Mathematics and Civil Society

Mathematics and Civil Society

1.  Introduction

         Civil society is a concept located strategically at the cross-section of important strands of intellectual developments in the social sciences (http://en.wikipedia.org). How is Mathematics related to Civil Society? People believe, Mathematics is a divine discipline. Some love Mathematics, while some fear it; some study Mathematics, while some worship it. Ancient Indian Mathematicians like Aryabatta or Bhaskara worshipped Mathematics and lived for it. It was not for any material benefit, but was out of their devotion. Again, the legend Srinivasa Ramanujan of India was a man who adored Mathematics. All over the world, there were and there are people who loved Mathematics as a divine subject. Hence it may be a very interesting topic of research, that how Mathematics affects the Civil Society.

         We know that Mathematics plays a very important role in the Modern World. We are living in a scientific era of rapid development. Things that were new or unheard of a few years ago seen commonplace today. Some of the new technical advancements may have little effect upon our personal life, but others may play a most important part in our existence. If we are to play a position on the team of our society, or even to watch intelligently from the sideline, we must have an understanding and appreciation of Mathematics. The advancement in the areas of Science and Technology are rapid and rather amazing. All these astounding advancements are indebted to Mathematics to a great extent. Everyone who is a beneficiary of these scientific and technological facilities may have to know a little of Mathematics for its fruitful and smooth utilization. Hence, Mathematics cannot be considered as a classroom discipline only. Every man may need it at any time (Anice James-2005). Not only an Academician; not only a Scientist; not only an Engineer; but, a shopkeeper needs it; a grocer needs it; a housewife needs it; a sportsman needs it; an employee needs it; and who does not? Just like a language, we need Mathematics to communicate! So the Mathematics that we teach in the classroom should cater the need of every individual. There is no need of teaching Higher Algebra or Topology to a grocer. A housewife does not need the statements or proofs of real Analysis. 

         In this paper, the authors wish to discuss these matters in detail. The need of formulating a curriculum, which suits the need of different types of people, is studied. The paper is based on a survey made in a locality of Trivandrum, which is one of the State-Capitals of India. Opinions from experts are also used to develop the paper. 

2.  Significance of Mathematics in the Civil Society 

         Why should everybody learn Mathematics? What is the significance of Mathematics in the Civil Society? What shall be the advantage of devoting so much effort, time and money of the Society to learn Mathematics? How does it make any contribution in the overall development of the members of the Civil Society? These are some of the questions that may come to our mind when we speak of the relation between Mathematics and Civil Society. These qualms in our mind will show us the way to explore the values of Mathematics (Kulshrestha-2005).

             Historians of Mathematics have the opinion that much of the impulse behind Mathematics has been economic. In the third and fourth decades of the twentieth century, for obvious political reasons, attempts were made to show that all vital Mathematics, particularly in application, is of economic origin. But, they admit that an aware of Mathematics, is essential for civilized living (Bell- 1940).

           Today economic tyranny has no more powerful friend than the calculating prodigy. Without knowledge of Mathematics, the grammar of size and order, we cannot plan the rational society in which there will be leisure for all and poverty for none. We should try to realize the reasons, which repel many people from studying this subject. As Mathematics has been taught and expounded in schools no effort is made to show its social history, its significance in our social lives and its immense dependence of civilized mankind upon it. We were neither told how the knowledge of Mathematics has been used in history to assist in the liberation of mankind from superstition nor shown how it may be used to defend the liberties of the people.

            Consider the sum:  0.1 + 0.01 + 0.001 +.…. However long we make the sum, it never grows bigger than 1/9. We know that this is nothing but about the convergence of an infinite series to a limiting value. The same fact can also be interpreted as if we go on piling up smaller and smaller quantities as long as we can, we may get a pile of which the size is not made measurably larger by adding any more. This provides a great social truth: Fruitful intellectual activity of the cleverest people draws its strength from the common knowledge which all of us share. Beyond a certain point, clever people can never transcend the limitations of the social culture they inherit. Our studies in Mathematics show us that whenever the culture of a people loses contact with the common life of mankind, it is becoming a priestcraft, which will perish. The Mathematician and the plain man each need one another. The democratization of Mathematics is a decisive step in the advance of a civil society (Hogben-1937).   

          History of Mathematics reveals that whenever a society gave due weightage to the knowledge of Mathematics, it made a tremendous progress. When Mathematics makes its contribution in the advancement of science and technology, society draws huge benefits. Its history presents a very good picture of the overall development of our civilization. What we possess in the form of Mathematical knowledge today is the fruit of the combined efforts of all human beings. Mathematics is the common heritage of mankind and it is not the exclusive property of any particular nation, race or country. So it is no exaggeration to say that history of Mathematics is the history of civilization.

          Ancient men felt their concern with Mathematics, motivated by their social needs and they had done their best on the computational front of their life. It has been found that Babylonians possessed the knowledge of multiplication and division of numbers, taking square and square root of numbers, finding areas of certain geometrical figures (http://www-groups.dcs.st-and.ac.uk). The Egyptian civilization is also owed to Mathematics. Aristotle says that Mathematics had its birth in Egypt, because there the priestly class had leisure needful for its study. They built pyramids at a very early period. The basis of both the Egyptian and the Mesopotamian civilizations were agriculture. In an agricultural economy, a reliable calendar, accurate with respect to both astronomy and arithmetic, is a necessity. When we think of Greek civilization, we could not help to remember the great Mathematicians, like, Thales (640-546 B.C), Pythagoras (580-500 B.C), Plato (429-348 B.C), Ptolemy, Archimedes (287-212 B.C), Apollonius, Pappus, Diophantus, etc. When we go through history, we can see further the contributions from Romans, Chinese, Japanese, Arabs and Indians to Mathematics. A close and careful study of the history will reveal the fact that ancient civilizations are very much related to the development of Mathematics.  

3.  Educational Values of Mathematics

        Broadly speaking Mathematics learning is multi-valued. Some of them are:

§  Practical or Utilitarian Values

§  Disciplinary Values

§  Cultural Values

§  Social Values

§  Moral Values

§  Aesthetic Values

§  Recreational Values

3.1.   Practical or Utilitarian Values

         A common man can get on sometimes ‘very’ well without learning how to read and write, but he can never pull on without learning how to count and calculate. Any person ignorant of Mathematics will be at the mercy of others and will be easily cheated. The knowledge of its fundamental processes and the skill to use them are the preliminary requirements of human being these days (Sidhu-1995).

         A person may belong to the lowest or the highest class of society, but he utilises knowledge of Mathematics in one form or other. Not to speak of an Engineer, a Businessman, an Industrialist, or Banker; even a Labourer has got to calculate his wages, make purchase from market, and adjust the expenditure to his income. Most individual as well as group projects in life fail for want of sense of calculation. A person with proper calculations, can anticipate all the possible handicaps to be faced and thus can adopt precautionary measures. An individual is the smallest unit of a Civil Society. The society can flourish only if the smallest unit flourishes. 

         In many occupations indirect or direct use of Mathematics is made. Many of the projects depend upon Mathematics for their successful functioning. It has become the basis of the world’s entire business and commercial system. Mathematical illiteracy in the masses is a formidable barrier in the way of a country’s progress. One is sometimes misled about the practical value of Mathematics on account of a feeling that whatever is taught in higher classes is of little use to live in the society. The common man seldom uses the knowledge in higher Mathematics in his later life. But the value of a subject cannot be measured in this way. The great Napoleon said, ‘the progress and the improvement of Mathematics are linked to the prosperity of the state’.              

3.2 Disciplinary Values

         Strengthening of mental power as well as acquisition of knowledge is considered as an important disciplinary value of Mathematics.  It is primarily taught on account of the mental training it imparts, and only secondarily on the account of the knowledge of facts it imparts. The mental power one gets from learning Mathematics is the acquisition of the art of proper thinking and effective reasoning. The study of Mathematics imbibe in the individual the values like honesty, truthfulness, open-mindedness, objectivity, self-confidence, self-reliance, patience, will-power, and orderly habits like concentration, punctuality, neatness, hard work, etc. Thus the study of Mathematics helps an individual to lead a well-disciplined life, which in turn helps him to constitute for a good Civil Society. 

         Certain modes of thinking provided by Mathematics learning are quite important in the successful building of society and nation. This analytical approach enhances the ability to take hold of a situation, to analyse the situation and to perceive correctly the state of affairs. The habit of carefully analysing the situation before decision making could be very helpful in complex life situations where decision making becomes very difficult. As Mathematics deals with facts, which are accurate and precise, there is no scope for uncertainty or vagueness. This makes the mind of the learner more broad and open. He enjoys a universal acceptance, without any barriers of countries, languages, climate, etc. the knowledge of Mathematics helps the members of the society to organise his ideas more logically and express his thoughts more accurately and explicitly. It trains the members not to take things for granted, or rely on tradition or authority, but rely on reasoning.

3.3    Cultural Values

         The essence of culture of a Civil Society is in the mode of living of its members. The culture reflects how they live, behave, dress, eat, drink, rear their children, and maintain their social relationship. The mode of living of the members of a society is greatly determined by the scientific and technological advancement, which in turn depends upon the progress and development of Mathematics. Therefore the changes in modes of living and thereby the culture has been continuously influenced by the progress in Mathematics. It is rightly said that, ‘Mathematics is the mirror of civilisation’. Thus the history of Mathematics portrays the culture and civilisation of a Civil Society. Mathematics also helps in the preservation and transmission of our cultural traditions.    

3.4   Social Values

         For become a Civil Society, any country should encourage its members to participate in the political process and to contribute to community services consistent with good citizenship. Interpersonal cooperation and social responsibility are encouraged.

         Mathematics helps in the proper organisation and maintenance of a fruitful social structure. It plays an important role in the proper setting up of social institutions such as banks, co-operatives, railways, post offices, insurance companies, industries, transports, navigation and so on. Effective business transactions, exports and imports, trade and commerce and communication cannot take place without Mathematics. Thus smooth and orderly functioning of the civil society is ensured by Mathematics.

          The success of an individual in a society depends on how well he is able to become a part of the society and what contributions he can make towards the progress of the society and how well he can be benefited by the society. Today, our social existence is totally governed by the scientific and technological knowledge, which can only be attained by the study of Mathematics. Mathematical methods and logics are used to investigate, analyse and draw inferences regarding the formation of various social laws and their compliance. More over the values acquired through learning Mathematics will help the individual to adjust himself and lead a harmonious life in the society.

3.5   Moral Values

          The Greek philosopher Dutton has rightly remarked that, ‘….gossip, flattery, slander, deceit – all speak for a slovenly mind that has not been trained by Mathematics’. This articulates the moral value of Mathematics. The study of Mathematics helps an individual in his character formation in many ways. It develops in him a proper attitude, as there is no space for prejudiced feelings, biased outlook, discrimination and irrational thinking, and aids him in objective analysis, correct reasoning, valid conclusions and impartial judgment. These moral values inculcated in the individual help him to become a successful member of his society.

3.6  Aesthetic Values

           Mathematics enriches with its aesthetic appeal. Moving considerably beyond the mere amusement found in games, the elegance and gracefulness of Mathematical relationships touches our emotions, much like music and art can reach inside the psyche and make us feel truly alive (Clawson –2004). When we go through the biographies of great Mathematicians, we see that almost all of them were attracted to this ‘divine discipline’, by realising its beauty. They were not studying Mathematics, but worshipping it. The fineness, the harmony, the symmetry everything adds its beauty. Music or art are simply the aftermath of this eternal beauty.

3.7   Recreational Values

          Mathematics gives a variety of recreational opportunities to grown up people as well as children. Mathematics entertains people. Mathematical game books are very popular, and many magazines end with some kind of ‘brain bogglers’ or ‘mind benders’ section, which is often filled with Mathematical puzzles. Various puzzles, games, riddles, etc., of Mathematics, give people recreation and entertainment. The modern video-computer games are all developed through proper use of Mathematics. The significance of this type of recreation is that, this enables one to develop his imagination, sharpen his intellect and draw satisfaction to his mind. The human brain is an organ that improves with exercise. The study of Mathematics thus gives sufficient exercise to the brain of an individual. For the practitioner of Mathematics, the daily joy of untwisting some strange Mathematical relationship is always entertaining. Thus Mathematics shares a place with other amusement activities from chess or cards.              

4.   Empirical Study

          A study is conducted in our locality in Trivandrum to learn more about the relationship between Mathematics and the Civil Society. We had selected individuals in the age group of 20-50 years. The study is mainly aimed at gathering the society’s opinion in the concerned problem. The main objectives of the study were:

ü  to evaluate the impact of Mathematics learning in individual life; and

ü  to evaluate the impact of Mathematics learning in social life.

             A survey was conducted and the sample consisted of 145 respondents including 32 women. Table-1 shows the classification of respondents according to their formal education in Mathematics.

 Table-1

Mathematics Education	No. of people	Percentage
Illiterate	Nil	-
In the Primary School only	34	23.45
Up to the Secondary School only	87	60.00
Beyond Secondary School	24	16.55
Total	145	100.00

   

As it is clear from the table, none of the respondents were illiterates, 34 of them (23.45 %) are having primary schooling (4 years of study), 87 of them (60%) having secondary school education (10 years of schooling) and 24 of them (16.55%) having formal education beyond secondary schools education.        

        Table-2 shows the classification of respondents according to their primary occupation.

Table – 2

Occupation	No. of people	Percentage
Unskilled	47	32.41
Skilled	58	40.00
Service	21	14.48
Professional	19	13.11
Total	145	100.00

              Of the 145 individuals 32.41 per cent were unskilled labourers, 40.00 per cent were skilled labourers, 14.48 per cent were in the Service category, while 13.11 per cent were Professionals.

Table-3 shows their responses towards the values of Mathematics learning.

Table-3

Values of Mathematics Learning	No. of people	percentage
Practical Value	145	100.00
Disciplinary Value	38	26.21
Social Value	35	24.13
Cultural Value	27	18.62
Recreational Value	12	8.27
Aesthetic Value	8	5.51
Moral Value	3	2.06

          All the 145 individuals agreed that they use Mathematical knowledge every day in one form or other. It is seen that all the 145 agree with the practical value of Mathematics learning. It is interesting to see that even some of the respondents in the group of ‘primary school Mathematics education’ admitted the practical value of Mathematics. But most of the respondents were unaware of other values of learning Mathematics.

          Only 26.21 per cent of the respondents agree for its disciplinary value. There were respondents even from the category of Professionals and Service group, who were unaware of the social value of learning Mathematics. Only 27 (18.62%) of the respondents appreciated the Cultural values. The respondents were as low as12 (8.27%) who admit the Recreational value of mathematics as 8 (5.51%) who admit the Aesthetic value of Mathematics. There were only 3(2.06%) respondents who know about the Moral value of the subject.

           The responses of the people who were included in the study, clearly shows that people are aware of the importance of mathematics in day-to-day life.  Even though people in the society are not fully aware of the different values of Mathematics, they all agree in the fact that, it is necessary for a societal man to know Mathematics, at least its fundamentals, and the facts of practical utility. Some of them gravely regretted that they could not study Mathematics when they were offered it.

5.   Conclusion

           Even though a good percentage of people are unaware of the relation between Civil Society and Mathematics, it does not mean that the relation is insignificant. The structure and functioning of the Society is highly depending on Mathematics. But the only thing is that the members of the Society, irrespective of their education level or occupation is highly ignorant towards this relationship. The authors like to compare the situation with the fact: ‘even though Oxygen is essential for life, nobody care for it’. In this world of technological savvy, we cannot think of a Mathematics-free society. Directly or indirectly, knowingly or unknowingly, every member of the society consumes Mathematics. Even after imbibing all the benefits, we are pretending like a stranger to the subject. It should be wiped off. We should see and admit the goodness in Mathematics. No doubt, this will make our society progress with enormous power. So there should be a move from the part of Mathematics Teachers and Academicians to make the public aware of the values of learning Mathematics, especially its Social values.

                The authors are now engaged in designing a study module to give basic mathematics education for school dropouts with special emphasis on budding Mathematical skills and developing practical application of Mathematics in their respective fields of work.