Mathematics thought in junior high school mathematics is a model essay I brought to you. Welcome to reading.

Abstract: Mathematics thoughts and methods are the essence of mathematics curriculum, and also the way to transform theoretical knowledge into practical ability.

At present, the thinking methods contained in junior high school mathematics curriculum mainly include: holistic thinking, inductive thinking, analogical thinking, dialectical thinking and so on.

Teachers should pay attention to cultivating students' mathematical thinking if they want to help students master learning methods and improve their mathematical literacy.

Keywords: mathematical thinking, junior high school mathematical method system

Mathematical thought is the understanding of the essence of mathematical knowledge and methods, the fundamental strategy to solve mathematical problems, and directly dominates the practical activities of mathematics; Mathematical thoughts and methods are the essence of mathematical knowledge and the bridge from knowledge to ability.

At present, in junior high school, the main mathematical thinking methods are: transformation thinking, equation thinking, classified discussion thinking, combination of numbers and shapes, etc.

First, change ideas.

So-called? Change your mind? It refers to a way of thinking that the problems to be solved or unsolved are reduced to problems that have been solved or are relatively easy to solve through transformation, and finally solve the problems.

In the process of mathematics learning, we often turn complex problems into simple ones and unfamiliar ones into familiar ones.

The process of solving mathematical problems is a series of transformation processes.

Transformation is a powerful means to simplify the complex, make the difficult easy and turn the unknown into the known. It is the most basic idea to solve problems and plays a positive role in improving students' ability to analyze and solve problems.

When learning the understanding of parallelogram and trapezoid, the understanding and learning of trapezoid can guide students to solve problems by making appropriate auxiliary lines, such as making the height of trapezoid, translating a waist or a diagonal to divide or supplement trapezoid into triangle and parallelogram.

As a result, unfamiliar new problems are transformed into familiar old problems, and difficult problems are transformed into easy problems.

Second, the idea of equation.

The so-called equation thought mainly refers to the thinking method of establishing equations (groups) to solve practical problems.

This way of thinking appears in a large number of textbooks, such as solving application problems with equations, finding the resolution function, and finding the value of letter coefficient by using the discriminant of roots and the relationship between roots and coefficients.

The educational value of equation modeling is embodied in two aspects: one is modeling, and the other is transformation.

The significance of students learning equations lies in: firstly, it is very difficult to abstract the most essential things from the complicated things in life, which is of great training value; The second is to follow the best way in operation and simplify complex problems. This optimization idea has a far-reaching impact on thinking habits.

In teaching, students can be consciously guided to find equivalence relations and establish equations.

Like talking? Determine the quadratic resolution function by undetermined coefficient method? Can inspire students to find that the key to determine the analytical formula is to find the coefficient, which can be regarded as three? Unknown quantity? Tell the students to solve with the idea of equation, and then the students will consciously find three equal relationships to establish the equation.

If you only explain the steps of doing the problem here, it will appear dull and stiff. Students only know what it is and don't know why.

Third, the idea of classified discussion.

? Classified discussion? It is a logical method, an extremely important mathematical thinking method in middle school mathematics and an important problem-solving strategy. When the problem studied contains many possible situations and cannot be generalized, it is necessary to discuss it according to the possible situations, so as to draw conclusions in various situations. This way of thinking to deal with problems is classified discussion thinking.

In recent years, it has been involved in the senior high school entrance examination questions in various places. Classified discussion? Problems are very common, because such problems not only examine our basic knowledge and methods of mathematics, but also examine the profundity of our thinking. When solving this kind of problems, we lose more points because of poor consideration. The main reason is that we lose more points in our usual study, especially in the review of the senior high school entrance examination. Classified discussion? In mathematics, when the objects given by the question cannot be studied uniformly, it is necessary to classify the research objects, then study each category separately and get the conclusion of each category, and finally synthesize the results of each category to get the answer of the whole question. Break the whole into parts, break them one by one, and then set zero as a whole? This method is called classified discussion.

1. Classification discussion is not only a logical method to solve problems, but also a mathematical idea, which is of great help to simplify the research object and develop people's thinking. Therefore, the mathematical proposition about classified discussion occupies an important position in the college entrance examination questions.

2. The so-called classified discussion means that when the objects given by the question cannot be studied uniformly, the research objects need to be classified according to certain standards, and then each category is studied separately, and the conclusions of each category are drawn. Finally, the answers to the whole question are obtained by synthesizing various results.

In essence, what is classified discussion? Break the whole into parts, one by one, and then add up to the whole? The mathematical strategy of.

3. Classification principle: the classification object is determined, the standard is unified, there is no repetition, no omission, and the discussion is conducted at different levels.

4. Classification method: clearly discuss the object, determine the overall object, determine the classification standard, and correctly classify; Discuss item by item and achieve phased results; Summarize and synthesize the conclusion.

Because the comprehensiveness of students' thinking is not perfect and they lack practical experience. In this way, students don't know from what aspects and angles to analyze and discuss problems in classification, which is a difficult point in the teaching process. Therefore, it is particularly important to cultivate students' classified thinking in the teaching process, that is, to introduce some necessary classified knowledge to students and guide them to discover, try and guide them.

Fourth, the idea of combining numbers with shapes.

? The number of missing shapes is not intuitive; It's hard to be nuanced, isn't it The combination of numbers and shapes is an important way of thinking in learning mathematics. It refers to a method that unifies the accurate description of algebra with the intuitive image of geometry and combines abstract thinking with intuitive thinking.

The idea of combining numbers with shapes runs through junior high school mathematics teaching.

The main contents of the combination of numbers and shapes are as follows: (1) Establish an appropriate algebraic model.

(2) Establish a geometric model to solve problems related to equations and functions.

(3) Algebraic and geometric synthesis problems related to functions.

(4) Application of presenting information in the form of images.

The key to solve the problem by combining numbers and shapes is to find the coincidence point of numbers and shapes.

If figures and shapes can be skillfully combined and effectively transformed into each other, some seemingly impossible problems will be solved and the result will be twice the result with half the effort

The combination of numbers and shapes is an important thinking method in mathematics, which combines abstract mathematical language with intuitive graphics to make algebraic problems geometric or algebraic, and provides a concise and clear way to solve problems.

In practice, we find that students often have no way to start when facing problems in the process of solving problems. At this time, if students can flexibly use the method of combining numbers and shapes, they can often find the trick to solve problems quickly.

In a word, in junior high school mathematics teaching, infiltrating mathematical thinking methods can overcome the problem-oriented topics and rigid models.

Mathematical thinking method can help us strengthen thinking analysis, seek the connection between the known and the unknown, improve our ability to analyze and solve problems, and thus improve our thinking quality and ability.

To improve students' mathematical quality, we must firmly grasp the important link of mathematical thinking method, because mathematical thinking method is an important guarantee to improve students' mathematical thinking ability and mathematical literacy.

References:

[1] Chen. Mathematics thinking method in middle school. Shanghai Science and Technology Education Press.

[2] Zheng Minxin. Mathematical methodology. Guangxi education publishing house