What is the root of the problem?

The root of the problem is not a concept, not a conclusion, but a problem. After the problem is standardized, it is actually a topic, just like examples in lectures, exercises in textbooks, and test questions in test papers. But it is not an isolated topic, nor is it a single individual in a pile of problems. It is the root of a theme family, the foundation of a theme system and the representative of a theme group. Grasping a topic root means grasping the topic family, the topic group and the topic system.

The book "The Roots of Mathematics in Senior High School" was formed on the basis of decades of research on the teaching theory of the roots of mathematics and its variants. The book takes the knowledge system of senior high school mathematics as a clue and important knowledge points as chapters. It is divided into 12 chapter ***46 sections, each with two roots and 92 * *. Through learning and experience, readers can clearly grasp the basic knowledge and methods and understand the essence of mathematical problems, thus helping to get rid of the "infinite sea of questions."

The columns under each topic root are set as follows:

The root cause analysis finds out the divergence points of information elements and variants in the root cause of the problem, and summarizes the core knowledge points and classical problem-solving methods in the process of detailed analysis of the root cause of the problem.

Variant network presents the direction and level of various variants. Such as the change of elements in the topic root, the strengthening and weakening of conditions, the analogy and induction of methods, and so on.

Try reading some chapters online.

Preface recommendation by Professor Zhang Dianzhou, a famous mathematics educator.

President Ni Ming, the reading assistant branch of East China Normal University Press, gave me a stack of manuscripts entitled "The Root of Mathematics Problems in Senior High School". The expression "topic root" is very attractive. ? One of the participants is Ping Huang, a familiar friend in the past and an innovative math teacher who is unwilling to be lonely. So, I read it carefully for a while and thought it was a teaching aid book with Chinese mathematics education characteristics.

Teaching AIDS are often regarded as the product of exam-oriented education, so they are widely criticized. In fact, supplementary books have a long history and great significance. In ancient China, many famous Confucian scholars annotated the Four Books and Five Classics, which actually provided teaching guidance for later study. I remember1At the end of 1970s, a set of "Mathematics Self-study Tutoring Series" in Shanghai was once expensive in Luoyang, which was in short supply and helped many young intellectuals to enter the university threshold. At present, many important documents are popular in compiling "reading guide" books, and its function is also "teaching assistant". Therefore, in my opinion, excellent teaching has infinite advantages, while shoddy teaching AIDS are harmful to people. Excellent supplementary books with high quality and China characteristics can also escort the teaching reform.

Most recent educational reforms focus on the first half of the cognitive process: creating situations, asking questions, group exploring, reporting and summarizing, and even finding something. This is a cognitive process from perceptual to rational. However, as we all know, there is a process of deepening and applying rational knowledge to practice in the second half. This is manifested in practice consolidation, reflection and summary, appreciation and observation, variant application, and even refined into mathematical thinking methods. Doing a good job in the second half of teaching requires a solid foundation in mathematics, not fancy performances. I think an excellent teaching aid book can be found in? The latter part plays an important role in the process of understanding.

The Roots of High School Mathematics by Ping Huang and Yin Dehao provides a platform for the "cognitive process in the second half" mentioned above. The basic idea is to find the root of the topic and weave it into a topic network through variants. The so-called "outline" is the "outline" of this network.

Many mathematical education researchers at home and abroad believe that an important feature of Chinese mathematical education lies in the "variant" treatment of mathematical problems. Professor Gu Lingyuan is an advocate of mathematical variant teaching. In recent years, the University of Hong Kong and the Chinese University of Hong Kong have written several doctoral dissertations on the role of mathematical variants. This book "The Root of Mathematics Problems in Senior High School" further summarizes the experience of front-line teaching practice, and systematically reviews teaching with "change" as the leading idea. Every root in the book will have several variants, forming a variant network, or background, or object, or rules, or conditions ... There are so many variants as never before, and there are many innovative elements. As for the columns such as "root analysis of topics", "classic variants" and "variant training", it is necessary to guide and pave the way for learners to improve their problem-solving ability and give full play to their "teaching assistance" function. It is conceivable that if we accumulate over time, looking for "topic roots" and variants may become a bright color in Chinese mathematics education.

I wrote some of the above ideas, hoping that everyone will cherish the dribs and drabs of Chinese mathematics education and stop begging with golden rice bowls.

catalogue

order

order

Chapter 1 Set and Proposition

Concept and operation of 1 section set

Section 2 Propositions and Necessary and Sufficient Conditions

Chapter II Basic Elementary Functions

Concept, definition and scope of function and inverse function in section 1

Monotonicity, parity and periodicity of functions in the second quarter

In the third quarter, linear function and quadratic function

Section 4 Power Function, Exponential Function and Logarithmic Function

Section 5 Translation and Folding of Functional Images

Section 6 Functions, Equations and Inequalities

Section 7 Application of Derivative in Function

Chapter III Trigonometric Functions

The relationship between the same angle ratio of the first 1 triangle

Brief introduction of the author

Ping Huang is a special teacher in Caoyang No.2 Middle School. In his honor list, there are: educational gardeners, top-notch talents in science and technology, May Day Labor Medal, and young and middle-aged experts who have made outstanding contributions. This is a high summary of his educational career. In his work experience, there are: teaching and research group leader, grade director, teaching department director, teaching room director, mathematics teaching and research researcher, senior teacher evaluation team leader and so on. This is the best evaluation of his teaching ability. He pays attention to scientific research, and is the leader of the topics of "Middle School Mathematics Thinking Teaching" and "High School Mathematics Variant Teaching", and has published more than 50 academic papers. Teaching, for him, is a familiar math problem? This pattern and its variants are very comfortable in his hands. The book "The Root of Mathematics Problems in Senior High School" is an excellent summary that comes from the front line of teaching and pays attention to teaching practice research.

Yin Dehao, senior teacher of Shanghai Yucai Middle School and senior coach of China Mathematical Olympics. People behave like their schools, just as their names suggest. Winner of "Shanghai Garden Award", leader of senior high school mathematics in Jing 'an District. It is his consistent pursuit to let students "enjoy mathematics and improve their wisdom", and the teaching results are remarkable, which is deeply loved by students. Combining teaching with scientific research, he presided over and participated in more than ten national, municipal and district-level scientific research projects, published dozens of papers in professional magazines, and participated in writing five books. At the same time, he also participated in the proposition work of many important exams. In recent years, I have devoted myself to the creation and research of mathematics test questions. Variants of learning problems and variant teaching are the focus of his research, and his wisdom and elegance can be seen from the chapter "The Root of Senior High School Mathematics Problems".