Junior High School Mathematics Key and Difficult Points - 16 Lectures (Junior High School Key and Difficult Points Learning Public Relations Series)

Author: Yang Zhengjia
Publisher:
Publish Date: 2005-05-01
Features: The level of mathematical learning for junior high school students is, on one hand, related to their talent, original mathematical foundation, and other factors. However, on the other hand, it is more closely linked to their love for mathematics, as well as their learning habits and methods. Teachers can guide students to gradually understand that mathematics follows certain rules, and learning mathematics is primarily about understanding its rather than relying on inspiration. As long as they follow the rules, every time they encounter a difficult problem, after thinking and trying, the problem can be solved. For this reason, we believe that the mission of a mathematics teacher is mainly to guide students in learning methods and to lead them in exploring mathematical rules. This is to help students gradually progress, understand mathematics, master the rules, solve problems, and thereby develop a greater love for mathematics. Based on this consideration, this book is divided into themes and methods in its content, covering the knowledge cluster of junior high school mathematics, various problem-solving methods, and related knowledge that is relatively concentrated. Readers can experience the natural and accessible nature of mathematics through smooth reading, and through step-by-step analysis and explanations, they can organize their thoughts and further learn that mathematics follows a certain structure.
The requirements of society for students' mathematical learning no longer satisfy merely being able to solve a few problems, memorize a few theorems, or recite a few formulas. Instead, it is increasingly inclined toward values of high quality, high efficiency, high ability, and low burden. Students should first understand some essential mathematical facts and then actively explore more important mathematical principles, including methods and ideas. The process of mathematical learning requires continuous accumulation, but it cannot rely solely on accumulation. It needs to be constructed, primarily by constructing the structure of mathematics and the thinking process of understanding mathematics. If, through learning, we can transform "yesterday's" mathematical knowledge into "today's" mathematical thinking and then use it to create "tomorrow's" scientific and cultural achievements, then we can truly say we have learned how to learn and are carrying forward the legacy of the past. Otherwise, learning mathematics would truly be like doing "gymnastics" every day.
The book is divided into two parts. The first part is a classified review of knowledge and methods. Each chapter begins with a detailed analysis of example problems, followed by further practice for students to try. When selecting example problems, emphasis is placed on important mathematical thinking and methods, and common mistakes are highlighted. Through the review in the first part, all key points can be systematically reviewed. The second part is a classified review by question type and difficulty level. Among them, "small and exquisite" problems refer to mid-level difficulty problems that do not contain too much knowledge or methods, but rather use common and important methods to solve them. Through the review in the second part, students can effectively improve their mathematical problem-solving skills.
During the use of this book, readers should not be greedy for speed but should focus on practical results. They should carefully read each example problem, understand the meaning of the problem, grasp the key points of the solution method, and clarify all the knowledge points covered. It is recommended that readers study the example problems according to the above requirements, then carefully and completely work through the example problems and their accompanying exercises, and finally make annotated notes on each problem regarding key points, solution methods, common mistakes, and key points. We propose the learning patience and responsibility of "solving problems to the end" and "doing small problems thoroughly." The "close reading" of mathematical learning can help us build a solid foundation. When we and "imitation," we may truly be able to break free from the "sea of problems."
We know that everyone has been very concerned about mathematical ability. In my opinion, at the junior high school level, at least the following abilities are included: proficient calculation and transformation skills, thorough understanding and analysis skills, organized argumentative and expressive skills, and accurate identification and judgment of concepts. Obviously, a thin book like this cannot help students fully achieve these levels of ability. However, we hope that students always take these as their own ability requirements and gradually achieve them through daily accumulation. This book can be used for self-study by readers or as a reference for teachers. The content of the entire book is based on the current mathematics curriculum for grades 7 to 9 in Shanghai.