THE DIFFERENCE OF STUDENTS ACHIEVEMENT IN MATHEMATICS BY USING GUIDED DISCOVERY LEARNING MODEL AND COOPERATIVE LEARNING MODEL JIGSAW TYPE AT SMA N 3 PEMATANGSIANTAR.
THE DIFFERENCE OF STUDENTS’ ACHIEVEMENT IN MATHEMATICS
BY USING GUIDED-DISCOVERY LEARNING MODEL AND
COOPERATIVE LEARNING MODEL JIGSAW TYPE
AT SMA N 3 PEMATANGSIANTAR
By:
Anna Angela Sitinjak
ID. Number 4113111004
Bilingual Mathematics Education Study Program
THESIS
Submitted to Fulfil Requirement for Getting
The Degree of Sarjana Pendidikan
MATHEMATICS DEPARTMENT
FACULTY OF MATHEMATICS AND NATURAL SCIENCES
STATE UNIVERSITY OF MEDAN
MEDAN
2015
i
iv
PREFACE
Give thankfulness to God that gives the God’s mercy and spirit so that
writer can finish this thesis. The title of this thesis is “The Difference of Students’
Achievement in Mathematics by Using Guided-Discovery Learning Model and
Cooperative Learning Model JIGSAW Type at SMA N 3 P.Siantar”. This thesis
was arranged to satisfy the requirement to obtain the Degree of Sarjana
Pendidikan from Faculty of Mathematics and Natural Science in State University
of Medan.
In the completion of this thesis, the writer received support from various
parts, therefore she was thanks fully to Dr. W. Rajagukguk, M.Pd as thesis
supervisor who has been guidance, direction, and advice to the perfection of this
thesis. Thanks fully are also due to Dr. Edy Surya, M.Si, Prof. Dr. Bornok Sinaga,
M.Pd, Dr. Izwita Dewi, M.Pd, as examiners who have provided input and
suggestion from the planning to the completion of this thesis, to Prof. Dr. Asmin,
M.Pd as academic supervisor and then thank you so much for all my lecturers in
FMIPA.
Thanks are extended to Prof. Dr. Syawal Gultom, M. Si. as rector of State
University of Medan and staff university, to Prof. Drs. Motlan, M.Sc., Ph.D as
Dean Faculty of Mathematics and Natural Sciences, to Coordinator of Bilingual
Prof. Dr. rer.nat. Binari Manurung, M.Si., Dr. Edy Surya, M. Si. as Chief of
Mathematics Department, Zul Amry, M. Si. as Chief of Mathematics Education
Study Program, Drs. Yasifati Hia, M. Si as Secretary of Mathematics Education,
and all of staff who have helped the author.
Thanks to Mr. Hinsa Simatupang as principle of SMA N 3 P.Siantar who
had given permission to writer doing research, Mr. Oloan Sinaga as mathematics
teacher and all teacher, staffs and also the students in class X-1 and X-6 SMA N 3
P.Siantar who had helped writer conducting the research.
v
Especially the writer would like to express gratitude to dear father, Jasman
Sitinjak (+) and dear mother, Rumia Manik that always be her hero and motivate
and be prayers forthe success of the writer in completing this thesis. Special big
thanks to her beloved sister Octa, Octi, Putri and brother Nahum that always give
support and all of her family for all pray, motivation, and support until the end of
writer’s study.
Writer wants to say thanks to her special friends Boby Simbolon, Vera,
Hotmauli Lestari, Johan Pasaribu, Summery, Dheina, Topas, Ayu, Yani, to her
best friends in Bilingual Mathematics Class 2011 for the valuable support and
motivation, and to her seniors of Bilingual Mathematics Class especially for
Khairunnisa Lubis, Abdul Tambunan, Siska Tambunan, Meiva, Nelly for their
suggestion. Thanks also for Kost Pondok Asri, especially Eva, Riva, Yuli, Hanna,
Susi, Lina.
The writer had given a big effort to prepare this thesis, and the writer know
that this thesis have so many weakness. So that, the writer needs some suggestions
to make it be better. And big wishes, it can be improve our knowledge.
Medan, July 2015
Author,
Anna Angela Sitinjak
ID. 4113111004
iii
THE DIFFERENCE OF STUDENTS’ ACHIEVEMENT IN MATHEMATICS
BY USING GUIDED-DISCOVERY LEARNING MODEL AND
COOPERATIVE LEARNING MODEL JIGSAW TYPE
AT SMA N 3 PEMATANGSIANTAR
Anna Angela Sitinjak (ID 4113111004)
ABSTRACT
The type of this study is a quasi-experiment study. The objectives of this
study is to know any difference of students’ achievement in mathematics which
using the model of guided discovery learning with cooperative learning model
JIGSAW type in class X SMA N 3 P. Siantar.
The population of this study is all students in SMA N 3 P. Siantar. The
sampling technique applied was cluster random sampling. The experimental class
I that chosen is X-1 consisted of 36 students, meanwhile the experimental class II
that chosen is X-6 consisted of 36 students. The instrument used to measure the
students’ mathematics achievement was a essay test. The normality test used was
Lilliefor’s test and the homogeneity test by using Fisher test. The data analysis
technique was t-test at the level of significance = 5%.
The study result showed that there is the difference of students’
achievement in mathematics which using the guided discovery learning model
with cooperative learning model JIGSAW type in grade X SMA N 3 P. Siantar
where obtained
= 2.504 at = 0.05 and
� � �
�� = (0.975,70) = 1.995,
then � � �
>
�� .
Keywords: Guided Discovery, Cooperative of JIGSAW Type, Mathematics
Achievement
ix
LIST OF TABLES
Table 1.1.
The Average Value of Students Learning
Pages
Outcomes for Mathematics in Grade X SMA
N 3 Pematangsiantar Academic Year 2014/2015
4
Table 2.1.
The Revised Cognitive Domain
14
Table 2.2.
Syntax of Cooperative Learning Model
28
Table 3.1.
Lattice of Mathematics Achievement Test
42
Table 4.1.
Summary of Descriptive Statistic
48
Tabel 4.2.
The Students’ Mathematics Achievement in
Experimental Class I
Table 4.3
The Students’ Mathematics Achievement in
Experimental Class I for Each Indicator
Table 4.4.
50
The Students’ Mathematics Achievement in
Experimental Class II
Table 4.5.
49
51
The Students’ Mathematics Achievement in
Experimental Class I for Each Indicator
52
Table 4.6.
Summary of Normality Result
54
Table 4.7.
Summary of Homogeneity Result
54
Table 4.8.
Summary of t-test Result
55
viii
LIST OF FIGURES
Pages
Figure 2.1. Cooperative Learning: JIGSAW
32
Figure 3.1. The Procedural of Study
40
Figure 4.1. The Histogram of Students’ Mathematics Achievement in
Experimental Class I
Figure 4.2. The Histogram of Students’ Mathematics Achievement in
Experimental Class II
49
52
x
LIST OF APPENDICES
Pages
Lesson Plan (Experiment Class I)
68
Worksheet of Experiment Class I
80
Lesson Plan (Experiment Class II)
104
Worksheet of Experiment Class II
116
Test of Mathematics Achievement
136
Alternative Solution
138
Lattice of Post-test
142
Guidance of Scoring for Mathematics Achievement Test
142
Validity of Students’ Mathematics Achievement
145
Reliability of Students’ Mathematics Achievement in Trial Class
153
Data Result of Students’ Mathematics Achievement
155
Normality Test
160
Homogeneity Test
163
Analysis of Hypothesis
164
r Product Moment Table
166
F - Distribution Table
167
Standard Normal Probilities
169
t-table
171
Observation Sheet of Learning Process
172
Documentations
184
Requirement Letters
186
1
CHAPTER I
INTRODUCTION
1.1.
Background of Study
It is undeniable that today education is needed more by society. Education
has an important role in everyone's life, without education, someone will be
difficult to obtain a better life. Education is a systematical process to acquire the
knowledge, experience, skills and a good attitude. Therefore, education does not
only provide knowledge, but also teaches the specific skills and how to be good.
Law of the Republic of Indonesia Number 20 of section 3 Year 2003 on
National Education System states that the national education has function to
develop skills and character development and dignify nation civilization in the
context of the nation life, aims to develop students' potential to be a man who has
faith and fear of God Almighty, have a noble moral, healthy, knowledgeable,
capable, creative, independent, and become democratic and responsible citizens.
The purpose of education above shows that the problem of education can
not be done only by one party namely school but also be the other responsibility
like as society, state and nation. Therefore, everyone needs to be involved in the
educational process. Formal education (schools) involving teachers and students,
is manifested in the form of teaching-learning interaction.
The purpose of teaching and learning process is to achieve the students’
success in learning. Today, teaching and learning process is expected to be fun,
challenging, and motivating for students to participate actively, creatively, and
innovatively according to their talents, proclivity, physical development, and
psychological. Therefore, highly expected the center of the teaching and learning
process is the students, not the teacher. But the teacher is not able to discharge of
their responsibilities, but still facilitate students.
2
Mathematics is one of the subjects taught in elementary school, junior high
school, senior high school and college. Mathematics is the science which is very
important to be mastered, because it is indispensable in daily life and a subject
which provides students with logical, analytical, systematic, critical, and creative
thinking. So the mathematics is one of the compulsive subjects taught in school
that certainly has an important role in achieving educational goals.
The purpose of studying mathematics according to the Education Minister
Regulation of the Republic Indonesia Number 22 Year 2006 on the Content
Standards are:
1.
To understand the concept of mathematics, explain the relationship between
concepts and apply concepts or logarithmic flexibly, accurately, efficiently
and appropriately in problem solving;
2.
To use the reasoning of pattern and characteristics, do manipulation of
Mathematics in making generalizations, arrange the evidence, or explain the
ideas and statements of mathematics;
3.
To solve problems which mean the ability to understand the problem, design
mathematical model, complete the model and interpret the obtained solution;
4. To communicate ideas with symbols, tables, diagrams, or other media to
clarify the situation or problem;
5.
To have respect for the usefulness of mathematics in daily life, namely having
curiosity, attention and interest in studying mathematics, also a tenacious
attitude and confidence in problem solving.
In order to achieve the goals of learning mathematics, it is needed the role
of various components such as: students, teachers, learning indicators, subject
content, learning model, methods, media, and evaluation. Teacher as one
component of teaching and learning activity has a very important role in achieving
the learning objectives and determine the success of the educational process.
Teacher must be able to motivate their students to engage in the teaching and
learning process.
3
Teachers are expected to develop their professionalism in teaching
students so that their function in class is not only as speaker. They should be able
to make every student be active in the teaching and learning activity. Students are
not as audiences as well, but also take active role in the teaching and learning
process.
Unfortunately, it is not easy to motivate students, especially senior high
school students to be active in teaching and learning activities because teachers
often apply the traditional learning model. So most of the teachers directly provide
mathematical formulas to the students and the students only see and memorize the
formulas. So do not be surprised if they think math is very bored and dreaded.
They think if they cannot memorize formulas they will get low score at math test
and worse when they just memorize formulas without knowing the actual math
concepts (how to get the formula). As the result, when teachers give a different
question from the example, the students are confused and fell difficult to solve it.
So the math scores of students are still low.
Martinus (2014: 75) says that to study mathematics is required a good
understanding of the concept in which in order to form the new concept
understanding, necessary understanding of the concept before. However, as
revealed by Ruseffendi and Wahyudi (in Martinus. 2014: 76) that many children
after studying mathematics, simple part was much he did not understand, because
many of the concepts are misunderstood, which means that the students'
understanding of the concept of the low. Team of science education developmentUPI (2007: 198) says that the learning and teaching process which is implemented
by teacher at the class is classically and only rely on textbooks with a teaching
method that emphasizes the process of memorizing rather than understanding the
concept. So that when students are given problems or test, will have difficulty in
solving and can get low score.
The low of students’ achievement for mathematics in Indonesia is also
proved from the results of international research. UNESCO shows that Indonesia
4
was ranked 36 of 49 countries in the Trends in International Mathematics and
Science Study (TIMSS) test (IBE, 2011: 25). The rank of Indonesia in math test,
held by PISA is 64 of 65 countries with a score of 375 which is a score below the
OECD average (http://www.theguardian.com/news/datablog/2013/dec/03/pisaresults-country-best-reading-maths-science).
This problem is also occurred in SMAN 3 Pematangsiantar. The math
teacher of SMA N 3 Pematangsiantar complained that the score average of daily
math test is still around 60 whereas KKM (minimum passing criteria) is 75. It
indicates that it does not achieve the value of KKM for math. Based on data
obtained from DKN in grade X SMA N 3 Pematangsiantar, the average of
students’ achievement for mathematics also has not been satisfactory as shown in
the following Table 1.1.
Table 1.1 The Average Value of Odd Semester Examination for Mathematics in Grade X
SMA N 3 Pematangsiantar Academic Year 2014/2015
No
Type of Test
The Average Value
KKM Value
1
Odd Semester Exam
61.7
75
From the table it can be seen that the value average of odd semester exam
of class X is below of the minimum passing criteria with the percentage of
students who have score below the minimum passing criteria is 83%. The odd
semester exam consists of level knowledge (C1), comprehension (C2) and
application (C3), which means that the achievement of students up to level C3 is
still low.
Trigonometry is one of the mathematical materials that generally
considered difficult by students. This is proved from a journal that is studied by
the Tuna and Kacar (2013) in which the pre-test (given before treatment) of
students' Kastamonu in grade X toward Trigonometry was 4.640 for the
experimental class and 4708 for control class whereas after had been given a
5
certain treatment by the researcher, students’ test scores average could reach 20.76
for experimental class and 16.00 for the control class. Hidayah (2013) also found
that students' achievement for trigonometry is still low. He revealed that from
observations, students of high school grade X considers mathematical material
especially for trigonometric ratios is difficult and students are still confused in the
use of formulas of trigonometric ratios. This is because most of students tend to
memorize trigonometric ratio values in a special angle. It is also the same as that
revealed by a math teacher in SMA N 3 P.Siantar that when asked about the
trigonometric ratios or exam, students often made the wrong formula which is
supposed for sinus, cosines, etc. Students also just like memorizing the formulas
and completion of the examples given by the teacher, which is known from the
students often ask the teacher how to memorize the formula.
The above problem must be overcome in order not be sustainable. One of
the ways is refinement to the arranging and application of learning models used by
the teacher. The learning model which is appropriate, effective and making the
students closed to the teacher will make students enjoy to study and be more
active, so students can improve their understanding of mathematics.
From some existing learning models, one way to deal with the above
problem is by guided-discovery learning model. Lefancois (in Depdiknas. 2013)
said that the discovery learning can be defined as the learning that takes place
when the student is not presented with the subject matter in the final form, but
rather is required to organize it himself.
According to Cetin (2004: 15) discovery learning makes students to be
brave to participate (active) during the instructional process, and they are able to
find out for him / invented the concept of the material being studied. For example,
the teacher presents a problem and students solve the problem until they find out
the interrelationship. But because students in high school are not accustomed to
find out own the solving of the problems presented, they still need the guidance of
6
the teacher and the model is known as the guided-discovery learning models. So
that, the closeness between teachers and students keeps well.
Guided-discovery learning model has been studied by Kholik and
Sugiyono (2013: 9), their journal entitled "Implementation of Guided Discovery
Learning Methods to
Improve Motivation and Mathematical Learning
Achievement" indicated that the average of learning achievement in mathematics
increased to 85.18 from 78.57. Akanmu and Fajemidagba (2013: 85) in the journal
entitled "Guided Discovery learning Strategy and Senior School students
Performance in Mathematics in Ejigbo, Nigeria" also reveal the same thing,
namely that students taught with guided discovery learning had a significantly
higher scores than students taught by non-guided discovery learning.
Cooperative learning model also can make students to be active. In
addition, "cooperative learning is the instructional use of small groups so that
students work together to maximize their own and others' learning” (Johnson, et al
in Bruce. 2002: 3).
Bruce added (2002: 3), “cooperative learning enables skills in working as
teams, skills that are in dire demand in the workplace”. Jigsaw is type of
cooperative learning model in which each student becomes a member of two
groups, namely the member of the home group and the member of the expert
group so that students do not get bored because the discussions during the lesson
they not only meet in one group. Jigsaw cooperative learning model makes every
student to be responsible and foster a desire / effort to understand the parts of the
lessons to be learned and deliver the material to the other group members. So that
students can develop the positive relationships among his friends who have
different capabilities, to help friends who have difficulty in understanding
mathematical concepts and improve self-esteem of student.
From the journal of mathematics education by Meilawati (2013: 41) with
the title "The Way to Improve Mathematics Result Through Jigsaw Cooperative
Learning” states that the use of cooperative learning model type of Jigsaw has a
7
positive impact in the learning process that is characterized by increase the
average of student’s achievement in mathematics into 83.59.
Based on the above description, the researcher is interested in conducting
research with the title "The Difference of Students’ Achievement in Mathematics
by Using Guided-Discovery Learning Model and Cooperative Learning Model
JIGSAW Type at SMAN 3 Pematangsiantar".
1.2 Problem Identification
Based on the background can be identified some of problems as follows:
1. Teachers tend using a learning model which centered to teacher, so that students
are less actively involved during the learning process.
2. Lack of students' understanding to mathematical concepts because students just
memorize the mathematical formulas so they have difficulty in doing math
problems.
3. There still needs the repair to students’ achievement in mathematics at SMAN 3
P. Siantar because there are students get low score of math test.
4. Guided-discovery learning model and cooperative learning model type of
JIGSAW have difference steps to presenting the mathematical material.
1.3
Problem Limitation
In order this study to be more specific and focused, this research is limited
in scope:
1. Students’ achievement in mathematics class X at SMA N 3 P. Siantar,
Academic Year 2014/2015
2. The learning models in this study are categorized by guided-discovery learning
model and cooperative learning model type of Jigsaw.
8
1.4
Problem Formulation
Based on problem limitation stated above, the formulation of the problem
in this study is:
Is there any difference of students’ achievement in mathematics which
using guided-discovery learning model with using cooperative learning
model Jigsaw type in class X SMA N 3 P. Siantar?
1.5
The Objective of Research
The purpose of this research is:
To know any difference of students’ achievement in mathematics
which using the model of guided discovery learning with cooperative
learning model JIGSAW type in class X SMA N 3 P. Siantar.
1.6
The Benefit of Research
1. For teachers, especially teachers of mathematics, this study can be
used as consideration in choosing learning model used in teaching and
learning activities at school.
2. For students, this research can make students more motivated to
increase their achievement in mathematics.
3. For researchers, this study can be used as a reference and to increase
knowledge of researcher about the problems that occurred in schools.
1.7
Operational Definition of Variable
Operational Definition is the definition of all variables that will be used in
a study based on properties of the term definition which is observed, so that the
reader / testers can easily interpret the meaning of the study.
In this study, the operational definition of the variables is:
9
1.
Guided-Discovery Learning Model
The guided-discovery learning model is learning model that directs teacher to
assist students in making the discovery. Form of guidance provided by the
teacher is the form of instructions or questions, so that students are expected
to conclude (generalize) in accordance with the design of the teacher.
Therefore, students need to really actively learn to find own the material
learned and have to prepare himself before class is started.
2.
Cooperative Learning Model JIGSAW Type
Cooperative learning model Jigsaw type is learning emphasized to students in
learning activities of group which consists of 4-6 students with heterogeneous
capability, and each student enters into two groups namely the origin and
expert groups. Each member of the expert group has to responsible for the
completeness of section discussed and delivering these materials to members
of the original group. Finally, every student realizes that he needs to have the
initial knowledge about material will be discussed.
3.
Student’s Achievement in Mathematics
The students’ achievement in mathematics is the results achieved by students
especially for domain of cognitive in level knowledge (C1), comprehension
(C2), Application (C3), using the test as a measure of student success.
Researcher determines the domain of cognitive in level C1, C2 and C3 with
reason that 83% of students do not able to reach value of semester
examination in level C1, C2 and C3 above the minimum passing criteria.
58
CHAPTER V
CONCLUSION AND SUGGESTION
4.1.
Conclusion
Based on the result of research, it can be concluded that:
1. There is difference of students’ achievement in mathematics which using
the model of guided discovery learning with cooperative learning model
JIGSAW type in class X SMA N 3 P. Siantar.
2. Students who are taught by guided discovery learning model have the
higher score that by cooperative learning model JIGSAW type.
4.2.
SUGGESTION
Based on the conclusion and the relevant study can be offered some
suggestions below:
1. Guided discovery learning model gives the higher students’ mathematics
achievement compared to the cooperative learning model JIGSAW type.
Therefore, the mathematical teachers are suggested to apply guided discovery
learning model in the learning activity.
2. Guided discovery learning model and cooperative learning model JIGSAW
type are applied to mathematical learning of trigonometric ratio in the
cognitive level of knowledge (C1), comprehension (C2) and application (C3),
for other researchers are suggested to take study for another subject, another
level of cognitive and also studied for the special students.
3. Teacher especially mathematics teacher is suggested to know more about
characteristics of students, be creatively in making problem about lesson
which will be given to students, considerate time with lesson effectively for
trigonometric ratio especially for sub matter of trigonometric identity and the
value sign of trigonometric ratio.
59
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BY USING GUIDED-DISCOVERY LEARNING MODEL AND
COOPERATIVE LEARNING MODEL JIGSAW TYPE
AT SMA N 3 PEMATANGSIANTAR
By:
Anna Angela Sitinjak
ID. Number 4113111004
Bilingual Mathematics Education Study Program
THESIS
Submitted to Fulfil Requirement for Getting
The Degree of Sarjana Pendidikan
MATHEMATICS DEPARTMENT
FACULTY OF MATHEMATICS AND NATURAL SCIENCES
STATE UNIVERSITY OF MEDAN
MEDAN
2015
i
iv
PREFACE
Give thankfulness to God that gives the God’s mercy and spirit so that
writer can finish this thesis. The title of this thesis is “The Difference of Students’
Achievement in Mathematics by Using Guided-Discovery Learning Model and
Cooperative Learning Model JIGSAW Type at SMA N 3 P.Siantar”. This thesis
was arranged to satisfy the requirement to obtain the Degree of Sarjana
Pendidikan from Faculty of Mathematics and Natural Science in State University
of Medan.
In the completion of this thesis, the writer received support from various
parts, therefore she was thanks fully to Dr. W. Rajagukguk, M.Pd as thesis
supervisor who has been guidance, direction, and advice to the perfection of this
thesis. Thanks fully are also due to Dr. Edy Surya, M.Si, Prof. Dr. Bornok Sinaga,
M.Pd, Dr. Izwita Dewi, M.Pd, as examiners who have provided input and
suggestion from the planning to the completion of this thesis, to Prof. Dr. Asmin,
M.Pd as academic supervisor and then thank you so much for all my lecturers in
FMIPA.
Thanks are extended to Prof. Dr. Syawal Gultom, M. Si. as rector of State
University of Medan and staff university, to Prof. Drs. Motlan, M.Sc., Ph.D as
Dean Faculty of Mathematics and Natural Sciences, to Coordinator of Bilingual
Prof. Dr. rer.nat. Binari Manurung, M.Si., Dr. Edy Surya, M. Si. as Chief of
Mathematics Department, Zul Amry, M. Si. as Chief of Mathematics Education
Study Program, Drs. Yasifati Hia, M. Si as Secretary of Mathematics Education,
and all of staff who have helped the author.
Thanks to Mr. Hinsa Simatupang as principle of SMA N 3 P.Siantar who
had given permission to writer doing research, Mr. Oloan Sinaga as mathematics
teacher and all teacher, staffs and also the students in class X-1 and X-6 SMA N 3
P.Siantar who had helped writer conducting the research.
v
Especially the writer would like to express gratitude to dear father, Jasman
Sitinjak (+) and dear mother, Rumia Manik that always be her hero and motivate
and be prayers forthe success of the writer in completing this thesis. Special big
thanks to her beloved sister Octa, Octi, Putri and brother Nahum that always give
support and all of her family for all pray, motivation, and support until the end of
writer’s study.
Writer wants to say thanks to her special friends Boby Simbolon, Vera,
Hotmauli Lestari, Johan Pasaribu, Summery, Dheina, Topas, Ayu, Yani, to her
best friends in Bilingual Mathematics Class 2011 for the valuable support and
motivation, and to her seniors of Bilingual Mathematics Class especially for
Khairunnisa Lubis, Abdul Tambunan, Siska Tambunan, Meiva, Nelly for their
suggestion. Thanks also for Kost Pondok Asri, especially Eva, Riva, Yuli, Hanna,
Susi, Lina.
The writer had given a big effort to prepare this thesis, and the writer know
that this thesis have so many weakness. So that, the writer needs some suggestions
to make it be better. And big wishes, it can be improve our knowledge.
Medan, July 2015
Author,
Anna Angela Sitinjak
ID. 4113111004
iii
THE DIFFERENCE OF STUDENTS’ ACHIEVEMENT IN MATHEMATICS
BY USING GUIDED-DISCOVERY LEARNING MODEL AND
COOPERATIVE LEARNING MODEL JIGSAW TYPE
AT SMA N 3 PEMATANGSIANTAR
Anna Angela Sitinjak (ID 4113111004)
ABSTRACT
The type of this study is a quasi-experiment study. The objectives of this
study is to know any difference of students’ achievement in mathematics which
using the model of guided discovery learning with cooperative learning model
JIGSAW type in class X SMA N 3 P. Siantar.
The population of this study is all students in SMA N 3 P. Siantar. The
sampling technique applied was cluster random sampling. The experimental class
I that chosen is X-1 consisted of 36 students, meanwhile the experimental class II
that chosen is X-6 consisted of 36 students. The instrument used to measure the
students’ mathematics achievement was a essay test. The normality test used was
Lilliefor’s test and the homogeneity test by using Fisher test. The data analysis
technique was t-test at the level of significance = 5%.
The study result showed that there is the difference of students’
achievement in mathematics which using the guided discovery learning model
with cooperative learning model JIGSAW type in grade X SMA N 3 P. Siantar
where obtained
= 2.504 at = 0.05 and
� � �
�� = (0.975,70) = 1.995,
then � � �
>
�� .
Keywords: Guided Discovery, Cooperative of JIGSAW Type, Mathematics
Achievement
ix
LIST OF TABLES
Table 1.1.
The Average Value of Students Learning
Pages
Outcomes for Mathematics in Grade X SMA
N 3 Pematangsiantar Academic Year 2014/2015
4
Table 2.1.
The Revised Cognitive Domain
14
Table 2.2.
Syntax of Cooperative Learning Model
28
Table 3.1.
Lattice of Mathematics Achievement Test
42
Table 4.1.
Summary of Descriptive Statistic
48
Tabel 4.2.
The Students’ Mathematics Achievement in
Experimental Class I
Table 4.3
The Students’ Mathematics Achievement in
Experimental Class I for Each Indicator
Table 4.4.
50
The Students’ Mathematics Achievement in
Experimental Class II
Table 4.5.
49
51
The Students’ Mathematics Achievement in
Experimental Class I for Each Indicator
52
Table 4.6.
Summary of Normality Result
54
Table 4.7.
Summary of Homogeneity Result
54
Table 4.8.
Summary of t-test Result
55
viii
LIST OF FIGURES
Pages
Figure 2.1. Cooperative Learning: JIGSAW
32
Figure 3.1. The Procedural of Study
40
Figure 4.1. The Histogram of Students’ Mathematics Achievement in
Experimental Class I
Figure 4.2. The Histogram of Students’ Mathematics Achievement in
Experimental Class II
49
52
x
LIST OF APPENDICES
Pages
Lesson Plan (Experiment Class I)
68
Worksheet of Experiment Class I
80
Lesson Plan (Experiment Class II)
104
Worksheet of Experiment Class II
116
Test of Mathematics Achievement
136
Alternative Solution
138
Lattice of Post-test
142
Guidance of Scoring for Mathematics Achievement Test
142
Validity of Students’ Mathematics Achievement
145
Reliability of Students’ Mathematics Achievement in Trial Class
153
Data Result of Students’ Mathematics Achievement
155
Normality Test
160
Homogeneity Test
163
Analysis of Hypothesis
164
r Product Moment Table
166
F - Distribution Table
167
Standard Normal Probilities
169
t-table
171
Observation Sheet of Learning Process
172
Documentations
184
Requirement Letters
186
1
CHAPTER I
INTRODUCTION
1.1.
Background of Study
It is undeniable that today education is needed more by society. Education
has an important role in everyone's life, without education, someone will be
difficult to obtain a better life. Education is a systematical process to acquire the
knowledge, experience, skills and a good attitude. Therefore, education does not
only provide knowledge, but also teaches the specific skills and how to be good.
Law of the Republic of Indonesia Number 20 of section 3 Year 2003 on
National Education System states that the national education has function to
develop skills and character development and dignify nation civilization in the
context of the nation life, aims to develop students' potential to be a man who has
faith and fear of God Almighty, have a noble moral, healthy, knowledgeable,
capable, creative, independent, and become democratic and responsible citizens.
The purpose of education above shows that the problem of education can
not be done only by one party namely school but also be the other responsibility
like as society, state and nation. Therefore, everyone needs to be involved in the
educational process. Formal education (schools) involving teachers and students,
is manifested in the form of teaching-learning interaction.
The purpose of teaching and learning process is to achieve the students’
success in learning. Today, teaching and learning process is expected to be fun,
challenging, and motivating for students to participate actively, creatively, and
innovatively according to their talents, proclivity, physical development, and
psychological. Therefore, highly expected the center of the teaching and learning
process is the students, not the teacher. But the teacher is not able to discharge of
their responsibilities, but still facilitate students.
2
Mathematics is one of the subjects taught in elementary school, junior high
school, senior high school and college. Mathematics is the science which is very
important to be mastered, because it is indispensable in daily life and a subject
which provides students with logical, analytical, systematic, critical, and creative
thinking. So the mathematics is one of the compulsive subjects taught in school
that certainly has an important role in achieving educational goals.
The purpose of studying mathematics according to the Education Minister
Regulation of the Republic Indonesia Number 22 Year 2006 on the Content
Standards are:
1.
To understand the concept of mathematics, explain the relationship between
concepts and apply concepts or logarithmic flexibly, accurately, efficiently
and appropriately in problem solving;
2.
To use the reasoning of pattern and characteristics, do manipulation of
Mathematics in making generalizations, arrange the evidence, or explain the
ideas and statements of mathematics;
3.
To solve problems which mean the ability to understand the problem, design
mathematical model, complete the model and interpret the obtained solution;
4. To communicate ideas with symbols, tables, diagrams, or other media to
clarify the situation or problem;
5.
To have respect for the usefulness of mathematics in daily life, namely having
curiosity, attention and interest in studying mathematics, also a tenacious
attitude and confidence in problem solving.
In order to achieve the goals of learning mathematics, it is needed the role
of various components such as: students, teachers, learning indicators, subject
content, learning model, methods, media, and evaluation. Teacher as one
component of teaching and learning activity has a very important role in achieving
the learning objectives and determine the success of the educational process.
Teacher must be able to motivate their students to engage in the teaching and
learning process.
3
Teachers are expected to develop their professionalism in teaching
students so that their function in class is not only as speaker. They should be able
to make every student be active in the teaching and learning activity. Students are
not as audiences as well, but also take active role in the teaching and learning
process.
Unfortunately, it is not easy to motivate students, especially senior high
school students to be active in teaching and learning activities because teachers
often apply the traditional learning model. So most of the teachers directly provide
mathematical formulas to the students and the students only see and memorize the
formulas. So do not be surprised if they think math is very bored and dreaded.
They think if they cannot memorize formulas they will get low score at math test
and worse when they just memorize formulas without knowing the actual math
concepts (how to get the formula). As the result, when teachers give a different
question from the example, the students are confused and fell difficult to solve it.
So the math scores of students are still low.
Martinus (2014: 75) says that to study mathematics is required a good
understanding of the concept in which in order to form the new concept
understanding, necessary understanding of the concept before. However, as
revealed by Ruseffendi and Wahyudi (in Martinus. 2014: 76) that many children
after studying mathematics, simple part was much he did not understand, because
many of the concepts are misunderstood, which means that the students'
understanding of the concept of the low. Team of science education developmentUPI (2007: 198) says that the learning and teaching process which is implemented
by teacher at the class is classically and only rely on textbooks with a teaching
method that emphasizes the process of memorizing rather than understanding the
concept. So that when students are given problems or test, will have difficulty in
solving and can get low score.
The low of students’ achievement for mathematics in Indonesia is also
proved from the results of international research. UNESCO shows that Indonesia
4
was ranked 36 of 49 countries in the Trends in International Mathematics and
Science Study (TIMSS) test (IBE, 2011: 25). The rank of Indonesia in math test,
held by PISA is 64 of 65 countries with a score of 375 which is a score below the
OECD average (http://www.theguardian.com/news/datablog/2013/dec/03/pisaresults-country-best-reading-maths-science).
This problem is also occurred in SMAN 3 Pematangsiantar. The math
teacher of SMA N 3 Pematangsiantar complained that the score average of daily
math test is still around 60 whereas KKM (minimum passing criteria) is 75. It
indicates that it does not achieve the value of KKM for math. Based on data
obtained from DKN in grade X SMA N 3 Pematangsiantar, the average of
students’ achievement for mathematics also has not been satisfactory as shown in
the following Table 1.1.
Table 1.1 The Average Value of Odd Semester Examination for Mathematics in Grade X
SMA N 3 Pematangsiantar Academic Year 2014/2015
No
Type of Test
The Average Value
KKM Value
1
Odd Semester Exam
61.7
75
From the table it can be seen that the value average of odd semester exam
of class X is below of the minimum passing criteria with the percentage of
students who have score below the minimum passing criteria is 83%. The odd
semester exam consists of level knowledge (C1), comprehension (C2) and
application (C3), which means that the achievement of students up to level C3 is
still low.
Trigonometry is one of the mathematical materials that generally
considered difficult by students. This is proved from a journal that is studied by
the Tuna and Kacar (2013) in which the pre-test (given before treatment) of
students' Kastamonu in grade X toward Trigonometry was 4.640 for the
experimental class and 4708 for control class whereas after had been given a
5
certain treatment by the researcher, students’ test scores average could reach 20.76
for experimental class and 16.00 for the control class. Hidayah (2013) also found
that students' achievement for trigonometry is still low. He revealed that from
observations, students of high school grade X considers mathematical material
especially for trigonometric ratios is difficult and students are still confused in the
use of formulas of trigonometric ratios. This is because most of students tend to
memorize trigonometric ratio values in a special angle. It is also the same as that
revealed by a math teacher in SMA N 3 P.Siantar that when asked about the
trigonometric ratios or exam, students often made the wrong formula which is
supposed for sinus, cosines, etc. Students also just like memorizing the formulas
and completion of the examples given by the teacher, which is known from the
students often ask the teacher how to memorize the formula.
The above problem must be overcome in order not be sustainable. One of
the ways is refinement to the arranging and application of learning models used by
the teacher. The learning model which is appropriate, effective and making the
students closed to the teacher will make students enjoy to study and be more
active, so students can improve their understanding of mathematics.
From some existing learning models, one way to deal with the above
problem is by guided-discovery learning model. Lefancois (in Depdiknas. 2013)
said that the discovery learning can be defined as the learning that takes place
when the student is not presented with the subject matter in the final form, but
rather is required to organize it himself.
According to Cetin (2004: 15) discovery learning makes students to be
brave to participate (active) during the instructional process, and they are able to
find out for him / invented the concept of the material being studied. For example,
the teacher presents a problem and students solve the problem until they find out
the interrelationship. But because students in high school are not accustomed to
find out own the solving of the problems presented, they still need the guidance of
6
the teacher and the model is known as the guided-discovery learning models. So
that, the closeness between teachers and students keeps well.
Guided-discovery learning model has been studied by Kholik and
Sugiyono (2013: 9), their journal entitled "Implementation of Guided Discovery
Learning Methods to
Improve Motivation and Mathematical Learning
Achievement" indicated that the average of learning achievement in mathematics
increased to 85.18 from 78.57. Akanmu and Fajemidagba (2013: 85) in the journal
entitled "Guided Discovery learning Strategy and Senior School students
Performance in Mathematics in Ejigbo, Nigeria" also reveal the same thing,
namely that students taught with guided discovery learning had a significantly
higher scores than students taught by non-guided discovery learning.
Cooperative learning model also can make students to be active. In
addition, "cooperative learning is the instructional use of small groups so that
students work together to maximize their own and others' learning” (Johnson, et al
in Bruce. 2002: 3).
Bruce added (2002: 3), “cooperative learning enables skills in working as
teams, skills that are in dire demand in the workplace”. Jigsaw is type of
cooperative learning model in which each student becomes a member of two
groups, namely the member of the home group and the member of the expert
group so that students do not get bored because the discussions during the lesson
they not only meet in one group. Jigsaw cooperative learning model makes every
student to be responsible and foster a desire / effort to understand the parts of the
lessons to be learned and deliver the material to the other group members. So that
students can develop the positive relationships among his friends who have
different capabilities, to help friends who have difficulty in understanding
mathematical concepts and improve self-esteem of student.
From the journal of mathematics education by Meilawati (2013: 41) with
the title "The Way to Improve Mathematics Result Through Jigsaw Cooperative
Learning” states that the use of cooperative learning model type of Jigsaw has a
7
positive impact in the learning process that is characterized by increase the
average of student’s achievement in mathematics into 83.59.
Based on the above description, the researcher is interested in conducting
research with the title "The Difference of Students’ Achievement in Mathematics
by Using Guided-Discovery Learning Model and Cooperative Learning Model
JIGSAW Type at SMAN 3 Pematangsiantar".
1.2 Problem Identification
Based on the background can be identified some of problems as follows:
1. Teachers tend using a learning model which centered to teacher, so that students
are less actively involved during the learning process.
2. Lack of students' understanding to mathematical concepts because students just
memorize the mathematical formulas so they have difficulty in doing math
problems.
3. There still needs the repair to students’ achievement in mathematics at SMAN 3
P. Siantar because there are students get low score of math test.
4. Guided-discovery learning model and cooperative learning model type of
JIGSAW have difference steps to presenting the mathematical material.
1.3
Problem Limitation
In order this study to be more specific and focused, this research is limited
in scope:
1. Students’ achievement in mathematics class X at SMA N 3 P. Siantar,
Academic Year 2014/2015
2. The learning models in this study are categorized by guided-discovery learning
model and cooperative learning model type of Jigsaw.
8
1.4
Problem Formulation
Based on problem limitation stated above, the formulation of the problem
in this study is:
Is there any difference of students’ achievement in mathematics which
using guided-discovery learning model with using cooperative learning
model Jigsaw type in class X SMA N 3 P. Siantar?
1.5
The Objective of Research
The purpose of this research is:
To know any difference of students’ achievement in mathematics
which using the model of guided discovery learning with cooperative
learning model JIGSAW type in class X SMA N 3 P. Siantar.
1.6
The Benefit of Research
1. For teachers, especially teachers of mathematics, this study can be
used as consideration in choosing learning model used in teaching and
learning activities at school.
2. For students, this research can make students more motivated to
increase their achievement in mathematics.
3. For researchers, this study can be used as a reference and to increase
knowledge of researcher about the problems that occurred in schools.
1.7
Operational Definition of Variable
Operational Definition is the definition of all variables that will be used in
a study based on properties of the term definition which is observed, so that the
reader / testers can easily interpret the meaning of the study.
In this study, the operational definition of the variables is:
9
1.
Guided-Discovery Learning Model
The guided-discovery learning model is learning model that directs teacher to
assist students in making the discovery. Form of guidance provided by the
teacher is the form of instructions or questions, so that students are expected
to conclude (generalize) in accordance with the design of the teacher.
Therefore, students need to really actively learn to find own the material
learned and have to prepare himself before class is started.
2.
Cooperative Learning Model JIGSAW Type
Cooperative learning model Jigsaw type is learning emphasized to students in
learning activities of group which consists of 4-6 students with heterogeneous
capability, and each student enters into two groups namely the origin and
expert groups. Each member of the expert group has to responsible for the
completeness of section discussed and delivering these materials to members
of the original group. Finally, every student realizes that he needs to have the
initial knowledge about material will be discussed.
3.
Student’s Achievement in Mathematics
The students’ achievement in mathematics is the results achieved by students
especially for domain of cognitive in level knowledge (C1), comprehension
(C2), Application (C3), using the test as a measure of student success.
Researcher determines the domain of cognitive in level C1, C2 and C3 with
reason that 83% of students do not able to reach value of semester
examination in level C1, C2 and C3 above the minimum passing criteria.
58
CHAPTER V
CONCLUSION AND SUGGESTION
4.1.
Conclusion
Based on the result of research, it can be concluded that:
1. There is difference of students’ achievement in mathematics which using
the model of guided discovery learning with cooperative learning model
JIGSAW type in class X SMA N 3 P. Siantar.
2. Students who are taught by guided discovery learning model have the
higher score that by cooperative learning model JIGSAW type.
4.2.
SUGGESTION
Based on the conclusion and the relevant study can be offered some
suggestions below:
1. Guided discovery learning model gives the higher students’ mathematics
achievement compared to the cooperative learning model JIGSAW type.
Therefore, the mathematical teachers are suggested to apply guided discovery
learning model in the learning activity.
2. Guided discovery learning model and cooperative learning model JIGSAW
type are applied to mathematical learning of trigonometric ratio in the
cognitive level of knowledge (C1), comprehension (C2) and application (C3),
for other researchers are suggested to take study for another subject, another
level of cognitive and also studied for the special students.
3. Teacher especially mathematics teacher is suggested to know more about
characteristics of students, be creatively in making problem about lesson
which will be given to students, considerate time with lesson effectively for
trigonometric ratio especially for sub matter of trigonometric identity and the
value sign of trigonometric ratio.
59
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Agarwal, R. and Nagar, N., (2011), Cooperative Learning, Kalpaz Publications,
India.
Akanmu, M. Alex and Fajemidagba, M. O., (2013), Online Mathematics Module:
Guided-Discovery Learning Strategy and Senior School Students
Performance in Mathematics in Ejigbo Nigeria, Journal of Education and
Practice 4: 82-90.
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