INCREASING OF STUDENTS MATHEMATICAL COMMUNICATION ABILITY BY USING GROUP INVESTIGATION (GI) LEARNING MODEL IN QUADRILATERAL OF GRADE VII AT SMP NEGERI 11 MEDAN ACADEMIC YEAR 2014/2015.
INCREASING OF STUDENTS’ MATHEMATICAL COMMUNICATION
ABILITYBYUSINGGROUPINSTIGATION(GI)LEARNINGMODEL
INQUADRILATERALOFGRADEVIIATSMPNEGERI
11 MEDAN ACADEMIC YEAR 2014/2015
By:
Mawaddah
ID 4113312010
Mathematics Education Study Program
THESIS
Submitted to Fulfill the Requirement for Getting
the Degree of Sarjana Pendidikan
MATHEMATICS DEPARTMENT
FACULTY OF MATHEMATICS AND NATURAL SCIENCES
STATE UNIVERSITY OF MEDAN
MEDAN
2015
iv
PREFACE
Give thankfulness to Allah SWT that gives the God’s mercy and spirit so
that writer can finish this thesis. The title of this thesis is “Increasing of Students’
Mathematical Communication Ability by Using Group Investigation (GI)
Learning Model in Quadrilateral of Grade VII at SMP Negeri 11 Medan
Academic Year 2014/2015”. 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 it was appropriate writer big thanks to Mrs. Dr. Izwita Dewi, M.Pd
as my thesis supervisor who has provided guidance, direction, and advice to the
perfection of this thesis. Thanks are also due to Dr. Asrin Lubis, M.Pd and Drs.
M. Panjaitan, M.Pd and Drs. Syafari, M.Pd as my examiners who have provided
input and suggestion from the planning to the completion of the preparation of the
research of this thesis. Thank you so much for all my lecturers in FMIPA.
My thanks are extended to Prof. Dr. Syawal Gultom, M.Pd as rector of
State University of Medan and employee staff in office of university head, Prof.
Drs. Motlan, M.Sc., Ph.D as Dean Faculty of Mathematics and Natural Sciences
and to coordinator of bilingual Prof. Dr. rer.nat. Binari Manurung, M.Si., Drs. Edi
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 employee staff who have helped the author.
Thanks to Mrs. Dra. Hj. Khairani, M. M as principle of SMP N 11 Medan
who has given permission to writer do research, Mrs. Sitti Khadijah S.Pd as
mathematics teacher and all teacher, staffs and also the students in grade VII-6
SMP N 11 Medan who have helped writer conducting the research.
Especially the writer would like to express my gratitude to my dear father
Prof. Dr. H. Syamruddin Nasution, M.Ag and my dear mother Mrs. Masdelina
Lubis S.PdI that always be my hero and continues to provide motivation and
prayers for the success of the writer completed this thesis. Special big thanks to
v
my beloved brother Mukhtarsyah Nasution S.H my beloved sister Mahmudah
Nasution M.Pd my Brother Muhammad Mu'az S.E my brother Abdul Hafiz
Nasution and Brother Yoneco Haref S.T, niece Adzkia Fitri big thanks to aunty
Siti Rabiah, uwak Rosliana and Sister Retnita Lubis, M. Pd that always give me
support even moril or material and all my family for all pray, motivation, and
support until the end of writer’s study.
Writer wants to say thanks to my best friends in Bilingual Mathematics
Class 2011, Leni, Sapta, Acy, Dwi, Nelly, Debby, Jo, Evan, Galang, Ozy, Yerni,
Lita, Dewi, Aprita, Kristin, Tari, Elvi, Sifa, Sam, Vera, Anna, Rony, Widi, and
Tika for the valuable support and motivation. Thanks also for 5 Serangkai (Mak
Leni, Kak Sapta, Dwi, and Acy). Big thanks also for my rented-house mates,
Zaitun, Dwi, Devi, Mbak Sari, Lely Wardani, Lely Harefa, Kia, Rina and Wulan
for support, motivation and always be my best family in Medan. Also thanks for
all my best friend Dannis and Aisyah that have give me the best experience.
The writer should give 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 increase our
knowledge.
Medan, July
Author,
Mawaddah
ID. 4113312010
2015
iii
INSREASING OF STUDENTS’ MATHEMATICAL COMMUNICATION
ABILITY BY USING GROUP INVESTIGATION (GI) LEARNING
MODEL IN QUADRILATERAL OF GRADE VII AT SMP
NEGERI 11 MEDAN ACADEMIC YEAR 2014/2015
By :
Mawaddah
4113312010
ABSTRACT
The purpose of this research were (1) to find out how the investigation
group learning model can improve the students' mathematical communication
ability, (2) to determine whether students' mathematical communication ability
increased after following the investigation of learning with group learning model.
The type of his research was belongs to Classroom Action Research (CAR),
which is implemented in SMP Negeri 11 Medan. The subjects in this research were
students of class VII-6 in 2014/2015 that have total of 47 people consisting of 20
men and 27 women. The object of this resarch were the students’ mathematical
communication ability and group investigative learning model.
Instruments used to collect the data were mathematical communication
ability test, observation sheet, and documentation. The research consists of two
cycles and for every end of cycle given students’ communication ability test.
Before given, at the first tests must be validity. Validity test done is contents
validity where expert as validator.
Repairs done to increase the communication mathematic ability is to make
students actively involved in the learning process and can be communicated, is
coordinating the state of classroom teachers, changing the group. is expected to
make increase of cycle 1 is no change cycle 2.
The results of this study can be seen: (1) The results of tests of mathematical
communication ability of students in the first cycle known average value of 65,39,
complete 4 people, 43 incomplete, 8,51% classical completeness and mathematical
communication ability of students categorized very low. (2) The results of tests of
mathematical communication ability of students in the second cycle known average
value of 86,81, complete 45 persons, 2 persons incomplete, classical completeness
87.50% and mathematical communication ability of students are middle
categorized. And (3) Learning by using the group investigation learning model can
make students’ activity were good categorized in learning.
From the results of this research can be concluded that the implementation
of the group investigative learning model can increase the students' mathematical
communication ability. The suggestion that given for teachers is to be able to
implement the group investigative learning model as an alternative in the learning
process that can increase communication skills.
vi
CONTENTS
Sheet of Agreement
Biography
Abstract
Preface
Contents
List of Figure
List of Table
List of Appendix
Page
i
ii
iii
iv
vi
ix
x
xii
CHAPTER I INTRODUCTION
1.1. Background
1.2. Problem Identification
1.3. Problem Limitation
1.4. Problem Formulation
1.5. Research Purpose
1.6. Research Benefits
1.7. Operational Definitions
1
1
7
7
7
8
8
9
CHAPTER II LITERATURE REVIEW
2.1. Theoretical Framework
2.1.1. Communication
2.1.2. Communication in Learning
2.1.3. Mathematical Communication
2.1.4. Mathematical Communication Ability
2.1.5. Cooperative Learning Model
2.1.6. Group Investigation Learning Model
2.1.7. Support Learning Theory
2.1.8. Content Materials
2.1.8.1. Rectangle
2.1.8.2. Square
2.2.
Relevant Research
2.3.
Conceptual Framework
2.4. Action Hypothesis
10
10
10
12
14
17
20
22
26
28
28
31
34
35
35
CHAPTER III RESEARCH METHODOLOGY
3.1. Type of Research
3.2. Location and Time of Research
37
37
37
vii
3.3.
3.4.
3.5.
3.6.
3.7.
3.8.
3.9.
3.2.1. Location of Research
3.2.2. Time of Research
Subject and Object of Research
3.3.1. Subject of Research
3.3.2. Object of Research
Procedure and Research Design
Cycle I
a. Problem I
b. Action Planning I
c. Action Implementation I
d. Observation I
e. Data Analysis I
f. Reflection I
Cycle II
a. Action Planning II
b. Action Implementation II
c. Observation II
d. Data Analysis II
e. Reflection II
Data Resources
Research Instrument
3.6.1. Mathematics Communication Ability Test
Observation Sheet
Data Analysis
Indicator of Succed
CHAPTER IV RESULTS AND DISCUSSION
4.1. Result of the Research
4.2 Description of Research Results
4.2.1.
37
37
37
37
38
38
39
39
40
40
41
41
42
42
42
42
43
43
43
46
46
46
48
49
53
54
54
54
Description The Result of Research Cycle I
54
4.2.1.1
Problem Cycle I
55
4.2.1.2.
Action Planning Stage I
55
4.2.1.3.
Action Implementation Stage I
56
1.
Meeting I
56
2.
Meeting II
59
Data Analysis Cycle I
62
1.
62
4.2.1.4.
Mathematical Communication Ability Test
viii
2.
4.2.1.5.
4.2.2
65
Reflection Cycle I
70
Research Cycle II
72
4.2.2.1.
Problem Cycle II
72
4.2.2.2.
Action Planning Stage II
72
4.2.2.3.
Action Implementation Stage II
73
1.
Meeting III
73
2.
Meeting IV
75
Data Analysis Cycle II
78
1.
Mathematical Communication Ability Test
78
2.
Observation
81
4.2.2.4.
4.2.2.5.
4.2.3
Observation
Reflection Cycle II
Increasing of Mathematical Communication Ability
1.
87
Increasing of Class Score in Mathematical
Communication Ability
4.3. Description of Observation Result
1.
87
Increasing of Mathematical Communication Ability
of Each Indicator
2.
84
Observation Result of Teacher Activities
89
89
89
4.4. Result of Interview
90
4.5. Research of Result
91
4.6. Discussion of Research Results
92
1.
Mathematical Communication Ability of Student’s
92
CHAPTER V CONCLUSION AND SUGGESTION
94
5.1. Conclusion
94
5.2. Suggestion
94
REFERENCES
APPENDIX
DOCUMENTATION OF RESEARCH
96
99
202
x
LIST OF TABLE
Page
Table 2.1
Scoring Criteria for Mathematics Communications
19
Table 2.2
Step of cooperative learning Model
21
Table 3.1
Description about Cycle I
41
Table 3.2
Description about Cycle II
45
Table 3.3
Scoring Guidelines Mathematical Communication Test
50
Table 3.4
The Category of Mathematical Communication Ability
51
Table 3.5
Criteria of Normalization
52
Table 4.1
The percentage of Students’ Mathematical
62
Communication Ability in Expressing or Illustrarte Cycle I
Table 4.2
The percentage of Describe through Mathematical Ideas by
62
Using Mathematical Symbols Cycle I
Table 4.3
The Percentage of Explaining Mathematical Model and
63
Doing Calculation Cycle I
Mathematical
64
Table 4.5
The Students’ Mathematical Communication Ability Test I
64
Table 4.6
The Observation Results of Teacher Activities Cycle I
66
Table 4.7
Observation of Students’ Activity in Cycle I
67
Table 4.8
Results Obtained from Cycle I
68
Table 4.9
The percentage of Students’ Mathematical Communication
78
Table 4.4
The
Percentage
of
Students’
Communication Ability Cycle I
Ability in Expressing or Illustrarte Cycle II
Table 4.10
The percentage of Describe through Mathematical Ideas by
78
Using Mathematical Symbols Cycle II
Table 4.11
The Percentage of Explaining Mathematical Model and Doing
79
Calculation Cycle I
Table 4.12
The Percentage of Students’ Mathematical Communication
Ability Cycle II
80
xi
Table 4.13
The Students Learning Completeness at Communication
80
Ability Test II
Table 4.14
The Observation Results of Teacher Activities Cycle II
81
Table 4.15
Observation of Students’ Activity in Cycle II
83
Table 4.16
Comparison Between Cycle I and Cycle II
85
Table 4.17
The Results Obtained from Cycle II
85
Table 4.18
The Increasing Mathematical Communication Ability of Each
88
Indicator
Table 4.19
The
Increasing
Average
Score
of
Mathematical
89
Communication Ability
Table 4.20
The Observation Results of Teacher Activity
90
xii
LIST OF APPENDIX
Page
Appendix 1
Lesson Plan I
99
Appendix 2
Lesson Plan II
104
Appendix 3
Lesson Plan III
108
Appendix 4
Lesson Plan IV
114
Appendix 5
Student Worksheet I
119
Appendix 6
Student Worksheet II
125
Appendix 7
Student Worksheet III
130
Appendix 8
Student Worksheet IV
135
Appendix 9
Alternative Solution of Student Worksheet I
140
Appendix 10 Alternative Solution of Student Worksheet II
142
Appendix 11 Alternative Solution of Student Worksheet III
145
Appendix 12 Alternative Solution of Student Worksheet IV
148
Appendix 13 Lattice of Initial Capability Test
151
Appendix 14 Lattice of Mathematical Communication Ability Test I
152
Appendix 15 Lattice of Mathematical Communication Ability Test II
153
Appendix 16 Initial Capability Test
154
Appendix 17 Mathematical Communication AbilityTest I
155
Appendix 18 Mathematical Communication Ability Test II
159
Appendix 19 Alternative Solution of Initial Capability Test
163
Appendix 20 Alternative Solution of Mathematical Communication
Ability Test I
166
Appendix 21 Alternative Solution of Mathematical Communication
Ability Test II
Appendix 22 Scoring Guidelines of Initial Capability Test
169
172
Appendix 23 Scoring Guidelines of Mathematical Communication
Ability Test
174
Appendix 24 Observation Sheet of Teacher Activity
176
Appendix 25 Guidelines for Interview
179
xiii
Appendix 26 Validation Sheet of Initial Capability Test
181
Appendix 27 Validation Sheet of Mathematical Communication
Ability Test I
182
Appendix 28 Validation Sheet of Mathematical Communication
Ability Test II
183
Appendix 29 Result Description of Initial Capability Test
184
Appendix 30 Result Description of Mathematical Communication Cycle I
185
Appendix 31 Result Description of Mathematical Communication Cycle II
187
Appendix 32 Result Observation Teacher Activities on Cycle I
189
Appendix 33 Result Observation Teacher Activities on Cycle II
191
Appendix 34 Result Observation Students’ Activities on Cycle I
193
Appendix 35 Result Observation Students’ Activities on Cycle II
194
Appendix 36 Result of Interview
195
CHAPTER I
INTRODUCTION
1.1 Background
Mathematics is the science that has the concept of hierarchically,
structured, logical and systematic concepts ranging from the simplest to the most
complex concepts. In learning mathematics, students are not only required to
memorize mathematical formulas, but students also need to understand the
concept of a material and can apply their knowledge to solve the existing
problems.
It is important for students to get five process standards of mathematics,
namely problem solving, mathematical reasoning, mathematical communication,
mathematical connections, and representations in mathematics learning. National
Council of Teachers of Mathematics (1989) also formulate learning objectives of
mathematics, namely: (1) learn to communicate, (2) learn to reason, (3) learn to
solve problems, (4) learn to associate the idea, and (5) learn to format a positive
attitude towards mathematics.
Obviously that mathematics is applied in field wherever in everyday life.
The development of science and technology is the role of mathematics. Therefore,
to master and create in the future technology needed a strong mastery of
mathematics from an early age by Departemen Pendidikan Nasional (2006).
Basically mathematics of school is function to develop the ability to count,
measuring, lowered and using mathematical formulas needed in everyday life.
Mathematics is also function to develop ability communicate ideas or ideas with
the language and symbols through a mathematical model which can be words and
mathematical equations, graph or table meaningful.
Many factors cause the mathematical achievement of students in Indonesia
is low, one of which is not yet optimized mathematical communication skills of
students. This is according to research conducted which showed that students'
mathematical communication skills are still low.
1
2
In the curriculum 2006 has been formulated five skill or proficiency
expected in the learning of mathematics, namely: (1) learning to communicate, (2)
learning to reason, (3) learning to solve the problems, (4) learning to associate the
idea, and (5) learning to establih of a positive attitude to mathematics. It relates to
the opinion about the importance of communication in learning mathematics,
communication is not only used in science but also in the overall of mathematics
learning activities.
Communication
skills
should
be
owned
by
every
student’,
communication skills can be built up in students’ self. This is in accordance with
the opinion expressed by Lindquist based on the National Council of Teachers of
Mathematics (NCTM) revealed that communication skills in mathematics needs
to be built so that students’ are able to : (1) express and explain their thinking
about mathematical ideas and relationship, (2) formulate a mathematical
definition and make generalizations obtained through investigation (discovery),
(3) express mathematical ideas orally and in writing, (4) read the discourse of
mathematics with understanding, (5) explain and apply well as expanding of math
questions that have been learned, and (6) appreciate the beauty and power of
mathematical notation, well as its role in developing ideas/mathematical ideas.
Communication is one of the purpose in the learning of mathematics. The process
of communication is helping students’ to build ideas, publicize the idea, and can
build a good social network in a classroom environment.
In the view of the experts, mathematical communication ability needs to
be developed among students’. Mathematical communication is the ability to
include and contain a variety of opportunities for students’ to communicate in the
form of: reflecting real objects, pictures, or ideas of mathematics, modeling
situations or problems using oral, written, concrete, graphs, and algebra, using
skills of reading, writing, listening, and study to interpret and evaluate ideas,
symbols, terms, and mathematical information.
Baroody (in Ansari, 2009 : 4) mentions at least two important reasons
why communication in learning mathematics should be cultivated among the
students’. First, mathematics is essentially a language for mathematics itself.
3
Mathematics is not just a thinking tool that helps us to find patterns, solve the
problem and make conclusion, but also a tool to communicate our thoughts about
various ideas with clear, precise and concise. In fact, mathematics is considered as
a "universal language" with symbols and unique structure.
The discussion group is another way to develop students' mathematical
communication skills. Discussion groups making students to practice
for to
express understanding. verbalize the process of thinking, and clarifying their
understanding or misunderstanding. In forming a group discussion to note a few
things, for example what kind of tasks which allow students can explore
mathematical abilities fine and true. Besides it is also need to design teacher's role
in the group of discussions. In the process of group discussion, will happen an
exchange of ideas and thinking between of students’. This will provide the
opportunity for students to build mathematical of understanding. Student's
conversation and teachers will also drive or strengthen a deeper understanding of
mathematical concepts.
This results in lower students' mathematical abilities. However
mathematical ability must be owned by the students’ to achieve the learning
objectives of the Mathematics. National council of teacher of mathematics (2000)
stated that in learning mathematics the students’ should have the mathematical
ability, namely communication, problem solving, reasoning, connections, and
mathematical representations to achieve the learning objectives of mathematics.
In fact, the students’ communication mathematics ability is still far from
expectations. This can be seen from the results of preliminary test performed by
researcher at the date of February, 6th 2015 at VIII–6 class of SMP Negeri 11
Medan as a sample. The test was given consist of 3 problems with the type is
essay test about quadrilateral as:
1. The floor area which shaped of a rectangular is 180 m2. comparison of the
length and width the room flooring is 5 : 4. stated in drawing and
mathematical model! calculated the circumference of the room floor.
4
2. Mr. Nasir has a squa
square-shaped rice fields with side length iss 54 m. Around the
rice fields planted
nted orange trees by the distance between orange
oran tree is 3 m.
Questions :
a. Data anythi
ything obtained from this problem
b. How do kno
know my much the orange trees are planted
ed around the rice
fields!
c. Calculate
te how much orange trees are planted around
und the rice fields!
d. Check com
come back the result obtained in question c! W
Whether much of
orange tre
trees are planted around the rice fields iss 88 tree
trees? Explain!
3. Mr. Irham will
ill make a fence around the banana garden
den which shaped
rectangular. The
eas the width is 10
he llength of a banana gardens is 20 m, whereas
m.
a. Describing
bing the problem
b. Based on the image, how to calculate the length of the fence to be
made byy Mr
Mr.Irham ?
c. Calculating
ting the length of the fence to be made by Mr. IIrham!
After the resul
sults of the students' answers were analyzed,
d, tthere were some
errors found are m
made by students. In the first case, from
om indicators of
communication, 90%
% of the students failed related the image too the mathematical
ideas and formulate
te m
mathematical ideas into mathematical mode
odels. This is one
picture of the students
nts' answer was wrong:
Picture
stion
re 1.1. The Student’s Answer for 1st Question
From the pictur
pictures of the student’ answers showed that stude
students’ are also
not able to calculatee the length and width of floor space with a rat
ratio of length and
width of which has been known that the
circumference cal
calculation results
5
obtained not appropri
opriate. This shows that the ability of students
nts tto communicate
mathematical ideas is low, so that the students’ are not able whe
when making the
mathematical models
ls aand solution final strategies of the problem..
The question
on number 2 found that 95% students cannot
annot answer the
question correctly,, ffrom the indicator of communication, st
students’ fail to
formulate the mathem
hematical idea into mathematical model and respons
espons a statement
in the argument, This
his iis one of the student’s wrong answer:
stion
Picture
re 1.2. The Student’s Answer for 2nd Question
that the students’
From the pict
pictures the students' answers we can see tha
students’ can not
analyze the wrong side and the distance between trees so that st
on ski
skills in terms of
calculate what is writt
ritten. This shows the lack of communication
orm of arguments.
making a mathematica
tical model to respond to a problem in the form
ustrates a problem
In question
on num
number 3 students’ were asked fatherly illust
ham, and calculate
that is known the leng
ngth and width of bananas garden the Mr. Irham
ribe mathematical
its length. Of indicat
cators of student’ communication fails describe
ideas and so cann not ccalculate the length of a banana garden.
re 1.3. The Student’s Answer for 3rd Question
tion
Picture
picture above, we can see that the student’ can
an not answer the
From the pictur
question at all. Theyy ccan not describe about a story that could not answer the next
6
question. It can also be used as real proof that students' mathematical
communication ability is low.
The analysis showed that from 25 students who take the diagnostic test,
which is the complete categorize with scored 75 only 4 people who completed
or about 16%, while 84% of students’ do not complete. Furthermore viewed from
mathematical communication ability category around 4% higher mathematical
communication ability, 12% medium, while 8% lower and 76% is very low. It
showed that students’ mathematical communication ability of students’ is still
low.
Based on the result of observation and interview that be done by researcher
to the one of the mathematics teacher in SMP Negeri 11 Medan, she is Mrs. Siti
Khadijah S.Pd date of January, 27th 2015 known that the student still have many
difficult in mathematical Communication. That is caused of the student still have
difficulties to understand the problem that was be asked in the problem especially
to know what they asked and they known in that problem, so the students still
were very difficult to communicate the problem.
Vygotsky learning theory argues that students forming knowledge as a
result of the thoughts and activities of the students themselves through language.
Vygotsky believed that development depends both on biological and social
factors, social factors are very important for the development of higher mental
functions for the development of the concept, logical reasoning, and decision
making. The learning process will occur if the child work or handle tasks that
have not been studied, but these tasks are still within their reach. Learning
Vygotsky's theory is a theory of learning that support cooperative learning model
Group Investigation.
One type of cooperative learning model that can be applied is Group
Investigation (GI). In the Group Investigation (GI) learning model, students’ in
groups conducting the investigation. This activity gives the possibility for students
to interact even more and did not close the possibilities the process of students’
answers communication because in the investigation process allows for more
than one answer.
7
Based on the above explanation, the researcher interested in conducting
the research reveal whether the learning model group investigation (GI) can
increse students’ mathematical communication skills which in turning will
increase students’ mathematics learning outcomes as one of academic human
contribution in increasing the quality of education in Indonesia. Therefore, this
research title is ‘’Increasing of Students’ Mathematical Communication
Ability by Using Group Investigation (GI) Learning Model in Quadrilateral
of Grade VII at SMP Negeri 11 Medan Academic Year 2014/2015”.
1.2 Problem Identifications
Based on the background described above, we can identify some problems
as follows :
1. Mathematical communication ability of students’ still low.
2. There are still many students’ who are not able to resolve the question
of the communication on the subject of the quadrilateral.
3. Students’ tend to be passive, just waiting for information from the
teacher. Students’ are less brave in stating his opinion.
4. The learning approach is still conventional so that so that students’ are
not trained to find their own knowledge and develop the ability of
communication.
1.3 Problem Limitation
Based on identification problem above, so the researches make the limited
the problem in: Increasing of students’ mathematical communication ability by
using Group Investigation (GI) in quadrilateral of grade VII at SMP Negeri 11
Medan Academic Year 2014/2015.
1.4 Problem Formulation
The problems formulation of this research are:
1. How is the increase communication math strategies on learning model
group investigation on the topic quadrilateral in SMP N 11 Medan?
8
2. How is the increase communication of mathematics after use Group
Investigation (GI) learning model in quadrilateral of grade VII at SMP N
11 Medan?
1.5 Research Objectives
The objective of this research are:
1. Increasing the students’ mathematical communication ability using Group
Investigation learning model.
2. Increasing whether of mathematical communication ability of student's
after the applied Group Investigation learning model.
1.6 Research Benefits
Benefit that hoped from this research is:
1. For students’ can construct the knowledge actively, able to develop the
communication ability, understanding in dealing the problems and can
improve the social relation and responsible to themselves and their
environment.
2. For Teachers can improve the quality of mathematics learning
achievement through the create mathematical communication and as one
of learning model alternative that can be used in mathematics learning.
3. For Researcher can become the comparative material about mathematical
communication rule, positive attitude and achievement motivation to the
learning result in mathematics learning, increase the experience and
thingking insight for writer about the scientific research.
4. For School expected can become the comparative material to apply the
group investigation learning model and expected can improve the
education quality in Indonesian.
9
1.7 Operational Defenition
To avoid the differencies in interpretation of the terms contained in the
problem formulation in this research, it should be noted the operational definition
as follows :
1. The ability of students’ mathematical communication is students’ ability
to (1) relate the picture, table, diagram and dailiy events into mathematical
idea, (2) formulate the mathematical idea to mathematical model, (3)
respons a statement or problem in the argument and (4) express the
description or mathematical paragraph with own language.
2. Group Investigation is a teaching method that engages students in groups
of 5-6 people from the planning, both in determining the topic as well as a
way to learn through investigation.
CHAPTER V
CONCLUSION AND SUGGESTION
5.1 Conclusion
Based on the research results presented in the previous section can be
concluded with regard to the application of investigative learning groups to
increase communication ability of junior high school students' mathematical
follows:
1. Strategies to discuss the role in evereyday life before the start of learning
and gives students’ awards have a positive impact forstudents’ is very high
enthusiasm categorized to good category.
2. The increase of students’ mathematical communication ability by the
implementation of Group Investigation (GI) model learning belongs to
moderate category with the normalized gain value is 0.62 where the
average of students’ mathematical communication ability percentage in
cycle I is 8,51% or categorized to bad category and in cycle II the average
of percentage is improved become 95,74% or categorized to good
category.
5.2 Suggestion
Based on these results, the authors propose some suggestions for learning
mathematics, especially in secondary schools, namely:
1. Learning mathematics with group investigative learning model can be
used as one of the effective learning alternative to increasing the students’
mathematical communication ability. But in the early days of learning the
teacher will have difficulty in preparing a child to perform cooperative
learning process, student learning is difficult to accept the changes they
have done so far with the constructivism learning through group learning
model investigation. Therefore, it is suggested that before the process of
learning to do, learning to familiarize teachers with cooperative learning
so that students will get used to communicate both orally and in writing to
convey ideas of mathematics.
94
95
2. To support the successful implementation of the investigative group
learning models necessary teaching materials of interest, to the student
activity sheet should be designed based on contextual issues close to
students' daily lives and challenges students to solve.
3. In the learning process so that learning outcomes can be maximized
teachers should pay attention to: (a) how to ask a question or type of
question that can evoke the curiosity of students, (b) how to settle disputes
over the students can have high confidence that they are not totally
dependent on teacher (c) the provision of scaffolding on students' prior
knowledge was limited to connecting students to their problem
solving. (D) how to create an atmosphere of discussion among students
with other students so that the discussion is not dominant mastered by
students who have high ability.
4. In the investigation group learning model, the teacher acts as a
facilitator. Therefore, teachers of mathematics who wish to apply this
learning need to pay attention to: (a) the availability of instructional
materials in the form of problems that lead to kemampun kontkstual to be
achieved, (b) required careful consideration for teachers in providing
assistance to the student so that the student is able to achieving the
expected competencies to the maximum, (c) the provision of assistance
may be needed if it is to encourage the development of students' potential.
5. In addition to increasing communication skills of mathematics and
learning outcomes, learning models can also spur investigation group of
students in a learning activity and can assist students in forming a positive
perception towards learning mathematics, therefore it is advisable to
learning as developed further on the topic - the topic of mathematics and
different levels of education.
6. This study only reveals the role of investigative group learning model in
increasing communication skills of mathematics. To complete the study of
the role of investigative learning model as a whole group needs to be
further research to look at the role of the investigative group learning
model in increasing problem-solving abilities, reasoning, and
mathematical connections.
96
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Ansari, Bansui.I, (2012). Komunikasi Matematik dan Politik, Pena, Banda Aceh
Ansari,B.I, (2009). Komunikasi Matematik, Yayasan Pena, Banda Aceh.TIMSS.
(2012). TIMSS 2011 International Results in Mathematics. Chestnut Hill:
TIMSS & PIRLS International Study Center.
Arthur, k. Ellis (1998). The Interdisiplinary curriculum. Eye on Education Inc.
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Arikunto, S., (2007), Prosedur Penelitian suatu Pendekatan Praktik, Rineka
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Asmin dan Abil Mansyur. (2012). Pengukuran dan Penilaian Hasil Belajar
dangan Analisis klasik dan modern. Larispa, Medan
Depdikbud, (2002), Kamus Besar Bahasa Indonesia, Ed ke -2, Balai Pustaka,
Jakarta
Depdiknas, (2006), Peraturan Menteri Pendidikan Nasional No. 22 tahun 2006
tentang Standar Isi, Jakarta
Gronlund, E & Linn, Robert. (2000). Measurement and Assesment in Teaching
(8th Edition). USA: Prentice-Hall, INC.
Hake, R. R., (2001), Suggestion for Administering and Reporting Pre/ Post
Diagnostic Test
Isjoni. (2013). Cooperative Learning. Alfabeta. Bandung
Kunandar, (2009), Guru Profesional, Rajawali Pers, Jakarta.
Lubis, Nurhadijah. (2014). Perbedaan Kemampuan Pemecahan Masalah dan
Metakognisi Matematika Antara Siswa yang Diberi Pembelajaran
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UNIMED. Medan.
Lia, Purba (2014). The Implementation of Group Investigation Learning Model to
Improve The Students’ Mathematical Communication Ability of Eighth Grade
SMP N 4 P.Siantar Academic Year 2014/2015. Skripsi, FMIPA UNIMED,
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Students’ Activitiesby Implementing PBL Model in Learning and
TeachingQuadrilateralsTopic in Seventh Grade of Mts. N 3 Medan in A.Y
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97
Muriana, 2013. Peningkatan kemampuan komunikasi dan disposisi Matematis
Siswa SMA di Kecamatan Medan Area dengan Menggunakan Model
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UNIMED. Medan
Nasution, wardani. (2013). Upaya meningkatkan kemampuan komunikasi
matematik siswa dengan penerapan startegi pembelajaran TTW pada
materi Faktorisasi bentuk Aljabar siswa kelas VIII SMP Negeri 1 Padang
sidempuan T.A 2013/2014. Skripsi, FMIPA UNIMED, Medan
National Council of Teachers of Mathematics (NCTM) (1989), Curriculum and
Evaluation Standards for School Mathematics, NCTM, Reston, Virginia
National Council of Teacher of Mathematics (NCTM), (2000), Principles and
Standards for School Mathematics, NCTM, Reston, Virginia
Purba, lia, (2014). The Implementation of Group Investigation Learning Model to
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Pembelajaran Kooperatif tipe STAD. Skripsi, FMIPA UNIMED, Medan
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Sulastri, (2014). Perbedan kemampuan komunikasi matematika siswa yang diajar
dengan model pembelajaran kooperatif tipe TPS dan pembelajaran
Konvensional pada kelas VIII SMP Yapim Namorambe T.A 2013/2014.
Skripsi, FMIPA UNIMED, Medan
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UNIMED, Medan
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Academic. Singapore
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Communication Ability By Using Think-Talk-Write (Ttw) Model In
Quadrilateral Of Grade Vii At Smp Negeri 1 Onan Ganjang. Skripsi,
FMIPA UNIMED, Medan
ii
BIOGRAPHY
Mawaddah was born in Pekanbaru on September 1th, 1993. Her father’s
name is Prof. Dr. H. Syamruddin Nasution M.Ag and her mother’s name is Hj.
Masdelina S.Pd. She is the fourth child of her family, and she has two brother,
Mukhtarsyah Nasution S.H, Muhammad Mu'az S.E, one sister, Mahmudah
Nasution M.Pd and one brother Abdul Hafiz Nasution. She was jointed in SD 031
Tampan Permai Pekanbaru on 1999 and then graduated in 2005. She was
graduated from SMP Negeri 1 Pekanbaru on 2008. And then she was graduated
from MAN 1 Pekanbaru on 2011. After graduated from Senior High School, she
continued her study in Unimed as student in Bilingual Class of Mathematics
Education 2011.
ABILITYBYUSINGGROUPINSTIGATION(GI)LEARNINGMODEL
INQUADRILATERALOFGRADEVIIATSMPNEGERI
11 MEDAN ACADEMIC YEAR 2014/2015
By:
Mawaddah
ID 4113312010
Mathematics Education Study Program
THESIS
Submitted to Fulfill the Requirement for Getting
the Degree of Sarjana Pendidikan
MATHEMATICS DEPARTMENT
FACULTY OF MATHEMATICS AND NATURAL SCIENCES
STATE UNIVERSITY OF MEDAN
MEDAN
2015
iv
PREFACE
Give thankfulness to Allah SWT that gives the God’s mercy and spirit so
that writer can finish this thesis. The title of this thesis is “Increasing of Students’
Mathematical Communication Ability by Using Group Investigation (GI)
Learning Model in Quadrilateral of Grade VII at SMP Negeri 11 Medan
Academic Year 2014/2015”. 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 it was appropriate writer big thanks to Mrs. Dr. Izwita Dewi, M.Pd
as my thesis supervisor who has provided guidance, direction, and advice to the
perfection of this thesis. Thanks are also due to Dr. Asrin Lubis, M.Pd and Drs.
M. Panjaitan, M.Pd and Drs. Syafari, M.Pd as my examiners who have provided
input and suggestion from the planning to the completion of the preparation of the
research of this thesis. Thank you so much for all my lecturers in FMIPA.
My thanks are extended to Prof. Dr. Syawal Gultom, M.Pd as rector of
State University of Medan and employee staff in office of university head, Prof.
Drs. Motlan, M.Sc., Ph.D as Dean Faculty of Mathematics and Natural Sciences
and to coordinator of bilingual Prof. Dr. rer.nat. Binari Manurung, M.Si., Drs. Edi
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 employee staff who have helped the author.
Thanks to Mrs. Dra. Hj. Khairani, M. M as principle of SMP N 11 Medan
who has given permission to writer do research, Mrs. Sitti Khadijah S.Pd as
mathematics teacher and all teacher, staffs and also the students in grade VII-6
SMP N 11 Medan who have helped writer conducting the research.
Especially the writer would like to express my gratitude to my dear father
Prof. Dr. H. Syamruddin Nasution, M.Ag and my dear mother Mrs. Masdelina
Lubis S.PdI that always be my hero and continues to provide motivation and
prayers for the success of the writer completed this thesis. Special big thanks to
v
my beloved brother Mukhtarsyah Nasution S.H my beloved sister Mahmudah
Nasution M.Pd my Brother Muhammad Mu'az S.E my brother Abdul Hafiz
Nasution and Brother Yoneco Haref S.T, niece Adzkia Fitri big thanks to aunty
Siti Rabiah, uwak Rosliana and Sister Retnita Lubis, M. Pd that always give me
support even moril or material and all my family for all pray, motivation, and
support until the end of writer’s study.
Writer wants to say thanks to my best friends in Bilingual Mathematics
Class 2011, Leni, Sapta, Acy, Dwi, Nelly, Debby, Jo, Evan, Galang, Ozy, Yerni,
Lita, Dewi, Aprita, Kristin, Tari, Elvi, Sifa, Sam, Vera, Anna, Rony, Widi, and
Tika for the valuable support and motivation. Thanks also for 5 Serangkai (Mak
Leni, Kak Sapta, Dwi, and Acy). Big thanks also for my rented-house mates,
Zaitun, Dwi, Devi, Mbak Sari, Lely Wardani, Lely Harefa, Kia, Rina and Wulan
for support, motivation and always be my best family in Medan. Also thanks for
all my best friend Dannis and Aisyah that have give me the best experience.
The writer should give 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 increase our
knowledge.
Medan, July
Author,
Mawaddah
ID. 4113312010
2015
iii
INSREASING OF STUDENTS’ MATHEMATICAL COMMUNICATION
ABILITY BY USING GROUP INVESTIGATION (GI) LEARNING
MODEL IN QUADRILATERAL OF GRADE VII AT SMP
NEGERI 11 MEDAN ACADEMIC YEAR 2014/2015
By :
Mawaddah
4113312010
ABSTRACT
The purpose of this research were (1) to find out how the investigation
group learning model can improve the students' mathematical communication
ability, (2) to determine whether students' mathematical communication ability
increased after following the investigation of learning with group learning model.
The type of his research was belongs to Classroom Action Research (CAR),
which is implemented in SMP Negeri 11 Medan. The subjects in this research were
students of class VII-6 in 2014/2015 that have total of 47 people consisting of 20
men and 27 women. The object of this resarch were the students’ mathematical
communication ability and group investigative learning model.
Instruments used to collect the data were mathematical communication
ability test, observation sheet, and documentation. The research consists of two
cycles and for every end of cycle given students’ communication ability test.
Before given, at the first tests must be validity. Validity test done is contents
validity where expert as validator.
Repairs done to increase the communication mathematic ability is to make
students actively involved in the learning process and can be communicated, is
coordinating the state of classroom teachers, changing the group. is expected to
make increase of cycle 1 is no change cycle 2.
The results of this study can be seen: (1) The results of tests of mathematical
communication ability of students in the first cycle known average value of 65,39,
complete 4 people, 43 incomplete, 8,51% classical completeness and mathematical
communication ability of students categorized very low. (2) The results of tests of
mathematical communication ability of students in the second cycle known average
value of 86,81, complete 45 persons, 2 persons incomplete, classical completeness
87.50% and mathematical communication ability of students are middle
categorized. And (3) Learning by using the group investigation learning model can
make students’ activity were good categorized in learning.
From the results of this research can be concluded that the implementation
of the group investigative learning model can increase the students' mathematical
communication ability. The suggestion that given for teachers is to be able to
implement the group investigative learning model as an alternative in the learning
process that can increase communication skills.
vi
CONTENTS
Sheet of Agreement
Biography
Abstract
Preface
Contents
List of Figure
List of Table
List of Appendix
Page
i
ii
iii
iv
vi
ix
x
xii
CHAPTER I INTRODUCTION
1.1. Background
1.2. Problem Identification
1.3. Problem Limitation
1.4. Problem Formulation
1.5. Research Purpose
1.6. Research Benefits
1.7. Operational Definitions
1
1
7
7
7
8
8
9
CHAPTER II LITERATURE REVIEW
2.1. Theoretical Framework
2.1.1. Communication
2.1.2. Communication in Learning
2.1.3. Mathematical Communication
2.1.4. Mathematical Communication Ability
2.1.5. Cooperative Learning Model
2.1.6. Group Investigation Learning Model
2.1.7. Support Learning Theory
2.1.8. Content Materials
2.1.8.1. Rectangle
2.1.8.2. Square
2.2.
Relevant Research
2.3.
Conceptual Framework
2.4. Action Hypothesis
10
10
10
12
14
17
20
22
26
28
28
31
34
35
35
CHAPTER III RESEARCH METHODOLOGY
3.1. Type of Research
3.2. Location and Time of Research
37
37
37
vii
3.3.
3.4.
3.5.
3.6.
3.7.
3.8.
3.9.
3.2.1. Location of Research
3.2.2. Time of Research
Subject and Object of Research
3.3.1. Subject of Research
3.3.2. Object of Research
Procedure and Research Design
Cycle I
a. Problem I
b. Action Planning I
c. Action Implementation I
d. Observation I
e. Data Analysis I
f. Reflection I
Cycle II
a. Action Planning II
b. Action Implementation II
c. Observation II
d. Data Analysis II
e. Reflection II
Data Resources
Research Instrument
3.6.1. Mathematics Communication Ability Test
Observation Sheet
Data Analysis
Indicator of Succed
CHAPTER IV RESULTS AND DISCUSSION
4.1. Result of the Research
4.2 Description of Research Results
4.2.1.
37
37
37
37
38
38
39
39
40
40
41
41
42
42
42
42
43
43
43
46
46
46
48
49
53
54
54
54
Description The Result of Research Cycle I
54
4.2.1.1
Problem Cycle I
55
4.2.1.2.
Action Planning Stage I
55
4.2.1.3.
Action Implementation Stage I
56
1.
Meeting I
56
2.
Meeting II
59
Data Analysis Cycle I
62
1.
62
4.2.1.4.
Mathematical Communication Ability Test
viii
2.
4.2.1.5.
4.2.2
65
Reflection Cycle I
70
Research Cycle II
72
4.2.2.1.
Problem Cycle II
72
4.2.2.2.
Action Planning Stage II
72
4.2.2.3.
Action Implementation Stage II
73
1.
Meeting III
73
2.
Meeting IV
75
Data Analysis Cycle II
78
1.
Mathematical Communication Ability Test
78
2.
Observation
81
4.2.2.4.
4.2.2.5.
4.2.3
Observation
Reflection Cycle II
Increasing of Mathematical Communication Ability
1.
87
Increasing of Class Score in Mathematical
Communication Ability
4.3. Description of Observation Result
1.
87
Increasing of Mathematical Communication Ability
of Each Indicator
2.
84
Observation Result of Teacher Activities
89
89
89
4.4. Result of Interview
90
4.5. Research of Result
91
4.6. Discussion of Research Results
92
1.
Mathematical Communication Ability of Student’s
92
CHAPTER V CONCLUSION AND SUGGESTION
94
5.1. Conclusion
94
5.2. Suggestion
94
REFERENCES
APPENDIX
DOCUMENTATION OF RESEARCH
96
99
202
x
LIST OF TABLE
Page
Table 2.1
Scoring Criteria for Mathematics Communications
19
Table 2.2
Step of cooperative learning Model
21
Table 3.1
Description about Cycle I
41
Table 3.2
Description about Cycle II
45
Table 3.3
Scoring Guidelines Mathematical Communication Test
50
Table 3.4
The Category of Mathematical Communication Ability
51
Table 3.5
Criteria of Normalization
52
Table 4.1
The percentage of Students’ Mathematical
62
Communication Ability in Expressing or Illustrarte Cycle I
Table 4.2
The percentage of Describe through Mathematical Ideas by
62
Using Mathematical Symbols Cycle I
Table 4.3
The Percentage of Explaining Mathematical Model and
63
Doing Calculation Cycle I
Mathematical
64
Table 4.5
The Students’ Mathematical Communication Ability Test I
64
Table 4.6
The Observation Results of Teacher Activities Cycle I
66
Table 4.7
Observation of Students’ Activity in Cycle I
67
Table 4.8
Results Obtained from Cycle I
68
Table 4.9
The percentage of Students’ Mathematical Communication
78
Table 4.4
The
Percentage
of
Students’
Communication Ability Cycle I
Ability in Expressing or Illustrarte Cycle II
Table 4.10
The percentage of Describe through Mathematical Ideas by
78
Using Mathematical Symbols Cycle II
Table 4.11
The Percentage of Explaining Mathematical Model and Doing
79
Calculation Cycle I
Table 4.12
The Percentage of Students’ Mathematical Communication
Ability Cycle II
80
xi
Table 4.13
The Students Learning Completeness at Communication
80
Ability Test II
Table 4.14
The Observation Results of Teacher Activities Cycle II
81
Table 4.15
Observation of Students’ Activity in Cycle II
83
Table 4.16
Comparison Between Cycle I and Cycle II
85
Table 4.17
The Results Obtained from Cycle II
85
Table 4.18
The Increasing Mathematical Communication Ability of Each
88
Indicator
Table 4.19
The
Increasing
Average
Score
of
Mathematical
89
Communication Ability
Table 4.20
The Observation Results of Teacher Activity
90
xii
LIST OF APPENDIX
Page
Appendix 1
Lesson Plan I
99
Appendix 2
Lesson Plan II
104
Appendix 3
Lesson Plan III
108
Appendix 4
Lesson Plan IV
114
Appendix 5
Student Worksheet I
119
Appendix 6
Student Worksheet II
125
Appendix 7
Student Worksheet III
130
Appendix 8
Student Worksheet IV
135
Appendix 9
Alternative Solution of Student Worksheet I
140
Appendix 10 Alternative Solution of Student Worksheet II
142
Appendix 11 Alternative Solution of Student Worksheet III
145
Appendix 12 Alternative Solution of Student Worksheet IV
148
Appendix 13 Lattice of Initial Capability Test
151
Appendix 14 Lattice of Mathematical Communication Ability Test I
152
Appendix 15 Lattice of Mathematical Communication Ability Test II
153
Appendix 16 Initial Capability Test
154
Appendix 17 Mathematical Communication AbilityTest I
155
Appendix 18 Mathematical Communication Ability Test II
159
Appendix 19 Alternative Solution of Initial Capability Test
163
Appendix 20 Alternative Solution of Mathematical Communication
Ability Test I
166
Appendix 21 Alternative Solution of Mathematical Communication
Ability Test II
Appendix 22 Scoring Guidelines of Initial Capability Test
169
172
Appendix 23 Scoring Guidelines of Mathematical Communication
Ability Test
174
Appendix 24 Observation Sheet of Teacher Activity
176
Appendix 25 Guidelines for Interview
179
xiii
Appendix 26 Validation Sheet of Initial Capability Test
181
Appendix 27 Validation Sheet of Mathematical Communication
Ability Test I
182
Appendix 28 Validation Sheet of Mathematical Communication
Ability Test II
183
Appendix 29 Result Description of Initial Capability Test
184
Appendix 30 Result Description of Mathematical Communication Cycle I
185
Appendix 31 Result Description of Mathematical Communication Cycle II
187
Appendix 32 Result Observation Teacher Activities on Cycle I
189
Appendix 33 Result Observation Teacher Activities on Cycle II
191
Appendix 34 Result Observation Students’ Activities on Cycle I
193
Appendix 35 Result Observation Students’ Activities on Cycle II
194
Appendix 36 Result of Interview
195
CHAPTER I
INTRODUCTION
1.1 Background
Mathematics is the science that has the concept of hierarchically,
structured, logical and systematic concepts ranging from the simplest to the most
complex concepts. In learning mathematics, students are not only required to
memorize mathematical formulas, but students also need to understand the
concept of a material and can apply their knowledge to solve the existing
problems.
It is important for students to get five process standards of mathematics,
namely problem solving, mathematical reasoning, mathematical communication,
mathematical connections, and representations in mathematics learning. National
Council of Teachers of Mathematics (1989) also formulate learning objectives of
mathematics, namely: (1) learn to communicate, (2) learn to reason, (3) learn to
solve problems, (4) learn to associate the idea, and (5) learn to format a positive
attitude towards mathematics.
Obviously that mathematics is applied in field wherever in everyday life.
The development of science and technology is the role of mathematics. Therefore,
to master and create in the future technology needed a strong mastery of
mathematics from an early age by Departemen Pendidikan Nasional (2006).
Basically mathematics of school is function to develop the ability to count,
measuring, lowered and using mathematical formulas needed in everyday life.
Mathematics is also function to develop ability communicate ideas or ideas with
the language and symbols through a mathematical model which can be words and
mathematical equations, graph or table meaningful.
Many factors cause the mathematical achievement of students in Indonesia
is low, one of which is not yet optimized mathematical communication skills of
students. This is according to research conducted which showed that students'
mathematical communication skills are still low.
1
2
In the curriculum 2006 has been formulated five skill or proficiency
expected in the learning of mathematics, namely: (1) learning to communicate, (2)
learning to reason, (3) learning to solve the problems, (4) learning to associate the
idea, and (5) learning to establih of a positive attitude to mathematics. It relates to
the opinion about the importance of communication in learning mathematics,
communication is not only used in science but also in the overall of mathematics
learning activities.
Communication
skills
should
be
owned
by
every
student’,
communication skills can be built up in students’ self. This is in accordance with
the opinion expressed by Lindquist based on the National Council of Teachers of
Mathematics (NCTM) revealed that communication skills in mathematics needs
to be built so that students’ are able to : (1) express and explain their thinking
about mathematical ideas and relationship, (2) formulate a mathematical
definition and make generalizations obtained through investigation (discovery),
(3) express mathematical ideas orally and in writing, (4) read the discourse of
mathematics with understanding, (5) explain and apply well as expanding of math
questions that have been learned, and (6) appreciate the beauty and power of
mathematical notation, well as its role in developing ideas/mathematical ideas.
Communication is one of the purpose in the learning of mathematics. The process
of communication is helping students’ to build ideas, publicize the idea, and can
build a good social network in a classroom environment.
In the view of the experts, mathematical communication ability needs to
be developed among students’. Mathematical communication is the ability to
include and contain a variety of opportunities for students’ to communicate in the
form of: reflecting real objects, pictures, or ideas of mathematics, modeling
situations or problems using oral, written, concrete, graphs, and algebra, using
skills of reading, writing, listening, and study to interpret and evaluate ideas,
symbols, terms, and mathematical information.
Baroody (in Ansari, 2009 : 4) mentions at least two important reasons
why communication in learning mathematics should be cultivated among the
students’. First, mathematics is essentially a language for mathematics itself.
3
Mathematics is not just a thinking tool that helps us to find patterns, solve the
problem and make conclusion, but also a tool to communicate our thoughts about
various ideas with clear, precise and concise. In fact, mathematics is considered as
a "universal language" with symbols and unique structure.
The discussion group is another way to develop students' mathematical
communication skills. Discussion groups making students to practice
for to
express understanding. verbalize the process of thinking, and clarifying their
understanding or misunderstanding. In forming a group discussion to note a few
things, for example what kind of tasks which allow students can explore
mathematical abilities fine and true. Besides it is also need to design teacher's role
in the group of discussions. In the process of group discussion, will happen an
exchange of ideas and thinking between of students’. This will provide the
opportunity for students to build mathematical of understanding. Student's
conversation and teachers will also drive or strengthen a deeper understanding of
mathematical concepts.
This results in lower students' mathematical abilities. However
mathematical ability must be owned by the students’ to achieve the learning
objectives of the Mathematics. National council of teacher of mathematics (2000)
stated that in learning mathematics the students’ should have the mathematical
ability, namely communication, problem solving, reasoning, connections, and
mathematical representations to achieve the learning objectives of mathematics.
In fact, the students’ communication mathematics ability is still far from
expectations. This can be seen from the results of preliminary test performed by
researcher at the date of February, 6th 2015 at VIII–6 class of SMP Negeri 11
Medan as a sample. The test was given consist of 3 problems with the type is
essay test about quadrilateral as:
1. The floor area which shaped of a rectangular is 180 m2. comparison of the
length and width the room flooring is 5 : 4. stated in drawing and
mathematical model! calculated the circumference of the room floor.
4
2. Mr. Nasir has a squa
square-shaped rice fields with side length iss 54 m. Around the
rice fields planted
nted orange trees by the distance between orange
oran tree is 3 m.
Questions :
a. Data anythi
ything obtained from this problem
b. How do kno
know my much the orange trees are planted
ed around the rice
fields!
c. Calculate
te how much orange trees are planted around
und the rice fields!
d. Check com
come back the result obtained in question c! W
Whether much of
orange tre
trees are planted around the rice fields iss 88 tree
trees? Explain!
3. Mr. Irham will
ill make a fence around the banana garden
den which shaped
rectangular. The
eas the width is 10
he llength of a banana gardens is 20 m, whereas
m.
a. Describing
bing the problem
b. Based on the image, how to calculate the length of the fence to be
made byy Mr
Mr.Irham ?
c. Calculating
ting the length of the fence to be made by Mr. IIrham!
After the resul
sults of the students' answers were analyzed,
d, tthere were some
errors found are m
made by students. In the first case, from
om indicators of
communication, 90%
% of the students failed related the image too the mathematical
ideas and formulate
te m
mathematical ideas into mathematical mode
odels. This is one
picture of the students
nts' answer was wrong:
Picture
stion
re 1.1. The Student’s Answer for 1st Question
From the pictur
pictures of the student’ answers showed that stude
students’ are also
not able to calculatee the length and width of floor space with a rat
ratio of length and
width of which has been known that the
circumference cal
calculation results
5
obtained not appropri
opriate. This shows that the ability of students
nts tto communicate
mathematical ideas is low, so that the students’ are not able whe
when making the
mathematical models
ls aand solution final strategies of the problem..
The question
on number 2 found that 95% students cannot
annot answer the
question correctly,, ffrom the indicator of communication, st
students’ fail to
formulate the mathem
hematical idea into mathematical model and respons
espons a statement
in the argument, This
his iis one of the student’s wrong answer:
stion
Picture
re 1.2. The Student’s Answer for 2nd Question
that the students’
From the pict
pictures the students' answers we can see tha
students’ can not
analyze the wrong side and the distance between trees so that st
on ski
skills in terms of
calculate what is writt
ritten. This shows the lack of communication
orm of arguments.
making a mathematica
tical model to respond to a problem in the form
ustrates a problem
In question
on num
number 3 students’ were asked fatherly illust
ham, and calculate
that is known the leng
ngth and width of bananas garden the Mr. Irham
ribe mathematical
its length. Of indicat
cators of student’ communication fails describe
ideas and so cann not ccalculate the length of a banana garden.
re 1.3. The Student’s Answer for 3rd Question
tion
Picture
picture above, we can see that the student’ can
an not answer the
From the pictur
question at all. Theyy ccan not describe about a story that could not answer the next
6
question. It can also be used as real proof that students' mathematical
communication ability is low.
The analysis showed that from 25 students who take the diagnostic test,
which is the complete categorize with scored 75 only 4 people who completed
or about 16%, while 84% of students’ do not complete. Furthermore viewed from
mathematical communication ability category around 4% higher mathematical
communication ability, 12% medium, while 8% lower and 76% is very low. It
showed that students’ mathematical communication ability of students’ is still
low.
Based on the result of observation and interview that be done by researcher
to the one of the mathematics teacher in SMP Negeri 11 Medan, she is Mrs. Siti
Khadijah S.Pd date of January, 27th 2015 known that the student still have many
difficult in mathematical Communication. That is caused of the student still have
difficulties to understand the problem that was be asked in the problem especially
to know what they asked and they known in that problem, so the students still
were very difficult to communicate the problem.
Vygotsky learning theory argues that students forming knowledge as a
result of the thoughts and activities of the students themselves through language.
Vygotsky believed that development depends both on biological and social
factors, social factors are very important for the development of higher mental
functions for the development of the concept, logical reasoning, and decision
making. The learning process will occur if the child work or handle tasks that
have not been studied, but these tasks are still within their reach. Learning
Vygotsky's theory is a theory of learning that support cooperative learning model
Group Investigation.
One type of cooperative learning model that can be applied is Group
Investigation (GI). In the Group Investigation (GI) learning model, students’ in
groups conducting the investigation. This activity gives the possibility for students
to interact even more and did not close the possibilities the process of students’
answers communication because in the investigation process allows for more
than one answer.
7
Based on the above explanation, the researcher interested in conducting
the research reveal whether the learning model group investigation (GI) can
increse students’ mathematical communication skills which in turning will
increase students’ mathematics learning outcomes as one of academic human
contribution in increasing the quality of education in Indonesia. Therefore, this
research title is ‘’Increasing of Students’ Mathematical Communication
Ability by Using Group Investigation (GI) Learning Model in Quadrilateral
of Grade VII at SMP Negeri 11 Medan Academic Year 2014/2015”.
1.2 Problem Identifications
Based on the background described above, we can identify some problems
as follows :
1. Mathematical communication ability of students’ still low.
2. There are still many students’ who are not able to resolve the question
of the communication on the subject of the quadrilateral.
3. Students’ tend to be passive, just waiting for information from the
teacher. Students’ are less brave in stating his opinion.
4. The learning approach is still conventional so that so that students’ are
not trained to find their own knowledge and develop the ability of
communication.
1.3 Problem Limitation
Based on identification problem above, so the researches make the limited
the problem in: Increasing of students’ mathematical communication ability by
using Group Investigation (GI) in quadrilateral of grade VII at SMP Negeri 11
Medan Academic Year 2014/2015.
1.4 Problem Formulation
The problems formulation of this research are:
1. How is the increase communication math strategies on learning model
group investigation on the topic quadrilateral in SMP N 11 Medan?
8
2. How is the increase communication of mathematics after use Group
Investigation (GI) learning model in quadrilateral of grade VII at SMP N
11 Medan?
1.5 Research Objectives
The objective of this research are:
1. Increasing the students’ mathematical communication ability using Group
Investigation learning model.
2. Increasing whether of mathematical communication ability of student's
after the applied Group Investigation learning model.
1.6 Research Benefits
Benefit that hoped from this research is:
1. For students’ can construct the knowledge actively, able to develop the
communication ability, understanding in dealing the problems and can
improve the social relation and responsible to themselves and their
environment.
2. For Teachers can improve the quality of mathematics learning
achievement through the create mathematical communication and as one
of learning model alternative that can be used in mathematics learning.
3. For Researcher can become the comparative material about mathematical
communication rule, positive attitude and achievement motivation to the
learning result in mathematics learning, increase the experience and
thingking insight for writer about the scientific research.
4. For School expected can become the comparative material to apply the
group investigation learning model and expected can improve the
education quality in Indonesian.
9
1.7 Operational Defenition
To avoid the differencies in interpretation of the terms contained in the
problem formulation in this research, it should be noted the operational definition
as follows :
1. The ability of students’ mathematical communication is students’ ability
to (1) relate the picture, table, diagram and dailiy events into mathematical
idea, (2) formulate the mathematical idea to mathematical model, (3)
respons a statement or problem in the argument and (4) express the
description or mathematical paragraph with own language.
2. Group Investigation is a teaching method that engages students in groups
of 5-6 people from the planning, both in determining the topic as well as a
way to learn through investigation.
CHAPTER V
CONCLUSION AND SUGGESTION
5.1 Conclusion
Based on the research results presented in the previous section can be
concluded with regard to the application of investigative learning groups to
increase communication ability of junior high school students' mathematical
follows:
1. Strategies to discuss the role in evereyday life before the start of learning
and gives students’ awards have a positive impact forstudents’ is very high
enthusiasm categorized to good category.
2. The increase of students’ mathematical communication ability by the
implementation of Group Investigation (GI) model learning belongs to
moderate category with the normalized gain value is 0.62 where the
average of students’ mathematical communication ability percentage in
cycle I is 8,51% or categorized to bad category and in cycle II the average
of percentage is improved become 95,74% or categorized to good
category.
5.2 Suggestion
Based on these results, the authors propose some suggestions for learning
mathematics, especially in secondary schools, namely:
1. Learning mathematics with group investigative learning model can be
used as one of the effective learning alternative to increasing the students’
mathematical communication ability. But in the early days of learning the
teacher will have difficulty in preparing a child to perform cooperative
learning process, student learning is difficult to accept the changes they
have done so far with the constructivism learning through group learning
model investigation. Therefore, it is suggested that before the process of
learning to do, learning to familiarize teachers with cooperative learning
so that students will get used to communicate both orally and in writing to
convey ideas of mathematics.
94
95
2. To support the successful implementation of the investigative group
learning models necessary teaching materials of interest, to the student
activity sheet should be designed based on contextual issues close to
students' daily lives and challenges students to solve.
3. In the learning process so that learning outcomes can be maximized
teachers should pay attention to: (a) how to ask a question or type of
question that can evoke the curiosity of students, (b) how to settle disputes
over the students can have high confidence that they are not totally
dependent on teacher (c) the provision of scaffolding on students' prior
knowledge was limited to connecting students to their problem
solving. (D) how to create an atmosphere of discussion among students
with other students so that the discussion is not dominant mastered by
students who have high ability.
4. In the investigation group learning model, the teacher acts as a
facilitator. Therefore, teachers of mathematics who wish to apply this
learning need to pay attention to: (a) the availability of instructional
materials in the form of problems that lead to kemampun kontkstual to be
achieved, (b) required careful consideration for teachers in providing
assistance to the student so that the student is able to achieving the
expected competencies to the maximum, (c) the provision of assistance
may be needed if it is to encourage the development of students' potential.
5. In addition to increasing communication skills of mathematics and
learning outcomes, learning models can also spur investigation group of
students in a learning activity and can assist students in forming a positive
perception towards learning mathematics, therefore it is advisable to
learning as developed further on the topic - the topic of mathematics and
different levels of education.
6. This study only reveals the role of investigative group learning model in
increasing communication skills of mathematics. To complete the study of
the role of investigative learning model as a whole group needs to be
further research to look at the role of the investigative group learning
model in increasing problem-solving abilities, reasoning, and
mathematical connections.
96
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ii
BIOGRAPHY
Mawaddah was born in Pekanbaru on September 1th, 1993. Her father’s
name is Prof. Dr. H. Syamruddin Nasution M.Ag and her mother’s name is Hj.
Masdelina S.Pd. She is the fourth child of her family, and she has two brother,
Mukhtarsyah Nasution S.H, Muhammad Mu'az S.E, one sister, Mahmudah
Nasution M.Pd and one brother Abdul Hafiz Nasution. She was jointed in SD 031
Tampan Permai Pekanbaru on 1999 and then graduated in 2005. She was
graduated from SMP Negeri 1 Pekanbaru on 2008. And then she was graduated
from MAN 1 Pekanbaru on 2011. After graduated from Senior High School, she
continued her study in Unimed as student in Bilingual Class of Mathematics
Education 2011.