How to develop your thinking quality in high school math problem training

The quality of thinking].

1) The profundity of thinking: refers to the depth of thinking, which is concentrated in whether it is good at thinking deeply, grasping the law and essence of things, and meeting the development and process of things.

2) The breadth of thinking: It refers to looking at the problem from the connection of all aspects of things based on rich knowledge and experience.

3) Agility of thinking: refers to the speed or rapidity of the thinking process, that is, the thinking quality of people to make decisions and solve problems quickly in a short period of time.

4) Flexibility of thinking: refers to the degree of improvisability to think about problems and solve problems.

5) Originality of thinking: whether it is good at analyzing and solving problems independently.

6) Critical thinking: good at criticizing the ideas and achievements of others and oneself.

7) Logical thinking: It refers to the clear thinking, clear organization, and strict compliance with logical laws when considering and solving problems. [Central Link].

Cultivate students' thinking qualities.

1) Strengthen the training of scientific thinking methods;

2) Use heuristic methods to emphasize the enthusiasm and initiative of students' thinking;

3) Strengthen verbal communication training;

4) play a positive role in the stereotype;

5) Cultivate students' thinking quality in solving practical problems.

Functions and equations thinking method.

Functions and equations are the core knowledge of the whole high school mathematics and play a pivotal role in high school mathematics. The essence of the idea of function is to use the viewpoint of motion and change to analyze and study the quantitative relationship in mathematics, to present the quantitative relationship between variables in the problem in the form of a function, and to solve the problem with the help of the image of the function. The idea of function is also reflected in the understanding of the essence of the concept of function and the grasp of properties, and the good use of function perspective to observe, analyze and solve problems.

The essence of equation thinking is to use the viewpoint of equations to analyze and study the equiquantitative relationship between variables in a problem, and present it in the form of equations or systems of equations. The solution of the problem is achieved with the help of the properties of equations or systems of equations, which embodies the idea of seeking stillness in motion and studying the relationship between equal quantities in motion. Therefore, in teaching, teachers should combine the characteristics of knowledge, start from the actual cognitive level of students, and focus on cultivating students' ideas of functions and equations, so that they can firmly grasp the properties and function images of various functions, and be able to solve mathematical problems with the help of them.

At the same time, teachers should also actively guide, inspire and induce students to discover and explore problems by themselves, be good at using the idea of functions and equations to present the quantitative relationship between variables in mathematical problems, express them with accurate and reasonable equations or functions, and use equations or functions to achieve the final solution of problems. In this way, students can develop a good sense of application of functions and equations and improve their problem-solving skills through continuous practice.

How to develop logical thinking ability in high school mathematics.

Combination of numbers and shapes, thinking methods.

The combination of numbers and shapes is an extremely important method of thought throughout the whole high school mathematics, which is mainly reflected in the two aspects of "using form to help numbers" and "using numbers to help forms". Its advantages are: students can use the vividness and intuitiveness of graphics to understand the abstract mathematical language or mathematical expressions in textbooks, and then grasp the essence and connotation of knowledge (that is, using graphics as a means and numbers as the purpose); At the same time, through the accuracy of numbers, the standardization and rigor of mathematical expressions, some attributes, characteristics and changes of images are revealed, which is conducive to the training of students' abstract thinking and flexibility, agility, divergence and profundity of three-dimensional thinking (i.e., using numbers as means and graphics as goals).

In the process of classroom teaching, students should first focus on grasping and understanding the concepts in the textbook, the geometric meaning represented by the operation and the algebraic characteristics of curves, and will analyze the conditions and conclusions in the exercises from the aspects of geometric meaning and algebraic meaning. Master the application method of parameters, and be able to properly set parameters, use parameters reasonably, and correctly determine the value range of parameters in combination with reality. Secondly, according to the cognitive level of students, teachers should actively and effectively guide students by creating appropriate problem situations, so that students can personally participate in mathematical problems, analyze mathematical problems, and solve mathematical problems, and pay attention to the penetration of the combination of numbers and shapes in the guidance process. In this way, it can not only cultivate students' good thinking quality, but also help stimulate students' interest in mathematics learning.