The result of reasonable reasoning is accidental, but it is not completely fictional. It is an exploratory judgment based on certain knowledge and methods. 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 emphasized the rigor of reasoning, overemphasized the importance of logical reasoning and neglected vivid and reasonable reasoning, making 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, and rational reasoning and deductive reasoning complement each other. Before proving a theorem, you should guess and discover the content of a proposition. Before making a complete proof, you should constantly test, improve and modify the conjecture put forward, and you should guess the idea of proof. You should synthesize the observed results before making an analogy. You must try again and again. In this series of processes, what you need to make full use of is not argumentation reasoning, but reasonable reasoning. The essence of rational reasoning is "discovery-conjecture". Newton has long said: "Without bold guesses, there will be no great discoveries."
First, cultivate the rational reasoning ability in "Number and Algebra"
In the teaching of "number and algebra", there must be certain "rules" in calculation-formulas, rules, reasoning rules and so on. Therefore, there is reasoning in calculation, and the quantitative relationship in the real world often has its own laws. For algebraic operation, it requires not only knowing how to operate, but also knowing arithmetic, controlling the operation through reasoning, and telling the concepts, operation rules and rules involved in each step of the operation. Algebra can't just focus on skilled and correct operation. For example, the addition rule of rational numbers is obtained by incomplete inductive reasoning with the help of the east and west movement of points on the number axis. In teaching, we should not only pay attention to the memory and application of rules, but also ignore the thinking of generating rules. For another example, all the algorithms of addition and multiplication are put forward in the form of incomplete inductive reasoning. Paying attention to this reasoning process (though insufficient) can not only explain the rationality of the algorithm, but also strengthen the perceptual knowledge and understanding of the algorithm. For another example, junior high school textbooks introduce the knowledge of mathematical number axis through image analogy and thermometer reasoning. Another example is: find the absolute value |-5|=? |+5|=? |-2|=? |+2|=? |-3/2|=? |+3/2|=? From the above operation, what do you find is the relationship between the absolute values of opposites? And briefly describe it. Through this example, teaching can cultivate students' rational reasoning ability, combine the number axis, let students get in touch with the problem-solving method of combining number and shape, and let students understand the geometric meaning of absolute value; Another example: when learning algebraic multiplication, the textbook uses the area of the graph to get the relevant laws of algebraic multiplication from the whole and local calculation methods. In this intuitive mode of combining numbers and shapes, students can easily understand and express the contents of the law.
In teaching, every knowledge point in the textbook should be prepared for the rationality or inevitability of knowledge before it is put forward, and the reasoning and reasoning process should be fully demonstrated to gradually cultivate students' reasonable reasoning ability.
Second, cultivate the rational reasoning ability in "space and graphics"
In the teaching of "space and graphics", we should not only attach importance to deductive reasoning. We should also attach importance to rational reasoning. In the teaching of the new curriculum standard "Space and Graphics" in junior high school mathematics, it is pointed out: "Reduce the inherent knowledge requirements of space and graphics, strive to follow students' psychological development and learning rules, pay attention to intuitive perception and operation confirmation, and start from the reality that students are familiar with, let students do it, try it and think about it, know the main characteristics of graphics and the basic nature of graphic transformation, and learn to know different graphics; At the same time, it is supplemented by appropriate teaching guidance to cultivate students' reasonable reasoning ability. " It also provides students with more opportunities for "intuitive thinking". In the actual operation process, students should constantly observe, compare, analyze and reason to get the correct answer. Such as: triangle interior and 180? In teaching, students cut and assemble three internal angles and then measure them. It is found that the internal angle of triangle is equal to 180? ; Axisymmetric graphics, lines, bottom midline, high line overlap (three lines in one), etc. None of them have been proved in the textbook, so students can confirm their existence by origami; In the teaching of circle, combined with the axial symmetry of circle, the vertical diameter theorem and its inference are found; By using the rotational symmetry of a circle, the relationship among arc, chord and central angle in the circle is found. Through observation and measurement, the quantitative relationship between the central angle and the circumferential angle is found. Using intuitive operation, the positional relationships between points and circles, straight lines and circles, and circles and circles are obtained. Wait a minute. After students explore the nature of graphics through observation, operation and transformation, they should also prove the nature of discovery, so that intuitive operation and logical reasoning can be organically combined, and reasoning and argumentation can be a natural continuation of students' observation, experiment and exploration, and in the process, students' reasonable reasoning ability can be developed. Paying attention to the exploration process of graphic nature and the organic combination of intuitive operation and logical reasoning are also helpful to the formation of students' spatial concept, and the reasonable reasoning method provides the direction for students to explore.
Thirdly, cultivate reasonable reasoning ability in Statistics and Probability.
Reasoning in statistics is reasonable and possible. Different from other reasoning, the conclusion drawn by statistical reasoning can not be tested by logical reasoning, but can only be confirmed by practice. Therefore, the teaching of statistics and probability should pay attention to the whole process of collecting data, sorting out data, analyzing data, inferring and making decisions. For example, what fruit is the most popular when preparing for the New Year's Eve dinner? First of all, students should investigate what kind of fruits the whole class likes, then sort out the results of the investigation into data and compare them, and then make decisions according to the processed data to determine what fruits should be prepared. This process is reasonable reasoning, and the result can only satisfy most students.
Probability is a subject that studies the laws of random phenomena. In teaching, students will learn some basic properties and simple probability models through a large number of experiments, such as coin toss, turntable, touch ball, computer simulation, etc., combined with specific examples, so as to deepen their understanding of its rationality.
In a word, cultivating students' rational reasoning ability in mathematics teaching can improve classroom 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 how to deal with new problems when they arise. Therefore, we should say loudly to our children: make bold guesses and demonstrate carefully!