Students’ Ability in Proving Pythagorean Theorem through Discovery Learning Model Using Geogebra Software
Proceedings of The 7th Annual International Conference (AIC) Syiah Kuala University and The 6th International
Conference on Multidisciplinary Research (ICMR) in conjunction with the International Conference on Electrical
Engineering and Informatics (ICELTICs) 2017, October 18-20, 2017, Banda Aceh, Indonesia
Students’ Ability in Proving Pythagorean
Theorem through Discovery Learning Model
Using Geogebra Software
1*
Fathiya Salsabila, 2Rahmah Johar and 3Susanti Panca Wahyuni
1,2
Department of Math Education, Faculty of Teacher Training and Education,
University of Syiah Kuala, Banda Aceh 23111, Indonesia;
2
Junior High School 6, Banda Aceh 23125, Indonesia;
*
Corresponding author: fathiyasalsabila11@gmail.com
Abstract
Learning math is like training logical thinking, intelligence, focus and
also systematics. One of the most important materials in math is
Pythagorean Theorem. It is used in many aspects of life and helps us to
solve daily problems. However, many students still cannot use it we
even they have learned it. The aim of this study research is to describe
the students’ learning ability process through discovery learning model
using GeoGebra software on Pythagorean Theorem. The subjects of this
study were the students of SMP Negeri 6 Banda Aceh 29 students of
grade VIII-8. The data which was analyzed is formed tasks which were
done in groups and video analysis. The results of study showed that the
students are able to accomplish worksheet through GeoGebra assisted
and all of them are able to take conclusion symbolically yet not by using
their own words. The first group was failed to count third area but they
succeeded on counting other areas which lead them to the right
conclusion. The second group’s fault was on naming a square
particularly on its third area however they were better taking the right
conclusion. The obstacles of learning process were (1) limitation of time,
(2) only some students practice using GeoGebra software, (3) laptops
used were slow and not responding, (4) even the student did not
understand the beginning explanations.
Keywords:
learning, discovery learning model, GeoGebra software,
Pythagorean Theorem.
Introduction
Math is a knowledge which has an important role in human life and it becomes a
beneficial subject to get connected to other studies. According to Scherer and
Beckmann (2014), math and science are significantly related to problem solving
ability in life. One of math materials which is frequently faced in daily life is
Pythagorean Theorem in junior High school. Murniasih (2016) argues that
Pythagorean Theorem is often used in daily life and it releases people to solve the
daily problem. It becomes the material that is used in another math material or
prerequisite material. Pythagorean Theorem material is also one of math test
questions which exist in National Examination (UN). Kurniawati (2015) declares that
students’ difficulty in comprehending Pythagorean Theorem material is unable to use
math concepts which have been learned previously.
717
Fathiya Salsabila, Rahmah Johar and Susanti Panca Wahyuni
Math case is dominated to real problem gotten in daily life, yet in math conventional
learning process, the teacher only teaches the materials. A concept, theorem,
proposition, and etc., appear as if they were taken for granted without past
discovery process or it is legacy of the past. This case causes students’ disability to
understand some logarithm (Offirstson, 2014). The observation done by Murniasih
(2015) showed that from 24 students who learned Pythagorean Theorem, only 15
students passed the Minimal Completeness Criteria (MCC); MCC applied in the
school is 65. According to Murniasih (2015), Student’s Mistakes in Pythagorean
Theorem concept are (1) students still misunderstand about story questions that
causes they failed to change it into math model, (2) students still failed in counting
quadratic values, and (3) students are careless in doing the tasks so it makes them
got a wrong final result. Furthermore, the research conducted by Arfiyanti, Irawan,
and Purwanto (2016) showed that the students still misunderstand about
Pythagorean Theorem. They face difficulty if the Pythagorean Theorem test is
formed
and not
. They are used to memorize the formula and
not understand the meaning of the formula which has been learned.
In learning process, the students have to be used to solve the problem, and to find
out their own ideas. According to Offirstson (2014), studying and learning have to
be packed into a learning process construction and not only taken from teachers’
teaching. In teaching math, teachers should facilitate the learning process by using
ways which make an information becomes valuable and relevant to the students.
Learning model which makes the students active and find their own concept is
Discovery Learning. According to Sund (1975) Discovery Learning is a learning
process that makes students find the idea without getting it directly from the
teachers. They get it by their selves. Purwatiningsih (2013) declares that Discovery
Learning used in learning process can increase students’ result achievement. The
statement above in line to Effendi’s research result (2012) claims that using
Discovery Learning assists students’ achievement ability and problem solving to be
better. In addition, Yang, Liao, Ching, Chang, and Chan’s study result (2010)
indicates that the learning process using Discovery Learning model produces
students’ concept retention better. While Joyce & Weil (1992, in Fajri, Johar &
Ikhsan:2016), the advantages of Discovery Learning are to support the students to
develop their intelligences and to increase their curiosity and to find out the answer
of the curiosity as well.
The rapid technology development with various technological models facilitates us to
do particular activities. One of activities we are easy with by technology is learningteaching process. Syah (2015) claims that to expand students’ thought in learning
process, mastering science and technology, math is extremely needed. Learning
principle based on Ministry National Education Republic of Indonesia 2016 Number
22 is to use media of information and communication technology increasing
efficiency and effectiveness in learning. Students can understand abstract contents
assisted by technology. In accomplishing the Pythagorean Theorem, teachers can
use technology. According to Wasriono, Syahputra and Surya (2015), visual
technology-assisted development need to be applied in teaching-learning process to
relieve students to understand the concepts. While Calder and Campbell (2016)
argue that particular characteristics in learning process using digital technology
enable alternative solutions. High-level thinking and problem solving skills related to
students’ ways of getting information by using digital technology.
One of technologies that can support the students nowadays is GeoGebra software.
Based on Hohenwarter (2008), GeoGebra is a computer program to facilitate
students to learn geometry concept and algebra and it also has 3 multirepresentation characteristics, they are: there is algebra figure, graphic, and
718
Proceedings of The 7th Annual International Conference (AIC) Syiah Kuala University and The 6th International
Conference on Multidisciplinary Research (ICMR) in conjunction with the International Conference on Electrical
Engineering and Informatics (ICELTICs) 2017, October 18-20, 2017, Banda Aceh, Indonesia
numerical. They are connected dynamically one another. And that leads students to
learn geometry objects particularly Pythagorean Theorem which is abstract.
According to Hohenwarter and Fuchs (2004), using GeoGebra software can lead
students to find out and demonstrate and visualize math concepts. Lubis and Listiani
(2016) state that the GeoGebra is applied to increase the concept of understanding.
Besides, Zulnaidi and Zakaria’s research result (2012) showed that the use of
GeoGebra can increase students’ achievement in comprehending concept and math
procedure.
Based on the explanation above, the research questions are:
1. How do the students’ ability in proving Pythagorean Theorem through
Discovery Learning Model Using GeoGebra software?
2. What are the obstacles of learning using Discovery Learning model using
GeoGebra software on Pythagorean Theorem?
Research Method
The study was conducted to describe students’ ability through Discovery Learning
model using GeoGebra software. The subjects of this research are 29 students of
SMP Negeri 6 Banda Aceh grade VIII-8 year 2017/2018.
This study was held on Monday, May 10th 2017. The instrument was the students’
worksheet worked in group. There were 5 groups consisting of 5-6 students who
were chosen randomly. Each group found Pythagorean Theorem concepts using
GeoGebra software. Then, the data was analyzed in descriptive qualitative.
Results and Discussion
The using of laptop in learning process made students enthusiastic and the tasks
which were done seemed so real. In the process of learning, teacher divided pupils
into 5 groups and all of them succeeded to conclude the argumentation symbolically
yet they were failed to take conclusion through their own words. Here are pictures of
students’ ability in proving Pythagorean Theorem until symbolic steps.
Figure 1. 1th group’s answer on symbolic step.
8. Determine the area of each equilateral triangle and write the solution on
the following worksheet:
Area 1 = Area ABE =Area triangle with base 4cm and height 3,46 cm
719
Fathiya Salsabila, Rahmah Johar and Susanti Panca Wahyuni
=
=
= 6.92 cm2
Area 2 = Area ACF = Area triangle with base 3 cm and height 2,6 cm
=
= 3,9 cm2
=
Area 3 = Area ABE = Area triangle with base 5 cm and height 4,33
=
=
= 10,71 cm2
Based on the student result: Area 6,92 + Area 3,9 = Area 10,71
Figure 2. 2ndgroup’s answer on symbolic step.
6. Determine the area of each square and write the solution on the following
worksheet:
Area 1 = Area ABGF = Area square with face 4 cm
=
=
= 16 cm2
Area 2 = Area ACHI = Area square with face 3 cm
=
=
= 9 cm2
Area 3 = Area BCFG = Area square with face 5 cm
=
=
= 25 cm2
Based on the student result:
Area 16 cm2 + Area 9 cm2 = Area 25 cm2
Figure 3. 3rdgroup’s answer on symbolic step.
720
Proceedings of The 7th Annual International Conference (AIC) Syiah Kuala University and The 6th International
Conference on Multidisciplinary Research (ICMR) in conjunction with the International Conference on Electrical
Engineering and Informatics (ICELTICs) 2017, October 18-20, 2017, Banda Aceh, Indonesia
6. Determine the area of each quadrant and write the solution on the
following worksheet:
Area 1 = Area BAD = Area quadrant with radius 4 cm
=
=
= 12,56 cm2
Area 2 = Area ACF = Area quadrant with radius 3 cm
=
=
= 7,065 cm2
Area 3 = Area BEC = Area quadrant with radius 5 cm
=
= 19,625 cm2
=
Based on the student result:
Area BAD + Area ACF = Area BEC
Figure 4. 4thgroup’s answer on symbolic step.
6. Determine the area of each square and write the solution on the following
worksheet:
Area 1 = Area ABGF = Area square with face 4 cm
=
=
= 16 cm2
Area 2 = Area ACHI = Area square with face 3 cm
=
= = 9 cm2
Area 3 = Area CBDE = Area square with face 5 cm
=
=
= 25 cm2
Based on the student result:
Area ABGF + Area ACHI = Area CBDE
First group was still failed in counting. It was supported by Murniasih’s research
(2015) which states that students who are less attention during task’s introduction
will produce bad final result. The example is on the picture below.
Figure 5. 1st group’s answer on 8th step.
Area 3 = Area ABE = Area triangle with base 5 cm and height 4,33
721
Fathiya Salsabila, Rahmah Johar and Susanti Panca Wahyuni
=
=
= 10,71 cm
2
= 10,82
Either first group or second group mistakenly understood the statement so it led
them to a wrong answer. In line to Priyanto, Suharto, and Trapsilasiwi’s research
(2015) that declare that question transformation error done by students amounts
49% like on the picture below:
Figure 6. 1stgroup’s answer on transformation.
Based on the student result:
Area 6,92 + Area 3,9 = Area 10,71
Area 1 + Area 2 = Area 3 or Area ABE + Area ACF = Area BCD
Figure 7. 2nd group’s answer on transformation.
Based on the student result:
Area 16 cm2 + Area 9 cm2 = Area 25 cm2
Area 1 + Area 2 = Area 3 or Area ABGF + Area ACHI = Area BCED
The second group’s second step was less precise in drawing and observing a
triangle. Furthermore, Priyanto, Suharto, and Trapsilasiwi (2015) support the
statement by their finding which found that 46% of students’ question
understanding error and it is added by Murniasih (2015) who argue that the
students are less precise to understand word problem in math and task finishing
process like the following pictures
Figure 8. 2nd group’s answer (fault on drawing a triangle).
722
Proceedings of The 7th Annual International Conference (AIC) Syiah Kuala University and The 6th International
Conference on Multidisciplinary Research (ICMR) in conjunction with the International Conference on Electrical
Engineering and Informatics (ICELTICs) 2017, October 18-20, 2017, Banda Aceh, Indonesia
Figure 9. 2nd group’s answer (fault on observing a triangle).
Area 3 = Area BCFG = Area square with face 5 cm
=
BCED
=
= 25 D
cm2
On conclusion section, all groups were less precise to take conclusion. Priyanto,
Suharto, dan Trapsilasiwi (2015) support the finding by stating that the fault in final
answer of students is amounts 61%. Conclusion section: first group could not
conclude that task. Second and third group would be 100% correct if they were not
failed to interpret the question. And the fourth and fifth groups were failed in
concluding. Those are showed in the pictures below.
Figure 10. 1st group’s answer on taking conclusion.
Figure 11. 2nd group’s answer on taking conclusion.
Figure 12. 3rd group’s answer on taking conclusion.
723
Fathiya Salsabila, Rahmah Johar and Susanti Panca Wahyuni
Figure 13. 4th group’s answer on taking conclusion.
Picture 10, 11, 12 and 13 are learners drawing conclusions according to the
definition. The last group did not write the answer on their worksheet. Nevertheless,
based on the video analysis they did it in another paper. The last group was failed to
count third area but they succeeded on counting other areas which lead them to the
right conclusion.
Figure 14. Fifth group’s answer.
1) Area 1 = Area BAD = Area quadrant with radius 4 cm
=
=
= 12,56 cm2
2) Area 2 = Area AEC = Area quadrant with radius 3 cm
=
=
= 7,065 cm2
3) Area 3 = Area FBC = Area quadrant with radius 6 cm
=
=
= 28,26 cm2
Based on the student result: Area BAD + Area AEC = Area FCD
Based on the data analysis, the summary is the students enable to accomplish
student worksheet through GeoGebra software and all of them enable to take
conclusion symbolically yet not by using their own words. The first group was failed
to count third area but they succeeded on counting other areas which lead them to
the right conclusion. The second group’s fault was on naming a square particularly
on its third area however they were better taking the right conclusion. Furthermore,
math teacher never uses computer software in learning process and also seldom
transforms students into groups. The statements were based on researcher and
math teacher’s interview section. The barriers faced by math teacher were a
limitation of time and computer availability. Barriers faced during learning process
were the students did not understand the beginning explanations, the laptops used
were slow and they were sometimes not responding that caused the students could
not finish the student worksheet on time.
724
Proceedings of The 7th Annual International Conference (AIC) Syiah Kuala University and The 6th International
Conference on Multidisciplinary Research (ICMR) in conjunction with the International Conference on Electrical
Engineering and Informatics (ICELTICs) 2017, October 18-20, 2017, Banda Aceh, Indonesia
Conclusions
GeoGebra software can be used as media or multimedia to learn Pythagorean
Theorem. From 5 groups mentioned, student can conclude the material symbolically
yet not by using their own words. In addition, the obstacles of learning process were
a limitation of time, in software socialization, only few of students wanted to try
using the software and the laptops used were slow, even the student did not
understand the beginning explanations, the laptops used were slow and they were
sometimes not responding that caused the students could not finish the student
worksheet on time. Teachers should more often integrate the media in learning.
References
Arfiyanti, D., Irawan, E. B., & Purwanto. (2016). Answers to problem analysis of the
concept of Pythagoras theorem in student of Class VIII. In Prosiding Seminar
Nasional Matematika dan Pembelajarannya “Tren Penelitian Matematika dan
Pendidikan Matematika Abad 21” (pp. 1-5). Malang: Universitas Negeri Malang.
Calder, N. & Campbell, A. (2016). Using mathematical apps with reluctant learners.
Digital Experiences in Mathematics Education, 2(1), 50–69.
Efendi, L.A. (2012). Mathematical learning with guided discovery methods to
improve representation and mathematical problem solving ability of junior high
school students. Jurnal Penelitian Pendidikan, 13(2), 1-10.
Fajri, H. N., Rahmah, J., & Ikhsan, M. (2016). Improvement of spatial ability and
student self-efficacy through multimedia based discovery learning model. Jurnal
Beta, 9(2), 180-196.
Hadiyanto, F.R., Susanto, H. & Qohar, A. (2017). Identify Class VII student error in
solving
geometry
problem.
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Matematika
dan
Pembelajarannya (pp. 332-339). Malang: Universitas Negeri Malang.
Hohenwarter, M. (2008). Teaching and learning calculus with free dynamic
mathematics software system GeoGebra. TSG 16: Research and Development in
the Teaching and Learning of Calculus ICME 11 (pp. 1-9). Monterrey, Mexico.
Hohenwarter, & M., Fuchs, K. (2004). Combination of Dynamic Geometry, Algebra
and Calculus in the Software System GeoGebra. In Computer Algebra Systems
and Dynamic Geometry Systems in Mathematics Teaching Conference 2004 (pp.
1-6). Pecs, Hungary.
Kurniawati, A. (2015). Diagnosis of junior student difficulties in problem solving on
pythagoras theorem material as well as its addressing efforts using scaffolding
(unpublished thesis). Universitas Negeri Malang, Malang.
Lubis, I., S. & Listiani, T. (2016). The effectiveness of Geogebra usage on the results
of mathematics student Class XII Science High School Daan Mogot West Jakarta
in material program linear Year 2014/2015. In Pengembangan 4C’s dalam
Pembelajaran Matematika:Sebuah Tantangan dalam Pengembangan Kurikulum
Matematika (pp. 229 – 235). Malang: Universitas Negeri Malang.
Murniasih, T., R. (2016). Use of manipulative media to enhance student concept
understanding on pythagoras theorem. In Pengembangan 4C’s dalam
Pembelajaran Matematika: Sebuah Tantangan dalam Pengembangan Kurikulum
Matematika (pp. 142 – 152). Malang: Universitas Negeri Malang.
Offirstson, T. (2014). Mathematics learning activity through Cinderella Software
Assisted Inquiry. Yogyakarta: Deepublish.
Priyanto, A., Suharto, & Trapsilasiwi, D. (2015). Analysis of student error in solving
mathematical story problems theory of pythagoras theorem based on category of
Newman Error in Class VIII A Junior High School 10 Jember. Artikel Ilmiah
Mahasiswa, 1-5
Purwatiningsih, S. (2013). Application of guided discovery methods to improve
student learning outcomes on surface area material and beam volume. Jurnal
Elektronik Pendidikan Matematika Tadulako, 1(1), 53-63.
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Fathiya Salsabila, Rahmah Johar and Susanti Panca Wahyuni
Scherer, R., & Beckmann, J. F. (2014). The acquisition of problem solving
competence: evidence from 41 countries that math and science education
matters. Large-scale Assess Educ, 2(1), 1-22.
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Merril Publishing Company.
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(Problem Based Instruction) in Class XI Science Senior High School 1 Cilegon.
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Wasriono, Syahputra, E., & Surya, E. (2015). Development of autograph assisted
learning tool to improve understanding of smk student mathematics concept
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Yang, E. F. Y., Liao, C. C. Y., Ching, E., Chang, T., & Chan, T.W. (2010). The
effectiveness of inductive discovery learning in 1: 1 mathematics classroom. In
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743-747). Putrajaya, Malaysia: Asia-Pacific Society for Computers in Education.
Zulnaidi, H., & Zakaria, E. (2012). The effect of using geogebra on conceptual and
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8(11): 102–106.
726
Conference on Multidisciplinary Research (ICMR) in conjunction with the International Conference on Electrical
Engineering and Informatics (ICELTICs) 2017, October 18-20, 2017, Banda Aceh, Indonesia
Students’ Ability in Proving Pythagorean
Theorem through Discovery Learning Model
Using Geogebra Software
1*
Fathiya Salsabila, 2Rahmah Johar and 3Susanti Panca Wahyuni
1,2
Department of Math Education, Faculty of Teacher Training and Education,
University of Syiah Kuala, Banda Aceh 23111, Indonesia;
2
Junior High School 6, Banda Aceh 23125, Indonesia;
*
Corresponding author: fathiyasalsabila11@gmail.com
Abstract
Learning math is like training logical thinking, intelligence, focus and
also systematics. One of the most important materials in math is
Pythagorean Theorem. It is used in many aspects of life and helps us to
solve daily problems. However, many students still cannot use it we
even they have learned it. The aim of this study research is to describe
the students’ learning ability process through discovery learning model
using GeoGebra software on Pythagorean Theorem. The subjects of this
study were the students of SMP Negeri 6 Banda Aceh 29 students of
grade VIII-8. The data which was analyzed is formed tasks which were
done in groups and video analysis. The results of study showed that the
students are able to accomplish worksheet through GeoGebra assisted
and all of them are able to take conclusion symbolically yet not by using
their own words. The first group was failed to count third area but they
succeeded on counting other areas which lead them to the right
conclusion. The second group’s fault was on naming a square
particularly on its third area however they were better taking the right
conclusion. The obstacles of learning process were (1) limitation of time,
(2) only some students practice using GeoGebra software, (3) laptops
used were slow and not responding, (4) even the student did not
understand the beginning explanations.
Keywords:
learning, discovery learning model, GeoGebra software,
Pythagorean Theorem.
Introduction
Math is a knowledge which has an important role in human life and it becomes a
beneficial subject to get connected to other studies. According to Scherer and
Beckmann (2014), math and science are significantly related to problem solving
ability in life. One of math materials which is frequently faced in daily life is
Pythagorean Theorem in junior High school. Murniasih (2016) argues that
Pythagorean Theorem is often used in daily life and it releases people to solve the
daily problem. It becomes the material that is used in another math material or
prerequisite material. Pythagorean Theorem material is also one of math test
questions which exist in National Examination (UN). Kurniawati (2015) declares that
students’ difficulty in comprehending Pythagorean Theorem material is unable to use
math concepts which have been learned previously.
717
Fathiya Salsabila, Rahmah Johar and Susanti Panca Wahyuni
Math case is dominated to real problem gotten in daily life, yet in math conventional
learning process, the teacher only teaches the materials. A concept, theorem,
proposition, and etc., appear as if they were taken for granted without past
discovery process or it is legacy of the past. This case causes students’ disability to
understand some logarithm (Offirstson, 2014). The observation done by Murniasih
(2015) showed that from 24 students who learned Pythagorean Theorem, only 15
students passed the Minimal Completeness Criteria (MCC); MCC applied in the
school is 65. According to Murniasih (2015), Student’s Mistakes in Pythagorean
Theorem concept are (1) students still misunderstand about story questions that
causes they failed to change it into math model, (2) students still failed in counting
quadratic values, and (3) students are careless in doing the tasks so it makes them
got a wrong final result. Furthermore, the research conducted by Arfiyanti, Irawan,
and Purwanto (2016) showed that the students still misunderstand about
Pythagorean Theorem. They face difficulty if the Pythagorean Theorem test is
formed
and not
. They are used to memorize the formula and
not understand the meaning of the formula which has been learned.
In learning process, the students have to be used to solve the problem, and to find
out their own ideas. According to Offirstson (2014), studying and learning have to
be packed into a learning process construction and not only taken from teachers’
teaching. In teaching math, teachers should facilitate the learning process by using
ways which make an information becomes valuable and relevant to the students.
Learning model which makes the students active and find their own concept is
Discovery Learning. According to Sund (1975) Discovery Learning is a learning
process that makes students find the idea without getting it directly from the
teachers. They get it by their selves. Purwatiningsih (2013) declares that Discovery
Learning used in learning process can increase students’ result achievement. The
statement above in line to Effendi’s research result (2012) claims that using
Discovery Learning assists students’ achievement ability and problem solving to be
better. In addition, Yang, Liao, Ching, Chang, and Chan’s study result (2010)
indicates that the learning process using Discovery Learning model produces
students’ concept retention better. While Joyce & Weil (1992, in Fajri, Johar &
Ikhsan:2016), the advantages of Discovery Learning are to support the students to
develop their intelligences and to increase their curiosity and to find out the answer
of the curiosity as well.
The rapid technology development with various technological models facilitates us to
do particular activities. One of activities we are easy with by technology is learningteaching process. Syah (2015) claims that to expand students’ thought in learning
process, mastering science and technology, math is extremely needed. Learning
principle based on Ministry National Education Republic of Indonesia 2016 Number
22 is to use media of information and communication technology increasing
efficiency and effectiveness in learning. Students can understand abstract contents
assisted by technology. In accomplishing the Pythagorean Theorem, teachers can
use technology. According to Wasriono, Syahputra and Surya (2015), visual
technology-assisted development need to be applied in teaching-learning process to
relieve students to understand the concepts. While Calder and Campbell (2016)
argue that particular characteristics in learning process using digital technology
enable alternative solutions. High-level thinking and problem solving skills related to
students’ ways of getting information by using digital technology.
One of technologies that can support the students nowadays is GeoGebra software.
Based on Hohenwarter (2008), GeoGebra is a computer program to facilitate
students to learn geometry concept and algebra and it also has 3 multirepresentation characteristics, they are: there is algebra figure, graphic, and
718
Proceedings of The 7th Annual International Conference (AIC) Syiah Kuala University and The 6th International
Conference on Multidisciplinary Research (ICMR) in conjunction with the International Conference on Electrical
Engineering and Informatics (ICELTICs) 2017, October 18-20, 2017, Banda Aceh, Indonesia
numerical. They are connected dynamically one another. And that leads students to
learn geometry objects particularly Pythagorean Theorem which is abstract.
According to Hohenwarter and Fuchs (2004), using GeoGebra software can lead
students to find out and demonstrate and visualize math concepts. Lubis and Listiani
(2016) state that the GeoGebra is applied to increase the concept of understanding.
Besides, Zulnaidi and Zakaria’s research result (2012) showed that the use of
GeoGebra can increase students’ achievement in comprehending concept and math
procedure.
Based on the explanation above, the research questions are:
1. How do the students’ ability in proving Pythagorean Theorem through
Discovery Learning Model Using GeoGebra software?
2. What are the obstacles of learning using Discovery Learning model using
GeoGebra software on Pythagorean Theorem?
Research Method
The study was conducted to describe students’ ability through Discovery Learning
model using GeoGebra software. The subjects of this research are 29 students of
SMP Negeri 6 Banda Aceh grade VIII-8 year 2017/2018.
This study was held on Monday, May 10th 2017. The instrument was the students’
worksheet worked in group. There were 5 groups consisting of 5-6 students who
were chosen randomly. Each group found Pythagorean Theorem concepts using
GeoGebra software. Then, the data was analyzed in descriptive qualitative.
Results and Discussion
The using of laptop in learning process made students enthusiastic and the tasks
which were done seemed so real. In the process of learning, teacher divided pupils
into 5 groups and all of them succeeded to conclude the argumentation symbolically
yet they were failed to take conclusion through their own words. Here are pictures of
students’ ability in proving Pythagorean Theorem until symbolic steps.
Figure 1. 1th group’s answer on symbolic step.
8. Determine the area of each equilateral triangle and write the solution on
the following worksheet:
Area 1 = Area ABE =Area triangle with base 4cm and height 3,46 cm
719
Fathiya Salsabila, Rahmah Johar and Susanti Panca Wahyuni
=
=
= 6.92 cm2
Area 2 = Area ACF = Area triangle with base 3 cm and height 2,6 cm
=
= 3,9 cm2
=
Area 3 = Area ABE = Area triangle with base 5 cm and height 4,33
=
=
= 10,71 cm2
Based on the student result: Area 6,92 + Area 3,9 = Area 10,71
Figure 2. 2ndgroup’s answer on symbolic step.
6. Determine the area of each square and write the solution on the following
worksheet:
Area 1 = Area ABGF = Area square with face 4 cm
=
=
= 16 cm2
Area 2 = Area ACHI = Area square with face 3 cm
=
=
= 9 cm2
Area 3 = Area BCFG = Area square with face 5 cm
=
=
= 25 cm2
Based on the student result:
Area 16 cm2 + Area 9 cm2 = Area 25 cm2
Figure 3. 3rdgroup’s answer on symbolic step.
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Proceedings of The 7th Annual International Conference (AIC) Syiah Kuala University and The 6th International
Conference on Multidisciplinary Research (ICMR) in conjunction with the International Conference on Electrical
Engineering and Informatics (ICELTICs) 2017, October 18-20, 2017, Banda Aceh, Indonesia
6. Determine the area of each quadrant and write the solution on the
following worksheet:
Area 1 = Area BAD = Area quadrant with radius 4 cm
=
=
= 12,56 cm2
Area 2 = Area ACF = Area quadrant with radius 3 cm
=
=
= 7,065 cm2
Area 3 = Area BEC = Area quadrant with radius 5 cm
=
= 19,625 cm2
=
Based on the student result:
Area BAD + Area ACF = Area BEC
Figure 4. 4thgroup’s answer on symbolic step.
6. Determine the area of each square and write the solution on the following
worksheet:
Area 1 = Area ABGF = Area square with face 4 cm
=
=
= 16 cm2
Area 2 = Area ACHI = Area square with face 3 cm
=
= = 9 cm2
Area 3 = Area CBDE = Area square with face 5 cm
=
=
= 25 cm2
Based on the student result:
Area ABGF + Area ACHI = Area CBDE
First group was still failed in counting. It was supported by Murniasih’s research
(2015) which states that students who are less attention during task’s introduction
will produce bad final result. The example is on the picture below.
Figure 5. 1st group’s answer on 8th step.
Area 3 = Area ABE = Area triangle with base 5 cm and height 4,33
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Fathiya Salsabila, Rahmah Johar and Susanti Panca Wahyuni
=
=
= 10,71 cm
2
= 10,82
Either first group or second group mistakenly understood the statement so it led
them to a wrong answer. In line to Priyanto, Suharto, and Trapsilasiwi’s research
(2015) that declare that question transformation error done by students amounts
49% like on the picture below:
Figure 6. 1stgroup’s answer on transformation.
Based on the student result:
Area 6,92 + Area 3,9 = Area 10,71
Area 1 + Area 2 = Area 3 or Area ABE + Area ACF = Area BCD
Figure 7. 2nd group’s answer on transformation.
Based on the student result:
Area 16 cm2 + Area 9 cm2 = Area 25 cm2
Area 1 + Area 2 = Area 3 or Area ABGF + Area ACHI = Area BCED
The second group’s second step was less precise in drawing and observing a
triangle. Furthermore, Priyanto, Suharto, and Trapsilasiwi (2015) support the
statement by their finding which found that 46% of students’ question
understanding error and it is added by Murniasih (2015) who argue that the
students are less precise to understand word problem in math and task finishing
process like the following pictures
Figure 8. 2nd group’s answer (fault on drawing a triangle).
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Proceedings of The 7th Annual International Conference (AIC) Syiah Kuala University and The 6th International
Conference on Multidisciplinary Research (ICMR) in conjunction with the International Conference on Electrical
Engineering and Informatics (ICELTICs) 2017, October 18-20, 2017, Banda Aceh, Indonesia
Figure 9. 2nd group’s answer (fault on observing a triangle).
Area 3 = Area BCFG = Area square with face 5 cm
=
BCED
=
= 25 D
cm2
On conclusion section, all groups were less precise to take conclusion. Priyanto,
Suharto, dan Trapsilasiwi (2015) support the finding by stating that the fault in final
answer of students is amounts 61%. Conclusion section: first group could not
conclude that task. Second and third group would be 100% correct if they were not
failed to interpret the question. And the fourth and fifth groups were failed in
concluding. Those are showed in the pictures below.
Figure 10. 1st group’s answer on taking conclusion.
Figure 11. 2nd group’s answer on taking conclusion.
Figure 12. 3rd group’s answer on taking conclusion.
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Fathiya Salsabila, Rahmah Johar and Susanti Panca Wahyuni
Figure 13. 4th group’s answer on taking conclusion.
Picture 10, 11, 12 and 13 are learners drawing conclusions according to the
definition. The last group did not write the answer on their worksheet. Nevertheless,
based on the video analysis they did it in another paper. The last group was failed to
count third area but they succeeded on counting other areas which lead them to the
right conclusion.
Figure 14. Fifth group’s answer.
1) Area 1 = Area BAD = Area quadrant with radius 4 cm
=
=
= 12,56 cm2
2) Area 2 = Area AEC = Area quadrant with radius 3 cm
=
=
= 7,065 cm2
3) Area 3 = Area FBC = Area quadrant with radius 6 cm
=
=
= 28,26 cm2
Based on the student result: Area BAD + Area AEC = Area FCD
Based on the data analysis, the summary is the students enable to accomplish
student worksheet through GeoGebra software and all of them enable to take
conclusion symbolically yet not by using their own words. The first group was failed
to count third area but they succeeded on counting other areas which lead them to
the right conclusion. The second group’s fault was on naming a square particularly
on its third area however they were better taking the right conclusion. Furthermore,
math teacher never uses computer software in learning process and also seldom
transforms students into groups. The statements were based on researcher and
math teacher’s interview section. The barriers faced by math teacher were a
limitation of time and computer availability. Barriers faced during learning process
were the students did not understand the beginning explanations, the laptops used
were slow and they were sometimes not responding that caused the students could
not finish the student worksheet on time.
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Proceedings of The 7th Annual International Conference (AIC) Syiah Kuala University and The 6th International
Conference on Multidisciplinary Research (ICMR) in conjunction with the International Conference on Electrical
Engineering and Informatics (ICELTICs) 2017, October 18-20, 2017, Banda Aceh, Indonesia
Conclusions
GeoGebra software can be used as media or multimedia to learn Pythagorean
Theorem. From 5 groups mentioned, student can conclude the material symbolically
yet not by using their own words. In addition, the obstacles of learning process were
a limitation of time, in software socialization, only few of students wanted to try
using the software and the laptops used were slow, even the student did not
understand the beginning explanations, the laptops used were slow and they were
sometimes not responding that caused the students could not finish the student
worksheet on time. Teachers should more often integrate the media in learning.
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