Question 1: What are the commonly used thinking methods in mathematics? 1. The idea of ??using letters to represent numbers

This is one of the basic mathematical ideas. In the second chapter of the first volume of Algebra, "Algebra" This idea is mainly reflected in "Preliminary Knowledge".

For example: Suppose the number A is a and the number B is b. Use the algebraic formula to express: (1) 2 times the sum of the two numbers A and B: 2 (a b) (2) 2 times the number A and B 5 times difference of numbers: 2a-5b

2. The idea of ??combining numbers and shapes

"The combination of numbers and shapes" is the most important and one of the most basic thinking methods in mathematics. , is an effective idea for solving many mathematical problems. "When a number lacks a shape, it is less intuitive, but when there are countless shapes, it is difficult to understand" is the famous saying of Professor Hua Luogeng, a famous Chinese mathematician. It is a high-level summary of the role of the combination of numbers and shapes. The following content in mathematics textbooks reflects this idea.

1. The one-to-one correspondence between points on the number axis and real numbers.

2. One-to-one correspondence between points on the plane and ordered pairs of real numbers.

3. The relationship between functional expressions and images.

4. Problems such as sum, difference, multiple and fraction of line segments (angles), make full use of numbers to reflect shapes.

5. Solve triangles, find angles and side lengths, and introduce trigonometric functions. This is to use algebraic methods to solve geometry problems.

6. In the chapter "Circle", the definition of a circle, the positional relationship between a point and a circle, a straight line and a circle, a circle and a circle, etc. are all treated as quantitative relationships.

7. Statistics The second method of preliminary statistics is to draw statistical charts, and use these charts to reflect the distribution of data, development trends, etc. In fact, it is through "shape" to reflect the data distribution situation, development trends, etc. In fact, the characteristics of numbers are reflected through "shapes", which is a direct application of the idea of ??combining numbers and shapes in practice.

3. Transformation thought (reduction thought)

Throughout junior high school mathematics, the transformation (reduction thought) has been running through it. Transformation thinking is to turn an unknown (to-be-solved) problem into a solved or easy-to-solve problem, such as turning complex into simple, difficult into easy, unknown into known, high order into low order, etc. It is the most basic idea for solving problems and one of the basic thinking methods of mathematics. The following content reflects this idea:

1. The solution of fractional equations is to transform the fractional equation into the solution of the previously learned quadratic equation. Here, the new problem to be solved is turned into a solved one. Problem solving embodies the idea of ??transformation.

2. Solve right-angled triangles; turn non-right-angled triangle problems into right-angled triangle problems; convert practical problems into mathematical problems.

3. Prove that the sum of the interior angles of a quadrilateral is 360 degrees. The quadrilateral is converted into two triangles. At the same time, exploring the sum of the interior angles of a polygon also uses the idea of ??transformation.

4. Classification ideas

Classification of rational numbers, classification of integers, classification of real numbers, classification of angles, classification of triangles, classification of quadrilaterals, positional relationship between points and circles, positional relationship between straight lines and circles, circles and circles The positional relationship, etc. are all discussed through classification.

Question 2: What are the commonly used mathematical methods in primary school mathematics? What are the commonly used mathematical methods: substitution method, elimination method, undetermined coefficient method;

Commonly used mathematical ideas Combination of numbers and shapes

Mathematical thinking methods mainly come from

observation and experiment, generalization and abstraction, analogy, induction and deduction, etc.

Question 3: Commonly used in primary school mathematics What are the teaching methods? (1) Lecture method Lecture method is a method in which teachers use oral language to systematically impart knowledge to students. Lecture method is one of the oldest teaching methods, and it is also the most widely used and common teaching method in the world. The basic form of the teaching method is that the teacher talks and the students listen. Specifically, it can be divided into three methods: telling, reading and explaining.

Narration: Teachers describe and describe things and phenomena to students.

Explanation: Teachers explain, explain, and demonstrate concepts, principles, formulas, etc. to students.

Teaching and reading: Teachers use textbooks to read and talk at the same time.

There are no strict boundaries between the above three methods, and they are often used in conjunction with each other in teaching activities.

The advantage of the lecture method is that it allows students to acquire a large amount of systematic knowledge in a relatively short period of time, which is conducive to teachers' leading role and conducive to the purposeful and planned teaching activities. The disadvantage of the lecture method is that it easily restrains students and is not conducive to students' active and conscious learning. It also relies heavily on the teacher's personal language literacy.

Teachers should pay attention to the following points when using teaching methods.

1. Ensure that the teaching content is scientific and ideological. The concepts, principles, facts, and opinions taught by teachers must be correct, which requires teachers to carefully prepare lessons and teach.

2. Lectures should be organized and focused. Only when the teaching logic is clear can students understand it clearly.

3. Pay attention to language arts. The teacher's language level directly determines the effect of the teaching method, so he must constantly pay attention to and improve his language accomplishment. First of all, the language must be clear, accurate and concise, both logical and clear; secondly, we must strive to be vivid and contagious, which is especially important for primary school students; thirdly, we should also pay attention to the pitch and speed of the voice. Speed ??and slowness, pay attention to cadence.

4. Pay attention to use it in conjunction with other teaching methods. The attention time of primary school students is limited, and it is difficult to achieve good results by completely using the lecture method in the entire class. Teachers should be good at interchanging the lecture method with other teaching methods and means to avoid students' fatigue and lack of attention due to long-term listening.

(2) Conversation method

Conversation method is a method where teachers guide students through comparison, analysis and judgment based on students’ existing knowledge and experience, with the help of inspiring questions and oral questions and answers. Teaching methods to acquire knowledge through other thinking activities. The basic form of the conversation method is that students learn through independent thinking under the guidance of teachers.

The advantage of the conversation method is that it can fully stimulate students' active thinking and promote students' independent thinking. It has a positive effect on the development of students' intelligence, and it also helps to exercise and improve students' language expression ability. . The disadvantage of the talking method is that compared with the lecture method, it requires more time to complete the same teaching tasks. In addition, when the number of students is large, it is difficult to take care of every student. Therefore, the conversation method is often used in conjunction with other methods such as lecture methods.

Teachers should pay attention to the following points when using the conversation method.

1. Be well prepared. What is the conversation centered around? What questions are asked? Which students are asked? And what responses might students give? How to guide students through further questioning? Etc., teachers should consider and arrange carefully in advance.

2. The conversation should be open to all students. Although conversations can only take place between the teacher and individual students, teachers can make an effort to engage all students. First of all, the content of the conversation should be issues that can attract the attention of all students and are universal and important in teaching. Secondly, teachers should try to make the interviewees as representative as possible, such as selecting students at different levels. Again, provide appropriate explanations and explanations as supplements at the right time during the conversation.

3. Summarize at the end of the conversation. In the conversation, students' understanding and mastery are often not expressed accurately and concisely enough. Therefore, in the final stage of the conversation, teachers should use standardized and scientific expressions to summarize the knowledge that students have gained through the conversation, thereby strengthening their gains.

(3) Discussion method

The discussion method is a method in which students express and exchange opinions around a certain issue under the guidance of teachers, and acquire knowledge through mutual inspiration, discussion, and discussion. teaching methods.

The basic form of the discussion method is that students learn through independent thinking and communication under the guidance of teachers.

The advantage of the discussion method is that students with similar age and development level can discuss together, which can easily stimulate interest and activate thinking, and help them listen, compare and think about different opinions, and carry out research on this basis. Think independently and promote the development of thinking ability. In addition, the discussion method can generally and fully give every student the opportunity to express his or her views and opinions, mobilize all students' learning enthusiasm, and effectively promote the development of students' oral language abilities. Disadvantages of the discussion method...gt;gt;

Question 4: What are the commonly used mathematical analysis methods? What level are you asking about?

1. The basic content of mathematical analysis methods is mathematics, modeling and computerization. From a mathematical perspective, many methods of practical value have been found in mathematics, such as linear programming, integer programming, dynamic programming, game theory, queuing theory, inventory models, scheduling models, probability statistics, etc., for quantitative analysis and decision-making It has played a major promoting role; from a modeling perspective, each mathematical method includes a specific mathematical model to solve decision-making problems, and people can use the model to find the answers to the questions they need to know; from a computerization perspective See, people can use electronic computers as a fast logical calculation tool to shorten the time to solve problems and enhance the accuracy of predictions. These "three modernizations" are interrelated, and their combination has brought about significant changes in decision-making technology and methods.

2. Another level: undetermined coefficient method, substitution method, mathematical induction method.

Question 5: What are the commonly used mathematical thinking methods in mathematics? What are the common mathematical matching methods, substitution method, elimination method, undetermined coefficient method;

Commonly used mathematical thinking number shapes Combination

Mathematical thinking methods mainly come from

observation and experiment, generalization and abstraction, analogy, induction and deduction, etc.