ANALYSIS OF THE SECOND SEMESTER MATHEMATICS STUDENTS’ METACOGNITIVE SKILL IN SOLVING MATHEMATICS PROBLEMS AT STATE UNIVERSITY OF MEDAN.
ANALYSIS OF THE SECOND SEMESTER MATHEMATICS STUDENTS’
METACOGNITIVE SKILL IN SOLVING MATHEMATICS
PROBLEMS AT STATE UNIVERSITY OF MEDAN
By:
Shinta Belaginary
IDN. 4123111078
Bilingual Mathematics Education Study Program
SKRIPSI
Submitted in Partial Fulfillment of The Requirements for The Degree of
Sarjana Pendidikan
FACULTY OF MATHEMATICS AND NATURAL SCIENCES
STATE UNIVERSITY OF MEDAN
MEDAN
2016
ii
BIOGRAPHY
The
author,
ShintaBelaginary,
actually
has
a
fullnameShinta
Bella
GinarySimanjuntak, was born in Jakarta, January 14th 1995. She is the sixth
children from ZainalAbidinSimanjuntak, S.E. and ResiannaSiahaan. In 2000, the
author started her study at SD Sultan AgungPematangsiantar and graduated in
2006. The author continued her study to SMP Sultan AgungPematangsiantar and
graduated in 2009. The author also continued her study to SMAN 2
Pematangsiantar and graduated in 2012. In 2012, she continued her study to
UniversitasNegeri Medan (Unimed) as a student in Mathematics Education Study
Program, Bilingual Class. Finally, the author completed her study of
undergraduated (S1) from Unimed in 2016.
ii
iii
ANALYSIS OF THE SECOND SEMESTER MATHEMATICS STUDENTS’
METACOGNITIVE SKILL IN SOLVING MATHEMATICS
PROBLEMS AT STATE UNIVERSITY OF MEDAN
Shinta Belaginary1, Amin Fauzi2
1.
Faculty of Mathematics and natural Sciences, State University of Medan
email: 14shintabellags@gmail.com
2.
Faculty of Mathematics and Natural Science, State University of Medan
email: amin_fauzi29@yahoo.com
ABSTRACT
The type of this research is descriptive research that use mixed method. The
objective of this research was to know the second semester Mathematics students’
metacognitive skill in solving Mathematics problems at State University of
Medan, to know the students’ metacognitive (scaffolding) questions if given
Mathematics problems and to know the relationship of metacognitive skill with
students’ learning outcomes. This research was held in Mathematics laboratory at
State University of Medan. Subject of this research was Mathematics students in
second semester who are taking Calculus II course which consist of 40 students.
Object of this research was Mathematics students’ metacognitive skill in solving
problems. Instrument of this research was researcher itself who are guided by
metacognitive questionnaire which adapted from Metacognitive Awareness
Inventory (MAI), test which has been validated by experts and interview
guidelines. Technique of data analyzing is consisted of descriptive statistics such
as data service by table/figure, mean calculation, percentage calculation and
correlation analysis. Based on questionnaire, the percentage of students’
metacognitive skill is 73.78%. Based on test, the percentage of students’
metacognitive skill is 73.84%. It means the average of the second semester
Mathematics students’ metacognitive skill is in medium category. In addition,
based on interview got that in the medium category, students understand the
problem but technically as it determines the time, set the time and think the
achievement of goals was not so aware of and also still less in explaining the way
of the problem solving smoothly. For metacognitive (scaffolding) question got
that the strategic question is the most often to give by students in solving
problems. For all indicators of metacognitive skill got r = 0.42 which means the
correlation is medium. It means metacognitive skill has a good influential enough
toward students’ learning outcomes in this study.
Keywords: Metacognition, Metacognitive Skill, Metacognitive Scaffolding,
Problem Solving, Learning Outcomes
iv
PREFACE
I wish to take the opportunity to give thanks firstly to God Almighty for
His amazing grace, health and knowledge He gave to the author so that the author
could complete this skripsi properly.
Skripsi which entitled “Analysis of The Second Semester Mathematics
Students’ Metacognitive Skill in Solving Mathematics Problems at State
University of Medan” is submitted in partial fulfillment of the requirements for
the degree of Sarjana Pendidikan from Mathematics Department, FMIPA in State
University of Medan.
The author wish to express thanks for all supports which have been given
for completing this skripsi. Special thanks is given to Dr. Kms. M. Amin Fauzi,
M.Pd as skripsi supervisor who has provided guidance and advices in completing
this skripsi. Great thanks are also given to Prof. Dr. P. Siagian, M.Pd, Dr. Edy
Surya, M.Si, and Drs. Zul Amry, M.Si, Ph.D as skripsi examiners who have
provided some suggestions in the completion of this skripsi. Thanks also to Dr.
Asrin Lubis, M.Pd as academic supervisor and Dean of Mathematics and Natural
Sciences Faculty. The author also express thanks to Prof. Dr. Syawal Gultom,
M.Si as rector of Unimed, Dr. Iis Siti Jahro, M.Si as Coordinator of Bilingual
Program, Dr. Edy Surya, M.Si as Head of Mathematics Department, Drs. Zul
Amry, M.Si, Ph.D as Head of Mathematics Education Study Program, Drs.
Yasifati Hia, M.Si as Secretary of Mathematics Education and also for the entire
lecturer and staff of FMIPA in State University of Medan which supported in
helping author. The author express thanks also to Mathematics students of Dik C
2015 who gave contributions and supports when the research was held.
The author also would like to give most special thanks to beloved parents,
father Zainal Abidin Simanjuntak and mother Resianna Siahaan for taking care,
supporting, and always praying for the author, also sisters and the one and only
brother Glenn Rival Simanjuntak S.H and his family who always have prayed and
supported the author for the completion of this skripsi and study in Mathematics
Department. Special thanks to AKBP Johnson Sianipar/br. Simanjuntak and
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family and also sister Dr. Mariati Purnama Simanjuntak, M.Si and family who
always prayed and supported the author during study in Unimed.
The author also thanks to beloved friends, all the members of Bilingual
Mathematics Education 2012, Adi, Aisyah, Aida, Desy, Erika, Febby Nestia,
Friska E., Friska S., Bowo, Rudi, Mutik, Dila, Ima, Rani, Totok, and Windy for
every moment, support, motivation, love, laugh, and everything in finishing this
skripsi and also during study in Unimed. Thanks for all teachers, staff, students,
and friends of PPLT Unimed in SMA Negeri 2 Balige, Rani R. Simanungkalit,
Arny, Carol, Corry, Ivana, Mariana, Descey, Rohani, Ruben, Arif, and Jerry who
have made my three months was memorable. Thanks to seniors and juniors in
Mathematics Department for sharing, discussion and all other supports. Thanks
also to everyone for prayers and supports that have been given to author.
The author considered that this skripsi has imperfections. So that any
suggestions and constructive critics are needed to improve the quality of this
skripsi. The author wishes that this skripsi would be useful to improve the
knowledge of everyone who read for now and future.
Medan, June 2016
Author,
Shinta Belaginary
IDN. 4123111078
vi
TABLE OF CONTENTS
Page
Legalization Page ................................................................................................... i
Biography ............................................................................................................... ii
Abstract ................................................................................................................. iii
Preface ....................................................................................................................iv
Table of Contents ..................................................................................................vi
List of Figures ..................................................................................................... viii
List of Tables ........................................................................................................ ix
List of Appendices ................................................................................................. x
Chapter I Introduction
1.1.
Background .............................................................................................. 1
1.2.
Problem Identification .............................................................................. 5
1.3.
Problem Limitation................................................................................... 5
1.4.
Problem Formulation ................................................................................ 5
1.5.
Research Objective ................................................................................... 5
1.6.
Research Benefit ....................................................................................... 6
1.7.
Operational Definition .............................................................................. 6
Chapter II Literature Review
2.1.
Theoretical Framework ............................................................................ 7
2.1.1.
Learning Mathematics ............................................................... 7
2.1.2.
Mathematical Problems and Problem Solving .......................... 9
2.1.3.
Metacognition and Metacognitive Skill .................................. 13
2.1.4.
Theories Support Metacognition ............................................. 22
2.1.5.
Metacognitive Skill in Solving Mathematical Problems ........ 26
vii
2.1.6.
Scaffolding in Metacognition.................................................. 28
2.1.7.
Application of Integral in Finding Area .................................. 31
2.1.8.
Descriptive Research ............................................................... 32
2.2.
Relevant Research .................................................................................. 32
2.3.
Conceptual Framework .......................................................................... 33
Chapter III Research Methodology
3.1.
Setting of Research ................................................................................. 35
3.2.
Subject and Object of Research .............................................................. 35
3.2.1.
Subject of Research ................................................................. 35
3.2.2.
Object of Research .................................................................. 35
3.3.
Type and Design of Research ................................................................. 35
3.4.
Procedure of Research ............................................................................ 36
3.5.
Data Collecting Technique ..................................................................... 37
3.6.
Instrument of Research ........................................................................... 38
3.7.
Data Analysis Technique ........................................................................ 39
Chapter IV Result And Discussion
4.1.
Result ...................................................................................................... 44
4.2.
Discussion .............................................................................................. 52
Chapter V Conclusion And Suggestion
5.1.
Conclusion .............................................................................................. 69
5.2.
Suggestion .............................................................................................. 70
Bibliography ........................................................................................................ 71
viii
LIST OF FIGURES
Page
Figure 3. 1. Research Design Schema ................................................................... 36
Figure 4. 1. Figure of Student's Answer in High Category for Number 1 ............ 55
Figure 4. 2. Figure of Student's Answer in High Category for Number 2 ............ 56
Figure 4. 3. Figure of Student's Answer in High Category for Number 3 ............ 57
Figure 4. 4. Figure of Student's Answer in High Category for Number 4 ............ 58
Figure 4. 5. Figure of Student's Answer in Medium Category for Number 1 ...... 59
Figure 4. 6. Figure of Student's Answer in Medium Category for Number 2 ...... 60
Figure 4. 7. Figure of Student's Answer in Medium Category for Number 3 ...... 61
Figure 4. 8. Figure of Student's Answer in Medium Category for Number 4 ...... 62
Figure 4. 9. Figure of Student's Answer in Low Category for Number 1 ............. 63
Figure 4. 10. Figure of Student's Answer in Low Category for Number 2 ........... 64
Figure 4. 11. Figure of Student's Answer in Low Category for Number 3 ........... 65
Figure 4. 12. Figure of Student's Answer in Low Category for Number 4 ........... 66
Figure 6. 1. Figure of Researcher When Research Was Held ............................. 116
Figure 6. 2. Figure of Research in Mathematics Laboratory .............................. 116
Figure 6. 3. Figure of Lecturer Guided Researcher in Looking at Students in
Doing Test ....................................................................................... 116
ix
LIST OF TABLES
Page
Table 3. 1.
Validator Evaluation Scale .............................................................. 39
Table 3. 2.
Table List of Validator ..................................................................... 39
Table 3. 3.
Criterion of Questionnaire ............................................................... 39
Table 3. 4.
Interpretation Criterion .................................................................... 40
Table 3. 5.
Metacognitive Skill’s Indicators ...................................................... 40
Table 3. 6.
Scoring Rubric of Metacognitive Skill ............................................ 41
Table 3. 7.
Categories of Metacognitive (Scaffolding) Question ...................... 42
Table 3. 8.
Interpretation Criteria of Correlation Coefficient ............................ 43
Table 4. 1.
Table Average of The Students' Metacognitive Awareness in
Planning ........................................................................................... 44
Table 4. 2.
Table of Students' Metacognitive Awareness in Planning............... 45
Table 4. 3.
Table Average of The Students’ Metacognitive Awareness in
Monitoring ....................................................................................... 46
Table 4. 4.
Table of Students’ Metacognitive Awareness in Monitoring .......... 47
Table 4.5.
Table Average of Students' Metacognitive Awareness in
Evaluation ........................................................................................ 47
Table 4. 6.
Table of Students' Metacognitive Awareness in Evaluation ........... 48
Table 4. 7.
Table Average of Test Result .......................................................... 49
Table 4. 8.
Table Result for Category High ....................................................... 50
Table 4. 9.
Table Result for Category Medium ................................................. 50
Table 4. 10. Table Result for Category Low ....................................................... 51
Table 4. 11. Questionnaire and Test Result Overall ............................................ 51
Table 4. 12. Table Result of Correlation in Each Indicator ................................. 52
x
LIST OF APPENDICES
.Page
Appendix 1
Metacognitive Awareness Questionnaire .................................
75
Appendix 2
Essay Test .................................................................................
77
Appendix 3
Alternative Answers of Students. .............................................
81
Appendix 4
Interview Guidelines ................................................................
86
Appendix 5
Validation Sheet of Metacognitive Rubric ...............................
87
Appendix 6
Validation Sheet of Questionnaire............................................
91
Appendix 7
Validation Sheet of Essay Test .................................................
94
Appendix 8
Validation Sheet of Interview Guidelines ................................
96
Appendix 9
Table Result of Essay Test .......................................................
100
Appendix 10 Table Result of Questionnaire ..................................................
103
Appendix 11 Table Result of Metacognitive Awareness for Planning ..........
105
Appendix 12 Table Result of Metacognitive Awareness for Monitoring ......
106
Appendix 13 Table Result of Metacognitive Awareness for Evaluation .......
107
Appendix 14 Scripts of Interview ..................................................................
108
Appendix 15 The Problems of F3 Examination at A.Y. 2015/2016 ..............
111
Appendix 16 Documentation .........................................................................
116
CHAPTER I
INTRODUCTION
1.1. Background
Learning Mathematics in college has a very important role in developing
thinking skills, problem solving and independent students. The development of
metacognition in university is also one of important effort that should be done. It
is related to one of higher education’s objectives that is transform and develop
students’ ability, include to design what will do, do what planned, monitor and
evaluate what is doing and what has been done, so that they will be critics,
creative, innovative, confident, and responsible (Peraturan Pemerintah no.17 year
2010 about Pengelolaan dan Penyelenggaraan Pendidikan).
Briefly, Louca (2003) states metacognition refers to all process about
cognition, such as sensing something about one’s own thinking, thinking about
one’s thinking and responding to one’s own thinking by monitoring and
regulating it.
Metacognition is often described as multidimensional and has been used
as a general term about higher level of cognitive skills. A common definition is
“thinking about thinking”. Metacognition is one’s ability to know what he knows
and what he does not know. It is also the ability to use one’s own prior knowledge
to plan a strategy for producing information, to take necessary steps in problem
solving and to reflect on the quality of one’s thinking about a particular concern.
The concept of metacognition was first defined in the seventies by Flavell (1979).
Flavell, who is considered to be the “father of the field” and thereafter a
considerable amount of empirical and theoretical research dealing with
metacognition can be registered. It seems that metacognition is a result of research
on cognitive development, memory and reading. Many mathematics educators
have shown great interest in this area as they realize that purely cognitive analysis
of mathematical performance are inadequate for studying problem solving.
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2
According to Schoenfeld (1992), metacognition has the potential to
improve the meaningfulness in learning and creating a “culture of mathematics” in
the class that best foster metacognition. Schoenfeld believe that “cultural world of
mathematics” would lead one to think about mathematics as an integral part of
everyday life, improve students’ skills in making or doing linkages between
mathematical concepts in different contexts, and build understanding in the
environment through problem solving mathematical either alone or together. In
connection with that, one component of the learning process is a very important
mathematical problem solving. According to Schoenfeld, a mathematics education
expert, there is one particular mathematical point of view regarding the role that
problems have in the lives of those who do Mathematics. This unifying theme is
that the work of mathematicians is solving problems.
Problem solving in Mathematics is the process to find the solution to a
problem when the method is not known to a problem-solver. Then the problemsolver has to use strategic skills to select the appropriate techniques for a solution.
The problem is often not completely understood until the problem-solver has tried
and failed to arrive at a solution using different strategies. It is a series of going
forward and backward among the stages.
Metacognition can be built when students carry solving (problem solving).
During the process of problem solving, awareness of students’ cognition can be
grown as provide guidance so that students ask themselves whether understand
what is being learned or thought. Students are guided to be aware of what is
known and what is unknown and how to solve it, making planning problemsolving approach, make the stages of the solution, giving the reasons why doing
so, monitor the process of solving problems and progress toward the goal when
implementing the plan, and evaluate what has been done.
Scaffolding is defined as providing assistance to a student on an as-needed
basis, fading the assistance as the competence of the student increases. In
innovative learning arrangements students need scaffolds to support their
metacognitive activities to improve the regulation of their cognitive activities,
which in improving their achievement (Molenaar, 2011).
3
Scaffolding is the assistance given to the students to learn and solve
problems. Such assistance may include guiding questions, hints (hint),
encouragement, warning in the form of intervention, provide examples and nonexamples, as well as other measures that conditioned the students can learn
independently. Problem solving itself includes high-level thinking skills such as
visualization, association, abstraction comprehension, manipulation, reasoning,
analysis, synthesis, generalization, that from every point requires an organizing
and coordinating. Therefore, metacognition learners have an important role in
solving the problem. Especially in regulating and controlling the cognitive activity
in solving mathematical problems. Thus learning and thinking that performed by
students in solving mathematical problems become more effective. Thus, based on
the explanation above, it can be said that metacognition has a significant role in
designing (planning), monitoring (monitoring) and evaluate (evaluation) processes
of a person's cognitive learning and thinking, thus learning and thinking are done
by someone into more effective and efficient (Fauzi, 2011). In this study,
scaffolding was directed at supporting the metacognitive activities of triads.
Before conducting the study, by observing some Mathematics lecturers in
class, researcher found some of them actually have used metacognitive approach,
in their teaching to develop students’ abilities in understanding the material and
improving the learning outcomes. It can be seen that by using presentation, giving
worksheet, discussion, and many else, many lecturers often provide the
opportunity for undergraduate students to develop their mathematical abilities, to
explore, try, adapt, and change the resolution procedures, including verifying
solutions which correspond to the new situation obtained because metacognitive
approach is a sequential process that is used to control cognitive activities and
ensure that the cognitive objectives have been achieved. Therefore, even though
the lecturers have been applied the metacognitive approach, in particular in order
to encourage the undergraduate students to understand the metacognition
processes that need to be developed, the metacognitive skill of Mathematics
students at State University of Medan have not known yet.
4
Inspired by the suggestion of Kiki Dewi Rahmawati in journal Artikel
Ilmiah Mahasiswa to take the higher level of subject research about analysis
metacognition and the research by Alvanda Candrasari in Journal of Chemical
Education that found metacognitive skill with learning outcomes have strong
correlation in his research so the researcher in this study has interests to do the
research about analysis metacognition for students in university.
In the class that will be chosen as subject, the lecturer as treatment
applicator, has applied this metacognitive approach dominantly in this semester
compared with the past. It can be known by interviewing that lecturer, he always
gives some worksheet which the questions has been matched with metacognitive
indicators with or without scaffolding questions. Because of this metacognitive
approach has been applied, the researcher can suppose that the students’ learning
outcomes will be increased in that class. Based on that, the researcher would like
to know how much metacognitive skill and learning outcomes are related.
The researcher is also found that the interesting of research about
metacognition in Mathematics Department at State University for S-1 students is
still low. This can be known from repository Unimed as retrieved at
http://digilib.unimed.ac.id that amount of skripsi about metacognition, especially
in Mathematics Department is not much. The researcher in this study just found 3
skripsi about metacognition and all of that are about metacognitive approach.
Then, the researcher has an interest to do research about the metacognition in
higher education, especially in Mathematics Department at State University of
Medan.
Based on background above, researcher interested in conducting research
entitled “Analysis of The Second Semester Mathematics Students’
Metacognitive Skill in Solving Mathematics Problems at State University of
Medan”.
5
1.2. Problem Identification
Based on the background presented above, can be identified the issue is:
1. The metacognitive skill of Mathematics students have not known yet.
2. The lack of attention in the research about metacognition in Mathematics
Department at State University of Medan.
1.3. Problem Limitation
In order for specific discussion, this study is needed to be limited. This study is
focused on the second semester Mathematics students’ metacognitive skill in
solving Mathematics problems that taken from recent F3 examination of Calculus
II about application of integral in finding area at State University of Medan.
1.4. Problem Formulation
Based on background and problem identification above, can be formulated the
problems of this research are:
1. How is the second semester Mathematics students’ metacognitive skill in
solving Mathematics problems at State University of Medan?
2. How is the students’ metacognitive (scaffolding) questions if given
Mathematics problems?
3. How is the relationship of metacognitive skill with students’ learning
outcomes?
1.5. Research Objective
The objective of this research is:
1. To know the second semester Mathematics students’ metacognitive skill in
solving Mathematics problems at State University of Medan.
2. To know the students’ metacognitive (scaffolding) questions if given
Mathematics problems.
3. To know the relationship of metacognitive skill with students’ learning
outcomes.
6
1.6. Research Benefit
The benefit of this research is:
1. As the development of the theory of metacognition.
2. As a basis for improving the quality of learning in higher education, in
particular in order to encourage the undergraduate students to understand
the metacognition processes that need to be developed.
3. The Mathematics students’ metacognitive skill is expected to be known
and it is used to learning reference for lecturers and all further research
soon.
1.7. Operational Definition
In order to avoid misconception about important terms contained in this research,
the operational definitions will be noted as:
1. Metacognitive skill is people’s extraordinary ability to evaluate and
control their cognitive processes.
2. Scaffolding is the assistance given to the students to learn and solve
problems.
3. Metacognitive approach is a sequential process that is used to control
cognitive activities and ensure that the cognitive objectives have been
achieved.
4. Mathematics problem is a problem that is amenable to being represented,
analyzed, and possibly solved with the methods of Mathematics.
5. Problem solving is the process to find the solution to a problem when the
method is not known to a problem-solver.
CHAPTER V
CONCLUSION AND SUGGESTION
1.1.
Conclusion
Data collection has been done by using test, questionnaire and interview.
Questionnaire is the efficient data collection technique if the researcher surely
know the variable that will be measured from respondents. The test is used to
know metacognitive skill score of students. This test is also used to know the
students’ metacognitive scaffolding questions toward Mathematics problems. And
interview in this study aims to reveal the profile of students’ metacognition.
So, based on data analysis from that questionnaire, test and interview and also
based on this research result, can be concluded generally that:
1. In the high category, students have used their metacognitive skill well. They
still less aware of planning but aware enough in evaluation. At the medium
category, student also have used their metacognitive skill but they still less
aware of planning and evaluation. While in the low category, students have
not used their metacognitive well. They still less aware in each indicator of
metacognitive skill. That is why they can not re explain their answer when
doing test. In this study, metacognitive skill of Mathematics students in
second semester is relative medium with average score of questionnaire is
73.78% and test is 73.84%.
2. Students’ metacognitive (scaffolding) questions that have been given can be
concluded as strategic question. It means that strategic question is the most
often to ask in helping them to do the test.
3. Metacognitive skill and learning outcomes are related which the correlation
value is 0.42. It means the correlation is good enough or can be said that
metacognitive skill is influential enough toward their learning outcomes in this
study.
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70
1.2.
Suggestion
In this research, got that in low category medium, student does not know to
explain more about the answer when doing test. Student even do not remember
what she wrote. Student also still less aware of planning, monitoring and
evaluation in solving problems. Researcher supposed that some of that result
caused by the time interval between test and interview is long enough and they do
not keep their test’ answer sheet when interviewed so that they can not remember
what they wrote when doing test. Besides that, because this research is descriptive
research so this research result can not be applied generally by another
researchers. And then this research is weak because it was not used any media
technically. So based on those descriptions, researcher needs to give some
suggestions, they are:
1. For educator, needed to give more exercises like worksheet, discussion, or
anything to improve students’ metacognitive skill.
2. For students, they are hoped to develop their metacognitive skill by
practicing so that students not just learn but also understand what they
have learned.
3. For next researchers, they are hoped to give more participation in
metacognition research in other research design so that the research result
can be used and applied generally, to care more about research timing and
instruments and to care more about media used in research.
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METACOGNITIVE SKILL IN SOLVING MATHEMATICS
PROBLEMS AT STATE UNIVERSITY OF MEDAN
By:
Shinta Belaginary
IDN. 4123111078
Bilingual Mathematics Education Study Program
SKRIPSI
Submitted in Partial Fulfillment of The Requirements for The Degree of
Sarjana Pendidikan
FACULTY OF MATHEMATICS AND NATURAL SCIENCES
STATE UNIVERSITY OF MEDAN
MEDAN
2016
ii
BIOGRAPHY
The
author,
ShintaBelaginary,
actually
has
a
fullnameShinta
Bella
GinarySimanjuntak, was born in Jakarta, January 14th 1995. She is the sixth
children from ZainalAbidinSimanjuntak, S.E. and ResiannaSiahaan. In 2000, the
author started her study at SD Sultan AgungPematangsiantar and graduated in
2006. The author continued her study to SMP Sultan AgungPematangsiantar and
graduated in 2009. The author also continued her study to SMAN 2
Pematangsiantar and graduated in 2012. In 2012, she continued her study to
UniversitasNegeri Medan (Unimed) as a student in Mathematics Education Study
Program, Bilingual Class. Finally, the author completed her study of
undergraduated (S1) from Unimed in 2016.
ii
iii
ANALYSIS OF THE SECOND SEMESTER MATHEMATICS STUDENTS’
METACOGNITIVE SKILL IN SOLVING MATHEMATICS
PROBLEMS AT STATE UNIVERSITY OF MEDAN
Shinta Belaginary1, Amin Fauzi2
1.
Faculty of Mathematics and natural Sciences, State University of Medan
email: 14shintabellags@gmail.com
2.
Faculty of Mathematics and Natural Science, State University of Medan
email: amin_fauzi29@yahoo.com
ABSTRACT
The type of this research is descriptive research that use mixed method. The
objective of this research was to know the second semester Mathematics students’
metacognitive skill in solving Mathematics problems at State University of
Medan, to know the students’ metacognitive (scaffolding) questions if given
Mathematics problems and to know the relationship of metacognitive skill with
students’ learning outcomes. This research was held in Mathematics laboratory at
State University of Medan. Subject of this research was Mathematics students in
second semester who are taking Calculus II course which consist of 40 students.
Object of this research was Mathematics students’ metacognitive skill in solving
problems. Instrument of this research was researcher itself who are guided by
metacognitive questionnaire which adapted from Metacognitive Awareness
Inventory (MAI), test which has been validated by experts and interview
guidelines. Technique of data analyzing is consisted of descriptive statistics such
as data service by table/figure, mean calculation, percentage calculation and
correlation analysis. Based on questionnaire, the percentage of students’
metacognitive skill is 73.78%. Based on test, the percentage of students’
metacognitive skill is 73.84%. It means the average of the second semester
Mathematics students’ metacognitive skill is in medium category. In addition,
based on interview got that in the medium category, students understand the
problem but technically as it determines the time, set the time and think the
achievement of goals was not so aware of and also still less in explaining the way
of the problem solving smoothly. For metacognitive (scaffolding) question got
that the strategic question is the most often to give by students in solving
problems. For all indicators of metacognitive skill got r = 0.42 which means the
correlation is medium. It means metacognitive skill has a good influential enough
toward students’ learning outcomes in this study.
Keywords: Metacognition, Metacognitive Skill, Metacognitive Scaffolding,
Problem Solving, Learning Outcomes
iv
PREFACE
I wish to take the opportunity to give thanks firstly to God Almighty for
His amazing grace, health and knowledge He gave to the author so that the author
could complete this skripsi properly.
Skripsi which entitled “Analysis of The Second Semester Mathematics
Students’ Metacognitive Skill in Solving Mathematics Problems at State
University of Medan” is submitted in partial fulfillment of the requirements for
the degree of Sarjana Pendidikan from Mathematics Department, FMIPA in State
University of Medan.
The author wish to express thanks for all supports which have been given
for completing this skripsi. Special thanks is given to Dr. Kms. M. Amin Fauzi,
M.Pd as skripsi supervisor who has provided guidance and advices in completing
this skripsi. Great thanks are also given to Prof. Dr. P. Siagian, M.Pd, Dr. Edy
Surya, M.Si, and Drs. Zul Amry, M.Si, Ph.D as skripsi examiners who have
provided some suggestions in the completion of this skripsi. Thanks also to Dr.
Asrin Lubis, M.Pd as academic supervisor and Dean of Mathematics and Natural
Sciences Faculty. The author also express thanks to Prof. Dr. Syawal Gultom,
M.Si as rector of Unimed, Dr. Iis Siti Jahro, M.Si as Coordinator of Bilingual
Program, Dr. Edy Surya, M.Si as Head of Mathematics Department, Drs. Zul
Amry, M.Si, Ph.D as Head of Mathematics Education Study Program, Drs.
Yasifati Hia, M.Si as Secretary of Mathematics Education and also for the entire
lecturer and staff of FMIPA in State University of Medan which supported in
helping author. The author express thanks also to Mathematics students of Dik C
2015 who gave contributions and supports when the research was held.
The author also would like to give most special thanks to beloved parents,
father Zainal Abidin Simanjuntak and mother Resianna Siahaan for taking care,
supporting, and always praying for the author, also sisters and the one and only
brother Glenn Rival Simanjuntak S.H and his family who always have prayed and
supported the author for the completion of this skripsi and study in Mathematics
Department. Special thanks to AKBP Johnson Sianipar/br. Simanjuntak and
v
family and also sister Dr. Mariati Purnama Simanjuntak, M.Si and family who
always prayed and supported the author during study in Unimed.
The author also thanks to beloved friends, all the members of Bilingual
Mathematics Education 2012, Adi, Aisyah, Aida, Desy, Erika, Febby Nestia,
Friska E., Friska S., Bowo, Rudi, Mutik, Dila, Ima, Rani, Totok, and Windy for
every moment, support, motivation, love, laugh, and everything in finishing this
skripsi and also during study in Unimed. Thanks for all teachers, staff, students,
and friends of PPLT Unimed in SMA Negeri 2 Balige, Rani R. Simanungkalit,
Arny, Carol, Corry, Ivana, Mariana, Descey, Rohani, Ruben, Arif, and Jerry who
have made my three months was memorable. Thanks to seniors and juniors in
Mathematics Department for sharing, discussion and all other supports. Thanks
also to everyone for prayers and supports that have been given to author.
The author considered that this skripsi has imperfections. So that any
suggestions and constructive critics are needed to improve the quality of this
skripsi. The author wishes that this skripsi would be useful to improve the
knowledge of everyone who read for now and future.
Medan, June 2016
Author,
Shinta Belaginary
IDN. 4123111078
vi
TABLE OF CONTENTS
Page
Legalization Page ................................................................................................... i
Biography ............................................................................................................... ii
Abstract ................................................................................................................. iii
Preface ....................................................................................................................iv
Table of Contents ..................................................................................................vi
List of Figures ..................................................................................................... viii
List of Tables ........................................................................................................ ix
List of Appendices ................................................................................................. x
Chapter I Introduction
1.1.
Background .............................................................................................. 1
1.2.
Problem Identification .............................................................................. 5
1.3.
Problem Limitation................................................................................... 5
1.4.
Problem Formulation ................................................................................ 5
1.5.
Research Objective ................................................................................... 5
1.6.
Research Benefit ....................................................................................... 6
1.7.
Operational Definition .............................................................................. 6
Chapter II Literature Review
2.1.
Theoretical Framework ............................................................................ 7
2.1.1.
Learning Mathematics ............................................................... 7
2.1.2.
Mathematical Problems and Problem Solving .......................... 9
2.1.3.
Metacognition and Metacognitive Skill .................................. 13
2.1.4.
Theories Support Metacognition ............................................. 22
2.1.5.
Metacognitive Skill in Solving Mathematical Problems ........ 26
vii
2.1.6.
Scaffolding in Metacognition.................................................. 28
2.1.7.
Application of Integral in Finding Area .................................. 31
2.1.8.
Descriptive Research ............................................................... 32
2.2.
Relevant Research .................................................................................. 32
2.3.
Conceptual Framework .......................................................................... 33
Chapter III Research Methodology
3.1.
Setting of Research ................................................................................. 35
3.2.
Subject and Object of Research .............................................................. 35
3.2.1.
Subject of Research ................................................................. 35
3.2.2.
Object of Research .................................................................. 35
3.3.
Type and Design of Research ................................................................. 35
3.4.
Procedure of Research ............................................................................ 36
3.5.
Data Collecting Technique ..................................................................... 37
3.6.
Instrument of Research ........................................................................... 38
3.7.
Data Analysis Technique ........................................................................ 39
Chapter IV Result And Discussion
4.1.
Result ...................................................................................................... 44
4.2.
Discussion .............................................................................................. 52
Chapter V Conclusion And Suggestion
5.1.
Conclusion .............................................................................................. 69
5.2.
Suggestion .............................................................................................. 70
Bibliography ........................................................................................................ 71
viii
LIST OF FIGURES
Page
Figure 3. 1. Research Design Schema ................................................................... 36
Figure 4. 1. Figure of Student's Answer in High Category for Number 1 ............ 55
Figure 4. 2. Figure of Student's Answer in High Category for Number 2 ............ 56
Figure 4. 3. Figure of Student's Answer in High Category for Number 3 ............ 57
Figure 4. 4. Figure of Student's Answer in High Category for Number 4 ............ 58
Figure 4. 5. Figure of Student's Answer in Medium Category for Number 1 ...... 59
Figure 4. 6. Figure of Student's Answer in Medium Category for Number 2 ...... 60
Figure 4. 7. Figure of Student's Answer in Medium Category for Number 3 ...... 61
Figure 4. 8. Figure of Student's Answer in Medium Category for Number 4 ...... 62
Figure 4. 9. Figure of Student's Answer in Low Category for Number 1 ............. 63
Figure 4. 10. Figure of Student's Answer in Low Category for Number 2 ........... 64
Figure 4. 11. Figure of Student's Answer in Low Category for Number 3 ........... 65
Figure 4. 12. Figure of Student's Answer in Low Category for Number 4 ........... 66
Figure 6. 1. Figure of Researcher When Research Was Held ............................. 116
Figure 6. 2. Figure of Research in Mathematics Laboratory .............................. 116
Figure 6. 3. Figure of Lecturer Guided Researcher in Looking at Students in
Doing Test ....................................................................................... 116
ix
LIST OF TABLES
Page
Table 3. 1.
Validator Evaluation Scale .............................................................. 39
Table 3. 2.
Table List of Validator ..................................................................... 39
Table 3. 3.
Criterion of Questionnaire ............................................................... 39
Table 3. 4.
Interpretation Criterion .................................................................... 40
Table 3. 5.
Metacognitive Skill’s Indicators ...................................................... 40
Table 3. 6.
Scoring Rubric of Metacognitive Skill ............................................ 41
Table 3. 7.
Categories of Metacognitive (Scaffolding) Question ...................... 42
Table 3. 8.
Interpretation Criteria of Correlation Coefficient ............................ 43
Table 4. 1.
Table Average of The Students' Metacognitive Awareness in
Planning ........................................................................................... 44
Table 4. 2.
Table of Students' Metacognitive Awareness in Planning............... 45
Table 4. 3.
Table Average of The Students’ Metacognitive Awareness in
Monitoring ....................................................................................... 46
Table 4. 4.
Table of Students’ Metacognitive Awareness in Monitoring .......... 47
Table 4.5.
Table Average of Students' Metacognitive Awareness in
Evaluation ........................................................................................ 47
Table 4. 6.
Table of Students' Metacognitive Awareness in Evaluation ........... 48
Table 4. 7.
Table Average of Test Result .......................................................... 49
Table 4. 8.
Table Result for Category High ....................................................... 50
Table 4. 9.
Table Result for Category Medium ................................................. 50
Table 4. 10. Table Result for Category Low ....................................................... 51
Table 4. 11. Questionnaire and Test Result Overall ............................................ 51
Table 4. 12. Table Result of Correlation in Each Indicator ................................. 52
x
LIST OF APPENDICES
.Page
Appendix 1
Metacognitive Awareness Questionnaire .................................
75
Appendix 2
Essay Test .................................................................................
77
Appendix 3
Alternative Answers of Students. .............................................
81
Appendix 4
Interview Guidelines ................................................................
86
Appendix 5
Validation Sheet of Metacognitive Rubric ...............................
87
Appendix 6
Validation Sheet of Questionnaire............................................
91
Appendix 7
Validation Sheet of Essay Test .................................................
94
Appendix 8
Validation Sheet of Interview Guidelines ................................
96
Appendix 9
Table Result of Essay Test .......................................................
100
Appendix 10 Table Result of Questionnaire ..................................................
103
Appendix 11 Table Result of Metacognitive Awareness for Planning ..........
105
Appendix 12 Table Result of Metacognitive Awareness for Monitoring ......
106
Appendix 13 Table Result of Metacognitive Awareness for Evaluation .......
107
Appendix 14 Scripts of Interview ..................................................................
108
Appendix 15 The Problems of F3 Examination at A.Y. 2015/2016 ..............
111
Appendix 16 Documentation .........................................................................
116
CHAPTER I
INTRODUCTION
1.1. Background
Learning Mathematics in college has a very important role in developing
thinking skills, problem solving and independent students. The development of
metacognition in university is also one of important effort that should be done. It
is related to one of higher education’s objectives that is transform and develop
students’ ability, include to design what will do, do what planned, monitor and
evaluate what is doing and what has been done, so that they will be critics,
creative, innovative, confident, and responsible (Peraturan Pemerintah no.17 year
2010 about Pengelolaan dan Penyelenggaraan Pendidikan).
Briefly, Louca (2003) states metacognition refers to all process about
cognition, such as sensing something about one’s own thinking, thinking about
one’s thinking and responding to one’s own thinking by monitoring and
regulating it.
Metacognition is often described as multidimensional and has been used
as a general term about higher level of cognitive skills. A common definition is
“thinking about thinking”. Metacognition is one’s ability to know what he knows
and what he does not know. It is also the ability to use one’s own prior knowledge
to plan a strategy for producing information, to take necessary steps in problem
solving and to reflect on the quality of one’s thinking about a particular concern.
The concept of metacognition was first defined in the seventies by Flavell (1979).
Flavell, who is considered to be the “father of the field” and thereafter a
considerable amount of empirical and theoretical research dealing with
metacognition can be registered. It seems that metacognition is a result of research
on cognitive development, memory and reading. Many mathematics educators
have shown great interest in this area as they realize that purely cognitive analysis
of mathematical performance are inadequate for studying problem solving.
1
2
According to Schoenfeld (1992), metacognition has the potential to
improve the meaningfulness in learning and creating a “culture of mathematics” in
the class that best foster metacognition. Schoenfeld believe that “cultural world of
mathematics” would lead one to think about mathematics as an integral part of
everyday life, improve students’ skills in making or doing linkages between
mathematical concepts in different contexts, and build understanding in the
environment through problem solving mathematical either alone or together. In
connection with that, one component of the learning process is a very important
mathematical problem solving. According to Schoenfeld, a mathematics education
expert, there is one particular mathematical point of view regarding the role that
problems have in the lives of those who do Mathematics. This unifying theme is
that the work of mathematicians is solving problems.
Problem solving in Mathematics is the process to find the solution to a
problem when the method is not known to a problem-solver. Then the problemsolver has to use strategic skills to select the appropriate techniques for a solution.
The problem is often not completely understood until the problem-solver has tried
and failed to arrive at a solution using different strategies. It is a series of going
forward and backward among the stages.
Metacognition can be built when students carry solving (problem solving).
During the process of problem solving, awareness of students’ cognition can be
grown as provide guidance so that students ask themselves whether understand
what is being learned or thought. Students are guided to be aware of what is
known and what is unknown and how to solve it, making planning problemsolving approach, make the stages of the solution, giving the reasons why doing
so, monitor the process of solving problems and progress toward the goal when
implementing the plan, and evaluate what has been done.
Scaffolding is defined as providing assistance to a student on an as-needed
basis, fading the assistance as the competence of the student increases. In
innovative learning arrangements students need scaffolds to support their
metacognitive activities to improve the regulation of their cognitive activities,
which in improving their achievement (Molenaar, 2011).
3
Scaffolding is the assistance given to the students to learn and solve
problems. Such assistance may include guiding questions, hints (hint),
encouragement, warning in the form of intervention, provide examples and nonexamples, as well as other measures that conditioned the students can learn
independently. Problem solving itself includes high-level thinking skills such as
visualization, association, abstraction comprehension, manipulation, reasoning,
analysis, synthesis, generalization, that from every point requires an organizing
and coordinating. Therefore, metacognition learners have an important role in
solving the problem. Especially in regulating and controlling the cognitive activity
in solving mathematical problems. Thus learning and thinking that performed by
students in solving mathematical problems become more effective. Thus, based on
the explanation above, it can be said that metacognition has a significant role in
designing (planning), monitoring (monitoring) and evaluate (evaluation) processes
of a person's cognitive learning and thinking, thus learning and thinking are done
by someone into more effective and efficient (Fauzi, 2011). In this study,
scaffolding was directed at supporting the metacognitive activities of triads.
Before conducting the study, by observing some Mathematics lecturers in
class, researcher found some of them actually have used metacognitive approach,
in their teaching to develop students’ abilities in understanding the material and
improving the learning outcomes. It can be seen that by using presentation, giving
worksheet, discussion, and many else, many lecturers often provide the
opportunity for undergraduate students to develop their mathematical abilities, to
explore, try, adapt, and change the resolution procedures, including verifying
solutions which correspond to the new situation obtained because metacognitive
approach is a sequential process that is used to control cognitive activities and
ensure that the cognitive objectives have been achieved. Therefore, even though
the lecturers have been applied the metacognitive approach, in particular in order
to encourage the undergraduate students to understand the metacognition
processes that need to be developed, the metacognitive skill of Mathematics
students at State University of Medan have not known yet.
4
Inspired by the suggestion of Kiki Dewi Rahmawati in journal Artikel
Ilmiah Mahasiswa to take the higher level of subject research about analysis
metacognition and the research by Alvanda Candrasari in Journal of Chemical
Education that found metacognitive skill with learning outcomes have strong
correlation in his research so the researcher in this study has interests to do the
research about analysis metacognition for students in university.
In the class that will be chosen as subject, the lecturer as treatment
applicator, has applied this metacognitive approach dominantly in this semester
compared with the past. It can be known by interviewing that lecturer, he always
gives some worksheet which the questions has been matched with metacognitive
indicators with or without scaffolding questions. Because of this metacognitive
approach has been applied, the researcher can suppose that the students’ learning
outcomes will be increased in that class. Based on that, the researcher would like
to know how much metacognitive skill and learning outcomes are related.
The researcher is also found that the interesting of research about
metacognition in Mathematics Department at State University for S-1 students is
still low. This can be known from repository Unimed as retrieved at
http://digilib.unimed.ac.id that amount of skripsi about metacognition, especially
in Mathematics Department is not much. The researcher in this study just found 3
skripsi about metacognition and all of that are about metacognitive approach.
Then, the researcher has an interest to do research about the metacognition in
higher education, especially in Mathematics Department at State University of
Medan.
Based on background above, researcher interested in conducting research
entitled “Analysis of The Second Semester Mathematics Students’
Metacognitive Skill in Solving Mathematics Problems at State University of
Medan”.
5
1.2. Problem Identification
Based on the background presented above, can be identified the issue is:
1. The metacognitive skill of Mathematics students have not known yet.
2. The lack of attention in the research about metacognition in Mathematics
Department at State University of Medan.
1.3. Problem Limitation
In order for specific discussion, this study is needed to be limited. This study is
focused on the second semester Mathematics students’ metacognitive skill in
solving Mathematics problems that taken from recent F3 examination of Calculus
II about application of integral in finding area at State University of Medan.
1.4. Problem Formulation
Based on background and problem identification above, can be formulated the
problems of this research are:
1. How is the second semester Mathematics students’ metacognitive skill in
solving Mathematics problems at State University of Medan?
2. How is the students’ metacognitive (scaffolding) questions if given
Mathematics problems?
3. How is the relationship of metacognitive skill with students’ learning
outcomes?
1.5. Research Objective
The objective of this research is:
1. To know the second semester Mathematics students’ metacognitive skill in
solving Mathematics problems at State University of Medan.
2. To know the students’ metacognitive (scaffolding) questions if given
Mathematics problems.
3. To know the relationship of metacognitive skill with students’ learning
outcomes.
6
1.6. Research Benefit
The benefit of this research is:
1. As the development of the theory of metacognition.
2. As a basis for improving the quality of learning in higher education, in
particular in order to encourage the undergraduate students to understand
the metacognition processes that need to be developed.
3. The Mathematics students’ metacognitive skill is expected to be known
and it is used to learning reference for lecturers and all further research
soon.
1.7. Operational Definition
In order to avoid misconception about important terms contained in this research,
the operational definitions will be noted as:
1. Metacognitive skill is people’s extraordinary ability to evaluate and
control their cognitive processes.
2. Scaffolding is the assistance given to the students to learn and solve
problems.
3. Metacognitive approach is a sequential process that is used to control
cognitive activities and ensure that the cognitive objectives have been
achieved.
4. Mathematics problem is a problem that is amenable to being represented,
analyzed, and possibly solved with the methods of Mathematics.
5. Problem solving is the process to find the solution to a problem when the
method is not known to a problem-solver.
CHAPTER V
CONCLUSION AND SUGGESTION
1.1.
Conclusion
Data collection has been done by using test, questionnaire and interview.
Questionnaire is the efficient data collection technique if the researcher surely
know the variable that will be measured from respondents. The test is used to
know metacognitive skill score of students. This test is also used to know the
students’ metacognitive scaffolding questions toward Mathematics problems. And
interview in this study aims to reveal the profile of students’ metacognition.
So, based on data analysis from that questionnaire, test and interview and also
based on this research result, can be concluded generally that:
1. In the high category, students have used their metacognitive skill well. They
still less aware of planning but aware enough in evaluation. At the medium
category, student also have used their metacognitive skill but they still less
aware of planning and evaluation. While in the low category, students have
not used their metacognitive well. They still less aware in each indicator of
metacognitive skill. That is why they can not re explain their answer when
doing test. In this study, metacognitive skill of Mathematics students in
second semester is relative medium with average score of questionnaire is
73.78% and test is 73.84%.
2. Students’ metacognitive (scaffolding) questions that have been given can be
concluded as strategic question. It means that strategic question is the most
often to ask in helping them to do the test.
3. Metacognitive skill and learning outcomes are related which the correlation
value is 0.42. It means the correlation is good enough or can be said that
metacognitive skill is influential enough toward their learning outcomes in this
study.
69
70
1.2.
Suggestion
In this research, got that in low category medium, student does not know to
explain more about the answer when doing test. Student even do not remember
what she wrote. Student also still less aware of planning, monitoring and
evaluation in solving problems. Researcher supposed that some of that result
caused by the time interval between test and interview is long enough and they do
not keep their test’ answer sheet when interviewed so that they can not remember
what they wrote when doing test. Besides that, because this research is descriptive
research so this research result can not be applied generally by another
researchers. And then this research is weak because it was not used any media
technically. So based on those descriptions, researcher needs to give some
suggestions, they are:
1. For educator, needed to give more exercises like worksheet, discussion, or
anything to improve students’ metacognitive skill.
2. For students, they are hoped to develop their metacognitive skill by
practicing so that students not just learn but also understand what they
have learned.
3. For next researchers, they are hoped to give more participation in
metacognition research in other research design so that the research result
can be used and applied generally, to care more about research timing and
instruments and to care more about media used in research.
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