Third learning series. Senior High School 2 Mathematics. Upper

Author: Liu Kun
Publisher:
Publish Date: 2004-08-01
Features: Preface to the Editor
I. The book is compiled with the purpose of "innovation—excellence—practicality—efficiency" and has six main characteristics:
1. This is a trial textbook specifically designed for "the third learning" In the past decade, many middle school students have been dissatisfied with their school education and hope to further improve their academic performance. This trial textbook, written for middle school students, is not a repetition of classroom teaching, a collection of materials for students to choose from, or a workbook as a supplement to classroom learning. Instead, it is a well-designed training textbook that has undergone repeated refinement, trial use, and revision, forming a self-contained and highly practical system. Once readers use it, they will recognize its value.
2. The book is the crystallization of long-term integration of mathematics teaching and research The author has been committed to combining teaching with research for 25 years, achieving fruitful results in both fields. This book is the culmination of these experiences. For example, the "scientific concept" and "scientific methods" of mathematical learning are the author's new research findings. Today, they are presented to the in this book and serve as the guiding principle throughout its compilation. Similarly, research on how to improve the quality of theoretical internalization, how to enhance the level of mathematical skill operation, and how to make the acquisition of mathematical experience, ideas, and concepts more effective are all embedded in the book. This elevates the book to a high standard.
3. The book is based on the renowned teaching methods of Beijing No. 4 High School Over the decades, Beijing No. 4 High School has been famous for its "strong emphasis on fundamentals and rigorous academic standards," accumulating extensive teaching experience and resources. The mathematics department of the school has been at the forefront of teaching reform in the country. The mathematics textbook for high school students, Beijing No. 4 High School High School Mathematics Textbook, was even used as a substitute for the People's Education Press textbook at the school for 10 years (1995 to the present). During the compilation and multiple revisions of this book, we fully absorbed the essence of these experiences and resources while also advancing them in line with the times.
4. The book features high-level foundational knowledge and detailed explanations of examples The teaching of Beijing No. 4 High School has always placed great emphasis on "building a solid foundation." "High-level classroom teaching" and "high-level learning guidance" are the hallmarks of the school's education. This book inherits this noble tradition. For foundational knowledge, we adopt the method of "deeply exploring theory" (definitions, theorems, formulas, and rules) to fully uncover the rich connotations of key points. On the other hand, we use unit reviews to connect these points into a sequence, forming a system that fully reveals the vertical and horizontal relationships between them, enabling students to "stand at a systemic height" and grasp the overall picture. This greatly enhances students' understanding of theoretical knowledge and lays a solid foundation for flexible application. For example, the book does not just teach problem-solving methods, leaving readers at the level of "knowing how to solve," but instead focuses on teaching "how to think" and further guides students to understand "why" and "how else" to approach problems, elevating problem-solving to the level of "understanding the principles." Only by reaching this level can students achieve the ability to generalize and apply knowledge effectively.
5. Closely integrating the explanation of mathematical content with learning guidance is another feature The book not only systematically explains the scientific concepts and methods of mathematical learning in the preface but also provides specific learning guidance tied to each chapter's content. We believe this approach will greatly inspire students.
6. Exercises are designed based on the principles of typicality, excellence, tiered difficulty, and appropriate quantity Currently, teaching and learning guides are filled with an overwhelming number of problems! We believe this is the result of the "sea of problems" strategy. In reality, students do not need or have the time to solve so many problems. Even if they sacrifice sleep to do so, the results may not be significant. We believe that problems are not about quantity but about being typical, excellent, and sufficient to achieve training goals. To cater to individual needs, we have also introduced a tiered and progressive principle: basic practice exercises, skill-enhancing exercises, and even attempts at real college entrance examination questions, which are arranged in ascending order of difficulty. This better meets the diverse needs of students without overburdening them. The inclusion of "Attempt Real College Entrance Examination Questions" is intended to show students how the exam evaluates each section and to provide advanced-level practice for those with extra time, preparing them for the exam in advance. All exercises in each chapter are provided with answers at the end of the book in the "Reference Answers and Hints" section, with some including hints or detailed solutions for verification. However, readers are encouraged not to look at the answers lightly but to compare them only after thorough reflection.
II. How to Use This Book To help readers achieve better results when using this book, we recommend the following methods:
1. About the Scientific Methods of Mathematical Learning
(1) First, recognize the psychological characteristics, learning tasks, and strategies of high school first-year students. Understanding these principles will help you seize the key period and avoid unnecessary detours, leading to ideal and higher levels of development. This is very important.
(2) Understanding the scientific concepts of mathematical learning and grasping the essence of learning methods will help you focus on the most effective areas, achieving twice the result with half the effort.
(3) The scientific methods of mathematical learning are designed to meet the needs of high school students at the critical stage of developing theoretical and abstract thinking abilities. On one hand, they help students learn more effectively; on the other hand, they greatly promote the development of their abstract thinking skills. Therefore, we encourage students to practice these methods and hope everyone will share their experiences and valuable suggestions for further improvement so that the book can be refined in future editions.
2. About the Synchronous Detailed Explanation of the Content of the Mathematics Textbook
(1) Pre-class Learning Preparation and Effectiveness Test This section is designed for pre-class preparation. Readers can solve and answer the test questions the night before class to identify what they have mastered and what needs improvement, ensuring they are well-prepared.
(2) Learning with Questions The questions in this section serve both to check the depth of your understanding of the theory and to help you delve deeper into it. Try answering them yourself before class to bring a clearer focus to your learning.
(3) Connecting and Systematizing Key Points This section outlines the theoretical structure of the chapter (or unit) and can also be seen as a "guide" for learning it. It connects the key points into a sequence, forms a system, and reveals the vertical and horizontal relationships between them, helping readers understand the development of the theory and the organic links between key points. This enables a holistic grasp of the unit's mathematical principles.
(4) In-depth Explanation of Key and Difficult Points This section lists the main key points of the chapter and provides a detailed analysis and explanation of them, which is crucial for enhancing understanding. To better absorb the content, we recommend that readers first explain each key point without referring to the book, then compare their explanations with those in the book to identify gaps and issues, and further analyze and reflect. This approach will lead to faster progress.
(5) Detailed Examples Each example in this section is explained in three parts: Thinking Process—how the solution approach was developed; Solution and Proof—the solution method (including standardized expression); Review and Insights—summarizing the problem-solving experience and explaining why the approach was chosen and how else it could be approached. If you fully grasp these three aspects, each example can serve as a model for solving other problems, enabling you to generalize and apply knowledge effectively. To improve your problem-solving skills and gain more insights, we recommend learning this section using the "Do—Compare—Summarize" method. Do—solve the problem without referring to the book's analysis or solution. Compare—contrast your approach with the one in the book. Summarize—identify differences and summarize your experience. This is a form of self-directed learning that is highly beneficial for skill development. Give it a try.
(6) Basic Practice Exercises These exercises are slightly more challenging than those in the textbook but remain fundamental and must be mastered.
(7) Skill-Enhancing Exercises These exercises are slightly more challenging than the review questions at the end of each chapter but are mostly still fundamental. They are essential for students preparing for college after graduation. The difficulty level increases progressively as you move through the exercises.
(8) Attempt Real College Entrance Examination Questions Most excellent college entrance examination questions related to the chapter (especially recent years) are included here. If you have extra time and are willing to try, you will definitely benefit from it. All exercises in each chapter are provided with answers at the end of the book in the "Reference Answers and Hints" section, with some including hints or detailed solutions for verification. However, readers are encouraged not to look at the answers lightly but to compare them only after thorough reflection.