Math 101
Mathematics is not primarily a matter of plugging numbers into formulas and performing rote computations. It is a way of thinking and questioning that may be unfamiliar to many of us.
Mathematics is all about illuminating relationships such as those found in shapes and in nature. It is also a powerful way of expressing relationships and ideas in numerical, graphical, symbolic, verbal and pictorial forms. It reveals hidden patterns that help us understand the world around us. This is the wonder of mathematics that is denied to most children.
The way Mathematics is introduced devoid of its daily application has been the root cause of the present scenario as experienced by everyone in the country. The conception of mathematics held by the teacher may have a great deal to do with the way in which mathematics is characterized. The subtle messages communicated about mathematics and its nature may, in turn, affect the way they grow to view mathematics and its role in their world.
When you ask hundreds of children, taught traditionally, to tell what mathematics is? They will typically say such things as “numbers” or “lots of rules”. Ask mathematicians what mathematics is and they will more typically tell you that it is “the study of patterns” or that it is a “set of connected ideas”.
How many students who attended mathematics classes would describe mathematics in this way? The image of mathematics presented in school mathematics classrooms has not given an opportunity to experience real mathematics. If you ask most school students what mathematics is, they will tell you it is a list of rules and procedures that need to be remembered. Their descriptions are frequently focused on calculations.
Why is mathematics so different? And why is it that students of mathematics develop such an unattractive view of the subject?
Reuben Hersh, a philosopher and mathematician, has written a book called ‘What is Mathematics, Really?’ in which he explores the true nature of mathematics and makes an
Important point –“people don’t like mathematics because of the way it is misrepresented in school”. The mathematics that millions of school children experience is an impoverished version of the subject that bears little resemblance to the mathematics of life or work, or even the mathematics in which mathematicians engage.
What is Mathematics, really?
Mathematics is a human activity, a social phenomenon, a set of methods used to help illuminate the world, and it is part of our culture. It is a language of science, a language to explain things around and brings order to the surroundings. It is the classification and study of all possible patterns. It is to be understood in a very wide sense, to cover almost any kind of regularity that can be recognized by the mind. The domain of pattern is not molecules or cells, but numbers, chance, form, algorithms, and change.
As a science of abstract objects, mathematics relies on logic rather than on observation as its standard of truth, yet employs observation, simulation, and even experimentation as a means of discovering the truth. Life, and certainly intellectual life, is only possible because there are certain regularities in the world.
A bird recognizes the black and yellow bands of a wasp; man recognizes that the growth of a plant follows the sowing of a seed. In each case, a mind is aware of the pattern.
However, the needs of the society may differ from the desires of individuals some may not be interested to learn mathematics because they do not see the use of it, especially when most applications in the environment are beyond their level, and to a certain extent they may not be interested in professions that require a lot of mathematics.
Although, not professionally but mathematical and data literacy, matters because it helps you make sense of the information you are surrounded by. Those who use mathematics engage in mathematical performances, they use language in all its forms, in the subtle and precise ways that have been described, in order to do something with mathematics. Students should not just be memorizing past methods; they need to engage, do, act, perform, solve problems, for if they don’t use mathematics as they learn it they will find it very difficult to do so in other situations, including examinations.
Mathematics is not about numbers, but about life. It is about the world in which we live. It is about ideas. And far from being dull and sterile, as it is so often portrayed, it is full of creativity.
Mathematics has different meanings to different people. People perceive mathematics according to their own experiences and these experiences differ from person to person. Most of the people come across an only certain aspect of mathematics of which nature of mathematics has special significance.
The Perceptions of the nature and role of mathematics held by our society have a major influence on the development of mathematics. The nature of any discipline has a significant impact on its pedagogy. Mathematics reveals hidden patterns that help us to understand the world around us. Thus, mathematics is a study of pattern and order dealing with numbers, geometrical objects, forms, algorithms, chance and change. More than merely being a study of arithmetic, algebra and geometry, mathematics today is a diverse discipline that deals with measurements, data analysis and observations from various fields of knowledge, inductive generalisations, proofs, logical deduction and mathematical modelling of natural phenomenon, of human behaviour and of social systems.
Mathematics empowers us to understand the information loaded world in which we live in a systematic and organized manner.
For example, arithmetic and basic algebra out of the need for counting and other simple operations required to solve basic life problems. Human quest possession of land and other properties needed measurement which led to the invention of geometry and trigonometry.
Mathematics is the only branch which may claim certainty. In all other branches experts, authorities have disagreed how often contended, and have not been able to convince each other on the world at large. Mathematics has a strong base on which new bricks are added every day and cemented with reason and logic
Mathematics has the inherent quality of generalizing various concrete concepts to abstract ones and in making systematic arrangements and classifications. The number concept itself enlarged from that of the whole numbers, irrational numbers to real numbers, to include successively fractional numbers, negative numbers, and imaginary.
Everybody cannot appreciate fully a beautiful piece of painting or musical art. Only a mathematician mind can appreciate these arts with some sense of confidence. Mathematics provides thus, a basis and background for aesthetic appreciation. The genius in mathematics finds in it pleasures akin to those in painting and music. They admire the delicate harmony of numbers and of forms.
Mathematics is everywhere! Mathematics is ‘‘a way of describing the world-a way of thinking, knowing, and problem-solving”.
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How can mathematics be so universal? First, human beings didn’t invent mathematics concepts; we discovered them. Also, the language of mathematics is numbers, not English or German or Russian. If we are well versed in this language of numbers, it can help us make important decisions and perform everyday tasks. Mathematics can help us to shop wisely, buy the right insurance, remodel a home within a budget, understand population growth, or even bet on the horse with the best chance of winning the race.
We likely use mathematics and mathematics language all the time but may not be aware of it. For example, when we do laundry and wash clothes separately based on color, we’re using the mathematics concepts of sorting and classifying. We also use mathematics concepts when you keep score during sporting events and explain how much your team is ahead or behind (number and operations), or give someone verbal directions to get from one place to another (spatial relationships).
On a basic level, you need to be able to count, multiply, subtract and divide. Mathematics is around us. It is present in different forms whenever we pick up the phone, manage the money, travel to someplace, play soccer, meet new friends; unintentionally in all these things mathematics is involved.
Mathematics can be seen in nature. If you look very carefully, the flower of a daisy you will notice that the seeds in the centre of the flower form spiral, some of which curve to the left and some to the right.
Remarkably, the measurements of various parts of the human body have the exact same relationship. Examples include a person’s height divided by the distance from tummy button to the floor; or the distance from shoulders to finger-tips, divided by the distance from elbows to finger-tips, the ratio turns out to be so pleasing to the eye. The ratio is also ubiquitous in art and architecture, featuring in the United Nations Building, the Greek Parthenon, and the pyramids of Egypt etc.
In fact, Mathematics can be compared to a pyramid. On the top of the pyramid are applications of mathematics to health, weather, movies and mobile phones. However, the top of this pyramid would not be so high if its base were not so wide. Only by extending the width of the base can we eventually build the top higher. This special feature of mathematics derives from its internal structure.
