A Comparative Study of Effectiveness of Teaching Mathematics

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A Comparative Study of Effectiveness of Teaching Mathematics through Conventional & Vedic Mathematics Approach,
ABSTRACT,
Keywords,
Significance of the study,
Operational definitions of the key terms used,
Effectiveness,
Achievement in mathematics,
Vedic mathematics approach,
Conventional method,
Objectives of the study,
Null Hypotheses,
Research tools,
Variables under the study,
Sample & sampling,
Delimitations of the study,
Experimental design,
The procedure of the study,
Analysis and interpretation of data,
Testing the hypothesis,
The calculation of effect size,
Discussion of the results

1. Educational Quest: An Int. J. of Education and Applied Social Science: Vol. 8, No. 2, pp. 453-458, August 2017
DOI: 10.5958/2230-7311.2017.00089.7
©2017 New Delhi Publishers. All rights reserved
A Comparative Study of Effectiveness of Teaching Mathematics
through Conventional & Vedic Mathematics Approach
Ajai Kumar Shukla1*, R.P. Shukla1 and Ajay Pratap Singh2
Faculty of Education (K), Banaras Hindu University, Varanasi, U.P., India
Department of Education, B.B.A. University, Lucknow, U.P., India
*Corresponding author: [email protected]
ABSTRACT
Vedic mathematics is the name given to the ancient Indian system of mathematics that was rediscovered
in the early twentieth century from ancient Indian scripture namely Atharvaveda. The study was intended
to compare the effectiveness of teaching mathematics through conventional and Vedic mathematics
approach in the terms of students’ achievement in mathematics. In this experimental study, pretest-
posttest equivalent control groups design was used having randomly selected sample of 30 students in
each group from BKT Inter College, Lucknow. The study covered the major topics of UP Basic Education
Board class VIII mathematics syllabus viz., square, square-root, factorization of algebraic expressions and
simultaneous simple equations. Mean, standard deviation, t-test and effect size were used for analyzing
the data collected through self-made Achievement Tests in Mathematics (ATM) as pretest and posttest.
Students’ achievement in mathematics of experimental group on posttest was significant over that of
control group. No significant difference was found between male and female students in each group on
posttest. Effect size was calculated as Glass’ ∆ which was 0.902. Thus the Vedic mathematics approach
is found highly effective for enhancing the students’ achievement in mathematics as well as that of male
and female students equally.
Keywords: Effectiveness, Vedic mathematics, conventional approach, achievement in mathematics
We use mathematics in our all endeavors; therefore in Mathematics have magic and mysteries. Our
it becomes a part of our life. Our imaginations do ancient scholars understood all these mysteries and
involve mathematics. From beggar to businessman, developed some simple ways and techniques to
everyone uses mathematics in their life. The solve mathematical problems. One such technique is
education commission (1964-1966) recommended Vedic mathematics as it helps to solve mathematical
mathematics as a compulsory subject for students problems very much faster than the traditional
at all school level. The National Policy on Education methods of solving problems. The National Policy of
(1986) has also considered the importance of Education (NPE-1986) stated “Mathematics could be
mathematics in general education and suggests that considered as a medium to train a child to develop
mathematics should be visualized as the vehicle to his thinking capacity, to develop his reasoning
train a child to think, reason, analysis and articulate power, and to coherent logically”. So mathematics
logically apart from being a specific subject. But due should be shown as a way of thinking, an art or
to lack of understanding its essence and technique form of beauty, and as human achievement and it
of teaching, mathematics is now considered as can be achieved easily through Vedic mathematics
a dry subject by many learners. Now a learner as it not only helps in generating interest and
shows no interest in learning mathematics, teacher concept clarity in students but also stabilizing the
is teaching and students are learning just for the knowledge for longer duration too.
sake of obtaining marks. Most of the problems

2. Shukla et al.
Need and significance of the study mathematics problem solving approach with high
speed and accuracy to educational planners and
Mathematics is the study of numbers, quantity,
curriculum developers.
space, structure and change. It is a branch of
science that uses numbers and symbols which are Operational definitions of the key terms used
arranged using systematic mathematics rules. It
can create moment of pleasure and wonder for all Effectiveness
pupils when they solve a problem for the first time,
discover a more efficient solution, or notice hidden In the study, effectiveness is described as significant
connection. But the essence and nature of teaching mean difference of a group over the other group
of mathematics is degrading day by day which on posttest in terms of students’ achievement in
creates a fear and phobia among students. Due to mathematics. In this fashion, the group having
excessive use of electronic gadgets and internet- greater mean is called more ‘effective’ than the
software, student and teacher both are diverting other group.
their path from efficient and effective teaching
Achievement in mathematics
learning process.
Now a student is laying less stress on mental Measurement of students’ grasp of knowledge
calculation and is more dependent on the gadgets or their proficiency in certain skills based on
and software for the solution. Vedic mathematics taught mathematical themes during experimental
is a unique method of solving problems by the use treatment. Here in this study it means achievement
of fast calculations. It is unique system as it helps score in mathematics obtained through ATM.
to solve all kinds of mathematical problems easily
Vedic mathematics approach
and efficiently. Tiwari, Gankhuyag, Kim & Cho
(2008) found that the proposed Vedic multiplier Solving mathematical problems easily with the
circuit seems to have better performance in terms help of some sutras, specifically based on the book
of speed. The goal of teaching mathematics is not Vedic Mathematics, authored by Sri Bharati Krishna
just academic achievement but its personal and Tirath Maharaja (1884-1960) of Govardhan Peetha,
professional growth also. Vedic mathematics not Puri (India). But it is originally rediscovered from
only helps in understanding the concept efficiently Atharvaveda (Sthapathya-subveda).
but also brings interest while learning mathematics
through magical techniques. Conventional method
And these techniques help the students to resist the A teacher centered traditional method of teaching
concepts for longer duration. Vedic mathematics with a due weightage to talk and chalk, based on
is found more effective in solving multiplication problem solving approaches given in class VIII
problems than traditional technique (Sharma, mathematics text-books of UP Basic Education
2014). Jiji (2012) also found Vedic mathematics is Board.
more effective, in terms of students’ achievement in
mathematics, than talk and chalk method. But almost Objectives of the study
all the studies were conducted on English medium To compare the means score on the achievement
students (e.g., Jiji, 2012; Sharma, 2014), covering in mathematics of the two groups of the
only few topics (e.g., multiplication and divisions in students on pretest.
arithmetic) and no practical significance (effect size)
was given. So to overcome this knowledge gap, the To compare the means scores on the achievement
present study was conducted on students of class in mathematics of the two groups of students
VIII Hindi medium government school of Lucknow. on posttest.
The study covered the major topics viz., square, To compare the means scores on the achievement
square-root, factorization of algebraic expressions in mathematics of male and female students of
and simultaneous simple equations. So the results of the control group on posttest.
the study can contribute an effective and interesting To compare the means scores on the achievement
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3. A Comparative Study of Effectiveness of Teaching Mathematics through Conventional...
in mathematics of male and female students of experimental group was taught using the Vedic
the experimental group on posttest. mathematics approach while the control group was
To calculate the effect size of the Vedic taught using traditional approach. The experiment
mathematics approach over conventional had been continued for 25 working days. The
approach on posttest. posttest was administered on both the groups, after
the treatment was over.
Null Hypotheses
Research tools
H01: There is no significant difference in the
mean scores of experimental and control group Self-made Achievement Tests in Mathematics (ATM)
on pretest. as pretest and posttest were administered for testing
the class VIII students’ achievement in mathematics.
H02: there was no significant difference in the
The test-retest reliability was established and it was
mean scores of experimental and control group
found that 0.87 and 0.83 respectively. The content
on posttest.
validity of the tests was evaluated by a committee,
H03: There is no significant difference in the which consisted of mathematics teachers and teacher
mean scores of male and female students of the educators. The validity was found satisfactory.
control group on posttest.
H04: There is no significant difference in the Variables under the study
mean scores of male and female students of the Independent variables: Approaches of teaching
experimental group on posttest. mathematics i.e. Vedic mathematics and conventional
(traditional) mathematics.
Dependent variables: Students’ achievement in
All the students of class VIII of Hindi medium mathematics.
schools of Lucknow district for the academic year
Variables uncontrolled: Interest and attitude, socio-
2015-16 following the UP Basic Education Board
economic status, self-concept.
syllabus were constituted the population for the
study. Variables controlled: Time, average-age, classrooms-
conditions.
Sample & sampling
Delimitations of the study
In the study, BKT Inter College, Lucknow was
selected using purposive sampling. Further eighth The present study was confined to the class VIII
standard 60 students from BKT Inter College, Hindi medium students from Lucknow district
Lucknow were randomly selected as the sample. under UP Basic Education Board curriculum
In this manner the selection and the assignment of only.
the students were performed randomly into two The present study was carried on class VIII
groups; Experimental group & Control group. So students’ in terms of their achievement in
the number of students in each group was 30. mathematics only.
The present study covered these topics only
Experimental design
viz., square, square-root, factorization of
Since the nature of the present study was algebraic expressions and simultaneous simple
Experimental. For this purpose the pretest- posttest equations. So only few Vedic mathematics
equivalent groups design was selected. sutras were used to teach these topics.
Procedure of the study Analysis and interpretation of data
The pretest was administered on the students in In analysis the collected data were tabulated and
order to acquire their pre-experimental achievement statistical techniques were employed as per research
score. The groups were randomly assigned to design of the study. All the hypotheses were tested
one control and another experimental group. The at 0.05 level of significance.
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4. Shukla et al.
Testing the hypothesis No. 1 in terms of students’ achievement in mathematics.
The null hypotheses No. 1 was that there was Testing the hypothesis No. 3
no significant difference in the mean scores of
The null hypothesis No.3 was that there was no
experimental and control group on pretest. This
significant difference in the mean scores of male
hypothesis was tested by calculating means,
and female students of the control group on
standard deviation and t-value. The means,
posttest. This hypothesis was tested by calculating
standard deviation and t-value are given in the
means, standard deviation and t-value. The means,
table 1 below:
standard deviation and t-value are given in the
Table 1: Mean, Standard deviation and t-value of table below:
Achievement in Mathematics on pretest
Table 3: Mean, Standard deviation and t-value of
Groups N Mean S.D. t-Value Null Achievement in Mathematics of Control group on
Hypothesis posttest
Experimental 30 5.97 2.32
Students N Mean S.D. t-Value Null Hypothesis*
Group 0.066 Failed to
Control 30 5.93 2.39 reject Male 18 6.56 1.93
Group
0.97 Failed to reject
Female 12 6.67 2.12
The null hypothesis was failed to reject on the
*Critical value of t with 28 df at 0.05 level is 2.05
basis of the above table and t-value was 0.066. This
indicates that there was no significant difference From the Table 3, it can be seen that the difference
between control and experimental group in terms in the achievement in mathematics of the male and
of their achievement in mathematics on pretest. female students from control group is not significant
therefore the null hypothesis was failed to reject.
Testing the hypothesis No. 2 This indicates the achievement in mathematics of
The null hypotheses No. 2 was that there was male and female students from control group were
no significant difference in the mean scores of same on posttest.
experimental and control group on posttest. This
Testing the hypothesis No. 4
hypothesis was tested by calculating means,
standard deviation and t-value. The means, The null hypothesis No. 4 was that there was no
standard deviation and t-value are given in the significant difference in the mean scores of male
table below: and female students of the experimental group on
posttest. This hypothesis was tested by calculating
Table 2: Mean, Standard deviation and t-value of means, standard deviation and t-value. The means,
Achievement in Mathematics on posttest
standard deviation and t-value are given in the
Groups N Mean S.D. t-Value Null table below:
Hypothesis
Experimental 30 8.53 1.31 Table 4: Mean, Standard deviation and t-value of
Group Achievement in Mathematics of Experimental group
4.214 Rejected
on posttest
Control 30 6.60 2.14
Group Students N Mean S.D. t-Value Null Hypothesis*
Male 17 8.24 1.53
The null-hypothesis was rejected and the research 1.027 Failed to reject
Female 13 8.92 2.21
hypothesis was accepted on the basis of the Table 2,
i.e. it can be seen that the difference in the means of *Critical value of t with 28 df at 0.05 level is 2.05
students’ achievement in mathematics from Control
From the Table 4, it can be seen that the difference
Group and Experimental Group is significant. Thus
in the achievement in mathematics of the male
Vedic mathematics approach is effective over the
and female students from experimental group is
conventional approach of teaching mathematics
not significant therefore, the null hypothesis was
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5. A Comparative Study of Effectiveness of Teaching Mathematics through Conventional...
failed to reject. This indicates that the achievement terms of their achievement in mathematics while
in mathematics of male and female students from scores of remaining 81.59% students of the control
experimental group were same on posttest. group were less than mean score of experimental
group. Thus we can say that the Vedic mathematics
The calculation of effect size approach is highly effective for enhancing the
After testing the hypotheses, the practical significance students’ achievement in mathematics. It may be
must be calculated (Sulivan & Feinn, 2012). Here noted that to calculate Glass’ ∆, there was used
Table No. 5 shows the calculation of effect size for standard deviation of control group because the
understanding the practical significance of Vedic control group is the original representative of
mathematics approach. the population and not affected by experimental
treatment (Coe, 2002). So this provided unbiased
Table 5: Calculation of Effect size (Glass’ ∆) effect size. On the basis of above findings, it can be
concluded that Vedic mathematics can be extended
Groups Mean S.D. Effect size (Glass’ ∆)
by teachers, curriculum developers for elementary
and secondary classes.
Experimental 8.53 1.31 (8.53 − 6.60)
Group ∆ E −C = In this context, every teacher should inculcate the
2.14
Control Group 6.60 2.14 habit of reading books related to Vedic mathematics;
= 0.902
at least some periods should be allotted in the class
to use Vedic mathematics tricks. So students can
Here Glass’∆ was calculated as effect size of Vedic
actively participate in solving problems. Schools
mathematics approach over conventional approach
should also realize the classrooms are not meant
of teaching mathematics which was 0.902.
only for transaction of knowledge but also for
Discussion of the results developing creative abilities and talents through
joyful teaching-learning approaches. With the
In this study, the control and experimental group help of Vedic mathematics students can score high
were found equivalent in the terms of their marks and also excel in competitive examinations.
achievement in mathematics at the time of starting In the present scenario, almost all the competitive
the treatment. So there is no need to use analysis examinations contain reasoning aptitude sessions,
of covariance (ANCOVA) in the study (Best & in which students have to score good marks. Since
Kahn, 2006). Vedic mathematics approach is found education has its main aim to transfer the cultural-
effective over the conventional approach of teaching heritage from one generation to other. In this order
mathematics in terms of students’ achievement in Vedic mathematics should be conserved as non-
mathematics. This finding is supported by many materialistic Indian cultural-heritage also.
studies only on the multiplication operation (e.g.,
Many further studies may be conducted at higher
Sharma, 2014); square and square-root (e.g., Jiji,
level of education through qualitative or mixed
2012). Whereas in the study, the Vedic mathematics
approach of the study, as the case may be; for testing
approach is found effective over the conventional
the effectiveness of Vedic mathematics in other
approach of teaching mathematics covering the
various terms viz., attitude towards mathematics,
experiment on the major topics viz., square, square-
interest in mathematics, motivation level, speed
root, factorization of algebraic expressions and
and accuracy in a particular time phase using
simultaneous simple equations. Conventional as
various Vedic sutras. Various problems faced by the
well as Vedic mathematics approach of teaching
students while using the Vedic mathematics may be
mathematics produce similar results on male and
diagnosed and remediated.
female students’ achievement, i.e. Vedic mathematics
is equally effective for male and female students. REFERENCES
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