How to improve junior high school mathematical thinking, eight thinking methods of junior high schoo

The eight thinking methods in junior high school mathematics are as follows:1. Abstract thinking.

2. Logical thinking.

3. Combination of numbers and shapes.

4. Classification discussion.

5. Equation thinking.

6. Universal thinking.

7. Dig deep into your thinking.

8. Naturalized thinking.

Through the complete analysis and research of the textbooks, we can clarify and grasp the system and context of the textbooks, and control the overall situation of the textbooks. Then, the interface relationship between various concepts, knowledge points or knowledge units is established, and their special properties and internal general laws are summarized and revealed. Further determine the combination point between mathematical knowledge and its thinking methods, establish a set of rich teaching examples or models, and finally form an active knowledge and thought interconnection network.

1. Conduct analogical thinking ability training.

Analogy is a way of thinking that guesses that some of the same or similar properties of two or two classes of things may also be the same or similar in other properties. Analogy is the most common method of scientific research.

There are many contents that can be used for analogical thinking training in junior high school mathematics textbooks.

For example, the derivation method of the multiplication rule of the same base power is used to study the multiplication rule of the power of the same base, and the division rule of the power of the same base; Factor factorization of analogous integers studies the factorization of polynomials; Analogous to the solution of binary linear equations, and study the solution of ternary linear equations;

The concept, properties, and operations of analogous fractions, the concepts, properties, and operations of fractions; The law of analogy merges the same term to study the addition and subtraction of quadratic radicals; The area formula of the triangle is analogous to the area formula of the sector to study the area formula; Analogy with the positional relationship between a straight line and a circle, the study of the positional relationship between a circle and a circle, and so on.

2. Carry out inductive thinking ability training.

Induction is the method of thinking that studies a number of individuals of a certain thing, discovers the common properties between them, and then deduces from this that the totality of such things also has this nature. There are also many contents in junior high school mathematics textbooks that can be used for inductive thinking training. Almost all of the inductions of the arithmetic rules of junior high school algebra are based on general induction.

From a subjective point of view, the thinking of junior high school students has not yet entered the stage of logical thinking, and it is impossible to give strict logical proofs when teaching these laws.

Objectively, this is a good time to train students in their inductive thinking skills. For example, the rules of addition, subtraction, multiplication and division of rational numbers, the exchange rate, the binding rate, the distribution rate, the rules of adding brackets and removing brackets for rational number operations, the rules of operation of powers of the same base, the relevant rules of integer multiplication and division, and the introduction of the basic properties of inequalities.

In addition, the relationship between the roots and coefficients of the unary quadratic equation can be explored and discovered by induction. The study of the image and properties of functions is based on the images and properties of individual specific functions, and the inductive method is also used.

1. Find the breakthrough point for the cultivation of mathematical thinking ability. The qualities of thinking include the profundity, agility, flexibility, criticality and creativity of thinking, which reflect the characteristics of different aspects of thinking, so there should be different means of cultivation in the teaching process.

2. Teach students how to think. Mathematical concepts and theorems are the basis of reasoning, argumentation and operation, and an accurate understanding of concepts and theorems is the premise of learning mathematics well.

3. Be good at mobilizing students' inner thinking ability. It is necessary to cultivate interest and let students burst into thinking. Teachers should carefully design each lesson to stimulate students' thinking and desire for knowledge, and often guide students to use the mathematical knowledge and methods they have learned to explain practical problems that they are familiar with. Laugh quietly.

Tease with lack of distraction are some ways to exercise the mathematical thinking of junior high school students:

Doing math problems: Mathematics is a subject that requires continuous practice, and by doing math problems, you can improve the mathematical ability and thinking ability of high school students, and exercise their problem-solving ability.

Cultivating Logical Thinking: Mathematics is a rigorous discipline that requires rigorous logical thinking skills. Logical thinking can be cultivated through methods such as reasoning, analysis, and induction.

Improve mathematical language skills: Mathematics is a special language, and students need to master the vocabulary, symbols, and expressions commonly used in mathematics in order to better understand and solve problems.

Pay attention to the accumulation of mathematical background knowledge: Mathematics is a subject that needs to be built on the basis of rich background knowledge, and students need to understand relevant mathematical knowledge and concepts in order to better master mathematical thinking.

Organize math activities: Some math games, math competitions and other activities can be organized so that students can learn and exercise math thinking in a relaxed and happy atmosphere. For example, Sudoku, math quizzes, team competitions, etc.

Guide students to learn independently: Mathematics is a subject that requires continuous thinking and excellence, and teachers can guide students to actively think about problems, find ways and ideas to solve problems, so as to improve their mathematical thinking ability.

1. Learn the basic knowledge of mathematics: The basic knowledge of mathematics is the basis for cultivating mathematical thinking ability. Middle school mathematics includes algebra, geometry, mathematical analysis, etc., and requires mastery of various mathematical concepts, formulas, and theorems.

Develop an interest in mathematics: Learning mathematics requires interest. Teachers, parents, and students themselves should all strive to create a positive, challenging, and fun learning environment. You can find interesting math problems, games, experiments and other ways to cultivate students' interest in mathematics.

2. Solving practical problems: Applying mathematics to practical problems can enable students to understand the essence of mathematics more deeply. For example, calculate area, volume, and so on.

In the process of solving problems, students learn important mathematical thinking skills such as how to observe, ask questions, propose solutions, and verify solutions.

Improve mathematical computing ability: The foundation of mathematical thinking ability is the ability to calculate. In junior high school, students need to master basic mathematical calculation methods, including oral arithmetic, columnar calculation, and the use of calculators.

These basic skills are a necessary prerequisite for further development of mathematical thinking skills.

3. Do more math problems: Mathematical thinking ability requires continuous training and practice. Doing more math problems can improve students' mathematical thinking skills.

To allow students to choose the right questions for themselves according to their level, not only do the problems in the workbook, but also try to solve other ** math problems.

4. Cultivate mathematical thinking ability: Mathematical thinking ability includes abstract thinking ability, logical thinking ability, spatial thinking ability, innovative thinking ability, etc. These abilities can be developed in the learning process of middle school mathematics.

For example, visualizing abstract concepts, building mathematical models, analyzing problems from multiple perspectives, trying to discover different solutions to problems, etc.

1. The method of combining numbers and shapes, the idea of combining numbers and shapes is to say that the problem of numbers can be solved by analyzing graphs, and the problem of shapes can also be thought about through the study of numbers.

2. The method of naturalization of thought, which means that when solving practical problems, it is often necessary to carry out equivalent conversion, transform unfamiliar topics into familiar topics, and summarize the laws of things through special to general, and can carry out appropriate variation and deformation.

3. Categorical discussion of ideas, and discussion of ideas by situation is the ideological method that needs to be divided into several situations to study the problem under study when a problem cannot be continued with a unified method.

4. Function and equation thinking method, function and equation thinking is to learn to use variables and functions to think about some mathematical problems, and learn to transform the relationship between the unknown and the known.