Journal of Physics: Conference Series

PAPER • OPEN ACCESS

The Use of Geogebra Software in Learning Geometry Transformation to

Improve Students’ Mathematical Understanding Ability
To cite this article: Moch. Rasyid Ridha et al 2020 J. Phys.: Conf. Ser. 1477 042048

View the article online for updates and enhancements.

This content was downloaded from IP address 115.164.221.246 on 10/11/2020 at 10:47

ICComSET 2019 IOP Publishing
Journal of Physics: Conference Series 1477 (2020) 042048 doi:10.1088/1742-6596/1477/4/042048

The Use of Geogebra Software in Learning Geometry

Transformation to Improve Students’ Mathematical
Understanding Ability

Moch. Rasyid Ridha1, Euis Eka Pramiarsih2, Widjajani3

1
Mathematic Study Program, Faculty of Teacher Training and Education, Universitas
Langlangbuana, Bandung, Indonesia
2
Economic Education Study Program, Faculty of Teacher Training and Education, Universitas
Langlangbuana, Bandung, Indonesia
3
Industrial Engineering Study Program, Faculty of Engineering, Universitas Langlangbuana,
Bandung, Indonesia

Abstract. This article reports the findings of one pretest-posttest design experiment with the control
group and with GeoGebra software learning application to examine the mathematical understanding
abilities and responses of students taking Geometry Transformation course. The subjects of this study
were 24 students of mathematics education study program in Universitas Langlangbuana. The
research instrument consisted of a mathematical comprehension ability test and a student response
questionnaire. Based on data analysis using SPSS 2.0.0 and Microsoft Excel 2013, the study found
that achievement and improvement in mathematical understanding skills and responses of students
who received learning with GeoGebra software were better than achievement and improvement in
student’s ability who obtain conventional approach for the high, middle and low categories. The
study also found a moderate relationship between mathematical understanding ability and student
response.

1. Introduction
Geometry of transformation is a compulsory subject for students of mathematics education study program
to be taken in the third semester. This subject is abstract so students need to learn more deeply for the
concept of transformation geometry to be accepted, understood and comprehended. Mathematics is
hierarchical or tiered, meaning that the concepts in the previous material will be the basis for further
material. Transformation geometry is a very important subject because it is the basis of other elective courses
in the following semester. If students experience difficulties in studying transformation geometry subject,
students will find it increasingly difficult to study elective courses in the following semester. This will have
an impact on high semester students who will take the Field Experience Practice (Praktek Pengalaman
Lapangan - PPL). In addition, it also has an impact on graduates as prospective mathematics teachers who
will later teach transformation geometry because the transformation geometry is available in the curriculum
of Junior High School (SMP/MTs) and High School (SMA/SMK/MA.)

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution
of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Published under licence by IOP Publishing Ltd 1
ICComSET 2019 IOP Publishing
Journal of Physics: Conference Series 1477 (2020) 042048 doi:10.1088/1742-6596/1477/4/042048

In the subject of transformation geometry, the accuracy of the size and accuracy of the drawing area is very
important. Differences in size can be a major problem, this is common when there is inappropriate use of
instructional media or less-thorough use of the media so that it results in inaccuracies in the measurement
data generated. From the existing problems, technological development can be used as an alternative
problem solving. Through technology, it is created media that can change the learning of transformation
geometry from abstract to concrete, from complex to simple so that it is easy to understand and support the
quality learning.
The development of science and technology especially information and communication technology
(ICT) can deliver the role and function of education to become more widespread and open. Thus the
computer becomes important and potential to be widely used in the world of education (Munir, 2009).
Information technology is developing so rapidly, thanks to the discovery of increasingly sophisticated means
of communication by experts.
In line with the opinions of the experts, computers have now entered the world of education and are no
longer a rare item, both at school and at the higher education level generally have computers. Even at the
university level, each student normally has a mobile computer (laptop). Utilization of computers is widely
used for the completion of administrative affairs as other offices in the field of non-education. Computers
in the world of education should not be used as a typewriter. Computers are very potential for learning so
they need to be widely used for learning. NCTM (National Council of Teachers of Mathematics) has
principles regarding mathematics education, one of which is the technological principle as follows: “The
NCTM Technology Principles: Technology is essential in teaching and learning mathematics; it influences
the mathematics that is taught and enhances student’s learning” [8].
NCTM clearly states that the use of technology is an important thing to support mathematics learning
in this era. The use of technology will influence how mathematics should be taught and improve student
learning outcomes. In line with NCTM, Arsyad [1] also stated that one of the functions of instructional
media is as a teaching aid that is also influenced by the climate, conditions and learning environment that
are arranged and created by someone, especially teachers in education. Computer technology has become
one of the media that has great potential to be used as an interactive tool in the learning process.
GeoGebra is software developed for the benefit of the world of mathematics education. Judith and
Markus Hohenwarter [3] explain that GeoGebra was developed by both of them for purely the interests of
the world of mathematics education, not for sale. In the GeoGebra manual [4] explained as follows:
“GeoGebra provides three different views of mathematical objects: a Graphics View, a numeric
Algebra View, and a Spreadsheet View. They allow you to display mathematical objects in three different
representations : graphically (e. g., points, function graphs), algebraically (e. g., coordinates of points,
equations), and in spreadsheet cells. Thereby, all representations of the same object are linked dynamically
and adapt automatically to changes made to any of the representations, no matter how they were initially
created”.
In its use, GeoGebra can run on Windows, Mac OS X, and Linux family operating systems, it is quite
easy to use because it can be run with basic commands such as scroll, zoom, delete, and can use hot keys
like in Windows. By using this program, various mathematical problems can be solved in the form of
arithmetic problems, algebra, trigonometry and calculus. By using GeoGebra, students will get better
visualization to analyze various problems.
The Geogebra Provider facilitates the development of GeoGebra software add-on by providing services
in various curricula and languages. On the site http://www.GeoGebra.org/forum/ you can find many posts
by math teachers from various countries. The contents of which are positive responses and suggestions from
them after using GeoGebra in class. Unfortunately there are no posts or contributions from Indonesian
teachers, so that Indonesia has not been included in the collection of GeoGebra development. This is an

2
ICComSET 2019 IOP Publishing
Journal of Physics: Conference Series 1477 (2020) 042048 doi:10.1088/1742-6596/1477/4/042048

indication that not many Indonesian teachers know and utilize GeoGebra. From such circumstances the
authors are interested in conducting research on the use of GeoGebra.
To further direct the implementation of the research, the problems that will be examined in this study
are formulated as follows: (1) Is the improvement of students' mathematical understanding abilities whose
learning use GeoGebra software better than students’ abilities whose learning use conventional learning in
transformation geometry course ?; (2) Are there differences in the improvement of students' mathematical
understanding abilities that obtain learning using GeoGebra software with students who obtain conventional
learning based on the KAM category (high, middle, low) in transformation geometry? (3) Is the increase in
mathematical response of students whose learning use GeoGebra software better than students whose
learning use conventional learning in transformation geometry course ?; (4) Is there a correlation between
mathematical understanding ability and mathematical response of students who have learned with GeoGebra
software.

2. Research Method
This research is a quasi-experimental study because the subjects in this study were not randomly grouped,
but the researchers accepted the research subject's condition as it is. The selection of this study is based on
consideration that the research subjects have been grouped into classes that already existed and it is not
possible to group students randomly. In this study, two classes were taken as samples, namely the
experimental class which was given treatment in the form of learning using GeoGebra software and the
control class using conventional learning. The design of this study uses the following non-equivalent control
group design [6][9]:

Experimental Class : O X O
Control Class :O O

Notes:
O: pretest and posttest of mathematical understanding ability
X: mathematics learning by using GeoGebra software
-----: Subjects are not randomly grouped
The population in this study was all semester III students who took the Transformation Geometry
course in the Mathematics Education study program FKIP UNLA Bandung academic year 2018/2019.
The sample of this study is students of class A as the experimental class and class B as the control class.
Sampling is determined based on purposive sampling, namely sampling based on certain considerations [7].
The type of data collected in this study is quantitative descriptive data consisting of 3 types, namely:
(1) Student activities during the learning process; (2) Student Learning Outcomes; (3) Student responses.

3. Result And Discussion

Quantitative data were obtained through tests of mathematical understanding ability at the beginning and
end of learning. The data was obtained from 24 students consisting of 12 experimental class students
(learning with GeoGebra software) and 12 control class students (conventional learning).
Mathematical understanding ability is obtained through pretest and posttest. From the pretest and
posttest scores, the normalized gain (N-gain) of the comprehension ability in the experimental class which
was learned by GeoGebra software and the control class was calculated by conventional learning.

3
ICComSET 2019 IOP Publishing
Journal of Physics: Conference Series 1477 (2020) 042048 doi:10.1088/1742-6596/1477/4/042048

Table 1. Descriptive Statistics of Mathematical Understanding Ability

KAM Statistics Experimental Class (GeoGebra) Control Class (Konvensional)
Category Data Pretest Postest N-gain Pretest Postest N-gain
High ̅ 16,17 32,33 0,82 16,33 28,50 0,62
s 1,17 1,21 0,06 1,63 1,05 0,07
Middle ̅ 11,22 25,61 0,58 12,90 22,65 0,42
s 2,28 3,53 0,13 1,48 1,90 0,09
Low ̅ 10,50 19,50 0,35 10,33 17,50 0,28
s 1,73 1,29 0,08 1,75 4,76 0,16
Total ̅ 12,03 26,09 0,60 13,06 22,78 0,43
s 2,83 4,67 0,17 2,41 4,22 0,14
Ideal Maximum Score = 36

Based on table 1 above, it can be seen that the mean score of the experimental class pretest using the GeoGebra
software approach is 12.03 while the average score of the conventional class pretest is 13.06. Pretest data for all
KAM categories in the experimental class and the control class are relatively the same. Based on these data both
reviewed as a whole student and in the KAM category it can be concluded that the initial abilities of students in
the two classes are the same.
The average posttest experimental class with the GeoGebra software approach is 26.09 while the posttest
conventional class is 22.78. In the low KAM category, the average posttest of the experimental class was 19.50
and the average posttest of the control class was 17.50. When seen as a whole, it was found that the experimental
class students got an average gain of 0.60 and a control class of 0.43. The data shows that the improvement of
the quality of the two classes is relatively the same, but the improvement in learning outcomes of the experimental
class is better than the control class. Thus it can be concluded that learning with GeoGebra software provides a
better contribution in the development of students' overall mathematical understanding abilities.
Finding out an increase in mathematical understanding in students whose learning uses learning models
with GeoGebra software and students whose learning uses conventional learning models will be done by testing
the difference in normalized gain. The statistical test used to prove the hypothesis stating "improvement of
mathematical understanding ability of students who obtain learning with GeoGebra software is better than
improvement of mathematical understanding ability of students who obtain conventional learning" namely the
test of the average difference in N-gain scores.

Table 2. Similarity Test of N-gain Score Average in Mathematical Understanding

Class T Df Sig. (2- Sig. (1- Note Conclusion
tailed) tailed)
Exp 4,25 22 0,00 0,00 H0 rejected Better
Cont

In table 2 you can see the sig value. (1-tailed) <α is 0,000. This shows that H0 is rejected. It means that the
improvement of students' mathematical understanding ability of the experimental class is better than the control
class. Thus it is proven that the hypothesis which states that increasing the ability of mathematical understanding
of students who get learning with GeoGebra software is better than students who get conventional learning.
Testing the difference in the average N-gain score based on KAM is done to find out whether there is a
difference in the increase in mathematical understanding ability of students who get learning with GeoGebra
software and students who get conventional learning in terms of the category of initial mathematical abilities
(high, middle, low). Therefore, t-test was used to determine the differences in the mean of the two data groups.

4
ICComSET 2019 IOP Publishing
Journal of Physics: Conference Series 1477 (2020) 042048 doi:10.1088/1742-6596/1477/4/042048

This analysis was conducted to see the effect of different treatments on the ability of mathematical understanding
in terms of the students' initial mathematical ability categories.

Table 3. Mean Similarity Result Based on KAM Category

KAM Class T Df Sig. (2- Note Conclusion
Category tailed)
High Experimental 5,659 3 0,000 H0 rejected There are differences
Control
Middle Experimental 4,833 15 0,000 H0 rejected There are differences
Control
Low Experimental 0,754 3 0,473 H0 rejected There is no difference
Control

Based on table 3 above it can be concluded that the high and middle KAM categories of the experimental class
and the control class provide a significant difference to the students' mathematical understanding ability because
of the sig. <α = 0.05 which is 0,000. So it can be concluded that there are differences in the improvement of
students' mathematical understanding abilities in each high and middle KAM category for students whose
learning uses an approach with GeoGebra software compared to conventional learning. Whereas for KAM it is
low because of the sig. > α = 0.05 which is 0.473, this means that there is no difference in the increase in students'
mathematical thinking abilities in the low KAM category.
The results of the response attitude scale have been converted in the form of intervals using the Method of
Successive Interval (MSI). The calculation uses STAT 97 software with the main software Microsoft Office
Excel 2010. The intended student response statistics include the number of students, minimum value, maximum
value, average, standard deviation, and normalized gain.

Table 4. Statistics Description of Responses Normalized Gain

Class Number of Xmin Xmaks Std. N-gain
Students (N) Deviation Interpretation
Geogebra 12 0,082 0,512 0,296 0,114 Low
Conventional 12 -0,182 0,347 0,131 0,116 Low

Table 4 contains the normalized gain data from the two learning groups. Based on the table, it can be seen that
the normalized gain of students 'responses whose learning using the learning model with GeoGebra software is
higher than the normalized gain of students' responses whose learning uses conventional learning models.
Similarity Test of the normalized response gain uses t-test. The statistical hypothesis is a one-way
hypothesis, the hypothesis testing criteria if 1/2 sig. (2-way) = sig. (1-way)> 0.05 then H0 is accepted, whereas
if otherwise the H0 is rejected. The results of the calculation of the normalized average of the response to the
normalized gain can be seen in table 5 below :

Table 5. Mean Similarity Test of Responses Normalized Gain

Class T df Sig. (2- Sig. (1- Note Conclusion
tailed) tailed)
Experimental 5,798 22 0,000 0,000 H0 rejected There are differences
Control

5
ICComSET 2019 IOP Publishing
Journal of Physics: Conference Series 1477 (2020) 042048 doi:10.1088/1742-6596/1477/4/042048

Based on the results of the normalized gain calculation, it is obtained 1/2 sig. (2-way) = 0,000 <0.05, so H0 is
rejected. In other words, there is a difference in the final response improvement between students learning using
GeoGebra software and students using conventional learning models .
After presenting two ways of seeing improvement in student responses in the two groups of learning models, the
two test mean responses concluded the same thing, an increase in the response of students who use learning with
GeoGebra software is better than increasing responses of students who use conventional learning.
The next research question is about the correlation between improvement of mathematical understanding
ability and improvement of student responses after using learning with GeoGebra software. Furthermore, a
correlation test will be conducted between improvement of students' understanding and response skills.

Table 6. Correlation Test of Normalized Gain in Understanding and Response

Correlation Pearson Sig. Ket. Conclusion
Gain Understanding Ability and 0,589 0,000 H0 rejected There is a
Response correaltion

In Table 6 above it can be seen that the value of sig. = 0,000 < 0.01, so H0 is rejected in other words H1 is
accepted, so it can be concluded that there is a significant relationship between understanding and response. The
magnitude of the correlation coefficient between comprehension ability and 0.589 responses are included in the
category of sufficient correlation.

4. Conclusion
The following are conclusions from the research activities, namely:
1. Improvement of students' mathematical understanding abilities whose learning using GeoGebra software is
better than students whose learning uses conventional learning in transformation geometry courses.
2. There is a difference in the improvement of students' mathematical understanding abilities that obtain learning
using GeoGebra software with students who obtain conventional learning based on the KAM category (high,
middle, low) on the geometry of transformation.
3. The improvement of mathematical response of students whose learning using GeoGebra software is better
than students whose learning uses conventional learning in transformation geometry courses.
4. There is a correlation between students' mathematical understanding abilities and mathematical responses of
students who have learned with GeoGebra software

References
[1] Arsyad, Azhar. (2002). Media Pembelajaran. Raja Grafindo Persada: Jakarta.
[2] Hohenwarter, M. & Fuchs, K. (2004). Combination of Dynamic Geometry, Algebra, and Calculus in the
Software System Geogebra. Tersedia: www.geogebra.org/publications/pecs_2004.pdf.
[3] Judith Howenwarter dan Markus Hohenwarter (2008). Introduction to GeoGebra. E-book:
www.geogebra.org.
[4] Judith Howenwarter dan Markus Hohenwarter (2009). GeoGebra Help. Buku Manual resmi. E-book:
www.geogebra.org.
[5] Munir. (2009). Implikasi Teknologi Informasi dan Komunikasi dalam Pendidikan.Makalah pada Seminar
Pendidikan Mahasiswa Universitas Pasundan. Bandung.
[6] Ruseffendi, E. T. (2010). Dasar-Dasar Penelitian Pendidikan & Bidang Non-Eksakta Lainnya. Bandung:
Tarsito.
[7] Sugiyono. (2009). Metode Penelitian Pendidikan: Pendekatan Kuantitatif, Kualitatif dan R&D. Bandung:
Alfabeta.
[8] Zakiyudin. (2010). Pembelajaran Matematika dengan Media GeoGebra. UIN Bandung

6
ICComSET 2019 IOP Publishing
Journal of Physics: Conference Series 1477 (2020) 042048 doi:10.1088/1742-6596/1477/4/042048

[9] Dwipriyoko, E., Bon, A. T. B., Sukono, F., (2019), Enterprise Architecture Planning as New Generation
Cooperatives Research Methods, In Journal of Physics: Conference Series (Vol. 1179, No. 1, p. 012094),
IOP Publishing.