Study on the Culture-oriented Mathematics Education
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Abstract. Mathematics has a close connection with the life of people all over the world. The mathematical culture refers to the integration of the mathematical spirit, perspective as well as concepts into the cultures. In this paper, the author carries out a study on the mathematics education, which is oriented at the cultures.
Key words: Culture-orientation; Mathematics; Education； Exploration
1. Mathematical Culture in Life
When the mathematical culture is being discussed, the history of the mathematics can be easy to step into the minds of the people. Indeed, making a macro observation on the mathematics as well as investigating the progress of the mathematics from the perspective of the history is two of the most important methods to reveal the mathematical culture.
However, in addition to such a macro historical investigation, there is a microscopic analysis at the same time. In other words, the inside information of the mathematical culture is revealed from the perspectives of the specific mathematical concepts, the mathematical methods as well as the mathematical thoughts. Therefore, in the following, some new perspectives will be used by the author to make an introduction, for the purpose of displaying the mathematical culture from multiple levels.
1.1 Mathematics and Literature
Mathematics is interlinked with the literature in the aspect of the thinking approach. For example, there is "symmetry" in the mathematics course of the middle school, while there is "antithesis" in the literature. Symmetry is a kind of transformation, in which the things have been changed but still keep something unchanged in nature. The rotational symmetry refers to the fifty percent division based on a symmetric axis, in which the shape and size of the figures remain unchanged. However, what's the "antithesis"? Actually, it means a matching of both sound and sense in two lines, while some characteristics of the words as well as the sentences are still unchanged. The unchanged properties in the changing-over things are universally in existence in culture, literature as well as mathematics. The "dual theorem" in mathematics as well as the variant and invariant in the topology is the embodiment of the above idea.
In the mean time, the artistic conception of the literature owns some interlinked aspects with the mathematical concepts. Mr. Xu Lizhi pointed out very early that the verse "a lonely boat is at distance and the blue sky is clean" just gives a very close artistic conception to the limit concept in mathematics.
1.2 Mathematics and Language
One of the forms of the mathematical culture is integrating the mathematics into the languages. As a Chinese commonplace saying goes, everything will be done regardless of the "three times seven equals twenty-one", and this touches upon a multiplication formula; a task will be completed within the time of calculating "three, down five, take away two", and this touches upon a Chinese counting-frame formula.
Also, for example, the phrase "absolutely safe" is used to express that a person is positive about a thing the Chinese language. However, this phrase can be deliberated deeply by combining with the "small probability event" in mathematics. More importantly, "there is 0.1% chance for an accident" is absolutely not allowed in the spacecrafts.
1.3 Mathematics and Aesthetics
Take a look at the "1/2 + 1/3 = 2/5". Could you feel there is a harmonious beauteousness? Is the root solving formula of the quadratic equation beautiful? All of these questions involve the aesthetics. The trigonometry classroom teaching should touch upon the music. The three-dimensional geometry teaching must touch upon something about painting and how to draw the three-dimensional graphics paintings on the plane.
2.The Connotation of the culture-oriented mathematics education
Different views as well as different values on the mathematics may give rise to the different concepts of mathematics education. As a result, the different mathematics educations come into being all over the world. If the mathematics is regarded as a collection of the mathematical knowledge, the mathematics education will be regarded as the teaching of the mathematical skills. If the mathematics is regarded as a kind of thinking activity, the mathematics education will be regarded as the teaching of activities of the mathematical teaching way.
In recent years, the researches on the teaching of the mathematics have obtained a series of the important achievement, which have been accepted by a wide range of the workers in the mathematics education and have exerted a very far-reaching influence at the same time. If the mathematics is compared to be a kind of cultural system, the mathematics education should be regarded as the mathematical culture education, which will be a totally new mathematics teaching concept in contrast to the above two mathematical educational methods.
Mathematical concept is the core of the mathematical culture. Besides, the mathematical spirit, the mathematical consciousness, the mathematical thought as well as the mathematical way of thinking all are the very important parts of the mathematical concept system. The influence of the mathematics on the students is realized through the influence of the mathematical concepts on the values and behavioral ways of the students.
However, the influence of the mathematics education on the society is realized through the influence of the mathematical concepts on the social concepts. As the concepts of common people are the core factors composing of the mental quality and also the social concepts are the core factors composing of the national quality, this essentially decides that the mathematical culture education is a quality education.
In the "mathematics education which is oriented at the culture", the cultural value of the mathematics should be utilized fully and also the mathematics should be used completely to train the mathematical quality in the processing of teaching the mathematics. In the mean time, the students take full advantage of the learning of the mathematical culture, so as to make an enhancement to the abilities in the thinking way as well as analyzing and resolving the problems.
However, the mathematical culture education is aiming to making the students acquire the advanced mathematical culture and then serve for the needs of society through the succession of the mathematical culture knowledge and create a new mathematical culture at the same time. As a result, they can push forward the progress of the whole society.
3.Difference between the Culture-oriented Mathematics Education and the Ability-oriented Mathematics Education
In the mathematics education which is oriented at the culture, high importance is attached to the mathematical concept and especially the educational value of the mathematical spirit. And this is actually one of the most fundamental characteristics of the mathematics education which is oriented at the culture.
Certainly, the ability-oriented mathematics education also lays a stress on the development of the mathematical concept, but its focal point is different from that of the mathematics education which is oriented at the culture. In the ability-oriented mathematics education, developing the mathematical concept of the students is only regarded as the method of improving the thinking way of the mathematics. However, for the culture-oriented mathematics education, developing the mathematical concept of the students is not only one of the means, and also is one of the most important goals of the education.
Therefore, it is necessary for the culture-oriented mathematics education not only to bring the intelligence education value of the mathematical concept into full play, and also pay more attention to the exertion of the role of the mathematical concept and especially the great role of the mathematical spirit in the promotion of the personality development of the students.
4.Several Aspects Necessary to be stressed in the Culture-oriented Mathematics Education
With the purpose of developing the rational spirit of the students as well as the consciousness of seeking truth, it is highly necessary to highlight the important position of logical reasoning as well as deduction.
In such a process, however, the difficulty of teaching will be increased all the time, and the professional characteristics of the mathematics education t will be emphasized excessively. As a result, the difficulties will be increased to the learning of the students. However, this goes against the original goal of the mathematical culture education at the same time.
4.1 The Emergence and Development Process of the Mathematics Knowledge
It is necessary for the mathematics courses to give a full expression to the emergence process of the mathematical thinking way and make the students know well the occurrence of the mathematical thoughts and then the thinking process of the mathematicians can reappear. In the mean time, it is necessary to add the teaching of the history of the mathematics into the teaching process and advocate the learning of the mathematical knowledge from the perspective of the mathematical culture, and ultimately get a real understanding of the mathematical thought, make an enhancement to the mathematical training and cultivate the mathematical quality.
4.2 The Connection between Mathematics and Life
In the traditional sense, mathematics is thought as the most fundamental tool to get an understanding of other science and engineering disciplines. As a result, a majority of the students only have the ability to solve the written questions of the mathematics, but can't make use of the mathematical knowledge to resolve the simple practical problems, not mention to applying the mathematical ideas and thinking methods to the work and practices. Culture originates from life and in turn exerts an influence on the life, and therefore is the relationship between practice and theory.
In the mean time, it is highly necessary to make an enhancement to the connection of the mathematics with the production and actual life and improve the qualities in mathematics without a stop. As a result, people can appreciate, learn and make use of the mathematical knowledge from a broad perspective.
4.3The Non-intelligence quality training in Mathematics education
In the previous time, the mathematics teaching only attached importance to the training of the three major abilities of the students and the acquisition of the mathematical knowledge.
As a result, the cultural knowledge in the mathematics courses as well as the training of the cultural qualities of the students is ignored. Besides, the non-intelligence quality is not directly involved in the learning activity of the mathematics, but will exert an influence on the non-cognitive factors such as emotion, will and motivation of the mathematics learning.
Therefore, in the mathematics education, it is necessary to strengthen the influence of the non-intelligence quality, integrate the patriotism stimulate the interest of the students in learning, and mobilize the leaning enthusiasm, and arouse the inner motivation of the students in learning.
4.4 The Rich and Colorful Mathematical Activities
The stories about the mathematicians, the frontier development situation of the mathematics, and the background of the famous mathematical questions as well as the mathematical aesthetics belong to the mathematical culture. In the mean time, all these can provide the chances for the students to accept the influence and baptism of the mathematical culture in the mathematical activities.
Therefore, through the combination with the mathematics knowledge and skills in the inheritance of the mathematical culture knowledge as well as the emotion, attitudes and values, the influencing and permeation force of the mathematical culture can be strengthened, and subsequently the students can obtain the mathematical culture in the process of training the mathematical culture quality.
5. Conclusion
From the above analysis, it can be clearly known that the cultivation of the cultural quality as well as the emergence of the concepts mainly refers to the inheritance of the cultures. And this gives a reflection to the sociality of the cultural education.
On the one hand, the formation of the mathematical idea is mainly a kind of the "cultural inheritance". Different from the skills and abilities, the mathematical concept in the modern times can't be established through the practices, because its formation is a subtle process.
On the other hand, the specific cultural inheritance behaviors are completed one by one. Therefore, it can be clearly known that the culture-oriented mathematics education attaches higher impotence to the individual characters of the students.
In addition, the culture-oriented mathematics education puts forward new requirements on the knowledge structure of the teachers at the same time. In the mean time, the mathematics education, which is oriented at the culture, requires the teachers to have the professional knowledge as well as much broader knowledge vision. Besides, the mathematics education in realities is necessary to have multiple levels and perspectives.
Through the above analysis, it can be clearly learnt that the ability-oriented mathematics education and the culture-oriented mathematics education can exert a role in the improvement of the qualities of the students. The difference between the ability-oriented mathematics education and the culture-oriented mathematics education lies in the key points.
Therefore, with the purpose of giving full play to the role of the mathematics education in the improvement of the students' quality and even the national quality, it is necessary for the mathematics education in China to be inclusive and comprehensive, to contain the knowledge education, ability education and cultural education, and make an adjustment to the key points in accordance with the different educational objects and stages.
References
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