THE IDENTIFICATION OF MATHEMATICS STUDENTS’ CHARACTERISTIC AND METACOGNITIVE LEVEL IN MATHEMATICAL PROBLEM SOLVING AT SECOND SEMESTER STATE UNIVERSITY OF MEDAN.
THE IDENTIFICATION OF MATHEMATICS STUDENTS’ CHARACTERISTIC AND METACOGNITIVE LEVEL
IN MATHEMATICAL PROBLEM SOLVING AT SECOND SEMESTER STATE
UNIVERSITY OF MEDAN
By:
Aisyah Tohar Nasution IDN 4123312002
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
(2)
(3)
iii
THE IDENTIFICATION OF MATHEMATICS STUDENTS’ CHARACTERISTIC AND METACOGNITIVE LEVEL
IN MATHEMATICAL PROBLEM SOLVING AT SECOND SEMESTER STATE
UNIVERSITY OF MEDAN
Aisyah ToharNasution (ID.4123312002)
ABSTRACT
Metacognition is needed in solving mathematics problem. It is defined as the knowledge, awareness, and control of one’s thinking process. In solving mathematics problem, not all students are able to use their metacognitive that are able to process the thinking. The objective of this research was to describee Mathematics Students characteristics and level of metacognition in mathematical problem solving and to know students’ scaffolding question metacognitive in answer the question of problem solving at second semester State University of Medan. This research use qualitative data which is described to get the students’ metacognitive representation in mathematical problems. That is why this research is included in descriptive qualitative research.
Held in second semesters students’ of Mathematics regular class C 2015 State University of Medan. The subject in this research is the whole mathematics students’ who’s taking Calculus II at State University of Medan. The students’ given test then grouped into three groups that us high level ability, medium and low ability. Every group is taken two subjects to have interview to get more credible data. Then, the data is analyzed to get conclusion from each group. The result of the research is obtained that the high level ability students has reflective cognitive use. Medium level ability students have strategic metacognitive use. Low level ability students have aware use and tacit use.
Scaffolding questions given in the test should be help students in completing the problem. From the result of this research is hoped will be source of information and input material for mathematics lecturer, researchers, and all side which needed especially in Faculty of Mathematics and Natural Science State University of Medan’s environment.
Keywords : metacognitive, metacognitive level, problem solving, mathematics problem, scaffolding.
(4)
iv
iv
ACKNOWLEDGEMENT
This thesis could not be accomplished without Allah SWT grace, love, guidance, suggestions and comments from lecturers and several people.
Praise to Allah SWT for His amazing grace, His wonderful love, the strength and the health which have been given so the author could finish this thesis. The author’s special sincerest thanks are expressed to:
1. Mr. Dr.Kms M. Amin Fauzi, M.Pd as his thesis supervisor for his advice, encouragements, suggestions and knowledge that have been contributed to help the author in compiling this thesis so that this thesis could be finished. May Allah SWT always bless him and his family now and forever.
2. Mr. Dr. Edi Surya, M.Si, Drs. Zul Amry, M.Si, Ph.D, Denny Haris, S.Si, M.Pd as thesis examiners who have provided builded suggestion and revision in the completion of this thesis .
3. Mr. Prof. Dr. Bornok Sinaga, M.Pd as academic supervisor and also for all lecturers in FMIPA Unimed.
4. Mr. Prof. Dr. Syawal Gultom, M.Pd as the Rector of State University of Medan, Mr. Dr. Asrin Lubis, M.Pd as the Dean of Faculty of Mathematics and Natural Sciences, Mr. Dr. Edy Surya, M.Si as the Head of Mathematics Department, Mr. Drs. Yasifati Hia, M.Si as the Secretary of Mathematics Department and Mrs. Dr. Iis Siti Jahro, M.Si as the Coordinator of Bilingual Program for all the valuable guidance and contribution to complete this thesis. 5. All the lectures of Mathematics Department and administrative staff at the
faculty, department and bilingual program for their guidance and administrative assistance given.
The author also thanks for author’s best friends PPLT Unimed in SMA N 1 Plus Matauli Pandan especially Evi, Lady, Witaloka, Rina, Putriwita, Findi, Cici and Aldo.
And for my besties Angga Mahardika Hadibroto, Fitria Amanda, Reza Septiani Sinaga, and Fitri Hidayah Hasibuan that give me courage and support my thesis until complete.
(5)
v
v
Then this thesis was compiled from the togetherness, strength, spirit, and endless friendship ever given by my special best friends Aida, Erika, Febby, Mutiara, Rahima, Shinta and Windy. Also big thanks for family of bilmath 2012 : Adi, Desy, Friska Elvita, Friska Simbolon, Bowok, Rudi, Dila, Rani and Totok.
And the author also thanks to authors’ roomates, Arimbi,Aqlia and Silvia for togetherness, happiness,sadness,hardship for this last four years.
And the last, this thesis can’t be compiled well without the everlasting love and pray from author’s beloved parents, Safri Tohar Nasution and Jawadah Syarief, also for authors’s beloved twin brother and sister Kurniawan Tohar Nasution and Rahma Yanti Tohar Nasution, and for my lovely young brother Siarruddin Tohar Nasution and for their support, motivation, material and pray so that author can face the problem during his academic year at the university.
The author should give a big effort to prepare this thesis, and the author knows that this thesis has so many weaknesses. The author needs some suggestions to make it better. At last, may this thesis can be helpful and improve our knowledge.
Medan, August 2016 The author,
Aisyah Tohar Nasution 4123312002
(6)
vi
TABLE OF CONTENTS
Pages
Ratification Sheet i
Biography ii
Abstract iii
Acknowledgment iv
Table of Contents vi
List of Tables ix
List of Figures x
List of Appendices xii
CHAPTER I INTRODUCTION 1
1.1. Background 1
1.2. Problem Identification 5
1.3. Problem Limitation 5
1.4. Problem Formulation 6
1.5. Research Objective 6
1.6. Research Benefit 6
1.7. Operational Definition 6
CHAPTER II RELATED LITERATURE 8
2.1. The Theoretical Framework 8
2.1.1. Defenition of Metacognitive 8 2.1.2. Component of Metacognitive 10
2.1.3 The Metacognitive Level 15
2.1.4. Students’ Characteristic 16
2.1.5. Mathematical Problem Solving 18 2.1.6. Metacognitive in Mathematical Problem Solving 21
2.2 Scaffolding Theory 23
2.3 Qualitative Approach 24
(7)
vii
2.4 Material Research 26
2.4.1 Derivative 27
2.4.2 Mind Mapping 30
2.4.3 Introduction 31
2.4.4 The Area between A Curve and The x-axis 31
2.5 Relevant Research 37
2.6 Conceptual Framework 38
CHAPTER III RESEARCH METHODOLOGY 39
3.1. Approach and Type of Research 40
3.2. Time and Location Research 41
3.3. Subject and Object Research 41
3.3.1 Subject of Research 41
3.3.2 Object of Research 41
3.4. Type and Design of Research 42
3.5. Procedure of Research 42
3.6. Data Collection Technique 45
3.7. Instrument Research 46
3.7.1 Initial Test 47
3.7.2 Test 47
3.8. Data Analysis 48
3.9. Validity and Reliability 49
CHAPTER IV RESULT AND DISCUSSION 50
4. 1 Result 50
4. 2 Discussion of Result 51
CHAPTER V CONCLUSION AND SUGGESTION 105
5. 1 Conclusion 105
5. 2 Suggestion 106
REFFERENCES 107
(8)
viii
LIST OF TABLES
Pages
Table 2.1. Metacognitive Level 15
Table 3.1. Rubric Problem Solving 47
Table 4.1. Result of Mathematical problem Solving 50 Table 4.2. Categorizing of Mathematical Problem Solving 51
(9)
ix
LIST OF FIGURES
Pages Figure 1.1 Student 1 Answer the Initial Test no 3 4 Figure 1.2 Student 1 Answer the Initial Test no 3 4 Figure 2.1 Typology of metacognitive Components 22
Figure 2.2 Mind Mapping 30
Figure 2.3 Graph 1 31
Figure 2.4 Graph 2 35
Figure 2.5 Graph 3 36
Figure 3.1 Prosedure of Research 44
Figure 3.2 Data Collection Technique 46 Figure 4.1 Worksheet S1 Problem 1 52 Figure 4.2 Worksheet S1 Problem 2 54 Figure 4.3 Worksheet S1 Problem 3 56 Figure 4.4 Worksheet S1 Problem 4 58 Figure 4.5 Worksheet S2 Problem 1 60 Figure 4.6.a Worksheet S2 Problem 2 62 Figure 4.6.b Worksheet S2 Problem 2 63 Figure 4.7.a Worksheet S2 Problem 3 65 Figure 4.7.b Worksheet S2 Problem 3 66 Figure 4.8 Worksheet S2 Problem 4 68 Figure 4.9 Worksheet S3 Problem 1 70
(10)
x
Figure 4.10 Worksheet S3 Problem 2 72 Figure 4.11 Worksheet S3 Problem 3 74 Figure 4.12 Worksheet S3 Problem 4 76 Figure 4.13.a Worksheet S4 Problem 1 78 Figure 4.13.b Worksheet S4 Problem 1 79 Figure 4.14 Worksheet S4 Problem 2 81 Figure 4.15.a Worksheet S4 Problem 3 83 Figure 4.15.b Worksheet S4 Problem 3 84 Figure 4.16.a Worksheet S4 Problem 4 86 Figure 4.16.b Worksheet S4 Problem 4 87 Figure 4.17 Worksheet S5 Problem 1 89 Figure 4.18 Worksheet S5 Problem 2 91 Figure 4.19 Worksheet S5 Problem 3 93 Figure 4.20 Worksheet S5 Problem 4 95 Figure 4.21 Worksheet S6 Problem 1 97 Figure 4.22 Worksheet S6 Problem 2 99 Figure 4.23 Worksheet S6 Problem 3 101 Figure 4.24 Worksheet S6 Problem 4 103
(11)
xii
APPENDICES LIST
Page
Appendix 1. Initial Test 110
Appendix 2. Alternative Solution of Initial Test 111
Appendix 3. Blueprint of Test 112
Appendix 4. Essay Test 113
Appendix 5. Alternative Solution of Test 117
Appendix 6. Rubric 121
Appendix 7. Guidances of Scoring Problem Solving Test 130 Appendix 8. Rubric of Metacognitive Level 139 Appendix 9. Interview Guidelines 142
Appendix 10. Script of Interview 144
Appendix 11. Validation Sheet 151
Appendix 12. Formative Test 3 2015/2016 159
(12)
1
CHAPTER 1 INTRODUCTION
1.1 Background
Mathematics is a universal science which very important in the aspects of technological progress and multidisciplinary. In Indonesia mathematics is regarded as one of disciplines which very important and has the most influence on the other multidisciplinary. The mathematics used as a compulsory subject and has been given early in the world of education in Indonesia. This is confirmed by Undang-Undang RI No. 20 Th. 2003 Tentang Sisdiknas (Sistem Pendidikan Nasional) Pasal 37 stated: “Mata pelajaran Matematika merupakan salah satu mata pelajaran wajib bagi siswa pada jenjang pendidikan dasar dan menengah.”
From the explanation above it is said that learning and knowing about the mathematics is very important. Mathematics it’s not only related with other multidisciplinary but also the development of modern technology and the power of human thought. So that it’s very needed in dimensions of knowledge and skills which is supporting in learning mathematics deeply. One of dimension aspect of knowledge and skills that interesting to be studied more deeply, especially in learning mathematics is metacognition.
The importances of metacognition in learning mathematics supported by the statement of two mathematician expert in education who is well known from USA, Garofalo and Lester (Safitri, 2015 : 470): “There is also growing support for the view that purely cognitive analyses of mathematical performance are inadequate because they overlook metacognitive action.” Furthermore Livingston (1997) also stated: “Metacognition refers to higher order thinking which involves active control over the cognitive processes engaged in learning. Activities such as planning how to approach a given learning task, monitoring comprehension, and evaluating progress toward the completion of a task are metacognitive in nature.”
(13)
2
From Brown (Hacker, 2009 : 7) that view the concept of metacognition as having four historical roots, each of which has provided foundation for approaches to strategies instruction, which we will take up in the next section. The first root is the issue of verbal reports as data—how reliable are people’s reports of their thinking processes? What we can express about what we know, or how does what we can express relate to what we know? The second root is the notion of executive control, which is derived from information processing models. These models feature a central processor that can control its own operations, which include planning, evaluating, monitoring, and revising. The third root is self-regulation, processes by which active learners direct and continuously fine-tune their actions. The fourth root that Brown et al. see underlying metacognition is what they call other regulation, or the transfer of control from other to self. This kind of regulation is based on Vygotsky’s theory that all psychological processes begin as social and then transformed through supportive experience to the intrapersonal, number of metacognition components that Brown et al. discuss within the four roots have relevance for reading. Actions such as self-regulating, planning, evaluating, and monitoring align well with what researchers have come to see as the processes in which readers need to engage in order to achieve successful comprehension. As Baker and Brown (Hacker, 2009 : 7) put it: “Since effective readers must have some awareness and control of the cognitive activities they engage in as they read, most characterizations of reading include skills and activities that involve metacognition”.
And the Mevarech & Kramarski (1997 : 2) called IMPROVE, emphasizes the importance of providing each student with the opportunity to construct mathematical meaning by involving themselves in metacognitive discourse. The IMPROVE method is based on self-questioning via the use of metacognitive questions that focus on: (a) comprehending the problem (e.g.,”What is the problem all about”?); (b) constructing connections between previous and new knowledge (e.g., “What are the similarities/differences between the problem at hand and the problems you have solved in the past? and why?”; (c) using appropriate problem solving strategies (e.g., “What are the
(14)
3
strategies/tactics/principles appropriate for solving the problem and why?”; and in some studies, (d) reflecting on the processes and the solution (e.g., “What did I do wrong here?”; “Does the solution make sense?”).
From the two expert it can be seen the importances of metacognitive and it’s component. There are relation of thinking process and question in our mind to contruct the answer of problem. And other expert Keiichi (Mulbar, 2008 : 3) in his research on Metacognition in Mathematics Education produced some findings, namely:
a). Metacognition plays an important role in resolving the conflict; b). Students are more skilled at solving problems if they have knowledge
of metacognition; c). In the framework of solving problems, teachers often emphasize specific strategies to solve problems and lack of attention to important features activities solve other problems; d). The teacher expresses some achievement more impressive at the intermediate level in the elementary school where these things important in mathematical reasoning and problem posing strategies.
From the observations of researchers when conducted PFE (Practice Field Experience), researchers observed that the students’ metacognition ability is still low. It is characterized by the existencies of students’ who can not and difficult to explain the results of their work in front of the class and still confused with the question given by his friends. Another problem was found in research there are still many students who pay attention well, but when the test the students can not get maximum results. So the researchers concluded that the ability of learner metacognitive need to be further investigated. From some of the reviews mentioned the importance of metacognition in mathematics and problems in mathematics, it’s necessary important to know the extent of stdents’ metacognitive in solving mathematical problems.
Researchers choose undergraduated students as research subjects in importances of metacognition due to Baker statement cited from Dale (Safitri, 2015 : 471) : “Supervisory of activity more often used by the older children and adults compared with young children. However, older children and adults do not always monitor their understanding and often misjudged as to how well they understand the text.” Reseacher choose the Calculus subject as a test observation
(15)
4
because Calculus is a compulsory subject for students’ mathematics in the second semester and as general courses for several other major. Calculus II was selected because it is related to other subjects and is the foundation for further understanding of subjects, such as Differential Equations, Real Analysis, Algebra, also for the other subjects that are application. So it’s important to see students in understanding and solving mathematical problems in Calculus II.
In the initial observations which was held on February, 2nd 2016, with correspondents Students of mathematics education regular class C in 2015 amounted to 40 people. There were many students who still difficulty to understand the mathematical problems, so that influent their mathematical problem solving ability. Also found from the initial observation that the ability of students mathematics regular class C 2015 , there was no oversight of thinking activities and monitoring the mathematical problem understanding.
Here is an overview the results of initial observations:
Figure 1.1 The Student I Figure 1.2 The Student 2 Figure 1.1 and 1.2 are Answer of Student in Initial Test no.3
From four questions provided by the material derivatives in Calculus I is still a lot of students who didn’t understand and difficulty to solving the problems. Result of the initial observation test using problem solving rubric percentage yield obtained are:
Not understanding the real problem Wrong element in the
problem solving
Misunderstood derivatives Using a strategy that is
(16)
5
1. The number of students who were in the top group, or high characteristic is 11 people
2. The number of students who were in the group of moderate or medium characteristic is 12 people
3. The number of students who were in the bottom group or low characteristic is 19 people
This percentage is 47,5% of students who are in the lower group shows the lack of students' ability to solve the problems and the lack of awareness of thinking, the lack above oversight of thinking activities and monitoring.Based on the results, the researchers are interested in knowing metacognitive level students and its characteristics in solving problems Calculus II.
1.2 Problem Identification
1. The mathematical problem solving ability is still low.
2. Not aware of the mistake that made in mathematical problem solving. 3. Students are not aware of their advantages and disadvantages in solving
mathematical problems.
4. The use of students’ thinking activity is still low in mathematical problem solving.
5. Students are not aware of what knowledge that can be used in mathematical problem solving.
6. Learning Process which not support for the using of metacognitive knowledge in mathematical problem solving
7. The metacognition in mathematical problem solving is still low
1.3 Problem limitation
Based on the identification problems above, there is a wide scope of issues, so this research is limited to know the following:
1. Grouping students based on characteristics of high, medium and low in mathematical problem solving at second semester State University of Medan.
(17)
6
2. The use of metacognition to know the mathematical problem solving 3. The components of metacognition to identify the level of student
metacognition.
1.4 Problem Formulation
The problems formulation of this research are:
1. How is the students’ characteristics in mathematical problem solving? 2. How is the level of student metacognition in mathematical problem
solving?
3. How students' scaffolding question metacognitive if given mathematical problem solving at second semester at State University of Medan ?
1.5 Research Objective
Research objective in this research is to describe Mathematics Students characteristics and level of metacognition in mathematical problem solving and to know students’ scaffolding question metacognitive in answer the question of problem solving at second semester State University of Medan.
1.6 Research Benefits
1. For the lecturer, to identify the difficulties of the students’ mathematical problem solving and to know how the metacognitive level of students in problem solving and to improve the student learning outcomes using metacognition approach.
2. For students to know the thinkingt process in solving the problem, so that improve the students’ mathematical problem solving ability.
(18)
7
1.7 Operational Definitions
In order to avoid the differences of meaning clarity about important terms contained in this research, the operational definitions will be noted as following:
1. Metacognition is the word that is related to what the learners known about him as individual and how he controls also consciousnees of awareness , consideration and controling or monitoring toward the strategy as well as cognitive processes themselves.
2. Problem solving is how to find alternative solutions to a problem as learners.
3. Level metacognitive is describing the metacognition to know learners steps in answered.
(19)
105
CHAPTER V
CONCLUSION AND SUGGESTION 5.1 Conclusion
Based on the result and discussion of research in the previous chapter, can be concluded that:
1. The result of students’ characteristic in mathematical problem solving are high, medium and low.
2. The results of research metacognitive level that used in mathematical problem solving in each categorizing, namely: Students who are classified as high mathematical ability in metacognitive level is Reflective Use. Students with a metacognitive level in Reflective Use has metacognition activities and able to understand the problem well, able to plan with good problem-solving strategies, able to realize the concept and know how to count are used properly also able to evaluate properly. Students who are classified as medium mathematical problem solving ability in metacognitive level is Strategic Use. Students with a metacognitive level in Strategic Use has activities such able to understand the problem well, able to plan with good problem-solving strategies, quite capable of realizing the concept and know how to count are used properly also able to evaluation quite capable of doing well. Students who are classified as low mathematical ability in metacognitive level is Aware Use and also be classified on the level of Tacit Use Students with a metacognitive level in Aware Use has metacognitive activities as quite able to understand the problem well, quite capable to plan problem-solving strategies well, quite capable of realizing the concept and know how to count are used properly and also are quite capable to evaluate properly , While students with a metacognitive level Tacit Use has metacognitive activities as less able to understand the problem well, less able to plan problem-solving strategies well, students are less able to realize the concept and how to count are well used and also less able to do the evaluation with good.
(20)
106
3. Scaffolding questions given in the test should help students in completing the problem and questions always lead to the completion of the work so that measures students' can answer the questions on the test.
5.2 Suggestion
Based on the findings and conclusions on the researchers gave some suggestions are:
1. For students, the problem in mathematical problem solving should use metacognition to guide thinking in mathematical problem solving.
2. For Researches, the subjects of research less attention in though. It’s made
difficulties in research .it’s should be the researcher master in theory deeply
so that can categorize the subject at the level of metacognition.
3. For Lectures, while giving students the material, it’s should always be guided
the students’ thoughts and use the components metacognition in his thinking
(21)
107
REFRENCES
Amiripour,P.,Mofidi, and S.A.,Shahvarani,A., (2012), Scaffolding as effective method for mathematical learning, Indian Journal of Science and Technology, Vol. 5 No. 9.
Arikunto, S.,(2013), Dasar-Dasar Evaluasi Pendidikan Edisi 2, Bumi Aksara, Jakarta.
Bilingual Study Program Faculty of Mathematics and Natural Sciences State University of Medan, (2015), Guideline : Proposal and Skripsi Writing for Bilingual Program, FMIPA Unimed.
Cohors-Frosenborg & Kaune, (2007), Modelling Classroom Discussion and Categorizing Discursive and Metacognitive Activities, In proceeding of CERME 5.
Desmita,(2011), Psikologi Perkembangan Peserta Didik, PT Remaja Rosdakarya, Bandung.
Du Toit, S., and Du Toit,G., (2013), Learner metacognition and mathematics achievement during problem-solving in a mathematics classroom, The Journal for Transdisciplinary Research in Southern Africa.
Fakultas Matematika dan Ilmu pengetahuan Alam Universitas Negeri Medan, (2010), Buku Pedoman Penulisan Skripsi dan Proposal Penelitian Kependidikan, FMIPA Unimed.
Fakultas Matematika dan Ilmu pengetahuan Alam Universitas Negeri Medan, (2012), Matematika Umum I (Kalkulus), FMIPA Unimed.
Fakultas Matematika dan Ilmu pengetahuan Alam Universitas Negeri Medan, (2016), Matematika Umum II (Kalkulus II), FMIPA Unimed.
Flavell, J. H., (1976), Metacognitive aspects of problem solving. In L. B. Resnick (Ed.), The nature of intelligence, Hillsdale, NJ: Erlbaum.
Hacker, J.D.,Dunlosky,J., and Graesser,C.A., (2009), Handbook of Metacognition in Education, Routledge : New York.
Husamah, and Setyaningrum,Y.,(2011), Desain Pembelajaran Berbasis Pencapaian Kompetensi, Prestasi Pustaka, Bandung.
Kiong,P.L.N.,Yong,H.T.,(-)Scaffolding as a Teaching Strategy to Enhance Mathematics Learning in the Clasrooms, Mara University Of Technology Sarawak Campus.
(22)
108
Kitcher,K.S., (1983), Cognition, Metacognition, and Epistemic Cognition A Three-Level Model of Cognitive Processing, Jounal Mobile, Volume 26 No.4.
Kramarski, B., and Mevarech,Z., (-), Metacognitive Discourse in Mathematics Classrooms, In Proceeding of Thematic Group 8 European Research in Mathematics Education III, Bar-Ilan University : Israel.
Lai, Emily, (2011), Metacognition: A Literature Review.
http://images.pearsonassessments.com/images/trms/metacognitio_literatur e_review_final.pdf (accessed January 2016).
Lee,M., and Baylor A.L., (2006), Designing Metacognitive maps for Web-Based Learning, educational Technology & society, Volume 9 Nomer 1.
Livingston, J., (1997), Metacognition: An overview.
http://www.gse.buffalo.edu/fas/shuell/cep564/Metacog.htm (accessed January 2016).
Luckin,R., and Hammerton,L., (2002), Getting to know Me: Helping Learners Understand Their Own Learning Needs through Matacognitive Scaffolding, Volume 2363.
Mahromah, L.A.,(2013), Identifikasi Tingkat Metakognisi Peserta didik dalam Memecahkan Masalah Matematika Berdasarkan Perbedaan Skor Matematika, Journal of MATHEdunesa, Vol 02, No. 01.
Moleong,L.J.,(2014), Metodologi Penelitian Kualitatif, Rosda, Bandung. Mulbar, Usman, (2008), Metakognisi Peserta didik dalam Memecahkan
Masalaha Matematika pada Pembelajaran Matematika, Prosiding.
Polya, G., (1945), How to Solve It: A New Aspect of Mathematical Method, Second Edition.Princeton: Princeton University Press.
Pugalee,D.K., (2011), Writing, Mathematics, and Metacognition : Looking for Connections Through Students’ Work in Mathematical Problem Solving, Volume 101, Issues 5.
Purcell, E.J., (1994), Kalkulus dan Geometri Analitis Jilid 1, Edisi Kelima, Erlangga, Jakarta.
Safitri,K.R.,Minhayati,S.,(2015), Analisis Pemecahan Masalah Matematika Menggunakan Metakognisis, Prosiding Seminar Nasional Matematika dan Pendidikan Matematika, 470-485
(23)
109
Schoenfeld, A.H., (1987), Cognitive Science and Mathematics Education, London: Lawrence Erlbaum Associates Publishers.
Schoenfeld, A.H., (1992), Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In Grouws, D. (Ed.). Handbook for Research on Mathematics Teaching and Learning, New York: MacMillan.
Schoenfeld, A.H., (2007), What is Mathematical Proficiency and How Can It Be Assessed? In Schoenfeld A.H. (Ed.). Assessing Mathematical Proficiency, Cambridge: Cambridge University Press.
Sugiyono,(2015), Metode Penelitian Pendidikan, Alfabeta, Bandung. Wilson,Jeni, David,C., (2004), Toward the Modelling of Mathematical
Metacognition, Mathematics Edication Research Journal, University of Melbourne, Vol. 16 , No 2.
(1)
1.7 Operational Definitions
In order to avoid the differences of meaning clarity about important terms contained in this research, the operational definitions will be noted as following:
1. Metacognition is the word that is related to what the learners known about him as individual and how he controls also consciousnees of awareness , consideration and controling or monitoring toward the strategy as well as cognitive processes themselves.
2. Problem solving is how to find alternative solutions to a problem as learners.
3. Level metacognitive is describing the metacognition to know learners steps in answered.
(2)
CHAPTER V
CONCLUSION AND SUGGESTION
5.1 Conclusion
Based on the result and discussion of research in the previous chapter, can be concluded that:
1. The result of students’ characteristic in mathematical problem solving are high, medium and low.
2. The results of research metacognitive level that used in mathematical problem solving in each categorizing, namely: Students who are classified as high mathematical ability in metacognitive level is Reflective Use. Students with a metacognitive level in Reflective Use has metacognition activities and able to understand the problem well, able to plan with good problem-solving strategies, able to realize the concept and know how to count are used properly also able to evaluate properly. Students who are classified as medium mathematical problem solving ability in metacognitive level is Strategic Use. Students with a metacognitive level in Strategic Use has activities such able to understand the problem well, able to plan with good problem-solving strategies, quite capable of realizing the concept and know how to count are used properly also able to evaluation quite capable of doing well. Students who are classified as low mathematical ability in metacognitive level is Aware Use and also be classified on the level of Tacit Use Students with a metacognitive level in Aware Use has metacognitive activities as quite able to understand the problem well, quite capable to plan problem-solving strategies well, quite capable of realizing the concept and know how to count are used properly and also are quite capable to evaluate properly , While students with a metacognitive level Tacit Use has metacognitive activities as less able to understand the problem well, less able to plan problem-solving strategies well, students are less able to realize the concept and how to count are well used and also less able to do the evaluation with good.
(3)
3. Scaffolding questions given in the test should help students in completing the problem and questions always lead to the completion of the work so that measures students' can answer the questions on the test.
5.2 Suggestion
Based on the findings and conclusions on the researchers gave some suggestions are:
1. For students, the problem in mathematical problem solving should use metacognition to guide thinking in mathematical problem solving.
2. For Researches, the subjects of research less attention in though. It’s made difficulties in research .it’s should be the researcher master in theory deeply so that can categorize the subject at the level of metacognition.
3. For Lectures, while giving students the material, it’s should always be guided the students’ thoughts and use the components metacognition in his thinking in solving the problem.
(4)
REFRENCES
Amiripour,P.,Mofidi, and S.A.,Shahvarani,A., (2012), Scaffolding as effective
method for mathematical learning, Indian Journal of Science and
Technology, Vol. 5 No. 9.
Arikunto, S.,(2013), Dasar-Dasar Evaluasi Pendidikan Edisi 2, Bumi Aksara, Jakarta.
Bilingual Study Program Faculty of Mathematics and Natural Sciences State University of Medan, (2015), Guideline : Proposal and Skripsi Writing for
Bilingual Program, FMIPA Unimed.
Cohors-Frosenborg & Kaune, (2007), Modelling Classroom Discussion and
Categorizing Discursive and Metacognitive Activities, In proceeding of
CERME 5.
Desmita,(2011), Psikologi Perkembangan Peserta Didik, PT Remaja Rosdakarya, Bandung.
Du Toit, S., and Du Toit,G., (2013), Learner metacognition and mathematics
achievement during problem-solving in a mathematics classroom, The
Journal for Transdisciplinary Research in Southern Africa.
Fakultas Matematika dan Ilmu pengetahuan Alam Universitas Negeri Medan, (2010), Buku Pedoman Penulisan Skripsi dan Proposal Penelitian
Kependidikan, FMIPA Unimed.
Fakultas Matematika dan Ilmu pengetahuan Alam Universitas Negeri Medan, (2012), Matematika Umum I (Kalkulus), FMIPA Unimed.
Fakultas Matematika dan Ilmu pengetahuan Alam Universitas Negeri Medan, (2016), Matematika Umum II (Kalkulus II), FMIPA Unimed.
Flavell, J. H., (1976), Metacognitive aspects of problem solving. In L. B. Resnick (Ed.), The nature of intelligence, Hillsdale, NJ: Erlbaum.
Hacker, J.D.,Dunlosky,J., and Graesser,C.A., (2009), Handbook of Metacognition in Education, Routledge : New York.
Husamah, and Setyaningrum,Y.,(2011), Desain Pembelajaran Berbasis
Pencapaian Kompetensi, Prestasi Pustaka, Bandung.
Kiong,P.L.N.,Yong,H.T.,(-) Scaffolding as a Teaching Strategy to Enhance
Mathematics Learning in the Clasrooms, Mara University Of Technology
(5)
Kitcher,K.S., (1983), Cognition, Metacognition, and Epistemic Cognition A
Three-Level Model of Cognitive Processing, Jounal Mobile, Volume 26
No.4.
Kramarski, B., and Mevarech,Z., (-), Metacognitive Discourse in Mathematics Classrooms, In Proceeding of Thematic Group 8 European Research in Mathematics Education III, Bar-Ilan University : Israel.
Lai, Emily, (2011), Metacognition: A Literature Review.
http://images.pearsonassessments.com/images/trms/metacognitio_literatur e_review_final.pdf (accessed January 2016).
Lee,M., and Baylor A.L., (2006), Designing Metacognitive maps for Web-Based
Learning, educational Technology & society, Volume 9 Nomer 1.
Livingston, J., (1997), Metacognition: An overview.
http://www.gse.buffalo.edu/fas/shuell/cep564/Metacog.htm (accessed January 2016).
Luckin,R., and Hammerton,L., (2002), Getting to know Me: Helping Learners Understand Their Own Learning Needs through Matacognitive
Scaffolding, Volume 2363.
Mahromah, L.A.,(2013), Identifikasi Tingkat Metakognisi Peserta didik dalam Memecahkan Masalah Matematika Berdasarkan Perbedaan Skor
Matematika, Journal of MATHEdunesa, Vol 02, No. 01.
Moleong,L.J.,(2014), Metodologi Penelitian Kualitatif, Rosda, Bandung. Mulbar, Usman, (2008), Metakognisi Peserta didik dalam Memecahkan
Masalaha Matematika pada Pembelajaran Matematika, Prosiding. Polya, G., (1945), How to Solve It: A New Aspect of Mathematical Method,
Second Edition.Princeton: Princeton University Press.
Pugalee,D.K., (2011), Writing, Mathematics, and Metacognition : Looking for Connections Through Students’ Work in Mathematical Problem Solving, Volume 101, Issues 5.
Purcell, E.J., (1994), Kalkulus dan Geometri Analitis Jilid 1, Edisi Kelima, Erlangga, Jakarta.
Safitri,K.R.,Minhayati,S.,(2015), Analisis Pemecahan Masalah Matematika Menggunakan Metakognisis, Prosiding Seminar Nasional Matematika dan Pendidikan Matematika, 470-485
(6)
Schoenfeld, A.H., (1987), Cognitive Science and Mathematics Education, London: Lawrence Erlbaum Associates Publishers.
Schoenfeld, A.H., (1992), Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In Grouws, D. (Ed.).
Handbook for Research on Mathematics Teaching and Learning, New
York: MacMillan.
Schoenfeld, A.H., (2007), What is Mathematical Proficiency and How Can It Be Assessed? In Schoenfeld A.H. (Ed.). Assessing Mathematical Proficiency, Cambridge: Cambridge University Press.
Sugiyono,(2015), Metode Penelitian Pendidikan, Alfabeta, Bandung. Wilson,Jeni, David,C., (2004), Toward the Modelling of Mathematical
Metacognition, Mathematics Edication Research Journal, University of