Mathematical culture paper submission 1
On the Course of Basic Mathematics Culture Education in China
First of all, what is mathematical culture?
There are many definitions of mathematical culture. Mathematical culture refers to not only that mathematics itself belongs to a cultural phenomenon of human society, but also that mathematics has a wide range of factors beyond its own significance and their great influence on human beings, so the occurrence, development and education of mathematics should be observed and understood in the whole social and cultural background. ?
? Because the mathematical object is not the real existence in the material world, but the product of human abstract thinking, mathematics is a kind of culture. ? In particular, a history of mathematics can reflect the occurrence and development of mathematical culture. Specific mathematical concepts, methods and ideas have rich cultural connotations, which are worth showing to everyone in teaching.
Second, the background of mathematical culture education
1. Stimulate students' interest in learning and improve the quality of mathematics education.
No matter in which country, mathematics education is the focus of basic education. However, mathematics has always been regarded by most students as boring and difficult to learn, lacking interest in mathematics learning, and even feeling scared and discouraged. However, mathematics education plays an irreplaceable role in cultivating every qualified social citizen. Interest is the best teacher. How to improve students' interest in learning mathematics is a problem that all educators are very concerned about. How to stimulate students' interest in learning mathematics has become a hot issue in mathematics education. Therefore, improving the quality of mathematics education is one of the reasons to advocate attaching importance to cultural education in mathematics education.
2. The need of quality education.
China is a big country in mathematics, but for a long time, we have paid too much attention to the instrumental value of mathematics education and neglected its value as a cultural aesthetic education that cultivates sentiment. Examination-oriented education is vigorous, and students' academic burden is too heavy. China students are the most diligent student group in the world, but China students' innovation ability is not high, and basic education does not reflect its most basic function: to cultivate high-quality qualified citizens for the society. We don't need nerds who only read dead books. Therefore, in order to improve the national quality, improve the quality of mathematics and the quality of mathematics education, cultural education in mathematics education is advocated by everyone.
3. Mathematics itself is a kind of culture, which has the value and function of cultural education.
At the beginning of the 20th century, there appeared an isolationist tendency in the field of mathematics, which was divorced from social culture, and it has been affecting today's China. The excessive formalization of mathematics makes people mistakenly think that mathematics is only the imagination of a few geniuses? Free creation? The development of mathematics does not need the promotion of society, its truth does not need the test of practice, and of course the progress of mathematics does not need the edification of human culture. So, what are the mathematical circles in the west? The revival of empiricism? . White's mathematical culture theory tries to return mathematics to the cultural level. Klein's Ancient and Modern Mathematical Thoughts, Mathematics in Western Culture and Mathematics: The Loss of Determinism were published one after another, trying to create a humanistic mathematical culture [3]. In recent years, mathematical culture has become a new perspective to discuss the development of mathematics. People are increasingly aware that the development of mathematics is closely related to human culture. Mathematics has always been the main cultural force of human civilization, and the development of human culture has greatly affected the progress of mathematics. Mathematics itself is not only a science, but also a culture, which has the value and function of cultural education. ? Excellent math culture will be a beautiful and moving math queen, handy servant and clever pet. With advanced mathematics culture, mathematics teaching will become lively and radiant. ?
Three stages of mathematical culture education in China's basic education
The first stage: the stage in which basic mathematical culture education was neglected (1949 to 1990s).
When our country was just founded, we had to do everything, and basic education was still in its infancy. At that time, it was difficult to guarantee qualified math teachers, not to mention the importance of cultural education in math education. Compared with the goal of mathematics education from 1958 in the early days of liberation, we find that mathematics education attaches importance to using the knowledge and skills learned to solve arithmetic application problems and simple calculation problems in daily life, while the teaching goals of knowledge, ability and ideological morality are not comprehensive and clear enough.
After that, influenced by the Great Leap Forward movement to catch up with the United States and Britain and the Great Leap Forward for ten years, China's education was seriously impacted. It was not until 1978 that the "Middle School Mathematics Teaching Outline (Trial Draft)" was promulgated every year that China's mathematics science education returned to the normal track. However, the revised syllabus added a lot of advanced mathematics content, which was obviously inconsistent with the reality of the low level of basic mathematics at that time, which increased the learning burden of students. In view of this situation, 1982 drew up the "six-year key middle school mathematics syllabus (draft)", adjusted the content of middle school mathematics appropriately, and compiled several sets of teaching materials with different depths and widths for different regions to choose corresponding teaching materials according to local specific foundations. At the same time, a large number of teaching material reform experiments have been actively and steadily carried out. 1986 "The Mathematics Teaching Syllabus for Full-time Middle Schools" was promulgated, which put forward new requirements for educational objectives to adapt to the specific situation at that time and future development [4]. Obviously, compared with today, everyone has no time to care about and mention the mathematical culture education in basic education.
The second stage: the stage in which the basic cultural education of mathematics was hotly discussed (from 1990s to 2004).
With the strengthening of national strength, and the sufficient attention and investment in education, China's mathematics education, especially basic education, is also in a leading position in the world. However, exam-oriented education is getting worse and worse. Many scholars and teachers find that, due to the influence of exam-oriented education, mathematics curriculum pays attention to imparting knowledge, but ignores the education of emotional attitudes and values, especially science subjects such as mathematics, which are all problems in students' eyes, not to mention the national Olympic fever. The Olympiad destroyed the interest and enthusiasm of China students in learning mathematics to a great extent, increased their fear of learning mathematics, occupied precious time for students to develop other qualities, and wasted too much manpower and material resources.
1993 02 13 the Central Committee of the Communist Party of China and the State Council, on the basis of summing up the practical experience of the vast number of educators, formulated and issued the Outline of Education Reform and Development in China (hereinafter referred to as the Outline). Should primary and secondary schools learn from it? Does exam-oriented education turn to the track of comprehensively improving the quality of the people? In order to implement the outline, the Central Committee of the Communist Party of China put forward at the national conference on education held in 1994:? Basic education must start from? Examination-oriented education should turn to the track of quality education, fully implement the educational policy and improve the quality of education in an all-round way. ?
With the development of the concept of quality education, the research on how to improve quality education has become more and more extensive. Having the desire, interest and methods of learning is more important than remembering some knowledge, which is also advocated by quality education. How to improve the quality of mathematics education and make mathematics education fully meet the purpose of quality education has become a hot topic for discussion. First of all, how to stimulate students' interest in learning mathematics and restore the educational value of mathematics itself has become a problem that everyone thinks deeply. In this context, mathematics culture education, which has been neglected, has become an important means to implement mathematics quality education. Obviously, our mathematics education ignores the cultural value of mathematics, the unique beauty of mathematics, the cultural education in mathematics education and the unique quality education function of mathematics education. While vigorously promoting quality education, mathematics education is no longer a simple calculation and proof reasoning, but attaches importance to cultural education in mathematics education, thus improving quality education.
How to carry out cultural education in mathematics education has become a hot spot. Among them, Professor Zhang Dianzhou of East China Normal University expressed the following views after studying this stage. Everyone tries to liberate mathematics from the circle of pure logical deduction, focusing on analyzing the history of mathematical civilization, fully revealing the cultural connotation of mathematics and affirming the value of mathematics as a cultural existence. Is this necessary? . At the same time, Professor Zhang also pointed out two shortcomings. One is? The study of mathematical culture can not only talk about the importance of mathematics, but also emphasize its contribution to human civilization. At the same time, we should also observe that mathematics is influenced by social culture and explain the cultural significance of mathematics with the help of social civilization. This helps people get close to mathematics. ?
At the level of middle school teachers, this idea has also been recognized by many people. In their teaching research papers, how to properly integrate cultural education into mathematics education to improve students' interest in learning is as follows.
A lot. However, not all leaders and teachers pay enough attention to the value and importance of mathematical culture in actual teaching or run through their own classroom teaching, and there is no official curriculum standard or textbook to give mathematical culture a corresponding position.
The third stage: Basic mathematics culture education is highly valued, appearing in textbooks and practical teaching (from 2004 to now).
? Mathematics is a kind of culture, and mathematics education is the education of mathematics culture. ? In the new curriculum reform since 2004? Pay attention to the value of mathematical culture? ,? Mathematics culture education should be consciously interspersed in teaching, and the history of mathematics appears in elective textbooks in the form of special topics. ? These ideas are embodied in the "Mathematics Curriculum Standards for Ordinary Senior High Schools (Experiment)" promulgated in 2003. The new curriculum reform points out that mathematics education is not only knowledge education, but also quality education. The new curriculum regards mathematics culture as an aspect of the content of senior high school mathematics curriculum, and gives a certain number of topics, puts forward specific goals and requirements, and properly grasps the contents and requirements of related topics in teaching. For example, how to combine the study of statistical thinking methods to grasp it? Data and reliability in advertising? ; How to design the right one in the right place? Mathematical problems arising from the golden section? Through practical problems, students can understand the extensive application of mathematics in architecture, art, aesthetics and optimization, and appreciate the value of mathematics culture.
After the new curriculum reform, the unconscious teaching of mathematical culture in the past has changed into conscious teaching of mathematical culture. The teaching of mathematical culture is not only an introduction to related materials, but also a reflection of the cultural value contained in the materials. Cultural education in mathematics education appears in the following two forms in actual teaching.
1. The introduction of mathematical culture is interspersed in the teaching of mathematical knowledge.
? Teachers can introduce the occurrence and development of some important basic concepts in class, so that students can understand the law of the occurrence and development of mathematics, and at the same time understand the process of human understanding of the objective world from the perspective of mathematics. For example, there are many materials about the establishment and development of analytic geometry and calculus. When selecting and sorting out mathematical materials, we should pay attention to those contents that reflect the mutual promotion of social development and mathematical development, or reflect the persistent spirit of mathematicians in pursuing truth, seeking truth and being pragmatic, reasoning, criticizing and questioning. With proper tips and guidance, students can understand the mathematical cultural value contained in relevant materials? .
? A few words, a story, a fragment, etc. In a word, while educating knowledge, we take knowledge as the carrier to let students know and understand the cultural value of mathematics, promote the formation of students' scientific outlook and improve students' mathematical literacy in an all-round way. ?
2. As the carrier of mathematical culture, the history of mathematics appears in new textbooks.
The elective series in the new curriculum includes lectures on the history of mathematics, which has entered the new curriculum of senior high school mathematics as an elective course. The selected textbooks bid farewell to the single content and methods of mathematics learning in the past, jump out of the ocean of mathematics knowledge and skill training, examine the historical evolution of mathematics from a macro perspective, understand the stormy course of the history of mathematics development, and understand how various mathematical thinking methods came into being, developed and applied.
The history of mathematics is the best carrier for integrating mathematics culture into mathematics curriculum. It shows the process of the emergence and development of mathematics. It is the concentrated expression of the hard work and wisdom of the working people, and it is a treasure house of mathematical knowledge, mathematical ideas and mathematical methods. ? By introducing the main figures, events and their backgrounds in the process of mathematics development, students can master the context of mathematics and understand the objective law of mathematics development and the interaction between mathematics and the development of human society. By understanding the biographies and basic mathematical thinking methods of mathematicians at home and abroad, we can draw rich nutrition and lessons from them, which will help students form a correct concept of mathematical thinking and establish an enterprising spirit of independent thinking and bold exploration. By comparing mathematics with different cultural backgrounds and introducing multicultural mathematics, students can understand the mathematical achievements of human civilization from a broader perspective and appreciate the colorful mathematical culture. ? In a word, the history of mathematics helps us to fully understand the cultural value of mathematics education and explore mathematics education under the guidance of mathematics culture. The educational value of the history of mathematics has appeared in the experimental area of curriculum reform.
Four. Concluding remarks
Mathematics is an important part of human culture, the product of human social progress and the driving force to promote social development. As a culture, mathematical literature is also a necessary scientific education for citizens. In American mathematics education, textbooks also emphasize the introduction of mathematics history knowledge. In the introduction, we should pay attention to the bright spots of mathematicians, educational materials, materials that arouse students' interest in learning mathematics and important mathematical facts from all over the world, so as to make students better understand the historical development of mathematics and broaden their horizons [8].
In China, one of the four ancient civilizations in the world, mathematical culture education, which was once absent in mathematics education, has been paid attention to. Mathematical culture? It is one of the important contents of the new curriculum, and mathematics education is the education of mathematics culture. Under the guidance of this concept, China's basic mathematics education can better stimulate students' interest in mathematics learning, change students' view of mathematics, establish students' self-confidence in learning, truly understand the beauty and history of mathematics, and then promote the healthy growth of students' personality, broaden their horizons and understand multicultural mathematics. This kind of mathematics education is the real quality education [9].
Submission of papers on mathematical culture II
Analysis of Mathematics Culture in Senior High School Mathematics Teaching
Abstract: Mathematical culture is an important part of human knowledge treasure house. It is not enough to impart mathematical knowledge and solve mathematical problems in mathematics teaching, but also to infiltrate mathematical culture. Through mathematical culture education, the beauty of mathematics and the charm of mathematical spirit are displayed, so as to stimulate students' interest in learning mathematics and cultivate students' good mathematical spirit and will quality. On the basis of introducing the main characteristics of mathematical culture, this paper analyzes how to infiltrate mathematical culture into senior high school mathematics teaching.
Keywords: high school mathematics; Mathematical culture; Main functions; infiltration
Mathematical culture refers to the sum of material products and spiritual products created by human beings in the process of mathematical activities, in which material products mainly refer to mathematical language, mathematical propositions, mathematical problems and mathematical methods, and spiritual products mainly refer to mathematical thoughts, mathematical consciousness and mathematical spirit. Infiltrating mathematical culture in senior high school mathematics teaching is the basic need of students' mathematics learning. Its purpose is to make students be infected by culture in the process of learning mathematics, appreciate the beauty of mathematics, realize the value of mathematics culture, and then stimulate students' interest in learning mathematics, cultivate students' good mathematical spirit and will quality, and promote the good development of students' personality.
1 Main features of mathematical culture
Mathematics is a kind of culture, and mathematics culture is an important part of human knowledge treasure house. Its characteristics mainly include the following aspects:
(1) Historicity. The development of mathematics is inseparable from the historical accumulation process, and people's understanding of the essence of mathematics also comes from the development of mathematics history. Therefore, it can be said that mathematical culture has certain social historicity. Mathematics learning should pay attention to mathematical methods, and the history of mathematics is an important basis for learning mathematical methods, so in a sense, all research related to mathematics is closely related to the history of mathematics. Understanding the history of mathematics can not only enhance the overall concept, but also stimulate the enthusiasm for learning.
(2) thinking. The main body of mathematical culture is mathematical knowledge and mathematical ideas and methods formed by using these knowledge. They are all the thinking results of the spatial forms and mathematical relations that can be applied to the real world summarized by human beings through mathematical language. Therefore, it can be said that thinking is the inner soul of mathematics, and mathematics is the basic embodiment of thinking.
(3) aesthetics. Mathematics is a science and an art, and the basic characteristics of mathematics such as simplicity, symmetry, unity and coordination are all important contents of mathematical beauty. What was mathematics in ancient China? Ceremony, music, shooting, imperial, book, number? One of the six arts, in the west, mathematics and harmony were once considered as the main source of the universe. So it can be said that mathematics has a strong aesthetic feeling, and the mathematical world is full of aesthetic feeling. The aesthetic feeling of mathematics is the reflection of mathematical culture on the cultivation of human will quality and noble sentiment.
2 the infiltration of mathematical culture in senior high school mathematics teaching
2. 1 Infiltrate the history of mathematics and cultivate the consciousness of mathematical culture.
In high school mathematics teaching, teachers should consciously infiltrate the history of mathematics and cultivate students' mathematical cultural awareness in the process of understanding the history of mathematics. In this regard, the history of mathematics can be infiltrated by offering an elective course in the history of mathematics. In elective courses, we can introduce some historical events with far-reaching significance related to mathematics, such as the historical events of the gradual evolution of mathematical ideas and the historical events of mathematicians gradually correcting mistakes. Or by recommending valuable works closely related to mathematics, such as Zhang Jingzhong's New Concept Geometry and Sioni? The Miracle of Mathematics written by pappas, etc. Or guide students to collect and find the stories of famous mathematicians at home and abroad through various resources such as the Internet, newspapers and periodicals, understand their main contributions to mathematics, broaden students' mathematical horizons and experience the cultural taste of mathematics.
2.2 infiltration of mathematical thinking methods to improve students' mathematical literacy
Mathematical thinking method refers to the regular and rational understanding of the formation of mathematical knowledge and methods, which provides guidance and problem-solving strategies for analyzing, handling and solving mathematical problems. Mathematics teaching in senior high school should not only be satisfied with imparting knowledge, but also help students master the essence of mathematics knowledge, guide students to solve practical mathematics problems with the help of mathematical thinking methods, and improve their own mathematics literacy. For example:
Known as x? [0, 1], the inequality X2COSA-x (1-x)+(1-x) 2sina >: 0 is a constant, so we can find the value range of A. Analysis: The result of this problem can be easily obtained by constructing thinking methods. Let f (x) = X2COSA-x (1-x)+(1-x) 2Sina = (COSA+Sina+1) X2-(1+2Sina) X+Sina. 0 ①; f( 1)= cosa & gt； 0 ②, under the condition ① ②, the axis of symmetry x=? [0, 1], at this time, as long as △ < 0, that is, sin2a & gt(3), and then (1), (2) and (3), the value range of a can be found. ..
2.3 Develop students' mathematical thinking and cultivate the spirit of mathematical rationality.
The key of mathematics teaching lies in developing students' mathematical thinking and cultivating the spirit of mathematical rationality. Mathematical thinking is an important form of rational thinking. Paying attention to the cultivation of students' mathematical thinking plays a very important role in improving students' thinking ability and enhancing their ability to solve problems. On the one hand, to develop students' mathematical thinking, we should pay attention to cultivating students' mathematical consciousness and sorting out students' thinking context. The knowledge points of mathematics are closely related. Therefore, in teaching, teachers should not only consider students' original knowledge base, but also consider the related knowledge content. Only in this way can we better stimulate students' thinking and gradually form the context of knowledge. On the other hand, we should pay attention to stimulate students' thinking motivation and improve their thinking level. Motivation is the inner strength of people's behavior. Stimulating students' thinking motivation is an important factor to cultivate their thinking ability. In mathematics teaching, teachers can create a reasonable problem situation, so that students can produce emotional * * * sounds, which in turn can trigger students' strongest thinking motivation and best thinking orientation, and form good mathematical thinking quality.
2.4 to carry out research-based learning on mathematical topics and realize the real value of mathematical culture.
In the actual mathematics teaching process, teachers can take some mathematical theorems and formulas as research topics to carry out research study, so that students can actively discover, test and demonstrate, experience the real process of mathematicians discovering mathematics, understand the formation process of mathematical concepts, theorems, formulas and conclusions, and gain the joy of re-creation, so as to grasp the essence of mathematics and realize the real value of mathematical culture. At the same time, in the process of carrying out research-based learning activities, teachers should give students appropriate guidance. If it continues? Derivation of linear equation? Sometimes, teachers can ask some questions appropriately to guide students to think: A. How do we often fix a straight line in our life? B. What conditions should be given to determine the equation of a straight line? How to find the general formula of its linear equation? When students finish their research, teachers can display their research results in time, carry out cooperation and exchange, and put forward different opinions, so as to keep students' enthusiasm for learning mathematics.
In a word, mathematical culture is the essence of mathematics. Paying attention to students' perception of mathematics culture can help students deepen their knowledge and understanding of mathematics, thus helping them learn mathematics well and fall in love with it.
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