1. The cultivation of mathematical culture helps students to better understand the essence of mathematics.
Mathematics is a rational thinking paradigm and cognitive model. It is not only some operating rules and transformation skills, but also a way of thinking that can benefit people for life. Therefore, we should always pay attention to this essential feature of mathematics in teaching practice, avoid the tendency of simply pursuing knowledge in mathematics learning, and pay attention to the cultivation of ability and thinking.
In teaching, students can fully perceive that mathematics is not only a tool of knowledge, language, nature and society, but also a collection of thinking methods and art with aesthetic characteristics by studying the connotation, existence value and national and global understanding of mathematics culture. Through the cultivation of students' mathematical culture, students can construct the connection between mathematical knowledge and deeply understand the essence of mathematics, so as to achieve the goal of lifelong benefit.
So as to better apply mathematics to society and create more wealth for society. 2. The cultivation of mathematical culture is helpful to improve students' mathematical literacy.
The cultural value of teaching materials should be fully explored in teaching. The connotation of mathematical culture is not only reflected in knowledge itself, but also in its history. Mathematics is a historical existence.
Therefore, in the teaching process, the whole process of the generation and development of mathematical knowledge has been fully revealed. Mathematics is both creative and inventive. As big as a subject and as small as a symbol, it always comes out of some kind of thinking under a certain cultural background.
Our mathematics education should strive to restore and reproduce this process of discovery or invention, explore the source of mathematics knowledge, rebuild the connection between separated mathematics knowledge and realistic background, and let students actively explore and grasp the background and essence of mathematics problems. In a word, both mathematics as a science and mathematics as a course show a cultural realm full of human creativity and imagination.
Through the cultivation of mathematical culture, students can think positively and express their mathematical thoughts in their own language, so as to put forward new ideas, new concepts and new methods reasonably. Combining the cultural background of mathematics, let students think and solve problems comprehensively and from multiple angles, and then cultivate their scientific attitude and rational spirit.
3. The cultivation of mathematical culture helps students to deeply understand the characteristics of mathematics. Through the study of mathematical thought, spirit, method, viewpoint, language and its formation and development, as well as the study of mathematical history, mathematicians, mathematical beauty, mathematical education, the intersection of mathematics and humanities, and the relationship between mathematics and various cultures, we can make the learned mathematical knowledge more systematic.
Students can deeply understand the characteristics of mathematics in the cultivation of mathematical culture: mathematics is abstract. The abstraction of mathematics has the following three characteristics: first, it retains the quantitative relationship or spatial form.
Secondly, the abstraction of mathematics is formed through a series of stages, and its degree of abstraction greatly exceeds the general abstraction in natural science. The form of mathematics is abstract, but the content is realistic.
As Lenin said: "All scientific (correct, solemn and not absurd) abstractions reflect nature more deeply, correctly and completely. Third, not only the concept of mathematics is abstract, but also the mathematical method itself is abstract.
Leonardo da vinci said: "Where a mathematical science cannot be applied, where it has nothing to do with mathematics, science has no reliability." Thus, the second characteristic of mathematics is accuracy, that is, the rigor of logic and the certainty of conclusions, and the third characteristic of mathematics is the universality of application.
In addition, mathematics has certain foresight. In engineering technology, the trajectory and impact point of rockets and missiles can be predicted by accurate calculation.
4. The cultivation of mathematical culture is helpful to stimulate students' curiosity and innovative spirit. The purpose of learning is to "apply what you have learned", and practice makes perfect in the process of application to make innovations.
Mathematics is not boring but full of vigor and vitality. It has its mysterious beauty. There are still some conjectures in mathematics, such as Riemann conjecture, Goldbach conjecture and four-color conjecture, which have not been completely solved.
In the process of effectively guiding students to try to solve these conjectures, the development process in the long history of mathematics should be appropriately introduced. Through the spread of mathematical culture and the cultivation of students' mathematical culture, students can wander in the ever-changing and developing mathematical culture, which will subtly stimulate students' thirst for knowledge and innovative consciousness and expand their thinking. "Learning comes from thinking, and thinking comes from doubt", "It is better to believe in books than to have no books", so that students dare to explore in doubt.
How to Improve the Function of Mathematics Culture in Mathematics Teaching
Mathematical culture and mathematical beauty are closely linked with mathematics. You have me and I have you. Mathematics is like a person, its professional knowledge is like a human skeleton, its culture is like a human muscle, and its beauty is better than human blood. A person should not only have a skeleton, but also have muscles and blood to become a person, a fresh person and an aura person. Therefore, mathematics culture and mathematics beauty are indispensable contents in mathematics teaching.
Following the footsteps of mathematicians' growth, we can understand the hard-working style, inspiring academic experience and lofty ideology and morality of our predecessors. They are extremely vivid ideological nourishment to stimulate learning interest, enthusiasm, scientific methods and national spirit in mathematics teaching. It can inspire students to climb the peak of science, cultivate the habit of respecting the law of scientific development and rational thinking such as seeking truth, reasoning, criticizing and questioning, and the scientific spirit of persevering in the pursuit of truth.
Showing the background of mathematical knowledge, the formation and development process of mathematical concepts and the process of putting forward mathematical theorems can guide students to understand the interaction between mathematical science and the development of human society, which can trace back to the source, broaden their horizons, help them to understand mathematical knowledge comprehensively and deeply, appreciate the value of mathematics, and improve their scientific literacy and cultural literacy.
This paper introduces the modern application of mathematical knowledge and mathematical thinking methods, shows the connection between mathematics and other natural sciences and interdisciplinary sciences, makes students feel the application value and social needs of mathematics, and realizes that "there is mathematics everywhere in life", thus correcting their misconceptions that the main function of mathematics is calculation, and the ultimate goal of mathematics learning is to stimulate students' creative desire for exams, so as to change passive learning into active learning.
Appreciating the beauty in mathematics, the beauty of unity, simplicity, symmetry and strangeness in mathematics can greatly change the boring situation of mathematics class at present, make students learn with great interest, improve their aesthetic ability in mathematics while enjoying beauty, enlighten their thinking, cultivate their quality, and promote the comprehensive and harmonious development of their personality and emotional experience.
Analysis on the present situation and problems of infiltrating mathematical culture and beauty into middle school mathematics teaching
Mathematics culture has gradually entered the middle school mathematics classroom, but we can see that the current teaching practice still only overemphasizes the instrumental role of mathematics, weakens the cultural value of mathematics and ignores the influence of mathematics on other disciplines, making mathematics an invisible culture for a long time. At present, the way of infiltrating mathematics culture in schools is generally only to introduce the history of mathematics. The teacher introduces a certain stage of mathematics development in one or two sentences, without excavating any connection between them or combining it with the contents of textbooks. Simple form, boring, lack of interest, systematicness and practicality are the present situation of infiltrating mathematics culture into middle school mathematics teaching. How can such teaching achieve the purpose of infiltrating mathematical culture, inheriting mathematical culture and stimulating students' mathematical learning?
The reasons are as follows:
First of all, the utility of teaching objectives. Under the command of the senior high school entrance examination, the teaching goal of school mathematics is still to implement "double basics of mathematics" [1], and the main task is to improve the enrollment rate. Therefore, the teaching method is generally used in mathematics classroom teaching, and teachers pay more attention to the cultivation of students' problem-solving ability, and strive to instill more mathematical conclusions and do more application problems in a limited time. Nature ignores the infiltration of mathematical culture. In fact, middle school mathematics teaching should aim at cultivating people with mathematical literacy, not a tool for mechanical calculation! In this way, the role of infiltrating mathematical culture can not be ignored.
Secondly, a single evaluation system. Examination is the only evaluation system of middle school teaching at present, and written examination can only examine students' mastery and application of knowledge to a certain extent, but can not comprehensively examine students' learning process and mathematics literacy, nor can it fully reflect a teacher's teaching level. Therefore, the evaluation system of mathematics teaching should be diversified, focusing on both the results and the process, and paying more attention to various factors affecting the teaching process and results. The correct evaluation system should include four aspects: the evaluation of course materials, the evaluation of teaching process, the evaluation of students' academic performance (mainly referring to students' mathematical thinking) and the evaluation of students' social adaptability.
Furthermore, isolated discipline construction. Every course in middle school is taught in relative isolation, and each course often only pays attention to the formation of knowledge system within disciplines and ignores the knowledge connection between disciplines, such as vectors. When learning vector, it is difficult for students to understand the concept of vector, and many teachers often can't explain its connection with physical mechanics in teaching. If we can understand from the aspect of physical mechanics and establish the connection between physics and mathematics, it will be much easier to understand the concept of vector.
Infiltrating mathematics culture and beauty in middle school mathematics teaching is like flesh and blood. We should not only study the theoretical knowledge of infiltrating mathematical culture and beauty into middle school mathematics teaching, but also put it into practice to make it really useful mathematics. This is a very important issue in the teaching reform, and it is hoped that it will receive universal attention and strong support from the society.
What is mathematical culture?
Mathematical culture refers to:
Narrow sense: mathematical thoughts, spirits, methods, viewpoints and languages, as well as their formation and development.
Broad sense: In addition to the above connotations, it also includes mathematicians, mathematical history, mathematical beauty and mathematical education. Humanistic elements in the development of mathematics, the relationship between mathematics and society, the relationship between mathematics and various cultures, and so on.
Mathematics, as a cultural phenomenon, has already become people's common sense. Historically, cultural celebrities in ancient Greece and Renaissance were often mathematicians themselves.
Plato, Thales, Leonardo da Vinci and other famous representatives. Recently, cultural celebrities such as Einstein, Hilbert, Russell and von Neumann were also the founders of mathematical civilization in the 20th century.
Extended data:
Cultural connotation
Out of the shadow of mathematical isolationism, the connotation of mathematics is very rich. However, in the field of mathematics education in China, there is often the concept of "mathematics = logic". The survey shows that students regard mathematics as "a collection of absolute truths" or "a game of symbols".
Mathematics follows the model of memorizing facts-using algorithms-executing memorized formulas-and getting answers. The formula of "Mathematics = Logic" has brought many negative effects. As a wise man said, a dynamic mathematical beauty has only skeleton in X-ray photos!
The connotation of mathematics includes observing reality from a mathematical point of view, building mathematical models, learning mathematical languages, charts and symbols, and conducting mathematical exchanges. Through rational thinking, cultivate rigorous quality, pursue innovative spirit and appreciate the beauty of mathematics.
More than half a century ago, the famous mathematician Courand wrote in the preface of his masterpiece What is Mathematics: "Today, the traditional position of mathematics education is in a serious crisis.
Mathematics teaching sometimes becomes an empty problem-solving training. There is a trend of over-specialization and over-emphasis on abstraction in mathematical research, while ignoring the application of mathematics and its connection with other fields.
Teachers, students and educatees all demand a constructive reform, the purpose of which is to truly understand that mathematics is an organic whole and the basis of scientific thinking and action. "
On August 20, 2002, Qiu Chengtong said in an interview with Oriental Time and Space: "I appreciate Historical Records as an opera." "Because I value history, and history is macro, so when I look at mathematical problems, it is often a macro view, which is different from others' views. "This is a mathematician's mathematical culture.
On August 2 1 2002, Wen Wei Po published Qian Weichang's article "The Pursuit of Gottingen School", which mentioned: "This made me understand:
Mathematics itself is beautiful, but don't be lost by it. The task of applied mathematics is to solve practical problems, not to perfect many mathematical methods. We take solving practical problems as our responsibility.
From this point of view, we should be excellent butchers who solve practical problems, not knife makers, not knife makers who appreciate how sharp their knives are all their lives without solving practical problems. "This is a mechanic's mathematical culture view.
Like all cultural phenomena, mathematical culture directly dominates people's actions. The mathematical culture of isolationism, on the one hand, makes people stay away from it, making people afraid of mathematics;
On the other hand, he is narcissistic and talks to himself, which makes people regard mathematicians as "weirdos". Mathematics in school, originally a favorite subject for teenagers, has become a "sieve" for filtering and a "stick" for beating people.
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.