**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 **

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**BIOGRAPHY**

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**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.

**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.

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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,

**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

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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

**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

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**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

**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

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**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

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 solver. Then the problem-solver 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 problem-solving 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.

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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 non-examples, 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.

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.

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**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.

**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.

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**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.

**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.

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