Mathematics and Civil Society
[Dr. P. G. Thomaskutty, Reader in Economics,
Mar Ivanios College, Trivandrum, India-695 015.
Dr. Mary George, Selection Grade Lecturer in Mathematics,
Mar Ivanios College, Trivandrum, India-695 015.]
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.
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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.
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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
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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
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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.
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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
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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,
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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
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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.
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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.
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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,
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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:
 to evaluate the impact of Mathematics learning in individual life; and
 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
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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.
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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
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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
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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.
Acknowledgement
The authors wish to thank University Grants Commission of India, for their
financial support in the form of Post-Doctoral Research Award to the second author in
pursuing this research.
References:
1.
Anice James,
Publications,
Teaching of Mathematics, (First Edition),
Neelkamal
Hyderabad, India, 2005
2.
Bell, E. T., The Development of Mathematics, McGraw Hill, New York, 1940
3.
Clawson, C. C., Mathematical Sorcery, Viva Books, India, 2004.
4.
Hogben, L., Mathematics for the Million, Norton &Company, New York, 1937.
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5.
Kulshrestha,
A. K. ,
Publications, Meerut,
6.
Sidhu,
K. S. ,
Teaching of Mathematics, (Third Edition), Surya
India, 2005
The Teaching of Mathematics, (Fourth Edition), Sterling
Publishers, New Delhi, India, 1995
Web Sites:
1.
http://en.wikipedia.org/wiki/Civil_society
2. http://www-groups.dcs.st-and.ac.uk/~history/Indexes/Babylonians.html
3. http://www-groups.dcs.st-and.ac.uk/~history/Indexes/Egyptians.html
4. http://www-groups.dcs.st-and.ac.uk/~history/Indexes/Greeks.html
5.
http://www-groups.dcs.st-and.ac.uk/~history/Indexes/Arabs.html
6.
http://www-groups.dcs.st-and.ac.uk/~history/Indexes/Chinese.html
7.
http://www-groups.dcs.st-and.ac.uk/~history/Indexes/Indians.html