### Metacognition Process of Students with High Mathematics Anxiety in Mathematics Problem-Solving

#### Abstract

This study aims to find out students’ metacognition process while solving the mathematics problem. It focuses on analyzing the metacognition process of students with high mathematics anxiety based on Polya’s problem solving phases. This study uses qualitative research with case study strategy. The subjects consist of 8 students of 7^{th }grade selected through purposive sampling. Data in the form of Mathematics Anxiety Scale (MAS) result and recorded interview while solving mathematics problems were analyzed qualitatively using Miles and Huberman steps. Before selecting the subjects, the researcher gave the Mathematics Anxiety Scale (MAS) to obtain students with high anxiety. Then, subjects were interviewed while solving the problem to investigate their metacognition process. The results show that: (1) The metacognition processes of students with high anxiety in understanding the problem involve *planning*, *monitoring*, and *evaluating* to explore and understand* *information of the given problem. (2) The metacognition processes of students with high anxiety in devising a plan involve *planning* and *monitoring* to identify the* *possible strategy for solving the problem. (3) The metacognition processes of students with high anxiety in carrying out the plan involve *planning *to use the strategy and procedures to find the solution. (4) In the final steps namely looking back, there is no metacognition process of students with high anxiety identified. Thus, it can be said that the high of mathematics anxiety can cause the lack of students’ metacognition process while solving the mathematics problem. Therefore, it is important for the teachers to consider students mathematics anxiety to design and plan better mathematics learning.

[1] NCTM 2000 Principles and Standards for School Mathematics NCTM 2000 (Virginia: NCTM)

[2] Jonsson B, Norqvist M, Liljekvist Y and Lithener J 2014 Learning Mathematics through Algorithmic and Creative Reasoning the J of Mathl Behaviour **36** 20-32

[3] Mullis I. V. S, Martin M. O, Foy P and Arora A 2012 TIMMS 2011 International Result in Mathematics (Chestnut Hill: TIMSS & PIRLS International Study Center)

[4] PISA 2016 Results Excellence and Equity in Education Volume I (Paris: OECD Publishing)

[5] Tambychik T and Mohd Meerah T S 2010 Students’ Difficulties in Mathematics Problem-Solving: What do they Say? Proc Soc and Behavioral Sc: Int Conf on Math Education Research 2010 **8** 142–151

[6] Sopia H. F 2015 Keefektifan Pendekatan Matematika Realistik Ditinjau dari Prestasi, Pemecahan Masalah, dan Kepercayaan Diri Siswa Seminar Nasional Mat dan Pend Mat UNY 2015 807-814

[7] Risnanosanti 2008 Kemampuan Metakognitif Siswa dalam Pembelajaran Matematika Phytagoras **4** 86-98

[8] Aljaberi N. M and Geith E 2015 University Students’ Level of Metacognitive Thinking and Their Ability to Solve Problems American Int J of Contemporary Research **5** 121-134

[9] Tuncer M and Dogan Y 2016 Relationships among Foreign Language Anxiety, Academic Self-Efficacy Beliefs, and Metacognitive Awareness: A Structural Equation Modelling Int J of Learning and Development **6** 31-41

[10] Akturk A. O and Sahin I 2011 Literature Review on Metacognition and its Measurement Proc-Soc and Behavioral Sc **15** 3731–3736

[11] Sengul S and Katranci Y 2015 Meta-cognitive Aspects of Solving Indefinite Integral Problems Proc-Soc and Behavioral Sc **197** 622-629

[12] Anggo M 2011 The Metacognitive Process of Teachers College Students in Solving Mathematical Problems Proc Int Seminar and the Fourth National Conf on Math Ed Building the Nation Character through Hum Math Ed (Yogyakarta: Department of Mathematics Education, Yogyakarta State University) 367-376

[13] Yimer A and Ellerton N. F 2006 Cognitive and Metacognitive Aspects of Mathematical Problem Solving: An Emerging Model Proc of the 29th Annual Conf of The Math Ed Research Group of Australasia (MERGA): Identities, Culture, and Learning Spaces. (Canberra, Australia: MERGA Inc.)

[14] Rozen M. T and Kramarski B 2014 Metacognition, Motivation, and Emotions: Contribution of Self-Regulated Learning to Solving Mathematical Problems Global Ed Review **1** 76-95

[15] Evans B. R 2015 Breakthrough Moments in Problem Solving Math Teaching-Research J Online **8**

[16] Carson, J 2007 A Problem with Problem Solving: Teaching Thinking without Teaching Knowledge the Math Educator **17** 7–14

[17] Ortiz E 2016 the Problem-Solving Process in a Mathematics Classroom Transformation **1** 4-13

[18] Lai Y, Zhu X, Chen Y and Li Y 2015 Mathematics Anxiety and Mathematical Metacognition on Word Problem Solving in Children with and without Mathematical Learning Difficulties PLOS One **10** 1-19

[19] Kurniawati A. D and Siswono T. Y. E 2014 Pengaruh Kecemasan dan Self Efficacy Siswa terhadap Kemampuan Pemecahan Masalah Materi Segiempat Siswa Kelas VII MTS Negeri Ponorogo Mathedunesia: J Ilmiah Pend Mat **3** 36-41

[20] Karasel N, Ayda O and Tezer M 2010 the Relationship between Mathematics Anxiety and Mathematical Problem Solving Skills among Primary School Students Proc-Soc and Behavioral Sc **2** 5804–5807

[21] Legg A. M and Locker L. Jr 2009 Math Performance and Its Relationship to Math Anxiety and Metacognition North American J of Psychology **11** 471-486

[22] Alikamar M. A, Alamolhodaei H and Radmehr F 2013 the Role of Metacognition on Effect of Working Memory Capacity on Students' Mathematical Problem Solving European J of Child Development, Education and Psychopathology **1** 125-139

[23] Moleong L. J 2007 Metodoogi Penelitian Kualitatif (Bandung: Remaja Rosdakarya)

[24] Zainal Z 2007 Case Study as a Research Method J Kemanusiaan **9** 1-6

[25] Sugiyono 2013 Metode Penelitian Pendidikan: Pendekatan Kuantitatif, Kualitatif dan RD (Bandung: Alfabeta)

[26] du Toit S and du Toit G 2013 Learner Metacognition and Mathematics Achievement during Problem-Solving in a Mathematics Classroom the J for Transdisciplinary Research in Southern Africa **9** 505-518

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PDF#### References

NCTM 2000 Principles and Standards for School Mathematics NCTM 2000 (Virginia: NCTM)

Jonsson B, Norqvist M, Liljekvist Y and Lithener J 2014 Learning Mathematics through Algorithmic and Creative Reasoning the J of Mathl Behaviour 36 20-32

Mullis I. V. S, Martin M. O, Foy P and Arora A 2012 TIMMS 2011 International Result in Mathematics (Chestnut Hill: TIMSS & PIRLS International Study Center)

PISA 2016 Results Excellence and Equity in Education Volume I (Paris: OECD Publishing)

Tambychik T and Mohd Meerah T S 2010 Students’ Difficulties in Mathematics Problem-Solving: What do they Say? Proc Soc and Behavioral Sc: Int Conf on Math Education Research 2010 8 142–151

Sopia H. F 2015 Keefektifan Pendekatan Matematika Realistik Ditinjau dari Prestasi, Pemecahan Masalah, dan Kepercayaan Diri Siswa Seminar Nasional Mat dan Pend Mat UNY 2015 807-814

Risnanosanti 2008 Kemampuan Metakognitif Siswa dalam Pembelajaran Matematika Phytagoras 4 86-98

Aljaberi N. M and Geith E 2015 University Students’ Level of Metacognitive Thinking and Their Ability to Solve Problems American Int J of Contemporary Research 5 121-134

Tuncer M and Dogan Y 2016 Relationships among Foreign Language Anxiety, Academic Self-Efficacy Beliefs, and Metacognitive Awareness: A Structural Equation Modelling Int J of Learning and Development 6 31-41

Akturk A. O and Sahin I 2011 Literature Review on Metacognition and its Measurement Proc-Soc and Behavioral Sc 15 3731–3736

Sengul S and Katranci Y 2015 Meta-cognitive Aspects of Solving Indefinite Integral Problems Proc-Soc and Behavioral Sc 197 622-629

Anggo M 2011 The Metacognitive Process of Teachers College Students in Solving Mathematical Problems Proc Int Seminar and the Fourth National Conf on Math Ed Building the Nation Character through Hum Math Ed (Yogyakarta: Department of Mathematics Education, Yogyakarta State University) 367-376

Yimer A and Ellerton N. F 2006 Cognitive and Metacognitive Aspects of Mathematical Problem Solving: An Emerging Model Proc of the 29th Annual Conf of The Math Ed Research Group of Australasia (MERGA): Identities, Culture, and Learning Spaces. (Canberra, Australia: MERGA Inc.)

Rozen M. T and Kramarski B 2014 Metacognition, Motivation, and Emotions: Contribution of Self-Regulated Learning to Solving Mathematical Problems Global Ed Review 1 76-95

Evans B. R 2015 Breakthrough Moments in Problem Solving Math Teaching-Research J Online 8

Carson, J 2007 A Problem with Problem Solving: Teaching Thinking without Teaching Knowledge the Math Educator 17 7–14

Ortiz E 2016 the Problem-Solving Process in a Mathematics Classroom Transformation 1 4-13

Lai Y, Zhu X, Chen Y and Li Y 2015 Mathematics Anxiety and Mathematical Metacognition on Word Problem Solving in Children with and without Mathematical Learning Difficulties PLOS One 10 1-19

Kurniawati A. D and Siswono T. Y. E 2014 Pengaruh Kecemasan dan Self Efficacy Siswa terhadap Kemampuan Pemecahan Masalah Materi Segiempat Siswa Kelas VII MTS Negeri Ponorogo Mathedunesia: J Ilmiah Pend Mat 3 36-41

Karasel N, Ayda O and Tezer M 2010 the Relationship between Mathematics Anxiety and Mathematical Problem Solving Skills among Primary School Students Proc-Soc and Behavioral Sc 2 5804–5807

Legg A. M and Locker L. Jr 2009 Math Performance and Its Relationship to Math Anxiety and Metacognition North American J of Psychology 11 471-486

Alikamar M. A, Alamolhodaei H and Radmehr F 2013 the Role of Metacognition on Effect of Working Memory Capacity on Students' Mathematical Problem Solving European J of Child Development, Education and Psychopathology 1 125-139

Moleong L. J 2007 Metodoogi Penelitian Kualitatif (Bandung: Remaja Rosdakarya)

Zainal Z 2007 Case Study as a Research Method J Kemanusiaan 9 1-6

Sugiyono 2013 Metode Penelitian Pendidikan: Pendekatan Kuantitatif, Kualitatif dan R&D (Bandung: Alfabeta)

du Toit S and du Toit G 2013 Learner Metacognition and Mathematics Achievement during Problem-Solving in a Mathematics Classroom the J for Transdisciplinary Research in Southern Africa 9 505-518

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