Solving problems and upgrading high school mathematics

Author: Zhang Yuezhu / Yang Jun (Editor-in-Chief)
Publisher:
Publish Date: 2005-06-01
Features:
This series of books is characterized by:
Comprehensive Analysis and Solutions: It provides in-depth analysis and solutions to typical problems related to knowledge points, key points, difficulties, and key examination points. It offers thinking angles for problem-solving, demonstrates the problem-solving process, and points out scientific problem-solving methods!
Training Package: Based on the examination points involved in the examples, it sets up targeted training for knowledge extension and expansion, allowing for learning by analogy!
Gas Station: Emphasizes important formulas, patterns, and problem-solving approaches, providing a boost for enhancing problem-solving skills!
Detailed Answers and Explanations: The answers to the training package are detailed, either revealing the problem-solving approach or providing analysis!
This book provides a comprehensive analysis and solution to typical problems related to knowledge points, key points, difficulties, and key examination points, serving as an auxiliary learning material with the nature of a problem-solving dictionary. However, it surpasses a problem-solving dictionary by not only demonstrating the problem-solving process but also providing a more detailed explanation of the thinking process and the selection of entry points, making its function of teaching methods and guiding thinking stronger.
Students must meet two conditions to improve their problem-solving skills: first, to build a solid foundation, and second, to apply the knowledge learned to analyze and solve problems. This book explains knowledge points, key points, difficulties, and key examination points through example analysis while providing the thinking process for problem-solving. It activates abilities while building a foundation and consolidates basic knowledge through problem-solving practice. Additionally, the training package set up according to the examples serves as a model for learning by analogy. Once these examples and exercises are mastered, similar problems can be solved effortlessly. Therefore, this book perfectly fulfills the role of improving problem-solving skills.
This book is organized by chapter order according to the curriculum standards and teaching progress, with examples and training questions set according to the examination guidelines for the middle school entrance examination. The examples are arranged in the order of basic questions first, then ability-based questions, and finally comprehensive questions, perfectly matching the rhythm of students' in-class learning and can be used at any time to solve the problem-solving issues students encounter.
Each example mainly includes three content items: analysis, solution, and notes, just like a teacher's lecture: first, it provides the analysis and thinking process, then solves the problem, and for difficult or easily mistaken questions, it explains the precautions, points out correct methods, and diagnoses errors. It is very easy to master.
The example analysis in this book has the following functions:
1. Links the knowledge system;
2. Explains knowledge points and examination points;
3. Interprets key points and difficulties;
4. Teaches methods and guides thinking;
5. Covers all types of questions;
6. Allows for learning by analogy.
Specifically, the examples in this book are set according to three principles:
1. Examples can explain knowledge points and examination points, meaning that for every knowledge point and examination point, there is a corresponding example;
2. The types of questions are comprehensive, including not only traditional classic questions but also new types of questions that have appeared in recent years in the middle school entrance examination, such as reading questions and situational questions;
3. Examples are typical in terms of question types and also typical in content, serving as a model for learning by analogy.
The examples in this book are closely related to examinations. First, the examination points in the textbook are all accompanied by example analysis. Second, the examples emphasize the purpose of ability, increasing application-based questions and ability-based questions, aligning with the trend of examination reform in middle school entrance examinations.