the discovery, proof and construction of mathematical system. For example, when we talk about Euler's formula, we can ask students such questions: "Is there a stable quantitative relationship between the number of vertices V, the number of edges E and the number of faces F of different convex polyhedrons?" Students may be at a loss when they come into contact with problems. At this time, teachers can put forward suggestions to solve the problem, that is, experimental observation, counting and induction of common polyhedrons. The proof can be left to students who are interested and have spare capacity to find materials to study after class.
Newton said, "Without bold speculation, there will be no great discovery." As early as 1953, the famous math educator Poliyan shouted, "Let's teach guessing." Guess before you prove it. This is the way most people find it. Therefore, in the usual study, we should use reasonable thinking ability to guess, and then use deductive thinking ability to judge whether the guess is correct. To reach a certain level of mathematical thinking ability, it needs usual efforts and long-term accumulation.