Mathematical thought is abstracted from some concrete mathematical cognitive processes, and its correctness has been repeatedly proved in subsequent cognitive activities, which has the characteristics of universal significance and relative stability. It reveals the universal law of the development of mathematics, plays a guiding role in the development of mathematics, directly dominates the practical activities of mathematics, and is the soul of mathematics. Engels described in the introduction of Dialectics of Nature that Descartes formulated analytic geometry, Naipur formulated logarithm, Leibniz and Newton formulated calculus, and pointed out that "the most important mathematical method has been basically determined". For mathematics, it can be said that the most important mathematical thought has also been basically determined. Therefore, in teaching, teachers must not think that cultivating students' mathematical thinking methods is to imprison students' thinking, and treat the precious thinking methods accumulated in historical practice as a hot potato and dare not touch them at all. On the contrary, they should regard it as a better and more efficient means and method to support students' independent and cooperative inquiry, especially primary school students, whose thinking is divergent, but the methods to solve problems are limited. In teaching practice, it is often difficult for students to find effective methods. I think the reason is that students still need guidance in solving problems. When we ask students to explore knowledge, it doesn't mean that even methods should be explored together. To some extent, guiding exploration is an efficient and high-quality educational means. For example, teaching the lesson "area calculation of parallelogram" will guide students to get the area calculation formula of parallelogram through splitting and splicing, and then guide students to recall, reflect and summarize the thinking method of equivalent transformation in the learning process; Students consciously use these mathematical thinking methods to solve problems when they continue to learn the area calculation of plane geometric figures such as triangles and trapezoid.
Second, explain the necessity of infiltrating mathematical thinking methods.
The standard points out: "Students can acquire important mathematical knowledge (including mathematical facts and experience in mathematical activities), basic mathematical thinking methods and necessary application skills through mathematics learning in compulsory education, so as to adapt to future social life and further development." It can be seen that the purpose of students learning mathematics is no longer simply to "accept mathematical knowledge" as the core, but to acquire some necessary mathematical ideas and methods.
In cognitive psychology, thinking method belongs to the category of metacognition, which plays a monitoring and regulating role in cognitive activities and plays a decisive role in the cultivation of ability. The purpose of learning mathematics "is to solve problems" (in Polish). The key to solving problems lies in finding suitable problem-solving ideas, and mathematical thinking methods are the guiding ideology to help build problem-solving ideas. Therefore, it is an important way to cultivate students' ability to analyze and solve problems by infiltrating some basic mathematical thinking methods into students and improving their metacognition level.
In addition, although mathematical knowledge itself is very important, it is not the only decisive factor. What really plays a long-term role in students' future study, life and work and benefits them for life is the mathematical thinking method. The future society will need a large number of talents with strong mathematical consciousness and quality. 2/KLOC-0 The fundamental goal of international mathematics education in the century is "problem solving". Therefore, it is the requirement of the future society and the inevitable result of the development of international mathematics education to infiltrate some basic mathematical thinking methods into students.
The fundamental task of primary school mathematics teaching is to improve students' quality in an all-round way, among which the most important factor is the quality of thinking, and the mathematical thinking method is the key to enhance students' mathematical concepts and form good thinking quality. If students' mathematical quality is regarded as a coordinate system, then mathematical knowledge and skills are like factors on the horizontal axis, and mathematical thinking method is the content on the vertical axis. Weakening or neglecting the teaching of mathematical thinking methods will not only hinder students from grasping the basic structure of mathematics from both vertical and horizontal dimensions, but also affect the development of students' ability and the improvement of mathematics quality. Therefore, infiltrating some basic mathematical thinking methods into students is a new perspective of mathematics teaching reform and a breakthrough of mathematics quality education.
Third, how to scientifically and reasonably infiltrate mathematical thinking methods.
1, teachers are sensitive and conscious.
Mathematical concepts, laws, formulas, properties and other knowledge are clearly written in the textbook, with a "shape", while mathematical thinking methods are implicit in the mathematical knowledge system, without a "shape", and are scattered in all chapters of the textbook systematically. Teachers don't talk, talk more and talk less, which is arbitrary. They often squeeze it out as a "soft task" because of the tight teaching time. The requirement for students is to calculate as much as they can. Therefore, as a teacher, we should first renew our ideas, constantly improve our understanding of the importance of infiltrating mathematical thinking methods, integrate both mastering mathematical knowledge and infiltrating mathematical thinking methods into teaching purposes, and integrate the requirements of teaching mathematical thinking methods into lesson preparation. Secondly, we should study the teaching materials deeply and try our best to find out all kinds of factors that can penetrate mathematical thinking methods. For each chapter and section, we should consider how the specific content permeates mathematical thinking methods, which mathematical thinking methods permeate, how to permeate, and to what extent. It is necessary to have an overall design and put forward specific teaching requirements at different stages.
2. Teachers grasp the feasibility of infiltration.
Mathematical thinking methods and some thinking strategies are always included in learning activities. For example, Cao Chong's image weighing process contains the mathematical thought of equivalent transformation, and Sima Guang's smashing cans contains the thinking strategy of reverse thinking. In students' learning activities, some mathematical thinking methods (such as analogy, association, statistics, correspondence, etc.) will also be used. ), but they may only use it this time. Therefore, we must grasp the opportunity of teaching mathematical thinking methods in the teaching process-the process of concept formation, conclusion derivation, method thinking, thought exploration and law revelation. At this time, I will guide students to reflect and summarize, help students understand the mathematical thinking methods used in learning activities, and let children master the golden key to learning mathematics, thus opening the door to the kingdom of mathematics more smoothly. At the same time, we should pay attention to the organic combination and natural infiltration in the teaching of mathematical thinking methods, consciously and imperceptibly inspire students to understand all kinds of mathematical thinking methods contained in mathematical knowledge, and avoid the counterproductive practices such as mechanically copying, generalizing and being divorced from reality.
3. Teachers pay attention to the repetition of infiltration.
Mathematical thinking method is gradually accumulated and formed in the process of enlightening students' thinking. Therefore, in teaching, we should first emphasize "reflection" after solving problems, because the mathematical thinking method refined in this process is easy for students to understand and accept. For example, through the regular comparison of scores and percentages, guide students to sum up the main points of solving such application problems, find the scores corresponding to specific quantities, and let students experience the corresponding ideas and reduction ideas themselves. Secondly, we should pay attention to the long-term nature of infiltration. It should be noted that the infiltration of students' mathematical thinking methods can not see the improvement of students' mathematical ability overnight, but a process. Mathematical thinking methods must be trained step by step and repeatedly, so that students can really understand.
Fourth, examples of infiltrating mathematical thinking methods
Dynamic classroom teaching is a teaching form actively advocated by the new curriculum reform, and inquiry is the lifeline of dynamic classroom teaching. The teaching method of inquiry for inquiry mentioned at the beginning of the article obviously does not meet the requirements of curriculum reform. As a teacher, we must find a necessary, scientific, natural and easy method for primary school students to explore. The author thinks that timely infiltration of mathematical thinking methods can greatly improve the efficiency of inquiry.
Throughout the ages, there are countless mathematical thinking methods, and each mathematical thinking method shines with the spark of human wisdom. One is that some mathematical thinking methods are difficult to accept because of the age characteristics of primary school students, and the other is that it is unrealistic to infiltrate so many mathematical thinking methods into primary school students. Therefore, we should selectively infiltrate some mathematical thinking methods to promote students' effective inquiry. The following mathematical thinking methods are not only easy for students to accept, but also have a good role in promoting the improvement of students' mathematical ability.
Example 1: Turn to thinking, and first closely link life with mathematics.
I listened to a lesson given by our school's third-grade teacher Zhou Meiqin-revealing the secrets of even and odd numbers. The teaching process begins with the practical problem-roulette game. There is a number of 10 on the turntable, odd numbers have big prizes and even numbers have small prizes. Rules of the game: turn the turntable, the pointer points to several squares, and then count down several squares from the next one, and the prize in that one is yours. Students naturally have questions after playing by themselves. They always wanted to win the grand prize, but they couldn't get it. What is the reason? Thus, the process of finding problems from life practice is realized, and the students' desire to solve problems is also stimulated. Through observation, independent thinking and group discussion, let students focus on the problem of even and odd numbers, and gradually turn the actual problem into a problem of even and odd numbers. Thus, the direction that students will explore is clarified and the learning efficiency is improved. The idea of transformation can turn a practical problem into a mathematical problem and a more complicated problem into a simple one through some transformation. Its basic characteristics are indirectness, reversibility and simplicity. The turntable problem has these three basic characteristics. This idea of reduction is also one of the manifestations of mathematical ability.
In the process of listening to the class, the author once thought about whether it is necessary for students to learn knowledge and improve their ability to solve problems. In fact, the mathematical knowledge in roulette is not profound, and it can be mastered by examples. However, after careful consideration, the author thinks that if the teacher simply takes out the question directly, the question will appear unfounded and meaningless. Depriving students of the right to practice perception is counterproductive to the cultivation of students' thirst for knowledge and questioning thinking. The class is a failure from the beginning, which will inevitably affect the quality of the whole class. )