Vedic Mathematics Newsletter No. 100
A warm welcome to our new subscribers.
Vedic Mathematics is becoming increasingly popular as more and more people are introduced to the beautifully unified and easy Vedic methods. The purpose of this Newsletter is to provide information about developments in education and research and books, articles, courses, talks etc., and also to bring together those working with Vedic Mathematics. If you are working with Vedic Mathematics - teaching it or doing research - please contact us and let us include you and some description of your work in the Newsletter. Perhaps you would like to submit an article for inclusion in a later issue or tell us about a course or talk you will be giving or have given. If you are learning Vedic Maths, let us know how you are getting on and what you think of this system.
This issue’s article is a report by Dr Arvind Prasad on the recent highly successful inaugural Online Vedic Mathematics Conference (14-15th March). Arvind is a researcher at the University of Queensland and was MC at the conference. We would like to extend our deepest thanks to him for all the work he has done before, during and after the conference.
FROM JODIE MASON IN NEW ZEALAND – 19th March
Damen and I have just completed two days with staff here in Murupara on Pebble & Vedic Maths. How amazing it was! The staff and also especially the children are continuing to embrace and engage with Pebble & Vedic Maths. Sometimes Damen and I find it hard to choose the words to describe just how thrilling things are going here. Damen and I also met yesterday with a Principal from another school, and she
immediately gave the go ahead for us to enter her school next week to run a Vedic/ Pebble Maths workshop with her staff... wow!
NEW BOOK – ‘THE ART OF CALCULUS’
This new book from Kenneth Williams is now available from the Bookstore. It is an elementary introduction to the subject using Vedic techniques. Getting gradients of curves and areas under them becomes extremely easy. Though this can be taught without the usual confusing notations and symbolism these are introduced too, later in the book. See:
An online course covering this material is under preparation.
NEW: ITALIAN PUBLICATION OF TEACHER’S MANUAL
The Elementary Teacher’s Manual has been translated into Italian and printed in Italy. This beautiful publication is available at:
NEW ONLINE JOURNAL ARTICLE
This is entitled “Cubing 3 Digit Numbers by the Ratio Method". And is in response to a question put in the March 2015 Vedic Maths Conference about extending Tirthaji’s cubing method, to 3 digit numbers. See:
JUST A SUTRA IS SUFFICIENT ! - from Badriya Raihani
In this case, no need to : « All From 9 and the Last From 10. »
Ekanyunena Purvena the third Corollary to the Nikhilam Sutra which means” By one less than the previous one” is used when multiplying any number by a number consisting only of nines: 9, 99, 999, 9999, etc.
Multiplying a number with a multiplier having equal number of 9’s digits
By using the Vedic formula « By One Less Than the One Before », and
« All From 9 and the Last From 10. »
Example: 763 x 999
-The left hand side of the answer will be found by subtracting 1 from 763, which is 762 "By one less than the one before"
-Then « All From 9 and the Last From 10 » is applied to 763 to get 237, which is the Right-hand side of the answer.
Learning while teaching !
In the above example , after getting the LHS of the answer , we ignore this half part of the answer and return to the text of question and apply the formula « All from nine and the last from ten » to 763.
I Notice that some students find it easier to finish the first half part of the answer already obtained by subtracting the digits 7, 6, and 2 from 9.
Or as a student suggests :
we can just apply the sutra « All From 9 and the Last From 10. »to get the RHS of the answer (763-----237)
And without using the sutra » « By One Less Than the One Before »,
We get the LHS of the answer by complements from 9 applying to the half answer already obtained (2, 3,7-------762)
So the answer is the same :
763x999 = 762 237
Like :As sometimes two or more sutras are used together to get the result
Also : Sometimes just applying one sutra is sufficient !
ARTICLE for VM Newsletter 100
by Dr Arvind Prasad
The inaugural online VM conference was held on the weekend of 14th-15th March, 2015, marking the 50th anniversary of the seminal book Vedic Maths by Bharathi Krishna Tirthaji. The conference also celebrated 14th of March as Swamiji’s birthday. The conference was aimed at providing a platform for VM practitioners to share their experiences and also to help beginners to VM get a glimpse of what VM has to offer. It brought together close to 80 participants representing 18 countries across 5 continents.
The conference was officially opened by Ken Williams. The conference hosted several different events over the 2 days, which are summarized briefly. The video links to each of these sessions have already been shared with the participants.
James’ Workshop: Day 1
James conducted a two-part 30 minute workshop where he showed the workings of the Anurupyena sutra, the first of the 13 upasutras given by Tirthaji. In the first part, he showed the sutra’s application in squaring and cubing 2-digit numbers. He also included the use of bar-numbers. He extended the application of this sutra in the second part to geometry and trigonometry, topping the session off with a one-line proof of the Pythagoras theorem. It is certainly worth going over the video again!
Global VM practices: Day 1
There were 21 speakers and as the name ‘global’ suggests, 5 continents were represented. The speakers shared their VM related work which extends from local sessions at libraries to teaching VM at a college as well as online resources for teaching VM. While the typical demographics of attendees to such VM classes and workshops included young children as well as adults, it was reported from America, and also highlighted, that unconventional attendees, such as adults looking to pass an exam to get employment and in correctional facilities, take to VM equally well. This is certainly an endorsement for the efficacy of VM. Experience reported from Switzerland was in some ways amusing; a child could be taught multiplication tables in a week using VM techniques while the child’s school, following the contemporary maths curriculum, had assigned a full year for the same subject matter.
The high point of this session was the growth in interest in VM. It was reported that one of the community schools in Manchester, UK has approved VM to be taught in the classroom. In addition, Pebble Maths, originating from Australia and already a success with young children, and Vedic Maths has been approved in a school in New Zealand as well. Presentation from Philippines suggests a massive VM movement. Nigeria has seen a similar interest and there is optimism that the Nigerian government will take up VM more rigorously. These are all a shot in the arm for the VM community.
Special Projects: Day 1 and 2
This session allowed individuals with larger initiatives to share their experiences. There were 7 speakers from 5 different countries. Typical projects being undertaken include books on VM (James and Ken), websites for teaching and/or to quantify the progress of pupils in maths (which may be extended to any subject) (Lokesh Tayal), and online courses being offered (Ken). Dr Kapoor spoke about a new way to look at BKTs’ Ganita-sutras, and his initiative to open a University where his new approach can be taught. Vera Stevens spoke about Pebble Maths in Australia and Karen Kwan shared her experiences with MathMonkey in several countries in Asia, both focussing on young children. Vinay Nair shared his experiences with the use of puzzles and pattern recognition with children. Due to technical difficulties, this session was held over two days instead of one, as originally planned.
Research papers: Day 2
The presentations in this session were divided into two categories – Mathematical (7 papers) and Dissemination (5 papers). Papers in the ‘Mathematical’ section included insight into the correlation between the sutras and the natural workings of the mind (James Glover), non-axiomatic geometry (Andrew Nicholas), recognition of patterns in raising numbers to higher powers (Robert McNeil) and the use of different approaches to maths for children with perceived learning difficulties (Vera Stevens). The section on ‘Dissemination’ included simple and non-symbolic approach of VM to teaching calculus (Ken Williams), comparison of VM methods with ancient Indian multiplication techniques (Arvind Prasad), challenges to disseminating VM (Swati Dave) and the use of modern technology to disseminate VM (Lokesh Tayal). Prof. Srivathsa’s paper could not be presented.
Panel discussion: Day 2
Panellists: James Glover, Ken Williams, Frank Morzano, Vera Stevens and Dr Kapoor (due to connection issues Dr Kapoor could not participate). Discussion conducted by Arvind Prasad.
The conference ended with a panel discussion where important questions were raised and discussed. At the outset, it must be kept in mind that there is no dichotomy in maths itself – VM and contemporary, but only a difference in approach to learning/teaching maths. The panellists agreed that the approach of contemporary maths has a problem, which starts at the primary school level and continues till college. For instance, while students get A’s in other subjects in college, the same students are failing high school maths. It seems that the problem in contemporary techniques lie in its rigid, formulaic, one-technique way to solve problems. The use of technology does not solve this problem. Besides, advanced technology i.e. calculators, laptops etc. are only accessible to the pupils in the affluent countries but not to the majority of the countries which are not as affluent. As such the use of technology in contemporary maths cannot be a global solution.
VM with its coherence and multiple-ways approach to solve a problem was seen as a logical solution to the challenge posed by contemporary maths. The way forward is to disseminate the knowledge about VM which can be done with a two-pronged bottom-to-top and top-to-bottom approach. The VM practitioners describing their work under the Global practises and Special Projects are at the grass-roots level. A long-term systematic effort is required to initiate and execute the top-to-bottom approach where administrative authorities are brought on board.
Part of dissemination at the grass-roots includes teaching VM to children and has three broad avenues of discussion, namely, Is VM beneficial for kids? How to teach VM to children? Once the children grow up learning VM, would they inherently teach VM to the rest of the community, and thereby disseminate VM?
Answer to ‘is it beneficial for the children?’ comes easy as VM allows their naturally curious minds and inquisitiveness to blossom. Vera’s experience with teaching VM to a current high school student is a testimony that students left behind in ‘contemporary maths classrooms’ can actually get exceptional at mathematics in a very short time. Furthermore, Gwen’s experience about a teacher teaching multiplication tables to her child in a few days using VM approach, when a full year is usually assigned in contemporary maths for the same subject matter, corroborates Vera’s experiences with children. Besides, based on the presentations at the conference, it is clear that pattern recognition assumes critical importance, which is, in fact, the VM approach. ‘How to teach VM to children?’ is perhaps an evolving question and depends on individual circumstances of teachers. Indeed, conferences such as the one conducted, provides a platform to exchange such ideas. Dissemination of VM in the future by current children is an open question and only time will tell. However, it stands to reason that the success of the VM approach in helping the children to learn maths would naturally put the VM in good light in the times to come.
An important question emerged through all the discussions – what is VM? As it currently stands, VM practitioners define VM differently. This could be a major hurdle for the top-down approach where senior authority figures need to be approached and convinced of the efficacy of VM. Without a firm definition of VM, the chances of success in such meetings could be significantly affected. Indeed, the VM practitioners at the grass-roots level too would benefit from a formal definition of VM. Perhaps developing a standardised curriculum for VM is the right step forward. Moreover, a firm definition of VM and a standard curriculum would help safeguard the VM, as quite often ‘maths tricks’ appear on the internet, which are essentially VM based methods, but with no acknowledgement to the original source.
End of article.
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Editor: Kenneth Williams
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21st April 2015