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
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.
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,
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 � � � > ��.
LIST OF TABLES
Pages Table 1.1. The Average Value of Students Learning
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 49
Table 4.3 The Students’ Mathematics Achievement in
Experimental Class I for Each Indicator 50
Table 4.4. The Students’ Mathematics Achievement in
Experimental Class II 51
Table 4.5. 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
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 49
Figure 4.2. The Histogram of Students’ Mathematics Achievement in
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
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.
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.
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 development-UPI (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.
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/pisa-results-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.
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 notbe 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.
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.
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".
1.2Problem 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
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.
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
CHAPTER V
CONCLUSION AND SUGGESTION
4.1. ConclusionBased 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
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