Every science has its history of development. As a historical science, it is both historic and realistic. Its reality is first manifested in the continuity of scientific concepts and methods. Today's scientific research is to some extent the deepening and development of scientific tradition in history, or the solution of scientific problems in history, so we can't separate the relationship between scientific reality and scientific history. Mathematical science has a long history. Compared with natural science, mathematics is an accumulative science, and its concepts and methods are more continuous. For example, the decimal notation and the four arithmetic rules formed in ancient civilization have been used to this day. Historical issues such as Fermat's conjecture and Goldbach's conjecture have long been hot topics in the field of modern number theory, and materials of mathematical tradition and history can be developed in practical mathematical research. Many famous mathematicians at home and abroad have profound cultivation or research on the history of mathematics, and are good at drawing nutrients from historical materials, making the past serve the present and bringing forth the new. Wu Wenjun, a famous mathematician in China, made outstanding achievements in the field of topology research in his early years. In the 1970s, he began to study the history of Chinese mathematics, which opened up a new situation in the research theory and method of the history of Chinese mathematics. Especially inspired by China's traditional thoughts of mathematical mechanization, he established a mathematical mechanization method for mechanical proof of geometric theorems, which was called "Wu Fa" in history. His works are worthy of being a model of making the past serve the present and revitalizing national culture.

The reality of the history of science also lies in providing experience and lessons for our scientific research today, making us clear the direction of scientific research, avoiding detours or mistakes, providing a basis for today's scientific and technological development decisions, and also providing a basis for us to foresee the future of science. If we know more about the history of mathematics, we won't have such absurd things as drawing the third part of the solution angle and proving the four-color theorem, and we will also avoid wasting time and energy on Fermat's last theorem and other issues. At the same time, summing up the experience and lessons in the history of mathematics development in China is beneficial to the development of mathematics in China today.

(2) the cultural significance of the history of mathematics

M Klein, an American mathematical historian, once said, "The general characteristics of an era are closely related to the mathematical activities of this era to a great extent. This relationship is particularly evident in our time. " Mathematics is not only a method, an art or a language, but also a rich knowledge system, which is very useful to natural scientists, social scientists, philosophers, logicians and artists and influences the theories of politicians and theologians. Mathematics has widely influenced human life and thought, and is the main force to form modern culture. Therefore, the history of mathematics reflects the history of human culture from one side and is the most important part of the history of human civilization. Many historians understand the characteristics and value orientation of other major ancient cultures through the mirror of mathematics. Mathematicians in ancient Greece (600 BC-300 BC) emphasized strict reasoning and the conclusions drawn from it, so they did not care about the practicality of these achievements, but educated people to make abstract reasoning and inspired people to pursue ideals and beauty. Through the investigation of the history of mathematics in Greece, it is very easy to understand why ancient Greece had beautiful literature, extremely rational philosophy and idealized architecture and sculpture that could not be surpassed by later generations. The history of Roman mathematics tells us that Roman culture is foreign, and the Romans lack originality and pay attention to practicality.

(3) the educational significance of the history of mathematics

When we have studied the history of mathematics, we will naturally feel that the development of mathematics is illogical, or that the actual situation of mathematics development is very inconsistent with the mathematics textbooks we have learned today. The mathematics content we learn in middle schools today basically belongs to the elementary mathematics knowledge before calculus in17th century, while most of the contents in the department of mathematics in universities are advanced mathematics in17th and18th century. These mathematics textbooks are compiled under the guidance of the principle of combining science with educational requirements. They are knowledge systems that compile historical mathematical data according to certain logical structure and learning requirements, and inevitably abandon the actual background, knowledge background, evolution process and various factors that lead to the evolution of many mathematical concepts and methods. Therefore, it is difficult to obtain the original appearance and panorama of mathematics only by studying mathematics textbooks. At the same time, it ignores those mathematical materials and methods that have been eliminated by history but may be useful to real science, and the best way to make up for this deficiency is through the study of mathematical history.

In the eyes of ordinary people, mathematics is a boring subject, so many people regard it as a daunting task. To some extent, this is because our math textbooks often teach some rigid and unchangeable math content. If the history of mathematics is infiltrated into mathematics teaching to make mathematics alive, it will stimulate students' interest in learning and help deepen their understanding and understanding of mathematical concepts, methods and principles.

The history of science is an interdisciplinary subject of arts and sciences. Judging from today's educational situation, the gap between arts and sciences leads to the fact that the talents trained by our education are increasingly unable to adapt to today's modern society with high penetration of natural science and social science. It is precisely because of the interdisciplinary nature of the history of science that it can show the role of communicating arts and sciences. Through the study of the history of mathematics, students in the department of mathematics can receive the training of mathematics major and get the cultivation of humanistic quality, while students in liberal arts or other majors can learn the general situation of mathematics and get the cultivation of mathematics and physics through the study of the history of mathematics. The achievements and moral character of mathematicians in history will also play a very important role in the personality cultivation of teenagers.

Mathematics has a long history in China. /kloc-Before the 4th century, it was the most developed country in the world. Many outstanding mathematicians have appeared and made many brilliant achievements. Its long history, calculation-centered, programmed and mechanized algorithmic mathematical model and the axiomatic mathematical model characterized by geometric theorem deduction and reasoning in ancient Greece reflect each other and alternately influence the development of world mathematics. Due to various complicated reasons, China became a mathematical superpower after16th century. After a long and difficult development process, it gradually merged into the trend of modern mathematics. Due to educational mistakes, under the influence of modern mathematical civilization, we often forget our ancestors and know nothing about the traditional science of our motherland. The history of mathematics can help students understand the brilliant achievements of ancient mathematics in China, the reasons for the backwardness of modern mathematics in China, the present situation of modern mathematics research in China and the gap with developed countries, thus stimulating students' patriotic enthusiasm and revitalizing national science.

From the perspective of general higher education

The Educational Function of Mathematics History Teaching

Mathematics teaching in China has always paid attention to the training of formal deduction of mathematical thinking, but neglected to cultivate students' understanding of mathematics as a scientific ideological system, cultural connotation and aesthetic value. The content of the history of mathematics added in the Mathematics Curriculum Standard for Ordinary Senior High School (Experiment) makes up for this deficiency. This paper aims to explore how its educational function is embodied.

Keywords:: the educational function of mathematical view in the history of mathematics

The Mathematics Curriculum Standard (Experiment) for Ordinary Senior High Schools (hereinafter referred to as the Standard) is full of new ideas. One of the highlights of the teaching content is the addition of the content of the history of mathematics, providing related topics of 1 1. It is pointed out that students should "realize the role of mathematics in the development of human civilization, improve their interest in learning mathematics and deepen their understanding of mathematics" through the study of mathematics history. Feel the rigorous attitude and persistent exploration spirit of mathematicians. "In the past, we always thought that mathematics belonged to science and we had to learn how to solve problems. But the history of mathematics, like the content of liberal arts, can be used as an extension of extracurricular knowledge, and it seems that it is not necessary to become a formal teaching content. This idea reflects our misunderstanding of the purpose and content of mathematics education: we only pay attention to the cultivation of formal logical reasoning ability, but ignore the learning of mathematics, a more internal scientific thing. Let's take mathematics as an example.

Studying the history of mathematics can help students understand mathematics and form a correct view of mathematics.

To learn a subject, we must first find out what kind of subject it is. The standard clearly puts forward that students should "understand the process of the emergence and development of mathematics and understand the role of mathematics in the development of human civilization", but at present, most of the senior high school students' views on mathematics remain at the perceptual level-boring and difficult to learn. What are the essential characteristics of mathematics? Most students don't fully understand the status of mathematics in today's science and its relationship with other disciplines.

Professor Fujitsu Hiroshi, a Japanese mathematician, pointed out in the report of the Ninth International Conference on Mathematics Education that there were four mathematical peaks in human history: the first time was the deductive mathematics period in ancient Greece, which represented the birth of mathematics as a scientific form and the first major victory of human "rational thinking"; The second is Newton-Leibniz's calculus period, which was produced to meet the needs of the industrial revolution and achieved great success in the fields of mechanics, optics and engineering technology. The third is the axiomatic period of formalism represented by Hilbert; The fourth is the new mathematics period marked by computer technology, and we are now in this period. The three major crises in the history of mathematics are the measurement of incommensurability in ancient Greece, the demonstration based on calculus in 17 and 18 centuries, and the paradox of set theory in the early 20th century. These three crises are closely related to the first three peaks. This connection is by no means accidental. It is the necessity of mathematics as a science that pursues perfection. From this connection, students can find that mathematics pursues clarity, accuracy and strictness, without confusion and ambiguity. At this time, students can easily understand the three basic characteristics of mathematics-abstraction, rigor and extensive application.

At the same time, introducing the necessary knowledge of the history of mathematics can help students have a deeper understanding of the background of the problems they have learned in their usual study, and realize that mathematics is by no means isolated, and it is closely related to many other disciplines, even the foundation and growth point of many disciplines, which plays a huge role in the development of human civilization. From the history of mathematics, mathematics and astronomy have always been closely related, and the discovery process of Neptune is a good example. It is also inseparable from physics. Newton, Descartes and others are all famous mathematicians and physicists. In the new mathematics period, mathematics (not only natural science) has gradually entered the field of social science and played an unexpected role. It can be said that all high technologies are supported by some kind of mathematical technology, which has become an important feature of the knowledge economy era. These understandings are necessary for a high school student who has studied mathematics for more than ten years.

Second, studying the history of mathematics is conducive to cultivating students' correct mathematical thinking mode.

Nowadays, mathematics textbooks are generally scrutinized repeatedly, and the language is very concise. In order to keep the knowledge systematic, the teaching content is arranged in the order of definition, theorem, proof, inference and example, lacking natural thinking mode, and introducing the connotation of mathematical knowledge and the creation process of corresponding knowledge is also less. Although it is helpful for students to accept knowledge, it is easy for students to produce mathematical knowledge by defining first and then summarizing properties and theorems. Therefore, there are such contradictions in the process of teaching and learning: on the one hand, educators systematize knowledge in order to let students master mathematics knowledge faster and better; On the other hand, systematic knowledge can't let students know that knowledge is gradually matured by asking questions, guessing, demonstrating, testing and perfecting, which affects the formation of students' correct mathematical thinking mode.

The study of the history of mathematics is conducive to alleviating this contradiction. By explaining some related mathematical history, students can have a clear understanding of the generation process of mathematical knowledge while learning systematic mathematical knowledge, thus cultivating students' correct mathematical thinking mode. There are many such examples, such as the generation of calculus: the traditional deductive system of European geometry can not produce calculus, which is the "exhaustive method" of Newton and Leibniz in ancient Greece. Inspired by the idea of "finding the arcuate area of parabola" to meet the needs of the first industrial revolution, the definition of "infinitesimal" was vague at the initial stage and not as strict as what we see now. With the continuous supplement and improvement of mathematicians, it gradually matured after decades.

The study of the history of mathematics can guide students to form the habit of exploration and research, and discover and understand what a problem really created from its emergence to its solution, and what ideas and methods represent the substantial progress of the content compared with the previous content. Understanding this creative process can make students realize a vivid and true mathematical thinking process, which is beneficial to students to form a deeper understanding of some mathematical problems. Understanding the realistic source and application of mathematical knowledge, rather than simply accepting the knowledge taught by teachers, can gradually form a correct mathematical thinking mode in the process of continuous learning, exploration and research.

Thirdly, studying the history of mathematics is conducive to cultivating students' interest in mathematics and stimulating their motivation to learn mathematics.

Motivation is a force that inspires people and pushes them to act. From a psychological point of view, motivation can be divided into two parts. People's curiosity, thirst for knowledge and hobbies constitute the internal motivation conducive to creation; The sense of social responsibility is an external motive force conducive to creativity. Interest is the best motivation. Japanese middle school students get the first place in the total score of international IEA survey, and at the same time, they find that the proportion of Japanese students who don't like mathematics is also the first, which shows that their good grades are obtained under the pressure of society, parents and schools. There is no comprehensive report on the situation in China. However, according to a survey of high school students in four middle schools in Xinxiang City, Henan Province, the proportion of students who "I don't like math, but I have to learn it well for the college entrance examination" is as high as 62.2 1%, while only 23.438+02% are interested in math. It can be seen that middle school students' learning motivation is not clear and their interest in mathematics is not enough. All these have greatly affected the effect of learning mathematics, but this is not because mathematics itself is boring, but because it is ignored in our teaching. Combining the history of mathematics properly in mathematics education is conducive to cultivating students' interest in mathematics and overcoming the negative tendency of motivation factors.

There are many contents in the history of mathematics that can cultivate students' interest in learning, mainly in these aspects: first, small games related to mathematics, such as skillfully holding matchsticks, Rubik's cube, businessmen crossing the river, etc. , strong operability, as a classroom activity or after-school research can achieve good results. Second, some famous mathematical problems in history, such as the Seven Bridges problem and Goldbach conjecture, often have vivid cultural backgrounds. It is also easy to arouse students' interest. There are also some famous mathematicians' lives and anecdotes, such as the success stories of some young mathematicians, such as "from Abel to Galois" mentioned in the standard. Abel proved at the age of 22 that there is no formula for finding the roots of algebraic equations with more than five degrees, and Galois was only 18 years old when he founded group theory. And Pascal, a French mathematician, became the founder of projective geometry at the age of 16. German mathematician Gauss solved the problem of drawing regular polygons at the age of 19, proved the basic theorem of algebra at the age of 20, and published "Arithmetic Research" which influenced the development of number theory in the whole 19 century at the age of 24. There are also many examples. Many mathematicians from poor backgrounds have finally made outstanding achievements in mathematical research through their own efforts. For example,/kloc-Steiner, a great geometer in the 9th century, was born in a peasant family and grew up as a farmer. He didn't learn to write until 14 years old, and 18 years old officially began to study. Later, he made a living as a private school teacher. After hard work, he finally made important work in mathematics at the age of 30. Become famous in one fell swoop If these students are interested in teaching and have knowledge, students' fear of mathematics will be eliminated, the attraction of mathematics will increase, and mathematics learning may no longer be compulsory.

Fourthly, studying the history of mathematics provides a stage for moral education.

Under the requirements of "Standards", moral education no longer focuses on politics, Chinese and history as before. With the addition of the history of mathematics, mathematics education has a stronger moral function. Let's discuss it from the following aspects.

First of all, studying the history of mathematics can educate students in patriotism. Most of the current middle school textbooks talk about foreign mathematical achievements, and seldom talk about China's contribution to the history of mathematics. In fact, China's mathematics has a glorious tradition, including a group of outstanding mathematicians such as Liu Hui, Zu Chongzhi, Zuxuan, Yang Hui, Qin, Zhu Shijie, and other mathematical achievements with world influence, such as China's remainder theorem, Zuxuan's axiom and secant. Many of these problems were studied many years earlier than those abroad. The third topic of "Selected Lectures on the History of Mathematics" in the standard is "Treasures of Ancient Mathematics in China", which refers to the representative achievements of ancient mathematics in China, such as Nine Chapters of Arithmetic and Sun Tzu Theorem.

However, at this stage, patriotism education can't just stop lamenting the glory of ancient mathematics in China. Since the Ming Dynasty, China's mathematics has gradually fallen behind the West. At the beginning of the 20th century, mathematicians in China began the difficult course of learning and catching up with western advanced mathematics. The "Lecture on the History of Mathematics" in the standard 1 1- The Development of Modern Mathematics in China also mentioned "the glorious course of mathematicians in modern China struggling hard to catch up with the advanced level of mathematics in the world". Under the requirements of the new era, in addition to enhancing students' national pride, we should also cultivate students' "international consciousness" and let students realize that patriotism is not reflected in "taking its strengths and saying its shortcomings". In scientific discovery, all mankind should learn from each other and improve together. We should respect foreign mathematical achievements and learn with an open mind.

Secondly, studying the history of mathematics can guide students to learn the excellent qualities of mathematicians. The road of any scientific progress and development is not smooth sailing. The discovery of irrational numbers, the creation of non-Euclidean geometry, the discovery of calculus and so on all illustrate this point. Mathematicians either stick to the truth and are not afraid of authority, or persevere and fight for it. Many people even dedicated their lives to it. Archimedes was still immersed in mathematical research at the moment when the enemy breached the city and endangered his life, in order to "I can't leave an incomplete theorem for future generations." Euler was blind in his right eye at the age of 3 1 year, and his eyesight was poor in his later years, but he continued his research with strong perseverance. His papers are numerous and long, so after his death 10, his papers were still published in the Journal of Chinese Academy of Sciences. For those students who give up when they encounter a little complicated calculation and a little complicated proof in their study, it will play an important role for them to correctly look at the difficulties encountered in the learning process and establish their confidence in learning mathematics by introducing stories about how some great mathematicians persist in pursuing when they encounter setbacks.

Finally, studying the history of mathematics can improve students' aesthetic cultivation. Mathematics is beautiful, and countless mathematicians are impressed by its beauty. Appreciating the beauty of mathematics is a basic quality of human beings, and the study of the history of mathematics can guide students to understand the beauty of mathematics. Many famous mathematical theorems and principles shine with the brilliance of aesthetics. For example, Pythagorean Theorem (Pythagorean Theorem) is a very simple and profound theorem that everyone is very familiar with in elementary mathematics. It is widely used. For more than two thousand years, it has aroused countless people's interest in mathematics, such as the famous Italian painter Leonardo da Vinci, Indian King Bascara, and the 20th President of the United States. Have given proof. 1938+0940, American mathematician loomis collected 370 proofs in the second edition of Pythagoras Propositional Art, which fully showed the infinite charm of this theorem. The golden section is also beautiful and charming. As early as the 6th century BC, Pythagoras School studied it. In modern times, people are surprised to find that it has a very close internal relationship with the famous Fibonacci sequence. At the same time, a good mathematical emotional experience can be formed when we sigh and appreciate the symmetrical beauty of geometric figures, the simple beauty of ruler drawing, the unified beauty of volume triangle formula and the singular beauty of non-Euclidean geometry.