Guangzhou Zhang Jingzhong

Over the past half century, mathematicians, educators and relevant government officials in China and other countries (especially developed countries) have actively explored the reform of mathematics education, and conducted a lot of research and practice in educational concepts, teaching methods and teaching contents. In recent years, my senior high school mathematics textbook edited by Hunan Education Press has carefully studied the advantages and disadvantages of similar textbooks at home and abroad, such as American textbooks, European textbooks, Asian textbooks and domestic traditional textbooks. And using new methods to solve the problems that the existing textbooks at home and abroad can't solve or can't solve well, reflecting its own characteristics, and compiling this set of high school mathematics textbooks that meet the needs of middle school teachers and students.

The authors of this textbook are mathematicians who teach in colleges and universities. They not only have profound attainments in mathematics, but also have long-term teaching experience in middle schools. They write the contents of middle school mathematics textbooks from the perspective of modern mathematics, and write them in person, which is easy to understand.

In the process of writing, many special middle school teachers were invited to read, and there were exercises. It should be said that this is a set of high-quality mathematics textbooks that meet the teaching requirements of middle schools today. If users really understand the content of this textbook, they should be able to face any form of middle school exams, including the college entrance examination.

Below, the writing concept and the arrangement of specific contents of this textbook are introduced in detail.

1. Writing concept

According to the spirit and requirements of "Basic Education Curriculum Reform Outline (Trial)", we have compiled a set of high school mathematics textbooks that reflect the characteristics of the times and reflect the mathematics culture, so that students can further improve their mathematics literacy as future citizens on the basis of nine-year compulsory education, and truly make teachers feel easy to teach and students feel eager to learn.

2. Differences between this textbook and domestic and foreign textbooks

2. 1 The similar textbooks at home and abroad have not revealed the internal relations between the parts of mathematical knowledge. This textbook pays attention to the internal relations of different mathematics contents and reveals the main lines of thoughts and methods hidden behind the diversity of mathematics to students.

For example, in similar textbooks, there is often no unified clue to the treatment of triangles, analytic geometry, vectors and complex numbers. We take vector as the main line, the content is simple and clear, and the problem-solving method is easy to learn and effective, which is more conducive to reducing students' burden, cultivating students' mathematical generalization ability and abstract thinking ability, and improving students' mathematical literacy.

For example, when talking about the general equation of a straight line, it is pointed out that the coefficient of the first term is the coordinate of the normal vector of the straight line. As long as the normal vector is well taught, this part of the linear equation can be spread all over the world without memorizing a lot of "knowledge" and formulas, which reduces the burden on students and greatly enhances their problem-solving ability.

2.2 In order to reduce the burden on students, similar textbooks at home and abroad often use the method of deleting content. This textbook not only deletes unnecessary tedious content, but also pays attention to improving efficiency by guiding students to master mathematical methods. Some new contents are very useful, which can help students save time when learning other contents or solving problems. Although it takes time, it is cost-effective and generally seems to reduce the burden. That's an added burden. When adding new content to the textbook, it is necessary to calculate whether it takes a lot of time to learn and whether it will be of great use after learning. It will be of great use if you are eager to learn. For example, the knowledge about vectors is not only easy to learn, but also an effective tool for studying plane geometry, analytic geometry, solid geometry, trigonometric formulas, complex numbers and physics in senior high school. It's a good deal to learn.

Fundamentally speaking, this is not a simple problem of reducing the burden, but a problem of improving learning efficiency: how to learn better and more useful things in a limited time. The main consideration is to improve efficiency, but this is not the only consideration. Sometimes it is necessary to toss and turn appropriately, maintain a certain burden and training intensity to exercise thinking, so as to master the necessary knowledge and cultivate ability more skillfully and firmly.

2.3 Similar textbooks at home and abroad do not pay enough attention to the logarithmic relationship, especially the role of geometry. This textbook pays special attention to the explanation and inspiration of geometric intuition to reasoning and algebraic operation.

For example, regarding the introduction of complex numbers, similar textbooks at home and abroad are often defined only from algebra.

Starting with geometric transformation, we show students that the appearance of complex numbers is the inevitable result of the exploration of geometric transformation, which is not only intuitive and easy to understand, but also conducive to embodying the thinking characteristics of mathematics and improving mathematical literacy.

For another example, when using vector method to prove geometric propositions, it is pointed out that all the operation rules of vectors have geometric significance, and when using these operation rules for vector operation, it is equivalent to using these basic geometric theorems for reasoning. Therefore, we ask students to understand its geometric meaning, and give their own geometric proofs through examples, so that students can deepen their understanding of the relationship between algebra and geometric connotation of vectors.

2.4 Questions raised in similar textbooks at home and abroad are related to practice, or students are allowed to apply known mathematical knowledge, or

It is to prepare for the mathematical concepts or methods to be introduced by simple analogy, or to give examples in life first, and then put forward general concepts, theories and laws through this example. However, if we only teach students general concepts, theories and laws through an example, it may make students form the wrong habit of incomplete induction. As long as you "present" the knowledge to the students, even through examples, you will still instill it in him instead of letting him discover it himself.

The way we take is not to "present" knowledge to students, but to ask them a question for students to try to solve; In the process of solving problems, introduce the required concepts and establish a set of theories and rules. We arrange mathematical experiments to make students realize the necessity and inevitability of introducing mathematical concepts in the process of using their hands and brains, so that students have the feeling of discovering themselves and the process of developing mathematical knowledge.

2.5 In similar textbooks at home and abroad, the rigor of mathematics is often opposed to intuitive learning, most of which are to reduce the difficulty, or to give up the rigor of mathematics too much for intuitive learning, and some are to increase the difficulty for rigor. Based on the research and practice of educational mathematics, this textbook focuses on improving the expression method of mathematical concepts to meet the needs of education, and at the same time, it is rigorous and easy. For example, we give the elementary expression and relatively rigorous demonstration of the basic theorem of calculus, so that students who have no chance to further study calculus in the future can understand this important achievement, which is called "the highest victory of human spirit." For students who continue to study calculus in the future, it is also a useful mathematical thinking to compare the elementary proof here with the strict limit method.

2.6 Similar textbooks at home and abroad generally focus on using pictures, stories or examples to enhance students' interest. This textbook not only pays attention to absorbing these advantages of similar textbooks, but also pays attention to guiding students to think deeply about some problems and explore the interest of mathematics itself. For example, similar textbooks at home and abroad often say that when a new type of number is introduced, an operation can pass unimpeded. When introducing plural numbers, this textbook asks, "Why not introduce a number and let 0 divide?" Discuss this problem, make students realize that the introduction of new numbers should conform to the law of the number system itself, and improve mathematics literacy in thinking.

2.7 Similar textbooks at home and abroad do not pay enough attention to the relationship between typesetting and content, and often put an important sentence or even a set of mathematical expressions on both sides of a page, which brings inconvenience to readers. We try to use "screen typesetting" to make form serve content, which enhances the readability of teaching materials, helps to improve teaching efficiency and helps to make electronic teaching plans.

2.8 It is our innovation to arrange math experiments in middle school textbooks. This standard advocates the integration of modern teaching methods, information technology and mathematics curriculum. The introduction of mathematical experiments in the preparation of teaching materials is the flavor of this integration. Some experiments directly enter the text content, while others are arranged in combination with the text content, which deepens the understanding of the text content and provides opportunities for exploring and studying the text content through experiments. For example, after introducing the concept of definite integral, it is arranged to calculate the area of unit circle by computer. Combined with geometric probability, pi is calculated by random point method, and some of them are closely combined with mathematics or physics courses as students' expanding exercises, such as drawing a spherical mirror to reflect parallel light to observe its focusing effect, drawing an image of spring vibration according to Hooke's theorem and observing whether it is sinusoidal, and so on.

We also provide teaching references, teaching plans, CDs, courseware and related materials for teachers and students to choose and apply.