2. The combination of numbers and shapes. The idea of the combination of number and shape is to make full use of "shape" to express a certain quantitative relationship vividly. That is, by making some graphs such as line segment, tree diagram, rectangular area diagram or set diagram, students can correctly understand the quantitative relationship and make the problem concise and intuitive. If there are many travel problems, students can clearly perceive the relationship between the total distance, the distance traveled and the remaining distance by using the line graph. Another example is the solution of fractional application problems, in which the relationship between the whole and the part is represented by a circle diagram or a line segment diagram, so that students can answer questions at a glance and understand clearly, which greatly improves their thinking and imagination.
3. Classified thinking method. The idea of classification is also an important way to train primary school students. The general classification requires the principles of mutual exclusion, no omission and simplicity. For example, if it is divisible by 2, integers can be divided into odd and even numbers; If we classify natural numbers by divisors, they can be divided into prime numbers, composite numbers and 1. Classification in geometry is more common. For example, when learning "angle classification", many concepts are involved, and the relationship between these concepts cultivates the law of quantitative change to qualitative change. Several angles are classified according to the degree, from quantitative change to qualitative change, and it is inferred that the largest angle in the triangle is greater than, equal to and less than 90, which can be divided into obtuse triangle, right triangle and acute triangle. Triangle can be divided into equilateral triangle and equilateral triangle, and equilateral triangle can be divided into equilateral triangle and isosceles triangle. Through classification and knowledge network construction, different classification standards will have different classification results, thus generating new mathematical concepts and the structure of mathematical knowledge.
4. Set the way of thinking. Modern classroom teaching should not only impart knowledge to students, but more importantly, consciously cultivate students' collective ideas contained in textbooks, which is conducive to cultivating students' abstract generalization ability and improving students' ability to analyze and solve problems. For example, in the teaching classification, some animals, plants and geometric figures with the same attributes are circled into a whole with a "circle" (closed curve), and this whole is a collection. When seeking the greatest common divisor of 8 and 12 in teaching, courseware or slides can be made to let students know clearly and intuitively that the common divisor of 8 and 12 is 1, 2 and 4, and the greatest common divisor is 4, thus breeding the idea of intersection.
5. Turn to the way of thinking. That is, when solving mathematical problems, we don't directly attack the problems, but adopt circuitous tactics to turn the problems to be solved into some solved problems through deformation, thus solving the original problems. Its basic forms are: turning difficulty into ease, turning life into maturity, turning complexity into simplicity, turning the whole into parts, turning music into straightness and so on. In primary school mathematics, there are all kinds of contents that can be answered by induction, so that students can learn inductive thinking methods initially. For example, to teach the calculation method of circular area, we should deduce the formula of circular area. In the process of derivation, we divide the circle into several equal parts, and then spell it into an approximate rectangle, thus deriving the formula of circle area. The process of splicing circular scissors into approximate rectangles here is the process of turning curves into straight lines.
6. Modeling thinking method. The so-called mathematical model is the mathematical structure of a specific research object in the real world, which is expressed in mathematical language after some necessary simplification and assumptions for a certain purpose. The idea of mathematical modeling is a mathematical idea and method to find, put forward and understand the unsolved or unsolved problems in the real world from the mathematical point of view, and simplify them into a kind of solved or easy-to-solve problems through the transformation process, and comprehensively apply the learned mathematical knowledge and skills to solve them.
Second, how can I cultivate students' mathematical thinking?
Combined with my own teaching practice, I will share with you how to cultivate and develop students' various mathematical ideas in my teaching practice:
First, pay attention to the training in the process of knowledge formation. Mathematical concepts, rules, formulas, properties and other knowledge. All of them are clearly written in textbooks, which are tangible, while the mathematical thinking method is implicit in the mathematical knowledge system, which is intangible and scattered in all chapters of textbooks in an unsystematic way. Therefore, mathematical thinking method must be realized through specific teaching process. Therefore, in teaching, we should grasp the opportunity to teach students mathematical thinking methods in the teaching process, and always run through the formation process of each concept, the derivation process of each conclusion, the thinking process of solving each problem, the exploration of ideas and the revealing process of laws. And consciously and imperceptibly inspire students to understand all kinds of mathematical thinking methods contained in mathematical knowledge.
Secondly, we should pay attention to the training in the process of solving problems. Mathematical thinking method exists in the process of solving problems, and the gradual transformation of mathematical problems follows the guidance of mathematical thinking method. Cultivating mathematical thinking methods can not only speed up and optimize the process of solving problems, but also achieve the effect of knowing one problem and knowing all the way. Through training, students should try their best to internalize mathematical thinking methods and improve their ability to acquire knowledge and solve problems independently.
Thirdly, we should pay attention to the cultivation in the process of repeated use. Mathematical thinking method plays a vital role in solving learning key points, breaking through learning difficulties and solving specific mathematical problems. The process of solving these problems is always a process of repeatedly applying mathematical thinking methods. Therefore, it is conditional and possible to pay attention to the application of mathematical thinking methods from time to time, which is an effective and universal way to carry out the teaching of mathematical thinking methods. Mathematical thinking method can only be consolidated and deepened through repeated application.
In short, strengthening the cultivation and training of students' mathematical thinking methods is not only an inevitable requirement of curriculum standards, but also an important intellectual help for children to learn to learn. In normal classroom teaching, paying attention to the cultivation of students' mathematical thinking methods is not only conducive to improving classroom teaching efficiency, but also conducive to improving students' mathematical cultural literacy and thinking ability. However, we should also clearly realize that the cultivation of students' mathematical thinking method is not achieved overnight, and it needs a process. Therefore, in the teaching process, we should organically combine the contents of mathematics knowledge, so as to achieve persistent, step by step and repeated training, so that students can truly understand mathematical thinking methods.