Effectiveness of GeoGebra in Developing the Conceptual Understanding of Definite Integral at Gongzim Ugyen Dorji Central School, in Haa Bhutan
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Asian Journal of Education and Social Studies
10(4): 60-65, 2020; Article no.AJESS.60967
ISSN: 2581-6268
Effectiveness of GeoGebra in Developing the
Conceptual Understanding of Definite Integral at
Gongzim Ugyen Dorji Central School, in Haa Bhutan
Kado1* and Nim Dem2
1
Gongzim Ugyen Dorji Central School, Ministry of Education, Post Office Box 15001, Haa, Bhutan.
2
Katsho Lower Secondary School, Ministry of Education, Post Office Box 15001, Haa, Bhutan.
Authors’ contributions
This work was carried out in collaboration between both authors. Author Kado designed the study,
performed the statistical analysis, wrote the protocol and wrote the first draft of the manuscript. Author
ND managed the literature searches. Both authors read and approved the final manuscript.
Article Information
DOI: 10.9734/AJESS/2020/v10i430276
Editor(s):
(1) Dr. Bashar H. Malkawi, University of Sharjah, United Arab Emirates.
Reviewers:
(1) Altaf Ahmad Bhat, Islamic University of Science and Technology, India.
(2) Alice Dhliwayo, Solusi University, Zimbabwe.
(3) Hafte Amsalu Kahsay, Wollo University, Ethiopia.
Complete Peer review History: http://www.sdiarticle4.com/review-history/60967
Received 28 June 2020
Accepted 01 September 2020
Original Research Article
Published 15 September 2020
ABSTRACT
As recommended by the Education Blueprint 2014-2020, education system in Bhutan transformed
from traditional instructions to technology-enriched and enabled teaching and learning environment
with adoption of emerging and relevant technology to produce the globally competent learners. The
integration of educational technology in the teaching and learning of definite integral creates a
conceptually rich learning environment. From this perspective, this study aims to
ascertain the effectiveness of a computer-assisted instruction method using GeoGebra in
developing the conceptual understanding of definite integral for grade 12 students. This study
employed a quasi-experiment static-group comparison design with 60 students from
Gongzim Ugyen Dorji Central School in Haa. The students were divided into two equal groups.
Group ‘A’ used the GeoGebra software, while group ‘B’ used the conventional method to learn
definite integral. The data were collected through Definite Integral Knowledge Test. An
Independent sample t-test was employed using the Statistical Package for the Social Sciences
(SPSS 22.0). Findings of the study showed that students who were taught using GeoGebra
_____________________________________________________________________________________________________
*Corresponding author: Email: kadoscs@education.gov.bt;Kado and Dem; AJESS, 10(4): 60-65, 2020; Article no.AJESS.60967
outperformed those who learned through conventional methods. The results confirmed that
GeoGebra software is capable of enhancing and significantly improving students’ conceptual
understanding of definite integral.
Keywords: Calculus; definite Integral; conceptual understanding; GeoGebra.
1. INTRODUCTION In literature, there is broad theoretical and
experimental evidence to support that limit,
The ideas of the calculus were independently derivative, and integral are epistemologically
th
discovered by Newton and Leibnitz in 17 difficult concepts for the learners, while the
century. Calculus means, “Small Stones” concept of definite integral is even harder for
because it is like understanding something by learners [7, 8, 9]. Learners could correctly use
looking at small pieces [1]. It is divided operational knowledge to manipulate the
into two branches, differential and integral algebraic functions symbolically, but they fail to
calculus. Differential calculus concerns interpret meaning. In a study that explored
with how things change with respect students’ understanding of definite integral
to time, while integral calculus integrate the concept, [9] found that most students’ do not
small pieces together to find how much is there have sufficient conceptual understanding of
[2] definite integral, their dominant knowledge was
the procedural knowledge and their ability for
Calculus is considered as vital topics in multiple representation of concepts were limited.
mathematics due to widespread application [10] administered a questionnaire that aimed at
across the multidisciplinary fields such as investigating students’ understandings of the
biological sciences, physical sciences, concepts associated with the definite integral as
engineering, social sciences, and economics [3]. well as their computation skills. He found that
Considering its significance, it is paramount to students’ understanding of definite integral is
focus the teaching and learning of integral rather instrumental or mechanical. Despite the
calculus on developing the relational wealth of literature available in this field in
understanding/conceptual understanding instead international context, there are limited academic
of instrumental or mechanical understanding. discourse in the Bhutanese context that focus on
From our search of the literature, it is clear that developing the conceptual understanding of
new calculus courses should place less definite integral. Thus, this research attempts to
emphasis on complex skills and emphasize enhance students’ conceptual understanding of
conceptual development [4].They also definite integral using the GeoGebra.
recommended future research to focus on
enhancing the conceptual development GeoGebra is open-source software developed by
as this understanding can have a profound Markus Hohenwarter in 2002 for teaching and
impact on students’ ability to solve in definite learning Mathematics from primary to the
integral. university level [11]. It combines many aspects of
different mathematical packages, and
Despite the importance of the emphasizing the dynamically joins Geometry, Algebra and
teaching and learning of calculus on conceptual Calculus. The numerous calculus- related
development, the conventional teaching and interactive worksheets and methods developed
learning of definite integral that relies on symbols by teachers and researchers are available
and notations, has been the preferred method of (www.geogebra.org). Based on the site,
calculus instructions for decades. There is a GeoGebra users have reached 100 million
body of evidence that suggest that teaching and students, while GeoGebra researchers based on
learning of definite integral focus more on Google Scholar have 15,800 published scientific
computational process rather than underlying papers [3].
concepts that resulted in routine algebraic
manipulations [5,6] . Thus the traditional Studies have shown that an improvement in
approach of teaching and learning helps to calculus concept can be achieved by integration
develop the skills of manipulating algebraically, of educational technology in teaching and
understanding instrumentally and memorizing the learning as it have potential to have positive
formulae instead of comprehending conceptual impact on students’ conceptual understanding of
or relational proficiencies. calculus[3, 12].Realizing the efficacy of
61Kado and Dem; AJESS, 10(4): 60-65, 2020; Article no.AJESS.60967
technology enriched and enabled learning of efficacy of GeoGebra in mathematics in
environment , Bhutan Education Blueprint 2014- general, calculus in particular.
2020 recommended a shift in educational system
by leveraging ICT to produce globally competent 1.1 Objectives of the Study
learners to address the need of fourth industrial
revolution[13]. Subsequently, Ministry of This study has two main objectives:
Education launched its education ICT master
plan called iSherig, on May, 2019, to harness the i. Developing the Conceptual or Relational
potential benefit of ICT in teaching and learning Understanding of Definite Integral
by creating a platform for effective ii. To compare the conceptual knowledge
communication, enabling access to information of students in treatment and control
and knowledge, and conceptually rich groups
learning environment where students construct
their own knowledge, visualize and experiment 1.2 Research Questions
[14].
What is the impact of GeoGebra software on the
As enshrine in our Education Blue print 2014- achievement of conceptual understanding of the
2020, teachers in Bhutan embarked the journey definite integrals?
of embracing educational technology to enhance
teaching and learning. The educational 2. MATERIALS AND METHODS
technology like GeoGebra software chosen as a
teaching method has the potential to visualize This study used a quasi-experimental static-
the conceptual definition of definite integral as group comparison design to compare the
the limiting process. Further support is given by effectiveness of the GeoGebra in developing the
[3] that generally asserts that GeoGebra is a conceptual understanding of definite integral for
digital tools that helps to develop the concept the students who received GeoGebra enriched
image of definite integral and helps to visualize instructions and students who received traditional
the abstract concept algebraically, numerically instructions. This method was the best approach
and graphically. The embedded mixed method as it attempts to study the effect of the treatment
design study showed that the computer assisted on intact groups rather than being able to
instructions method using GeoGebra had randomly assign participants to the experimental
significant influence on teaching and learning or control groups [17, 18].
outcome of definite integral. Additionally, this
study found to facilitate conceptual learning of The participants consist of 94 students from
the definite integral [15]. [16] conducted a quasi- grade 12 mathematics students at Gongzim
experimental study to investigate the efficacy of Ugyen Dorji Central School. The cluster random
developing conceptual understanding and sampling was adopted to select 60 out of 94
procedural knowledge of 124 high school students from 3 sections. The students were then
students in Indonesia. The finding revealed that divided into two groups; one was a treatment
treatment group showed significant gained in group and the other was the control. Students in
conceptual knowledge compared to control the treatment group were taught definite integral
group. using the GeoGebra software. Students in the
control group were taught through normal
In nutshell, it is clear from the extensive conventional learning.
evidences in literature that students’ knowledge
was rather an instrumental or mechanical as they A Definite Integral Knowledge Test (DIKT),
know how to manipulate the algebraic expression consisting of six questions modified from BHSEC
symbolically but had complexity in elucidating the Mathematics Book-II for Class XII students of
meaning. The present study was designed to Bhutan were used to collect the data (Malhotra,
enhance learners’ conceptual or relational Gupta, & Gangal, 2020). . Instrument was piloted
understanding in definite integral. Based on to ensure its reliability and validity. The average
literature research, no similar study was Item objective Congruence (IOC) was 0.89,
conducted in Bhutan; therefore, our study sheds validating the appropriateness for the study. The
light on the efficacy of digital tools like GeoGebra reliability of the instrument was proven high with
having significant impact for acquiring conceptual item reliability of 0.88. Comparative statistical
knowledge in definite integral. This study also analysis was done using the t-test. The
serves as stepping stone for further investigation independent sample t-test was used to compare
62Kado and Dem; AJESS, 10(4): 60-65, 2020; Article no.AJESS.60967
the learning achievement between the control experimental and control group as shown in the
and experiment group. The inferential t-test with Table 3.
p 0.05). Additionally Levene’s test for equality applied to these groups to identify differences
of variances of scores for two groups (EG& CG) caused by the treatment.
were conducted as shown in the Table 2.
An independent sample t-test conducted for
The Levene’s test indicated that the assumption comparison of post-test scores between
of homogeneity of variance of pre-test was met experimental and control group showed
as value is greater than 0.05 ( (1,62) = significant mean difference between EG ( =
6.571, = 0.78) .However, the variation of post- 56.95, = 4.66 ) and CG (M = 23.83, =
test scores for both the groups was not same as 10.52); (42.730) = 16.276, = 0.000(two tailed).
p-value is less than 0.05 ( (1,42.73) = The magnitude of the differences in the means
17.714, = 0.00). Thus, the assumption of equal (mean
variances had been violated. difference =
33.125,95% : 29.057 37.193) was very high
3.1 Comparison of Pre-test and Post-test (eta squared = 0.91). This indicates that there
was a statistically significant difference in post-
Scores of DIKT
test scores between experimental and control
group. The test scores of an experimental group
An independent sample t-test was conducted to
were significantly higher than the test scores of
determine the difference in DIKT between the
the control group.
Table 1. Test of normality with one-sample kolmogorov-smirnov test
Pretest-EG Posttest-EG Pretest-CG Posttest-CG
N 32 32 30 30
Kolmogorov-Smirnov Z .978 .944 .986 1.406
Sig. (2-tailed) .294 .335 .285 .038
Significant level: >0.05—no significant, 0.05—no significant, 0.05—no significant,Kado and Dem; AJESS, 10(4): 60-65, 2020; Article no.AJESS.60967
4. DISCUSSION AND CONCLUSION COMPETING INTERESTS
The results of the independent sample t-test Authors have declared that no competing
indicated that there were significant differences interests exist.
in DIKT between the experimental and control
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