How to effectively infiltrate mathematical thinking methods in the process of primary school mathematics teaching
If mathematics originated from the need of human survival, or from the need of human rational exploration of truth, then mathematical thinking method is accompanied by the emergence and development of mathematics. It is not only the essence of mathematics, but also the soul of mathematics teaching, an important aspect of embodying the essence of mathematics and the main basis for evaluating mathematics teaching. Therefore, in the process of primary school mathematics teaching, strengthening the infiltration of mathematical thinking methods will help teachers to deeply understand the content of mathematics, enhance students' mathematical concepts and consciousness, and form students' good thinking quality. Let's pay attention to mathematical thinking methods from the perspective of teaching process, and exchange some immature and incomplete understandings and opinions. 1. In the process of presenting knowledge, timely penetrate mathematical thinking methods. For mathematics, the process of knowledge is actually the process of thinking method. Therefore, the process of concept formation, conclusion derivation, method thinking, problem discovery, law revelation and so on. They all contain excellent opportunities to infiltrate mathematical thinking methods and train thinking. For students, the most common sources of difficulties are: a job, a discovery, a rule, ... rarely appear in the form used by the founder at first, but they have been condensed, hiding the tortuous and complicated thinking process and presenting rigorous, abstract and refined conclusions, while the thinking method that led to its birth is often hidden in the internal form and becomes an "internal river" with potential value in the mathematical structure system. An important task of our teaching work is to unveil the rigorous and abstract veil of mathematics, give students vivid teaching in the process of discovery, and let students personally participate in the process of "knowledge rediscovery", experience the tempering of exploration, and learn more thinking nutrition. For example, when teaching the area of a circle, students should be guided to recall the previous methods for calculating the area of parallelogram, triangle and trapezoid, and then transform the circle into a rectangle, so as to deduce the formula for calculating the area of the circle. We turn the problems to be solved into solved or easily solved problems in some ways, and finally solve the original problems. This kind of teaching activity makes students experience the process of knowledge formation, permeates the mathematical thought of reduction and limit, and plays a very important role in subsequent learning. 2. In the exploration of problem-solving ideas, the classroom teaching of mathematical thinking methods should be properly infiltrated, and students are the masters of learning. In the process of learning, we should guide students to actively participate, personally find problems, solve problems and master methods. In fact, the study of mathematical thinking method is no exception. In mathematics teaching, the process of exploring the thinking of solving problems is one of the most basic forms of activities, and the process of solving mathematical problems is the process of experiencing and acquiring mathematical thinking methods personally, and also the process of deepening understanding and understanding through application. For example, when solving the problem of "chickens and rabbits in the same cage", some students were at a loss when they first read the problem. At this time, teachers need to guide students to replace the large quantity in the original title of Sun Tzu's Art of War with a small quantity that is easy to explore, which is permeated with the thinking method of conversion; Solving problems by list method permeates the thinking method of function; Using arithmetic to solve problems permeates the hypothetical thinking method; Solving problems by equation method is permeated with algebraic thinking method; When sorting out the methods, we show stick figures with courseware to help students understand various algorithms. The thinking method of combining numbers and shapes is infiltrated, so that the infiltration of mathematical thinking method is closely combined with knowledge teaching to help students master the correct problem-solving methods and improve their divergent thinking ability. 3. In solving practical problems, it is the core of mathematics to flexibly penetrate mathematical thinking methods to solve problems. Students not only master and consolidate the basic knowledge of mathematics through solving problems, but also cultivate and develop students' mathematical ability because they focus on the whole process of solving problems. Teachers should guide students to solve problems, not solve problems for the sake of solving problems, but ignore the display of thinking process. In the process of solving problems, they should reveal the general thinking method of solving similar problems in the subsequent problem-solving activities. Therefore, it is necessary to strengthen the awareness of mathematical application, encourage students to analyze and solve practical problems in life by using mathematical thinking methods, guide students to abstract, summarize and establish mathematical models, and explore ways to solve problems, so that students can abstract practical problems into mathematical problems in the process of applying mathematical knowledge to solve practical problems, and further penetrate and understand mathematical thinking methods. For example, buses and trucks travel in opposite directions from the midpoint of two towns. Three hours later, the bus arrived in a town, and the truck was 30 kilometers away from b town. As we all know, the speed of freight cars is 3/4 of that of passenger cars. How many kilometers is it between town A and town B? Analysis: From the meaning of the question, we can see that the bus walked half in three hours, and the truck walked half in three hours, which was 30 kilometers less. If the distance between the two towns is Z kilometers, according to "the speed of freight cars is 3/4 of the speed of passenger cars", an equation can be drawn: most students choose this method. The teaching can't stop here, and continue to guide students to think in another way: change the known condition that "the speed of trucks is 3/4 of the speed of buses" into the narrative mode that "the speed ratio of trucks to buses is 3: 4". Because of the same driving time, the distance ratio between the truck and the bus is 3: 4, that is, the truck travels three times, the bus travels four times, and the truck travels less than the bus 1 time, 30 kilometers less. In this way, through transformation, students can realize that fractional application problems can also be solved by integer method, that is, proportional application problems can be solved, thus consolidating and improving students' ability to solve fractional application problems. More importantly, students can feel that the transformation method can simplify the complex, help cultivate the flexibility of thinking and overcome the rigidity of thinking. In fact, some thinking methods are often used in solving mathematical problems, such as the combination of numbers and shapes, transformation, symbolization and so on. Proper use of these thinking methods can not only improve the efficiency of solving problems, but also stimulate students' strong thirst for knowledge and creative spirit.