Mathematics: The Realm Of Meaning

This paper attempts to explore the value of mathematics from a new perspective,based on the update findings of mathematical philosophy and mathematical education philosophy study,with reflection on the prominent problems in mathematics education and analysis of the implications of the fundamental way back to the meaning of mathematics.The existence of human being is always related to the meaning,since human being is one kind of the existence of meaning and only the one full of meaning may bring about happiness.The meaning of mathematics has drawn much attention since Ancient Greece times.Plato indicated that if one forgets the fact that the ratio of diagonal lines to sides in square is non-commensurable,he deserves to be deprived of his name.He thought the one who ignores the importance of mathematics is as stupid as goose.With the promotion of the new round of mathematical curriculum reform,the meaning of mathematics meaning has become a hot topic in recent years.Although many people have carried out a large number of explorations and researches on this topic,most of them undertake the research only from one aspect in general.In a certain scope,those researches they carried out are more in a scientific position,but lack of the one in an educational position,and thereby those are not systematic, in-depth,and comprehensive.This paper focuses on the meaning of mathematics,with emphasis on the central subjects as follows:what is the essence of mathematics? Why does mathematics belong to the field of meaning? How to embody the meaning? Is mathematics education lacking in the meaning? What's the reason? What is the following concrete ways to deal with it and what are the philosophy perspectives in those ways?I believe that the root of failing to recognize the meaning is the ignorance of analysis from the perspective of meaning philosophy,cultural philosophy and educational philosophy,especially from the mathematical philosophy and mathematical education philosophy perspective.In fact,if we avoid taking the nature of mathematics into consideration,the controversy over mathematical meaning will never come to an end.Therefore,it will be impossible to propose a more convincing and satisfactory philosophical interpretation of the meaning and the nature of mathematics.In this paper,with the exploration on the nature of mathematics,the author considers mathematics as a kind of science and culture which embodying the characteristics of dynamic,misleading,experiential or to-be -experiential.Mathematics seeks to interpret the meaning of the physical world around us thoroughly and understand different models in our minds.It is a kind of science concerning models instead of a science only concerning numbers or figures.Based on these,I introduce -"Mathematics is a field related to the meaning"-this point of view,and make an in-depth discussion on the meaning of mathematics both in a scientific and educational position.Knowledge consists of three indivisible parts:symbolic feature,logic form and meaning.In this paper,the author proposes the idea that mathematics belongs to the field of meaning and explains that the meaning of mathematics relates mathematics to the physical,objective knowledge and spiritual world.Since there are many comments on the meaning of mathematics from the view of application and there are few discussions from the perspective of the development of human being which is concentrating on the standpoint of science rather than education,this paper will discuss on the meaning of mathematics from both the standpoint of scienco and education.From the perspective of science,mathematics is like a piece of music,the Queen of science,the servant of science,the company of science.From the perspective of education,mathematics is a prerequisite to become citizenship,which can equip one with excellent quality,the ability of thinking and aesthetic ability and so on.Investigations and studies show that the absence of mathematical meaning is common in mathematical education which directly leads to the alienation of mathematical teaching.Meanwhile there are some deviations in the understanding of mathematics teaching,both in the essence and the purpose and value of mathematics.Many students regard mathematics as a kind of symbol play to kill brain cells and invincible enemy.Learning mathematics is a process of compulsion and depression, which makes the learner standing the opposition towards the knowledge,the outcome and other learners.The deep reason behind this is that people have some misunderstanding of mathematics and mathematics teaching.It is considered that mathematics is as a tool for entering schools in mathematics teaching,the purpose of learning mathematics is to solve the problems,mathematics is an absolute truth,mathematical is equal to logic,mathematical teaching should emphasize on axiomatic system,mathematical teaching should be very abstract and so on.In this paper,I conduct an in-depth analysis on these ideas through the combination of the forefront results of researches on mathematical philosophy and the philosophy of mathematical education.I believe that all kinds of perplexities and confusions in the mathematical education are closely related to the absence of mathematical meaning.In the paper,I propose a new perspective of mathematical education——the meaning of mathematical education.And I believe,a mathematical education moving towards the meaning should be regarded as the new orientation and the pursuit of education.Then,how does the mathematical education return to mathematical meaning? Based on discussions on the three characteristics of mathematics-dialogue,culture and experience,together with reflection on all kinds of misconceptions in mathematical education,I put forward an idea that we can return to mathematical meaning from the "mathematical dialogue",the "mathematical culture" and the "mathematical experience" aspect.From the aspect of mathematics dialogue,the author suggests that the meaning can be obtained and becnme rich from the dialogue.Without dialogue,there is no communication and no real education.Those dialogues have great educational value and mathematics embodies the nature of dialogue,not only from the aspect of mathematical philosophy and development but also from the aspect of the mathematical knowledge.Therefore,it should make mathematical dialogues with students in mathematical teaching,with great attention paid to the mathematical communication and the value of process.From the aspect of mathematics culture,mathematics is an essential part of civilization and culture.In mathematics education,it should be considered from two aspects:concrete knowledge aspect and invisible culture aspect.There is deep introspection of mathematical knowledge education from the analysis of the characteristics,the losses,and the root of mathematical knowledge education. The author indicates that it is inevitable choice from knowledge education to culture education.From the aspect of mathematics experience,mathematics has a great empirical value.All learning about mathematics involve into the transference of experience.So it should return to the real life world with great importance paid to the mathematical experience and characterization in mathematics teaching.