The core connotation of integrated thinking: 1. Integrating and constructing knowledge system. The arrangement of junior high school mathematics textbooks follows the law that mathematical knowledge is the bright line and mathematical thinking method is the dark line. Teachers should proceed from the formation and development law of knowledge system structure and students' cognitive structure, grasp and deal with teaching materials from a global perspective, and guide students to fully grasp the knowledge structure and model structure of mathematics. By guiding students to organize themselves, review and reproduce mathematical knowledge, integrate scattered mathematical knowledge into a whole, expand and extend the cognitive structure, so that students' mathematical knowledge system is organized and systematic, and their comprehensive application ability is improved. Second, accurate analysis, improve thinking ability Mathematical thinking is the reorganization of cognitive structure caused by the interaction of students' old and new knowledge, activity experience and mathematical information. From the reality of life to mathematical problems, from simplicity to complexity, from the initial cognition of single knowledge to the comprehensive analysis of practical problems, it is essential in the process of forming systematic thinking. 1. Accurate attribution and perfection of cognitive structure based on experience. If the cognitive structure is defective, it will hinder the formation of systematic thinking. A complete and orderly cognitive structure helps to form systematic thinking. Therefore, in teaching, we should accurately attribute and take effective measures to improve students' ability to solve problems. For example, a student will not learn new content after an hour or two. Teachers think that students' understanding ability is poor and they don't understand the connotation and extension of knowledge, so the focus of training for a long time is to improve students' understanding ability; Parents mistakenly believe that their children's talent is insufficient and can't be compensated. The author tries to explain the following question to children: What is the minimum value of |x+ 1|+|x-2| when X is in what range? And find the minimum value. Connecting with the number axis, this paper explains the geometric meaning of absolute value, so that it can better understand the essence of this problem: when X is in what range, the sum of the distances from X to-1 and 2 is the smallest. However, the next day, students will not be able to test such questions. According to the requirements of systematic thinking, the author finds that the student can successfully complete the preparation stage, but lacks pattern recognition and memory in the analysis stage. After being reminded that he had done this kind of problem, he solved it smoothly at once. Secondly, the author trained the students in memory effectively. It can be seen that systematic thinking can play a correct attribution role in solving mathematical problems. 2. The combination of numbers and shapes is based on deepening the ability of method construction. Life prototype is a realistic material supported by activity experience, which is convenient for forming mathematical problems and for students to wander in the empirical world and the mathematical world and establish mathematical models. In the teaching process, teachers should actively create situations that are easy to construct knowledge, absorb the information and experience needed to solve mathematical problems, stimulate students to change their thinking from number to shape, and improve their cognitive structure.
For example, when reviewing "Elementary Function", the teacher designed the following problem groups: ① When x=0, find the value of the algebraic expression -2x+4; ② Solving equation:-2x+4 = 0; ③ Solve the following inequality:-2x+4 >; 0，-2x+4 & lt； 0。 Please solve the following problems according to the above information: ① Find the coordinates of the intersection of the function y=-2x+4 and the coordinate axis; ② Find the perimeter and area of the triangle surrounded by the linear function y=-2x+4 and the coordinate axis; ③ When y < 0, y=0 and y >; 0, find the range of independent variable x; ④ When -2
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The core connotation of integrated thinking
Zhiyang library
The core connotation of integrated thinking
First, the overall container, building a knowledge system.
The arrangement of junior high school mathematics textbooks follows the law that mathematical knowledge is the bright line and mathematical thinking method is the dark line. Teachers should proceed from the formation and development law of knowledge system structure and students' cognitive structure, grasp and deal with teaching materials from a global perspective, and guide students to fully grasp the knowledge structure and model structure of mathematics. By guiding students to organize themselves, review and reproduce mathematical knowledge, integrate scattered mathematical knowledge into a whole, expand and extend the cognitive structure, so that students' mathematical knowledge system is organized and systematic, and their comprehensive application ability is improved.
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Second, accurate analysis, improve thinking ability
Mathematical thinking is the reorganization of cognitive structure caused by the interaction between old and new knowledge, activity experience and mathematical information. From the reality of life to mathematical problems, from simplicity to complexity, from the initial cognition of single knowledge to the comprehensive analysis of practical problems, it is essential in the process of forming systematic thinking.
1. Accurate attribution and perfection of cognitive structure based on experience.
If the cognitive structure is defective, it will hinder the formation of systematic thinking. A complete and orderly cognitive structure helps to form systematic thinking. Therefore, in teaching, we should accurately attribute and take effective measures to improve students' ability to solve problems.