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Abstract,
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1. Introduction,
1.1 The Vedic Method,
2. Methodology,
3. Findings,
4. Conclusion,
1.
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Procedia Social and Behavioral Sciences 8 (2010) 129–133
International Conference on Mathematics Education Research 2010 (ICMER 2010)
Multiplication with the Vedic Method
Syed Azman bin Syed Ismail*, Pumadevi a/p Sivasubramniam
Faculty of Mathematics, Raja Melewar Teacher Training Institute
Abstract
This paper describes an action research that aimed at improving pupils’ performance in doing multiplication involving times tables more than
five, which is the six, seven, eight and nine times tables. This study involved five Year 4 Malaysian Primary school pupils who were selected
from 30 pupils who had sat for a test consisting of questions on multiplication. The study examines the use of the “Vedic Method” to do
multiplication problems involving times tables more than five by making use of times tables from zero to five. Hence, the five participants
chosen were pupils who demonstrated an ability to recall their one to five times table but had difficulties recalling the six to nine times tables.
The participants of the research were able to overcome their difficulties with the use of the “Vedic Method”.
© 2010 Elsevier Ltd. Open access under CC BY-NC-ND license.
Keywords: Multiplication; Vedic method; Primary school; Performance; Times tables; Basic multiplication facts; Sutras
1. Introduction
In today’s rapidly changing world, it cannot be denied that for an individual to be competent in mathematics their ability to
compute fluently is vital (National Council of Teachers of Mathematics, 2000). In the primary level, the basic computations are
addition, subtraction, multiplication and division. The Malaysian National Mathematics Curriculum for primary schools also
place great emphases on mastering these basic computing skills (Ministry of Education, 2003). Despite this emphasis in the
National Curriculum, many teachers’ experience and my experience is that there are pupils who never master these basic skills in
school. My most recent encounter was with a class of Year 4 pupils who were unable to do long multiplication problems not
because the algorithm was confusing but because they could not recall their six, seven, eight and nine times tables (see Figure 1).
Figure 1: Samples of pupils work showing poor recall of times table more than five
1.1 The Vedic Method
With the aim to find a method to recall times table more than five, I reviewed pertinent literature (Hall, 1998; Weisstein, 2010;
Urdhva Tiryak Sutra, 1971; Balin and Fred, 1979). I finally came across a method called the Vedic method.
Vedic Mathematics is the name given to the ancient system of Mathematics which was rediscovered from the Vedas between
1911 and 1918 by Sri Bharati Krishna Tirthaji (Ifrah.G, 1998). According to his research all mathematics is based on sixteen
Sutras or word-formulae.
* Corresponding author.
E-mail address: syed_kkb@yahoo.com
1877-0428 © 2010 Published by Elsevier Ltd. Open access under CC BY-NC-ND license.
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130 Syed Azman bin Syed Ismail and Pumadevi a/p Sivasubramniam / Procedia Social and Behavioral Sciences 8 (2010) 129–133
For example, ‘Vertically and Crosswise’ is one of these Sutras. These formulae describe the way the mind naturally works and
are therefore a great help in directing the student to the appropriate method of solution. One very useful application is helping
children who are having trouble with their tables above five. See Figure 2 for example of 7x8.
Figure 2: The Vedic method to calculate 7 x 8.
Hence the aim of this study was to describe the effects of the Vedic Method on pupils’ performance in recalling times tables
more than five to do multiplication problems.
2. Methodology
A pre-test was first administered to a class of 30 Year 4 pupils from a rural school in Malaysia. The test paper had four sections.
The first section had questions on times tables zero up to five. The second section had questions on times tables six up to nine.
The third section had long multiplication questions involving two 2-digit numbers based on times tables up to five and the fourth
section had long multiplication questions involving two 2-digit numbers based on times tables more than five. The pre-test had
no time frame attached. The test papers were marked and five pupils were selected as participants for this study. The five pupils
were then interviewed as a group.
The next day after the pre-test and interview, the participants were taught the Vedic Method during a one hour learning session.
After explaining eight examples of how to use the Vedic Method, Exercise 1 was given for the participants to practice the
application of the Vedic Method. Exercise 1 was handed in at the end of the first teaching and learning session. I marked
Exercise 1 and discussed it during the second teaching and learning session. Then I administered Exercise 2 and marked it as
pupils were doing the exercise. The questions were then discussed in class. The teaching and learning sessions were to
familiarize the participants to the Vedic Method to recall times tables more than five.
The post-test was administered the next day. The post-test is the same test as the pre-test. Again, no time frame was attached.
After the post-test, the five participants were interviewed as a group to express their views of the Vedic Method.
Field notes of observable behaviour were recorded during the pre-test, post-test and every teaching and learning session.
Interviews were audio taped. All test papers and exercise work were collected. A reflective journal was kept of every interaction
with the pupils by the researcher.
3. Findings
Thirty pupils sat for a pre-test which was administered under examination conditions. Pupils were seated apart, not allowed to
talk and were to raise their hands if they required anything. Some pupils appeared excited while others looked anxious. During
the test, some pupils were yawning and a look of boredom set in. They were informed that no time frame was set and so they
could pass up when they had finished. After about one and a half hours when one pupil handed in his paper, very quickly
everyone followed although some had not completed answering all the questions. Based on the pre-test data pupils who were
unable to recall times tables above five but able to recall their zero to five times table were selected as participants. There were
five pupils who met the criteria and were the participants for this study.
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The participants were then interviewed to explain their wrong answers. All five pupils stated that they found it difficult to
memorize all the times tables. One pupil said, “ I am so confused, it becomes bigger and bigger, can’t remember”.
The participants the next day were taught the Vedic method and given Exercise 1 as practice. Pupils enjoyed using the Vedic
method because it only required the zero to five times table to recall the six up to nine times tables. The following day the
Exercise 1 questions were discussed and then Exercise 2 was given. Exercise 2 was done more confidently and was discussed the
same day. Both exercises illustrated pupils been able to successfully employ the Vedic method to recall times tables more than
five and to do multiplication problems involving times tables more than five.
The post-test was administered on the fourth day, again under examination conditions and there was no time frame attached for
this test. The five participants were excited and they concentrated on the test. They hardly looked up until they had completed
answering all the questions.
The data for the pre-test and post-test are given in Table 1.
Table 1: Pre-test and post-test data
Pupil Section 1 Section 2 Section 3 Section 4 Overall
Pre-test Post-test Pre-test Post-test Pre-test Post-test Pre-test Post-test Pre-test Post-test
1 90 100 40 100 70 70 0 70 50 85
2 100 50 40 100 80 90 0 90 55 83
3 100 100 40 100 100 100 0 100 60 100
4 100 100 60 100 80 90 10 80 63 93
5 100 100 70 100 100 100 10 90 70 98
Mean 98 90 50 100 86 90 4 86 60 92
Examining the pre-test data shows that these five pupils have fared better in sections 1 and 3 which involves times tables less
than six compared to sections 2 and 4 which involves times tables more than five. This illustrates that generally these pupils do
not have a major problem with times tables from zero to five. Pupil 2 however showed a 50% decrease in score from the pre-test
to the post-test for section 1. This is because instead of recalling his multiplication facts for numbers less than six, he applied the
Vedic method for questions 1 to 5 in the post-test(see Figure 3).
Figure 3: Pupil applying the Vedic method for times tables less than 6 in the post-test
The Vedic method fails for times tables less than six. When I asked him why he stopped using the Vedic method after question 5,
he replied, “... the answers were wrong, you see. So I did like before for questions 6 to 10.” When I asked him why he did not
redo questions 1 to 5, he replied, “No time, others will finish first”. Although no time frame was attached for the post-test the
pupils wanted to complete the test at the same time that their friends completed it. All five pupils handed in their paper after 55
minutes with every question answered.
The pre-test scores for section 2 show that three out of the five pupils scored 40%. This is because all the five pupils were able to
answer correctly, 6x6, 7x7, 8x8 and 9x9. When I inquired about this ability, they told me that all of them knew the answers for
all the squares (they called it the two same numbers). They were unable to give a reason for this. The post-test scores show a
100% score from all five pupils for section 2. The pupils’ working showed that every pupil was able to successfully apply the
Vedic method on their own without any help to work out their six up to nine times tables.
For section 3 four out of five pupils show an increase in percentage score. One pupil showed no change. Examining his pre-test
paper and post-test paper revealed that he made errors in different questions in each paper but they were all due to poor recall of
basic multiplication facts and not a lack of understanding of the long multiplication algorithm (see Figure 4 and Figure 5).
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Figure 4: Poor recall of the four times table in the pre-test (left) but good recall in the post-test (right)
Figure 5: Good recall of the three times table in the pre-test (left) but poor recall in the post-test (right)
Section 4 shows an 82% increase from the pre-test to the post-test. This section showed the highest increase in percentage score.
This is because in the pre-test the pupils could not recall their multiplication tables above five and hence could not arrive at the
correct answer (see Figure 6).
Figure 6: The incorrect answer obtained because of poor recall of multiplication tables more than five in the pre-test (Pupil 3)
In the post-test with the use of the Vedic method the pupils were able to recall their multiplication tables more than five and
hence arrived at the correct answers (see Figure 7).
Figure 7: The correct answer obtained because recall of multiplication tables more than five was done using the Vedic method in
the post-test (Pupil 3)
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The overall increase in percentage score of 32% from the pre-test to the post-test are mainly contributed by the percentage
increase in sections 2 (50% increase from pre-test to post test) and section 4 (82% increase from pre-test to post test). Sections 1
had an 8% decrease while section 3 had a 2 % increase from the pre-test to the post-test scores.
A marked increase in section 2 is mirrored in section 4 but the changes in percentage in section 1 are not mirrored in section 3
because the errors in section 1 and 3 are basically careless mistakes and the pupils as a whole are able to recall up to their five
times table. Hence improving recall of basic multiplication facts does improve performance in multiplication problems. The
Vedic method has shown to enable pupils successfully to work out the times tables more than five by using the times tables up to
The interview after the post-test revealed that pupils realised the usefulness and appropriate application of the Vedic method. A
pupil said, “I don’t need to memorise the above times tables any more”, referring to the times tables more than five. Another
claimed that he was more confident to do mathematics because before learning the Vedic method he had problems with
multiplication. Yet another advised me, “Teacher, you should teach all my friends too. I am sure they can do multiplication very
well with the Vedic method”. Hence the pupils were comfortable with the Vedic method and it had enhanced their confidence not
only to do multiplication problems but also to learn mathematics.
4. Conclusion
The Vedic method has positive effects on pupils’ performance in recalling times tables more than five to do multiplication
problems. It enables pupils to calculate the six, seven, eight and nine times tables easily by employing the zero up to five times
tables. However, pupils must be reminded that the Vedic method will fail if applied to work out the product of two numbers less
than or equal to five. As for doing long multiplication problems other factors also play a role such as understanding the place
value system and a clear knowledge of the long multiplication algorithm.
The pupils in this study were successful in completing the long multiplication problems involving times tables more than five
correctly after learning the Vedic method because their only problem was recalling the times tables more than five. Should the
participants of this research have had any of the other problems the Vedic method would not be a powerful tool to enhance the
pupils’ performance in doing multiplication problems.
Another problem with the Vedic method is that the pupils are using it in a mechanical manner as one uses a tool such as a
calculator. Why it works is not understood by the pupils and trying to explain the algorithm is beyond the capacity of the
understanding of Malaysian Primary school pupils and beyond the scope of the Malaysian Primary school curriculum. Further
research into the Vedic Method’s algorithm in a meaningful way and result in increase performance in doing multiplication
problem by all primary school pupils in Malaysia is deemed necessary.
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