First, the cultivation of reasoning ability is organically integrated into the mathematics teaching process.
The development of ability is by no means equal to the acquisition of knowledge and skills. 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 themselves "understand" the truth, laws and thinking methods. This "realization" can only be carried out in mathematical activities, so teaching activities must provide students with a space for exploration and communication, organize and guide students to "experience the process of observing, experimenting, guessing and proving mathematical activities", and organically integrate the cultivation of reasoning ability into such a "process". Any attempt to "impart" the ability to students and train the ability to "try your best in the first world war" can't really achieve good results.
Second, the cultivation of reasoning ability is implemented in the four areas of standard division.
The course contents in four fields, such as number and algebra, space and graphics, statistics and probability, practice and comprehensive application, all provide rich materials for developing students' reasoning ability.
In the teaching of number and algebra, calculation should be based on certain "regular" formulas, rules and operation rates. , so there is reasoning in the calculation; Recognize that the quantitative relationship in the world often has its own laws. The process of describing quantitative relations with algebraic expressions, equations, inequalities and functions also involves analysis, judgment and reasoning. In the teaching of Space and Graphics, we should attach importance to both deductive reasoning and perceptual reasoning. Even in the teaching of the nature of plane graphics, students should be organized to experience the process of operation, observation, guess and proof, so as to combine perceptual reasoning with deductive reasoning. Compared with the original mathematics syllabus, the standard strengthens the relevant content of three-dimensional space set and provides more opportunities for students to "just think".
The inference in Statistics and Probability belongs to a reasonable category and is a possible inference. Different from other inferences, the conclusions drawn from statistical inference can not be tested by logical methods, but can only be proved by practice. Therefore, the teaching of statistics and probability should pay attention to the whole process of collecting, sorting out, analyzing data, inferring and making decisions.
Third, develop students' reasoning ability in daily life and game activities.
For example, people often need to make judgments and reasoning in daily life, and many game activities also imply the requirement of reasoning. Therefore, we should further broaden the channels for developing students' reasoning ability, let students feel that they have "learning" in their daily life and other activities, and form the habit of being good at observation and diligent in thinking.
Fourthly, to cultivate students' reasoning ability, we should pay attention to hierarchy and difference.
The standard emphasizes that mathematics teaching should be closely linked with students' real life, starting from students' life experience and existing knowledge. The cultivation of reasoning ability must fully consider students' physical and mental characteristics and cognitive level, and pay attention to hierarchy. Generally speaking, the difficulty of operation, experiment, observation and guess is easy to grasp, so the cultivation of reasonable reasoning runs through the whole process of mathematics teaching in compulsory education. To cultivate students' deductive reasoning ability, we should pay attention to both the hierarchy and the differences of students. Let every student understand the necessity of proof, make learning deductive reasoning a conscious requirement of students, and overcome the blindness of "proving for the sake of proof"; At the same time, we should pay attention to the control of "quantity" and the requirements of order and moderation.
Fifth, inspire students to think positively and fully mobilize students' subjective initiative in teaching.
The role of teachers in teaching is to impart knowledge and solve doubts. In teaching, teachers should get along with students equally, care about them and get along with them. Only in this way can students dare to approach you and tell you their own shortcomings and ignorance in learning, so that you can know the students' mastery of knowledge in time and the teachers can solve the students' confusion in learning in time. In the teaching of proof questions, the author not only teaches students to prove a certain problem or a certain kind of problem, but also pays attention to cultivating students' reasoning and argumentation ability. After writing a question, ask students to think for a few minutes first, so that in these few minutes, students with good grades may solve the problem as a whole, while students with medium grades have a basic understanding of a certain part of the problem, at least some constructive understanding of a certain problem, while students with poor foundation have not formed any valuable understanding. In the long run, students' reasoning ability has been exercised and improved.
Sixth, pay attention to the correctness of students' reasoning when correcting students' homework.
When correcting students' homework, we should gradually approve and revise them one by one, so that on the one hand, we can find some mistakes and urge teachers to improve teaching methods; On the other hand, we may find some good argumentation methods from it. Isn't it a good example that the teacher refines these good argumentation methods and then tells them to the students? Doing so is conducive to training students' reasoning and argumentation ability. It is not only necessary to refer to the reference answers, but also to type the correct reasoning argument wrong, which is not conducive to the cultivation of students' reasoning ability.
The above is my experience in cultivating students' mathematical reasoning ability in mathematics teaching, which is summarized as follows to promote future teaching.