Mathematics can be regarded as the science of proof, but this is only one aspect, and it completes the mathematical theory. How to analyze the cultivation of students' reasoning ability in junior high school mathematics teaching?

With the comprehensive promotion of educational reform, the new textbook corrects the old textbook's overemphasis on the rigor of reasoning and the importance of logical reasoning, but puts forward new viewpoints? Reasonable reasoning? This is a major feature of the new textbook. This paper explores the cultivation of students' reasoning ability in junior high school mathematics teaching under the new situation.

Keywords junior high school mathematics reasoning ability training

For a long time, middle school mathematics teaching has always emphasized the rigor of teaching, overemphasized the importance of logical reasoning and neglected vivid and reasonable reasoning, which made people mistakenly think that mathematics is a purely deductive science. In fact, every important discovery in the history of mathematics development, besides deductive reasoning, rational reasoning also plays an important role. For example, Goldbach conjecture, Fermat's last theorem and four-color problem were discovered. Some important discoveries in other disciplines are also made by scientists through reasonable reasoning, putting forward conjectures, hypotheses and hypotheses, and then through deductive reasoning or experiments. For example, Newton was inspired by the fall of an apple, and after reasonable reasoning, he put forward the conjecture of universal gravitation, which was later confirmed by Coulomb's Newskell experiment. The discovery of Neptune is a model of rational reasoning. Rational reasoning and deductive reasoning complement each other. Paulia and other mathematics educators believe that. Rational reasoning has certain risks, and its application in mathematics is as extensive as deductive reasoning. Strict mathematical reasoning is based on deductive reasoning, and the process of drawing and proving mathematical conclusions can only be found through reasonable reasoning. Therefore, we should cultivate students' rational reasoning ability as well as their deductive reasoning ability. Mathematical conjecture can be obtained through observation, experiment, induction and analogy. And further proof, proof or counterexample. In other words, students are required to go through the process from perceptual reasoning to deductive reasoning when obtaining mathematical conclusions. What is the essence of rational reasoning? Did you find it? Guess what? Therefore, paying attention to the cultivation of rational reasoning ability is helpful to cultivate students' innovative spirit. Of course, the' conjecture' obtained by reasonable reasoning needs to be proved by deductive reasoning or denied by quoting counterexamples. The conditions and conclusions of rational reasoning are based on conjecture and association, and intuitive thinking is the thinking basis of conjecture and association. Cultivating students' thinking habit of being good at rational reasoning is to form mathematical intuition and develop mathematical thinking. Therefore, in mathematics teaching, we should not only emphasize the rigor of thinking and the correctness of results, but also attach importance to the intuitive exploration and discovery of thinking, that is, attach importance to the rationality and necessity of rational reasoning in mathematics, give full play to the role of classroom teaching, gradually and orderly cultivate the ability of rational reasoning in mathematics, improve students' quality and promote their healthy and all-round development.

Mathematician Paulia said: Mathematics can be regarded as the science of proof, but this is only one aspect. It has completed the mathematical theory. Expressed in the final form. It seems that it can only be proved by proof. With the comprehensive promotion of educational reform, the new textbook corrects the old textbook's overemphasis on the rigor of reasoning and the importance of logical reasoning, but puts forward new viewpoints? Reasonable reasoning? This is a major feature of the new textbook. This paper explores the cultivation of students' reasoning ability in junior high school mathematics teaching under the new situation.

Based on deductive reasoning, mathematical reasoning discovers the process of drawing and proving mathematical conclusions through reasonable reasoning. So what is reasonable reasoning? It is a form of thinking in which one or several known judgments lead to another unknown judgment. Rational reasoning is based on the existing knowledge and experience, and draws the conclusion of energy in a certain situation and process. Reasonable reasoning is a kind of reasonable reasoning, which mainly includes observation, comparison, incomplete induction, analogy, conjecture, estimation, association, consciousness, epiphany and inspiration. The result of reasonable reasoning is accidental, but it is not completely fictional. It is an exploratory judgment based on certain knowledge and methods. Therefore, it is a subject worth pondering to cultivate students' rational reasoning ability in normal classroom teaching.

Today's educational reform is advancing in an all-round way. Cultivating students' innovative consciousness and ability is the goal of the new round of educational reform. Rational reasoning is the means and process of cultivating innovative ability. People think that mathematics is a purely deductive science, which is inevitably too biased and ignores reasonable reasoning. Rational reasoning and deductive reasoning complement each other. Before proving a theorem, you must guess.

To discover the content of a proposition, before it is fully proved, we must constantly test, improve and modify the conjecture put forward, and we must also speculate on the idea of proof. The essence of rational reasoning is:? Found a guess? . Newton has long said; ? Without bold guesses, there is no great discovery. ? As early as 1953, the famous mathematics educator Paulia put forward: Let's guess. Test first, then prove. This is the way to find most things? . Therefore, in mathematics learning, we should also attach importance to the intuitive exploration and discovery of thinking, that is, to the cultivation of mathematical reasoning ability. The perceptual reasoning ability in mathematics can be roughly divided into the following four aspects: 1. Properly create situations and guide students to observe rational reasoning, instead of blindly guessing. Based on some known facts in mathematics, it guides students to observe and create situations by selecting appropriate materials. Euler once said: Mathematics is a science that needs observation and experiment. Observation is the gateway for people to know the objective world. Observation can mobilize students' various senses, generate associations on the basis of existing knowledge, and reduce the blindness of guessing through observation. At the same time, observation is also an important ability of people. Therefore, students should be given necessary time and space to observe, cultivate good observation habits, improve observation ability and develop reasonable reasoning ability in teaching.

For example, put the six numbers 20, 265, 438+0, 22, 23, 24 and 25 in six circles respectively, so that the sum of the three numbers on each side of the triangle is equal. By observing the figure and these six numbers, we should think that the larger number or the smaller number cannot be on one side of the triangle at the same time, otherwise the sum will be too big or too small, that is to say, we can put the smaller three numbers on the three vertices respectively, and then put the larger three numbers on the corresponding opposite sides.

Second, carefully design experiments to stimulate students' thinking. Gauss once mentioned that many of his theorems were discovered through experiments and induction and proved to be only auxiliary means. In mathematics teaching, the correct and appropriate application of mathematics experiments is also the need of implementing quality education at present. George Polya, a famous mathematics educator, once pointed out that mathematics has two sides. On the one hand, it is Euclid's rigorous science. From this perspective, mathematics is like a systematic deductive science. On the other hand, mathematics in the process of creation is more like an experimental inductive science? From this point of view, mathematical experiments play an important role in stimulating students' innovative thinking.

Third, carefully design questions to stimulate students to guess. Mathematical conjecture is reasonable reasoning in mathematical research and the premise of mathematical proof. Only by guessing mathematical problems can we stimulate students' interest in solving problems and inspire their creative thinking, so as to find and solve problems. Mathematical conjecture is a specious judgment of unknown quantity and its law on the basis of existing mathematical knowledge and facts, and it is the embodiment of scientific hypothesis in mathematics. Once proved, it will rise to mathematical theory. Without bold speculation, there will be no great discovery. Mathematicians pass? Ask questions? Analyze the problem? Guess? Inspection certificate? Open up new fields and create new theories. In middle school mathematics teaching, the discovery of many propositions, the derivation of nature, the formation of ideas and the creation of methods can be obtained through mathematical conjecture. It is not only helpful for students to master knowledge firmly, but also helpful for cultivating their reasoning ability.

In a word, cultivating students' rational reasoning ability in mathematics teaching can improve teaching efficiency, increase the interest of classroom teaching, optimize teaching conditions and improve teachers' teaching level and professional level. For students, it can not only help them learn knowledge and solve problems, but also help them master the thinking method of how to deal with new problems when they arise.

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