How to master mathematics knowledge?

Mathematics learning method

Here we talk about the methods of mathematics learning. This is what we put forward according to the characteristics of mathematics subject by applying foreign fast learning methods. Because of the difference between algebra learning method and geometry learning method, we discuss it separately.

First, algebra learning method.

Copy the title, browse and set the target.

Read and record key content.

Try to make an example.

Do exercises quickly and summarize the questions.

Memory summary

Second, the four steps of geometry learning.

1.① Write the title and browse the teaching materials.

(2) self-study, write the directory.

2.① Read the textbook according to the catalogue.

② Self-study geometric concepts and theorems.

3.① Read the examples and form ideas.

(2) The process of writing examples of solving problems.

4.① Do exercises quickly.

② Summarize the problem-solving methods.

3. Learning methods of mathematical concepts.

There are many concepts in mathematics. How to make students master the concept correctly should explain what kind of process is needed and to what extent. Mathematical concept is a form of thinking that reflects the essential attributes of mathematical objects. Its definition is descriptive, indicating the extension of alien species, and there is a way to add concepts to categories. A mathematical concept needs to remember the name, describe the essential attributes, realize the scope involved, and use the concept to make accurate judgments. These questions are not required by teachers. Without learning methods, it is difficult for students to study regularly.

Let's summarize the learning methods of mathematical concepts:

Read concepts and remember names or symbols.

Recite the definition and master the characteristics.

Give two positive and negative examples to understand the scope of conceptual reflection.

Practice and judge accurately.

Fourth, the learning method of learning formula

The formula is abstract, and the letters in the formula represent infinite numbers in a certain range. Some students can master the formula in a short time, while others have to experience it repeatedly to jump out of the ever-changing digital relationship. Teachers should clearly tell students the steps needed in the process of learning formulas, so that students can master formulas quickly and smoothly.

The learning method of the mathematical formula we introduced is:

Write a formula and remember the relationship between the letters in the formula.

Understand the ins and outs of the formula and master the derivation process.

Check the formula with numbers and experience the law embodied in the formula in the process of concretization.

Make various transformations on the formula to understand its different forms of change.

Imagine the letters in the formula as an abstract framework, so that the formula can be used freely.

Fifth, the learning method of mathematical theorems.

A definite reason consists of two parts: conditions and conclusions. This theorem must be proved. Proving process is a bridge connecting conditions and conclusions, and learning theorem is to better apply it to solve various problems.

Let's summarize the learning methods of mathematical theorems:

Recite theorems.

Conditions and conclusions of discriminant theorem.

The proof process of understanding theorem.

Applying theorems to prove related problems.

Understand the internal relations between theorems and related theorems and concepts.

Some theorems contain formulas, such as Vieta Theorem, Pythagorean Theorem and Sine Theorem, and their learning should be combined with the learning method of the formula with the same sign.

Sixth, the learning method of geometric proof for beginners.

In the second semester of senior one, students have just started to learn solid geometry, and students always find it difficult to get started. Many old teachers agree with the following methods, which can be carried out in class or taught by themselves.

Look at the questions and draw pictures. (Look, write)

Examining questions to find ideas (listening to the teacher's explanation)

Read the proof process in the book.

Recall and write the proof process.

7. The reduction method to improve the ability of geometric proof.

After mastering the basic knowledge and methods of geometric proof, how to improve the ability of geometric proof on the basis of fluent and accurate expression of the proof process? It is necessary to accumulate the proof ideas of various geometric problems and know some proof skills. In this way, we can achieve the above goal by focusing on the teacher's explanation or reading some geometric proof questions.

Reduction is a method to classify the unknown into the known. When we encounter a new geometric proof problem, we need to pay attention to its question type and find the key steps, and it will be over when it falls into the known question type. At this time, the most important thing is to remember the steps of transformation and the idea of proving the problem, and no longer pay attention to the detailed expression process.

The reduction method to improve the ability of geometric proof;

1. Review the questions, find out the known conditions and verify the conclusions.

2. Draw a picture as an auxiliary line and find a way to prove the problem.

3. Record the key steps of the method to prove the problem.

4. Summarize the idea of proof, so that the process of proof can form a clear impression in the brain.

Eight, Paulia's problem-solving thinking method.

Foresight method

Collect information and sort it out.

Identify and recall, enrich and rearrange.

Separation and combination.

review

Method of solving problems.