High School Math Problem Misunderstanding Diagnosis and Treatment Manual (Grade 12)

Author: Xie Wenquan (Editor-in-Chief)
Publisher:
Publish Date: 2005-03-01
Features: We often observe a phenomenon where many students spend their days doing homework—post-class exercises, unit tests, and exam preparation drills. They have a mountain of materials and have worked through several exercise books, yet their academic performance doesn’t improve, and their test results remain unsatisfactory. Why is this? The reason lies in their failure to fully grasp the fundamental principles of the textbook and their lack of mastery in scientific problem-solving methods. Understanding principles is the fundamental guarantee of learning well; mastering methods is a powerful weapon for tackling difficult problems. Only by clarifying the basic principles can one think clearly and approach problems with ease; only by mastering methods can one generalize from examples and apply knowledge flexibly. No matter how challenging the problem, one can handle it with confidence and solve it effortlessly; no matter what exam one takes, one can perform beyond expectations and achieve success! The set of books we have meticulously planned and published, The Complete Guide to Problem-Solving Methods for Chinese Students, aims to provide students with the most comprehensive, systematic, practical, and thorough problem-solving methods. Based on the new curriculum standards, it emphasizes quality-oriented education, stimulates innovative thinking, enhances practical application, and cultivates problem-solving skills. The books include case studies with targeted exercises, methodical guidance, and expanded thinking. The methods are flexible and ingenious, the question types are systematic and comprehensive, the reasoning is clear and smooth, and the commentary is just right. In short, this book is a treasure trove for students to master their studies and a new weapon for conquering difficult problems. May this book become a fulcrum for your learning, lifting you to a vast blue sky of knowledge!
This book is compiled in accordance with the spirit of the Newly Revised Full-Time Senior High School Mathematics Teaching Syllabus issued by the Ministry of Education, following the order of the compulsory and elective senior high school mathematics textbooks published by the People’s Education Press in recent years. It is divided into three volumes for senior high school grades one, two, and three, respectively, and is synchronized with the curriculum. Considering the reality of changes in mathematics textbook content due to shifts in educational values and the potential future trends of mathematics teaching, this book primarily focuses on the exercises, review questions, and key question types from domestic senior high school mathematics textbooks, as well as a selection of typical problems beneficial for learning mathematics from newly published domestic and international materials. Each problem is meticulously analyzed and written, with each entry consisting of six sections: [Problem], [Misunderstanding], [Obstacle Analysis], [Rational Conceptualization], [Correct Solution], and [Varied Practice]. From the formulation of the problem to the diagnosis of misunderstandings and the conceptualization of the correct solution process, attention is paid to the principles of guidance, typicality, practicality, universality, and forward-looking development. Additionally, comments and extensions are provided for several influential issues.