Improve the adaptability of High School Mathematics Learning

Improving the adaptability of Mathematics Learning in high school Zhang Cheng, a graduate student in the Mathematics Department of Capital Normal University

Shortly after entering the first year of high school, many students felt very difficult in learning new knowledge and were not as comfortable as junior high school. For a long time, some students are disgusted with mathematics learning and even have fear. In the face of this problem, how should we adjust ourselves to adapt to High School Mathematics Learning?

I. Understanding the features of high school mathematics knowledge

After three years of study in junior high school, especially the review and consolidation Before the senior high school entrance exam, the students have mastered junior high school knowledge and have some experience in some of the mathematical ideas and methods. The knowledge of high school is more advanced than that of junior high school in both depth and breadth. Therefore, it is normal to feel certain difficulties in learning. One of the solutions is to first understand the characteristics of high school knowledge, so that we have a "Number" in our hearts ". Kochi knowledge and its learning methods have the following characteristics:

1. abstract concepts

After entering high school, the students felt that the concept of mathematics was not easy to understand. Indeed, many of the concepts we have learned in junior high school are defined only after obtaining perceptual knowledge from the relationship between intuitive examples or actual things, the acquisition of the concept of high school requires more rational thinking.

Taking the function concept as an example, in junior high school, we consider the correspondence between variables X and Y, that is, each value of X has a unique y correspondence. When a senior high school contacts a function again, the relationship between elements in two non-empty number sets A and B is considered. Through comparison, we can also see that there are differences in function learning in the two stages. First of all, in the symbolic representation, junior high school only requires us to express the function with a specific analytical expression, such as:, etc, in the high school stage, we use a more abstract form to facilitate the study of the general nature of functions. Secondly, in the junior high school stage, after learning the concept of functions, consolidate the concept of a function by applying specific functions. In the high school stage, we can deeply understand and consolidate the function concepts by discussing and applying the general functions.

The above analysis tells us that if we can compare the same concepts of junior and senior high school, we can have a better understanding of the abstract concepts of Senior High School.

2. Language Refining

Starting from the chapter of set and function, some mathematical symbols, such as Attention, attention, and. Phi, have been widely used in the beginning, and the redundant languages are simple and accurate.

For example, the empty set Phi can indicate that the equation has no solution. For another example, if the solution set of the equations is f, the solution set of the equations is and respectively. If we want to express the relationship between F and, it is easy to use a set language, that is.

3. Comprehensive knowledge

The knowledge of each chapter of high school mathematics is not isolated. There is a close relationship between the chapter and chapter, and between the chapter and the section. We need to use it comprehensively.

For example, after learning about the solution to the inequality, let's look at the following questions:

Three inequalities are known:

To make the X value that satisfies the inequality (3) satisfy at least one of the inequality (1) and (2), evaluate the value range of.

The analysis of this problem involves not only the issue of inequality solutions, but also the distribution of the root of the equation, the value of a function at a certain point, the intersection between several sets of inequality solutions, and so on, we need to make full use of the learned knowledge.

Ii. Consciously build a bridge for the transition of mathematical knowledge

1. grasp the concept and nature of the Set

Collective Knowledge is the first bridge between junior high school and senior high school.

First, the set table method simplifies the representation of natural data sets, rational data sets, and real data sets learned in junior high school, thus simplifying the presentation of complex problems. Second, relational operations between sets can help us better understand new knowledge, such as the solution of inequality or equations. Third, collections, as a mathematical idea, penetrate into many of the knowledge to be learned in the future. Therefore, it is very important to learn a set of knowledge at the beginning of high school.

2. Strengthen Association and Analogy

The relationship between high school knowledge and junior high school knowledge is very close. A lot of high school knowledge can be converted into junior high school knowledge in the form of dimensionality reduction and power reduction, but this requires us to be able to compare and associate them.

Taking ry as an example, we have proved that the distance from any point in the triangle to the three sides is equal to the height of the triangle, and it is easy to prove through the area and equal.

Can we prove that the distance from any point in the front body to four faces is equal to the height of the triangle, similar to the three-dimensional high-school ry?

In fact, we can see that this problem is very similar to the problem of plane ry above. Here we will promote the two-dimensional problem to three-dimensional. The two-dimensional problem can be solved by area. What can we do with the three-dimensional problem? Maybe we can use the volume method? If you are interested, try it.

Of course, Lenovo and analogy are based on understanding and mastering knowledge.

3. deepen understanding of mathematical computing

Mathematical computation has different learning requirements at different stages in middle school. In the high school stage, what is required is no longer simply to use calculation rules for calculation, but to master the calculation methods and understand the calculation principles, such as the construction method, split item method, variable replacement method, mathematical induction method, and so on.

For example, when we learn the summation of a series, we encounter the following problem: "1! + 2! 2 + 3! 3 +... + n! N and ". Obviously, formulas are powerless. In this case, we need to construct an algorithm. We may wish to use the wildcard n! Start with N and find it and (n + 1 )! , N! N! N = (n + 1 )! -N !, In this way, the split-item method is used to solve this problem.

Iii. Several learning suggestions

1. carefully read the teaching materials

It is impossible for most students to learn High School Mathematics only through classroom lectures. We are required to carefully read the teaching materials under the course, while still thinking. Only in this way can we deeply understand the connection between knowledge and knowledge.

2. Understanding, understanding, and using mathematical methods

Mathematical thinking and methods are the essence of mathematical knowledge. Junior high school students have some experience in the comprehensive analysis and reverse verification. In comparison, the mathematical thinking methods involved in high school are much richer. For example, a set of ideas, function ideas, analogy methods, mathematical induction, analysis methods, and other commonly used mathematical thought methods penetrate into all parts of the knowledge and need to be carefully understood.

3. Pay attention to the relationship between knowledge

In daily learning, you must: ① consider the connection between different mathematical knowledge; ② pay attention to the connection between examples and exercises. Understand the logical relationship between knowledge, so as to systematically and flexibly master high school mathematics.