The Use of Geogebra Software in Improving Student’s Mathematical

Abilities in Learning Geometry

Antonius K. A. P. Simbolon

, Lasma Melinda Siahaan

Lecturer in Department of Accounting, Universitas Prima Indonesia

Universitas Quality Medan

Keywords: Geometry, Geogebra, Mathematical Ability.

Abstract: Learning geometry has not paid attention to aspects of mathematical ability maximally so that learning

outcomes are not optimal either. Technology has been developing rapidly, one of which is the emergence of

geogebra software version 6.0 which can help the learning process of mathematics but has not been used in

learning. This study aimed to determine the magnitude of the increase in mathematics learning activeness and

achievement in geometry material using geogebra software. This research was conducted in class IX SMP

Negeri 2 Tanjung Morawa, totaling 210 students. The method used is a class action research method which

consists of two cycles, the analysis used is descriptive comparative by comparing the data between cycles.

Geogebra is used to visualize geometric objects that will be transformed. Through the visualization process

students try, reason, and finally find the concept of transformation. The results showed an increase in student

activity during learning. The test results for each cycle showed an increase in the number of students who

achieved minimum completeness (KKM). At the end of the cycle, students who completed learning reached

85.24%. Based on this, learning using geogebra software can improve mathematical abilities.

1 INTRODUCTION

21st-century learners are familiar to the pictorial

culture of learning mathematics as well as other

contents via wide access to internet site and various

applications that are related to mathematics. In this

regard, the traditional lecture-based method of

teaching mathematics is not working as expected by

mathematics tutors. This could be most of the

mathematics teaching and learning which is not

aligned to the pictorial culture. The central obstacles

in teaching mathematics could be concepts without

adequate illustrations (Dahal, 2019).

In Indonesia’s curriculum, geometry is one of the

essential materials that taught from elementary school

until college. It allows people to understand the world

by comparing shapes, objects and their connections

(Jelatu, 2018).

In facing the challenges of the 4.0 industrial

revolution era, an increase in human resources is

needed to be able to compete in the international

realm. One area that we can use as a bridge to improve

quality human resources is education (Adelabu,

2019). One branch of science that plays an important

role in education is mathematics. Mathematics as one

of the areas of learning in schools is an area that gets

attention in the development of learning.

Mathematics in junior high school, for example, tends

to be abstract. This causes mathematics to be a subject

that is considered difficult for students. One part of

mathematics that is abstract is geometry.

The need to visualize concepts and support the

materials in Mathematics learning by forming the

pictures or by using existing draw, becoming what is

needed by the students in improving their

mathematical development and understanding.

GeoGebra can combine dynamic visualization of

geometry and the results of mathematical calculations

simultaneously (Sur, 2020).

Technology developments rapidly bring new

challenges in education. New technology has

capability to make change in education. Many people

already use and explore the new and existing

technology for greater benefit of education. Putra

(2012) in his book stated that it's not chalk and talk

anymore, but (more) to school approach to

developing student's digital literacy.

With the progress in the technological change

process in the education field, we ought to admit that

the mobile education is a part of a new scene. It

352

Simbolon, A. and Siahaan, L.

The Use of Geogebra Software in Improving Student’s Mathematical Abilities in Learning Geometry.

DOI: 10.5220/0010311800003051

In Proceedings of the International Conference on Culture Heritage, Education, Sustainable Tourism, and Innovation Technologies (CESIT 2020), pages 352-360

ISBN: 978-989-758-501-2

provides personal distant learning, non-official

learning and automatic learning through the use of

mobile devices by students of all ages and

backgrounds. It enables them to interact, cooperate

and learn through different ways (Alkhateeb, 2019).

Long before, in year 2002, UNESCO has

advocated the use of technology in education. This

trend is still continuing until today, as recently Leung

(2016), Oktaviyanthi and Supriyani (2015), Loong

(2014) and Saadati (2014) exploring the use of

technology in regard to learning and education.

Specifically, Fathurrohman and Porter (2012)

advocate the use of technology for mathematics

teachers. Recently in year 2017 they explain the

teachers’ real and perceived of technology

availability for teaching and learning, while Hatlevik,

Throndsen, Loi and Gudmundsdottir (2018) explain

the students believe and their actual achievements in

regard to ICT experiences. Vongkulluksn, Xie, and

Bowman (2017) argues on teacher belief as one of

important factors in technology integration.

Karadeniz and Thompson (2018) proposed the use of

calculator, and Wares (2018) argues on the use of

dynamic geometry, while in particular, Martinovski

(2013), Quinlan (2016), Segal, Stupel, & Oxman

(2016), States & Odom (2016) promoting GeoGebra

as a tool for technology use in mathematics teaching

and learning.

Either science or technology is believed can

provide a great opportunity for students to do a deep

exploration of their understanding about a certain

concept. Some technology-based learning tools that

usually used during university level mathematics

learning such as Maple, Matlab, GeoGebra, SPSS, or

Fluent, the needs to find effective and efficient

software to assist them in doing a better

understanding still become educators’ top concern

(Safrida, 2018).

One of mathematics concepts is geometry. Atiah

in Hoherwarter and Jones (2007) said it is important

to learn geometry and algebraic geometry. Geometry

concepts and the ideas of geometry have been

introduced to students since their study in elementary

school level, for example for the introduction of line,

plane and space. However, many geometry concepts

and ideas in high school level presented in the abstract

concept for students, not in concrete as before. This is

one of the reasons why the students still get some

difficulty when learn geometry. Quadrilateral is a

mathematics concept in geometry for junior high

school level. Quadrilateral topic consists of concept

and definitions of abstract geometry that is required

to solve problems related with geometry use in daily

life. It is acknowledged that the students' cognitive

development at the stage of junior high school age is

the formal-operational stage. At this stage, the student

should have the capacity to use abstract principles, so

that students must be able to learn abstract learning

materials such as Quadrilateral. Kabaca (2017)

provided classroom note for understanding geometry,

however it is not enough for this case.

Written in the Regulation of the Minister of

National Education No. 16/2007 emphasized that one

of the pedagogical competencies that SMP / MTs

mathematics subject teachers must have is to be able

to utilize information and communication technology

for learning purposes. Meanwhile, for professional

competence, teachers must be able to take advantage

of Information and Communication Technology

(ICT) to communicate and develop themselves. The

main application of technology in learning

Mathematics is the integration of software (software)

for learning Mathematics. This has led to a lot of

software being developed and utilized.

According to Sumeda (Bawono, 2015)

mathematics is generally defined as a field of science

that studies the patterns of structure, change and space

of life, because in every daily activity, whether it is

based on it or not, we definitely use mathematics.

Mathematics equips students to be systematic, critical

and creative, therefore mathematics must be mastered

by everyone.

However, based on the 2011 TIMMS report,

Indonesian grade IX students occupy the 38th

position among 42 countries participating in the math

test with an average score of 406 while the

international standard standard score is 500. The

TIMMS survey results regarding the mathematical

abilities of Indonesian students are not much different

from the results of surveys from other institutions

such as PISA (Programme International for Student

Assesment). Based on the results of the 2012 PISA

survey, Indonesian students' mathematical abilities

rank 64 out of 65 countries with an average score of

375, while the average international score set by PISA

is 494.

The domain of the question content in the PISA

test is geometry. The content sub-components tested

are changes and linkages, space and form, quantity,

uncertainty and data. Many geometric problems

require visualization in problem solving and in

general students find it difficult to construct

geometrical spatial shapes, as experienced by

students at SMPN 2 Tanjung Morawa.

One of the efforts to visualize mathematical ideas

so that mathematics can be understood by students,

especially on geometry material, is through more

innovative learning strategies. Among them are

The Use of Geogebra Software in Improving Student’s Mathematical Abilities in Learning Geometry

353

innovative media with the use of advances in

Information and Communication Technology (ICT)

in the form of geographic media as a learning

resource and learning media.

Computer programs can be used as an alternative-

effective solution. One of the computer programs that

can be freely used is GeoGebra. GeoGebra is Non-

Commercial Free Software for use by mathematics

educators (teachers and lecturers) in Indonesia. The

use of GeoGebra in mathematics teaching and

learning enable students to draw geometry objects in

fast and specific. Enable to animate and manipulate

visual to understand geometry concept, evaluating, to

study geometry object (Syahbana, 2016). Many

researches show positive effects of teaching and

learning with GeoGebra, such as Zengin, Y (2017)

and Hähkiöniemi, M., (2017).

Geogebra is software designed to solve geometry,

calculus and algebra material as well as applications

fordesigning spaces and buildings (Saputra, 2019). It

can serve for development of instructional materials

in mathematics in many different forms, types and

styles, and for all levels of mathematical education. It

is free to be downloaded form a website, while

nothing but a Java 6 platform is necessary for its full

operation. GeoGebra seems to be particularly easy

and intuitive to learn. Files can be saved in “.ggb”

format, or as dynamic web pages. GeoGebra can

output files as pictures (.png) or as encapsulated

postscript for publication quality illustrations.

GeoGebra user interface offers a rich graphics

menu for drawing various objects, while the complete

construction protocol is saved and it appears in any

chosen language from the available 45 versions,

therefore no translation is necessary and free sharing

of developed instructional materials is genuinely

supported all over the world. Users are encouraged to

visit GeoGebra webpage and GeoGebra user’s forum

GeoGebraWiki, a free pool of teaching materials for

this dynamic mathematics software where everyone

can contribute and upload materials. GeoGebra has a

built-in Cartesian coordinate system, and accepts both

geometric commands (drawing a line through two

given points, a conic section determined) and

algebraic ones (drawing a curve with a given

equation). Among its more interesting features is the

ability to draw tangent lines to algebraic and even

transcendental curves at given points, while equation

of this tangent line is available immediately too. This

double representation: the geometric-synthetic one

and the algebraic-analytic one is one of the greatest

advantages of GeoGebra software that mostly suits to

didactic aims of full comprehension of basic

mathematical concepts.

GeoGebra software can be installed on a personal

computers, android devices, and direct use on the web

anytime and anywhere. In addition, the '.ggb' file

extension, as outcomes of the learning process using

GeoGebra, can be stored and disseminated for the

next session of learning. This output file is commonly

called the GeoGebra Applet. This is one of features in

GeoGebra that can be used, modified, and/or

developed by educators for dynamic and interactive

mathematics teaching and learning.

Publications, there is no GeoGebra Applets

closely linked and aligned to the Indonesia national

curriculum in accordance to the mandated approach.

The availability would be benefit for mathematics

teaching and learning and the implementation of the

national curriculum. In addition, various discovery

learning activities can be carried out, by using the

GeoGebra Applet. For that reason, there is a need to

develop GeoGebra Applet closely linked and aligned

to the Indonesia national curriculum, in this case is to

facilitate the mathematics teaching and learning in

quadrilateral concept, in accordance to the scientific

approach.

GeoGebra separates mathematical objects into

free objects and dependent objects. Where the

dependent objects are defined by an explicit

construction (algebraic or geometric) the construction

steps can be encapsulated into a tool. Once the tool

has been defined a new button appears on the tool bar

and a corresponding function name is available to the

user. Such tools are essentially functions, and may

operate with geometric objects such as circles, lines

and points. The tools function within GeoGebra is

interesting because it allows geometrical functions to

be defined, which illustrate a key mathematical

process: encapsulation or compression. Using these

tools it is possible to extend the software in natural

ways, just as mathematical domains are extended

during normal teaching.

The Indonesia national curriculum, called year

2013 curriculum, mandates the essence of scientific

approach in teaching and learning, including for

mathematics. Through a scientific approach

(observing, questioning, associating, experimenting,

and networking stages), the students are directed to

establish the ability to thinking scientifically that

emphasizes inductive reasoning rather than

deductive, and guiding the students to research,

instead of being told. At the time of research project,

checked through available

According to Aliviah (2012) during this time the

learning of geometry in the classroom was only

taught using whiteboard media and not yet utilizing

learning media such as computers. The submission of

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354

material that is often done by the teacher is

conventional learning such as lectures, so that there

are students who have difficulty understanding the

material presented. For this it is necessary that other

media can help students understand the geometry.

One of the technology-based mathematics learning

media that can help students to represent

mathematical problems is GeoGebra software. One of

the learning media that can represent a mathematical

model or represent a linear equation of two variables

into the form of graph using the help of GeoGebra

software media. According to Hohenwarter et al

(2008) GeoGebra is a dynamic mathematical

software that combines geometry, algebra, and

calculus.

Meanwhile, according to Wulandari (2015)

GeoGebra is an easy-to-use mathematical software,

both on geometry, algebraic, and calculus material.

From some of the definitions of GeoGebra above it

can be concluded that GeoGebra is one of the

mathematical software that can be used in learning

mathematics that includes material geometry,

algebra, and calculus. GeoGebra serves as a math

learning medium that can visually help students to

understand abstract mathematics material. Not only

that GeoGebra can also help students in

understanding the concept of straight line graphs in

more detail with a varied and interesting look. In

addition to the teachers themselves, GeoGebra can be

used as a math learning tool to create interactive

learning that allows students to explore various

mathematical concepts that are abstract.

Furthermore, according to Preiner (2008),

"Computer algebra systems, dynamic geometry

software, and spreadsheetsare the main types of

educational software currently used for

mathematicsteaching and learning. Each of the

programs has its own advantages and isespecially

useful for treating a certain selection of mathematical

topics orsupports certain instructional approaches ".

Geogebra Software is one of the technology

products that are widely used in mathematics

learning. This Software is widely utilized as a tool to

construct, demonstrate or visualize abstract problems

in mathematics that can not be resolved manually

especially in the field of geometry.

Apart from the standalone application, GeoGebra

also allows the creation of interactive web pages with

embedded java applets. These targeted learning and

demonstration environments are freely shared by

mathematics educators on collaborative online

platforms like the GeoGebraWiki. The number of

visitors to the GeoGebra website has increased since

2004 from 2000 per month to over 300,000 per month

coming from over 180 countries.

The International GeoGebra institute has been

established, coordinating the work of thousands of

volunteers all over the world in the structure of

accredited national GeoGebra institutes in different

countries. GeoGebra dynamic spreadsheets enable to

produce interactive presentations directly on the web

serving as electronic instructional sources for e-

learning solutions in the form of dynamic cognitive

tools. These html pages can be used directly from

Internet and are presentable in all common web-

browsers, while there is no need to install GeoGebra

software in the user’s computer. The only necessary

prerequisite in addition to the web-browser is the

installed Java support that is essential.

Based on exposure to background problems, the

problem is obtained in this research activity is,

whether the use of software GeoGebra media can

improve the mathematical ability of class IX students.

From the formula above, the purpose of this research

activity is to know whether the use of media software

GeoGebra can improve the mathematical ability of

junior high school students 2 Tanjung Morawa class

IX.

2 LITERATURE

Understanding geometry is important to yourself and

to understand other areas of mathematics. Geometry

is the study of the relationships between points, lines,

surfaces, angles, and shapes. So naturally, drawing

diagrams is a must! The relationships, properties, and

theorems will be easier to understand when you have

a diagram! ... Just be sure to pay attention to the

proportion of lines and angles. When you start

studying geometry, it is important to know and

understand some basic concepts.

Geometry comes from the Greek meaning ‘earth

measurement’ and is the visual study of shapes, sizes

and patterns, and how they fit together in space. You

will find that our geometry pages contain lots of

diagrams to help you understand the subject. When

you’re faced with a problem involving geometry, it

can be very helpful to draw yourself a diagram

(Pamungkas, 2019).

Geogebra is one of software to visualize and

demonstrate mathematical concepts, especially

geometry and algebra. Geogebra is recommended to

be included in the school curriculum because it has

potential in mathematics education. For this function,

students can use algebraic and geometrical functions

The Use of Geogebra Software in Improving Student’s Mathematical Abilities in Learning Geometry

355

simultaneously with interactive dynamics that will

enhance their cognitive abilities (Zetriuslita, 2020).

Various benefits of computer program application

in mathematics learning is expressed by Kusumah

(2003). According to him, computer programs are

ideal to be used in learning mathematical concepts

that demand high accuracy, repetitive concepts or

principles, precise, fast, and accurate chart

completion. Furthermore Kusumah (2003) also

suggested that the innovation of learning with

computer assistance is very good to be integrated in

learning mathematical concepts, especially those

involving the transformation of geometry, calculus,

statistics, and graphs of functions.

Computer utilization in mathematics learning is

intended to support and facilitate students in

understanding mathematical concepts. Thus,

understanding the concept of students should get a top

priority instead of only increasing the mechanistic

ability of students in utilizing computer programs. In

this case teacher teaching is indispensable to associate

a variety of animation or application of computer

programs produced by students with relevant and

underlying concepts. In many ways, understanding

the concept must precede various computer program

utilization. However, within certain boundaries,

computer programs can be utilized in the process of

the concept of constructlifing by students. Although

based on its functionality, computer learning media

can be applied to enhance students ' mathematical

skills, and to construct concept mastery skills.

Hohenwarter (2008) said the GeoGebra program

is very beneficial for both teachers and students.

Unlike the use of commercial software that usually

only bias used in schools, Geogebra can be installed

on personal computers and utilized when and

anywhere by students. For teachers, GeoGebra offers

an effective opportunity to create an interactive online

learning environment that allows students to explore

various mathematical concepts.

3 METHOD

This research was conducted in SMPN 2 Tanjung

Morawa, Class IX with 210 students. This research

method is Classroom ation research. The subjects of

the study were students of class IX 1-year semester

2020/2021 lessons of 210 students. The Data

examined in this class action study is the guidance of

student learning and the mathematical abilities of

students in the learning process. Data is collected

using a document technique from the pretests result

as an initial condition. The guidance of learning is

derived from the students' mathematical ability to

solve geometry problems through phase I cycle test

and cycle II. The data that has been collected is then

analyzed using two ways: quantitative data of

learning results Analyzed with comparative

descriptive, which compares the value of learning

outcomes in initial conditions, cycle I, and cycle II.

Qualitative Data of the learning process as a

description of student percentage in the mathematical

skills of students are analyzed with qualitative

descriptive. Qualitative Data compared between

initial conditions, cycle I, and cycle II. The research

procedure can be seen in Figure 1.



Figure 1: Research procedure Diagram.

Based on Figure 1 shows that the research process

is conducted with two cycles that contain aspects of

planning, action, observation, and reflection.

Planning research activities include identifying

issues, drafting a learning Implementation plan for

each action activity, student worksheets, evaluation

and media tools, tools and materials needed in

learning, and forming randomly-generated groups.

Action includes preliminary, core and closing

activities. Observation of learning activities is

conducted during the implementation of teaching and

learning activities to know the course of learning. At

the end of the cycle ends with tests. Based on

observation and test result, the next stage can be done.

Data gathered from observation results include study

results data, learning process data in the classroom,

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and observation data from completion of student

worksheets in view of students ' mathematical skills.

The reflection in this class action study is an

attempt to assess what has happened, or that has not

been completed in a previous step or attempt. The

results of reflection were used to take further steps in

an effort to achieve research objectives. Data

obtained from the observation, analyzed and

evaluated with the teacher observer. The findings

may still not be maximized, need to get noticed for

the next meeting. Reflection activities include

knowing the number of students who have a value

below the minimum completeness criteria,

constraints experienced by students and teachers and

the possibility of increasing the level of

understanding.

4 RESULTS AND DISCUSSIONS

4.1 Initial Conditions

Prior to the commencement of the research, the

learning carried out only used the lecture method and

only occasionally used the discussion method.

Teachers often explain all material orally without

using other learning models, teaching aids, and

software used in mathematics that can arouse student

interest in learning. Students not interested in learning

mathematics resulted in students being less active in

the learning process. The inactivity of students is

caused by students only listening without being

actively involved in the learning process.

Students only take notes without asking many

questions so that their level of understanding is not

known. At the end of the lesson each material is tested

and the results are many students whose scores are

below the KKM as shown in Figure 2 below:

Figure 2: Pretest Students Math Skills.

This is because students memorize more material

so that most students are unable to solve math

problems correctly. Learning using geogebra

software will be easier for students to solve geometry

problems. The discovery of geometric concepts in the

previous year was mostly done manually. The

application of the lecture model was felt to be less

attractive to students' interest and activity. Thus

learning has not met the desired standards, corrective

steps are needed.

The learning outcomes showed that 21 out of 210

students (10%) had completed their mathematical

abilities, while 189 other students (90%) had not yet

reached the KKM. In graph 2, it can be seen that the

results of daily tests are directly proportional to

students' mathematical abilities in the learning

process. Learning outcomes will increase if students

are taught using geogebra software in the learning

process of geometry material.

4.2 Description of Research on Cycle I

After the learning action carried out in cycle I, the

researcher identified the problems that were found

during the learning. Based on the results of

observations and observations of researchers during

the learning process, there are several things that are

considered by researchers so that they become

material for improvement for the next cycle, namely:

a. Students did not understand the use of geogebra

software after teaching in cycle I, so it is

necessary to re-teach using the geogebra

The Use of Geogebra Software in Improving Student’s Mathematical Abilities in Learning Geometry

357

software, so that students are able to solve

geogebra questions correctly.

b. The mathematical ability of students in solving

the problems in the first cycle that had not

reached the completeness level was 97 students

or 46.19%, while the students who had reached

the completeness level were 113 students or

53.81%. Thus it can be said that the class has not

finished solving geometry problems, namely

that there are not ≥ 80% of students who have a

complete level of mathematical ability in cycle

The following is presented in graph 3, the students'

mathematical abilities in cycle I are as follows:

Figure 3: Student mathematical skills on the I cycle.

4.3 Description of Research on Cycle II

After carrying out the learning action in cycle II it was

found that the students' mathematical abilities had

improved from before. This can be seen from:

a. The mathematical ability of students in

solving problems in cycle II with a very high

level of ability was 35 students or 16.67%,

high ability levels were 46 students or 21.90%,

medium ability levels were 98 students or

46.67%, low ability level as many as 16

students or 7.62%, and very low ability level

as many as 15 students or 7.14%. Meanwhile,

students who have reached the completeness

level are 179 students or 85.24%. Thus it can

be said that the average grade IX student has

completed solving geometry problems,

namely there are ≥ 80% of students who have

a level of completeness. Mathematical

abilities in cycle II can be seen in the graph

below:

Figure 4: Mathematical abilities of students on cycle II.

b. From graph 4 can be seen that there is an

increase in the number of students who reach

the level of completeness on geometry

material using geogebra software in cycle II

is 85.24%, whereas in cycle I the level of

completeness of students' mathematical

abilities was obtained at 53.81%. So the

increase in the completeness of students'

mathematical abilities from cycle I to cycle

II was 31.43%.

Some students are still not able to solve the given

questions, but the number of students who have not

been able to solve the questions has decreased from

before. This can be seen from the results of students'

mathematical ability tests in cycle II.

From the results of data analysis, it can be

concluded that students' mathematical abilities have

increased and students have reached the expected

level of learning completeness. This shows the

success of learning action in cycle II.

Based on the explanation above, from the initial

conditions to the final conditions in cycle II, many

students were active in following the learning process

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due to the use of geogebra applications in solving

geometry problems.

5 CONCLUSION AND

SUGGESTION

5.1 Conclusion

Based on the results of the research and discussion,

the conclusion is that: Learning using Geogebra

software can improve students' mathematical abilities

and the number of students who have reached the

KKM on geometry material after using geogebra

software from initial conditions to cycle I and cycle I

to cycle II increases.

Therefore, geogebra software can be used in the

learning process on the subject of geometry and other

subjects that have the same characteristics.

5.2 Suggestion

From the results of this study, the advice that I can

give to school principals and mathematics teachers at

SMP Negeri 2 Tanjung Morawa, should be in the

teaching and learning process of mathematics

teachers also use mathematics learning software to be

able to improve students' abilities in learning

mathematics.

ACKNOWLEDGEMENT

The researcher humbly expresses his gratitude to the

Research and Technology / Head of the National

Research and Innovation Agency (RistekBRIN) for

grant assistance for Junior Lecturer’s Research (PDP)

Year 2020 under in the Announcement of Receipt of

Research Funding in Non-PTNBH Colleges in 2019

No: B / 87 / E3 / RA.00 / 2020 and Amendments to

the Single Year 2020 Budget Year Research Contract

between Region I Higher Education Service

Institutions (LLDikti Wilayah 1) and Prima Indonesia

University, No: 282 / LL1 / PG / 2020.

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