Second Phase Curriculum Reform: High School Mathematics Guide: New and Difficult Questions Strategies for the National College Entrance Examination in Mathematics

Author: Li Zhengxing
Publisher:
Publish Date: 2006-12-01
Features: This book has the following characteristics:
1. Chapter Overview – Focusing on the Knowledge System, Clicking the Exam Point Network
The entire high school mathematics curriculum is constructed under the framework of the curriculum standards, including basic courses, extended courses, and inquiry and practical courses. Therefore, when reviewing, it is essential to first have a comprehensive understanding of each chapter, organize and construct knowledge chains, and grasp key and difficult points. This process is indispensable in the review process, as it may lead to the expansion of knowledge and the exploration of problems.
2. Unit Review – Guiding Problem-Solving Techniques and Teaching Mathematical Thinking
Each chapter is divided into several lessons, presented in the form of specialized topics. Each lesson first summarizes and organizes the basic knowledge, and then provides typical examples in a step-by-step progressive manner. Each problem includes [Strategy Tips]: guiding students to find problem-solving approaches, [Problem Solution] providing the entire problem-solving process, advocating multiple solutions to a single problem, and [Analysis and Extension]: analyzing, summarizing, and concluding on mathematical thinking to broaden students' problem-solving perspectives and enable them to apply knowledge to different scenarios.
3. Problem Exploration and Ability Expansion – Implementing Three-Dimensional Goals and Advocating Exploration and Innovation
Mathematics originates from the real world, and real-world perception is the medium for mathematical knowledge. Mathematical problems are the heart of mathematics, and the needs of reality are the driving force for learning. In this section, I first use the philosophical quotes of mathematical masters from all over the world to inspire students' interest in exploring problems and their enthusiasm for learning mathematics. The examples provided here are either applied problems or comprehensive exploratory problems, all of which have emerged in recent years and are high-stakes questions in college entrance exams. The focus is on [Thinking and Exploration]: teaching students to face a large amount of information, learn to judge, learn to make choices, learn to model, and learn to integrate and apply knowledge. The key to the reform of mathematics education should be the transformation of one-dimensional goals into three-dimensional goals, with the development of students as the core. This means not only mastering mathematical knowledge and skills but also understanding the process and methods, and more importantly, stimulating learning interest and improving mathematical literacy. The two accompanying articles, "Analysis of the New Curriculum Standards and the New Trends of College Entrance Exam Questions" and "80-Day Strategy for College Entrance Examination Mathematics – Correct Methods, No Problem to Improve by 15 Points," are provided for students to refer to when reviewing to grasp the direction. Additionally, five sets of "College Entrance Examination Mathematics Level Tests" and some provincial and municipal college entrance exam papers from 2006 are attached for students to practice before the exam. The reference answers are provided at the end of the book.