How do we simplify the teaching of Mathematics?
Knowledge has expanded like wildfire with the rapid advancement of information technology. The Worldwide Web has allowed millions of people to cross boundaries in the past two decades, resulting in interconnecting individuals and groups hitherto detached and separated from one another by thousands of miles and by differences in languages, traditions and cultures. It will probably take less than a couple of decades more for us to see a blurring of such cultural differentiation and witness a confluence of ideas and activities that produce a more homogenous or, better still, a somewhat unified global community that can eventually sing a common popular song, dance a common dance or even speak a single language at any given time.
Is it too hard to suppose that we will one day see more and more people among the nations deciding to do a common activity – not unlike watching a World Cup football game or a U2 concert – or to pursue a single purpose for the common good – not unlike coming together to help the victims of Haiti? This may be too idealistic or fanciful; but it is certainly one good reason for trying to break down all the physical and psychological walls of partition that exist between people and nations today.
For there is one particular field of human knowledge that has long broken down walls of separation that often exist in other areas such as religion, ideology, politics and economics. We are talking about Mathematics – the language of Nature, as someone once said. Numbers and their operations, in whatever language, remain the same. Hence, a foreign tourist wanting to buy two souvenir t-shirts in Hong Kong need only raise two fingers to a vendor to do so. The price tag would most probably be in Arabic numerals to make the transaction possible without speaking at all.
Once also referred to as the very foundation of all sciences, Mathematics has provided humans the essential tools for understanding, describing, analyzing and harnessing the multifarious benefits of natural and even artificial processes or concepts to make life more convenient, enjoyable and even more tolerable. Think of the cell phone which allows us not only to make calls or send messages but also to watch movies, listen to music and play games wherever we may go. Information technology owes much to Mathematics for giving us this potent tool we can no longer seem to live without.
Yet, the teaching of Mathematics has remained a formidable challenge for many individuals and, much more so, for societies that feel they are disadvantaged due to their inability to access educational opportunities readily available in other societies. The progress of a nation in terms of economic standards requires a citizenry that is not only literate but also mathematically in-step with other nations.
Unfortunately, the teaching of basic Mathematics has remained almost a standardized method for the past half-century or so. Whatever advancements or innovations that may have been incorporated (matrix distribution or quantum applications) are so specialized that the general pursuit of mastery in the essentials remains the critical area most educators must engage in.
But how does one improve the teaching of Mathematics if the processes or methods have not changed at all? How can an elementary teacher simplify multiplication of single digit numbers, for instance, such that students need not resort to the use of long multiplication tables or of tedious memorization? As students ourselves, we have had our own painful struggles at what we now consider as such simple chores. If we can teach the youth today to attain knowledge and proficiency in Math without the accompanying trauma that we normally assume must come with the task, then it would be a great step forward for us all.
What is Vedic Math?
Vedic Mathematics is a modern label to a system used in ancient India. Taken from the Sanskrit word “veda” meaning knowledge, it is essentially a simple and easy-to-learn method of solving basic and even advanced mathematical problems.
The Vedas were ancient writings (previously passed on orally from generation to generation) consisting of many documents which covered such subjects as Grammar, Architecture, Psychology, Philosophy, Astronomy, Archery and others. The writings show a great deal of structure and interrelationship. For instance, Architecture and Astronomy, as gleaned from India’s historic sites and rich cultural heritage, would not have developed as it did without a highly developed system of Mathematics just as it helped fuel the Industrial Revolution in the Western world in the early part of the 20th century.
Sanskrit scholars who translated the Vedic documents and were surprised at the depth and breadth of knowledge contained in them. Some documents headed “Ganita Sutras”, which means mathematics, could not be interpreted by them in terms of mathematics. Some verses referred only to historical events and had no relation to Math.
Bharati Krishna Tirthaji, who rediscovered Vedic Math, lived from 1884 to 1960. He was a brilliant student, obtaining the highest honours in all the subjects he studied, including Sanskrit, Philosophy, English, Mathematics, History and Science. When he heard what the European scholars were saying about the parts of the Vedas which were supposed to contain mathematics he resolved to study the documents and find their meaning. Between 1911 and 1918 he was able to reconstruct the ancient system of mathematics which we now call Vedic Mathematics.
Bharati Krishna wrote sixteen books expounding this system, but unfortunately these have been lost and when the loss was confirmed in 1958, Bharati Krishna wrote a single introductory book entitled “Vedic Mathematics”. This is currently available and is a best-seller.
Vedic Mathematics is best appreciated as you apply the various Sutras in solving the sample problems. Here are some main points to consider:
- The system rediscovered by Bharati Krishna is based on sixteen formulae (or Sutras) and some sub-formulae (sub-Sutras). These Sutras are given in word form: for example, Vertically and Crosswise and By One More than the One Before. In this text they are indicated by italics. The Sutras can be related to natural mental functions such as completing a whole, noticing analogies, generalization and so on.
- Not only does the system give many striking general and special methods, previously unknown to modem mathematics, but it is far more coherent and integrated as a system.
- Vedic Mathematics is a system of mental mathematics (though it can also be written down).
Many of the Vedic methods are new, simple and striking. They are also beautifully interrelated so that division, for example, can be seen as an easy reversal of the simple multiplication method (similarly with squaring and square roots). This is in complete contrast to the modem system. Because the Vedic methods are so different to the conventional methods, it is best to practice the techniques to gain familiarity.
It is quite unfortunate that the Philippines itself, having been colonized by Spain for almost four centuries and by the US for half-a-century, had no significant exposure to this system from its neighbor and traditional trade-partner in that nearby Asian peninsula. Some experts in Vedic Math did come to visit us and impress us with their almost magical abilities in handling numbers but such visits were quite sparse and did not make a mark in the minds of our officialdom or our citizenry.
Perhaps, it is but proper and beneficial that in looking more closely at the rich cultural and historical treasures found in Asia, Filipinos are now beginning to rediscover their own identity as an Asian nation and not as hybrid nation that is neither here nor there – which is basically a description of its social, economic and political status. Hopefully, with the great interest shown for this system, we will see a resurgence in our country’s education as private groups and individuals spread this wonderful tool that took centuries to reach our shores.
But the very, very long wait is now over. Finally, you will have at the tip of your fingers the products of the proverbial patience and wisdom of the gurus and the swamis of India. May this bring a dawning of Mathematical and general intellectual brilliance in the Philippines as well as in other countries.