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Abstract,

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1. Introduction,

1.1 The Vedic Method,

2. Methodology,

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4. Conclusion,

Abstract,

Keywords,

1. Introduction,

1.1 The Vedic Method,

2. Methodology,

3. Findings,

4. Conclusion,

1.
Available online at www.sciencedirect.com

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: [email protected]

1877-0428 © 2010 Published by Elsevier Ltd. Open access under CC BY-NC-ND license.

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: [email protected]

1877-0428 © 2010 Published by Elsevier Ltd. Open access under CC BY-NC-ND license.

2.
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.

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.

3.
Syed Azman bin Syed Ismail and Pumadevi a/p Sivasubramniam / Procedia Social and Behavioral Sciences 8 (2010) 129–133 131

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).

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).

4.
132 Syed Azman bin Syed Ismail and Pumadevi a/p Sivasubramniam / Procedia Social and Behavioral Sciences 8 (2010) 129–133

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)

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)

5.
Syed Azman bin Syed Ismail and Pumadevi a/p Sivasubramniam / Procedia Social and Behavioral Sciences 8 (2010) 129–133 133

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.

Agrawala, V. S. (1971). Vedic Mathematics. Delhi: Motilal Banarsidas. Ancient Multiplication Methods. (n.d.). Retreived February 17, 2010, from

http://www.pballew.net/old_mult.htm

Bibhutibhushan, D., & Avadesh, N. S. (2001). History of Hindhu Mathematics. Delhi: Bharatiya Kala Prakashan.

Booker, G., Bond, D., Sparrow, L., & Swan, P. (2004). Teaching Primary Mathematics. Malaysia: Pearson Education Australia.

Chapin, H. S., & Jhonson, A. (2000). Math Matter. USA: Math Solution Publication.

Fennel, F. (2008). Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics. The National Council of Teacher of Mathematics,1– 15. Retreived

February 17, 2010, from http://www.nctm.org/standards/content.aspx?id=7564

Jeniffer, S., Andrew, D., & Maria, G. (2006). Mathematical Knowledge for Primary Teacher (3rd ed.). Washington, DC: David Falton Publication.

Mrilyn, N. S. (1985). Improving Multiplication Skills. Arithmetic Teacher, 32(7), 52.

Robert, A. C., & Marilyn, J. C. (1974). Arithmetic of Whole Numbers. New York:John Wiley & Sons Inc.

Rumming, J. (1968). Multiplication Methods. Primary Mathematics, 6(1), 20 – 27.

Tapson, F. (2004). Multiplication Methods. Retrieved February 17, 2010, from http://www.cleavebooks.co.uk/trol/trolfg.pdf

Vedic Mathematics. (n.d.). Retrieved February 17, 2010, from http://www.hinduism.co.za/vedic.htm

William, D. H. (1989). Using Arrays for Teaching Multiplication. Arithmetic Teacher, 2, 20 – 21.

Williams, K. (1999). Vertically and Crosswise. Retrieved February 17, 2010, from http://vedicmaths.org/Free%20Resources/Articles/article%20vx/article-

vx%20text.asp

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.

Agrawala, V. S. (1971). Vedic Mathematics. Delhi: Motilal Banarsidas. Ancient Multiplication Methods. (n.d.). Retreived February 17, 2010, from

http://www.pballew.net/old_mult.htm

Bibhutibhushan, D., & Avadesh, N. S. (2001). History of Hindhu Mathematics. Delhi: Bharatiya Kala Prakashan.

Booker, G., Bond, D., Sparrow, L., & Swan, P. (2004). Teaching Primary Mathematics. Malaysia: Pearson Education Australia.

Chapin, H. S., & Jhonson, A. (2000). Math Matter. USA: Math Solution Publication.

Fennel, F. (2008). Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics. The National Council of Teacher of Mathematics,1– 15. Retreived

February 17, 2010, from http://www.nctm.org/standards/content.aspx?id=7564

Jeniffer, S., Andrew, D., & Maria, G. (2006). Mathematical Knowledge for Primary Teacher (3rd ed.). Washington, DC: David Falton Publication.

Mrilyn, N. S. (1985). Improving Multiplication Skills. Arithmetic Teacher, 32(7), 52.

Robert, A. C., & Marilyn, J. C. (1974). Arithmetic of Whole Numbers. New York:John Wiley & Sons Inc.

Rumming, J. (1968). Multiplication Methods. Primary Mathematics, 6(1), 20 – 27.

Tapson, F. (2004). Multiplication Methods. Retrieved February 17, 2010, from http://www.cleavebooks.co.uk/trol/trolfg.pdf

Vedic Mathematics. (n.d.). Retrieved February 17, 2010, from http://www.hinduism.co.za/vedic.htm

William, D. H. (1989). Using Arrays for Teaching Multiplication. Arithmetic Teacher, 2, 20 – 21.

Williams, K. (1999). Vertically and Crosswise. Retrieved February 17, 2010, from http://vedicmaths.org/Free%20Resources/Articles/article%20vx/article-

vx%20text.asp