Main Article Content
Abstract
The purpose of this research was to find out the thinking processes of a concrete student in solving two- dimensional problems. The research method used is descriptive qualitative. The research subjects were two students taken using purposive sampling. The instrument used was the Test of Logical Operations and problem-solving tests. Stages of data analysis used are researching all data, making a cognitive classification of students, choosing concrete students to be used as research subjects, reviewing the results of concrete student work in solving mathematical problems, verify data and data sources that have been classified and transcribed in the presentation or exposure of data. The results showed that at the stage of understanding the problem and re-checking the answers, concrete students use the assimilation at the stage of planning to solve the problem of doing the disequilibration. At the stage of carrying out a plan to solve a problem, concrete students carry out the accommodation. During this study, it was found that students 'habits in mathematical problem-solving did not plan to solve problems, did not re-examine answers, and there were students' habits by interpreting the final results of problems. It can be concluded that the students' concrete thinking processes in solving two- dimensional problems vary according to the stages of problem-solving.
Keywords
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References
- Abdullah, A. H., Abidin, N. L. Z., & Ali, M. (2015). Analysis of students’ errors in solving Higher Order Thinking Skills (HOTS) problems for the topic of fraction. Asian Social Science, 11(21), 996–1005. https://doi.org/10.5539/ass.v11n21p133.
- Adi, I. M. S., Meter, I. G., & Kristiantari, M. G. R. (2014). The effect of RME learning model assisted by semi-concrete media on mathematics learning outcomes of elementary students in class V of cluster 8 in Gianyar district, Gianyar regency, academic year 2013/2014 [in Bahasa]. Jurnal Mimbar PGSD Universitas Pendidikan Ganesha, 2(1), 1–11.
- Akbar, P., Hamid, A., Bernard, M., & Sugandi, A. I. (2017). Analysis of problem solving ability and mathematical disposition in eleventh-grade students of Putra Juang senior high school on opportunity material [in Bahasa]. Jurnal Cendekia : Jurnal Pendidikan Matematika, 2(1), 144–153. https://doi.org/10.31004/cendekia.v2i1.62.
- Amir, A. (2014). Reasoning and communication ability in mathematics learning [in Bahasa]. Logaritma: Jurnal Ilmu-Ilmu Pendidikan dan Sains, 2(01). https://doi.org/10.24952/logaritma.v2i01.211.
- Anisa, W. N. (2014). Improvement of problem solving ability and mathematical communication through learning realistic mathematics education for junior high school students in Garut [in Bahasa]. Jurnal Pendidikan Dan Keguruan, 1(1).
- Annamma, S. A. (2015). Whiteness as property: Innocence and ability in teacher education. Urban Review, 47(2), 293-316. https://doi.org/10.1007/s11256-014-0293-6.
- Barrouillet, P. (2015). Theories of cognitive development : From Piaget to today. Development Review, 38, 1–12. https://doi.org/10.1016/j.dr.2015.07.004.
- Blake, B., & Pope, T. (2008). Developmental Psychology: Incorporating Piaget’s and Vygotsky’s Theories in classrooms. Journal of Cross-Disciplinary Perspectives in Education, 1(1), 59-67.
- Bormanaki, H. B., & Khoshhal, Y. (2017). The Role of equilibration in piaget’s theory of cognitive development and its implication for receptive skills: A theoretical study. Journal of Language Teaching and Research, 8(5), 996-1005. https://doi.org/10.17507/jltr.0805.22.
- Creswell, J. W. (2009). Research design: Qualitative, quantitative, and mixed methods approaches (3rd ed). Sage Publication
- Creswell, J. W. (2012). Educational research: Planning, Conducting and evaluating quantitative and qualitative research. Pearson.
- Effendi, L. A. (2012). Mathematics learning with guided discovery method to improve mathematical representation and problem solving ability of junior high school students [in Bahasa]. Jurnal Penelitian Pendidikan, 13(2), 1–10.
- Elstad, E., & Christophersen, K.-A. (2017). Perceptions of digital competency among student teachers: Contributing to the development of student teachers’ instructional self-efficacy in technology-rich classrooms. Education Sciences, 7(1), 27. https://doi.org/10.3390/educsci7010027.
- Fauziyah, I. N. L., Usodo, B., & Ekana, C. H. (2013). The tenth-grade students' creative thinking process in solving geometry problems based on wallas stages in terms of students' Adversity Quotient (AQ) [in Bahasa]. Jurnal Pendidikan Matematika Solusi, 1(1), 1–16.
- Fitriyani, H., Widodo, S. A., & Hendroanto, A. (2018). Students’ geometric thinking based on Van Hiele’ S Theory. Infinity Journal, 7(1), 55–60. https://doi.org/10.22460/infinity.v7i1.p55-60.
- Hasibuan, A. M., Saragih, S., & Amry, Z. (2018). Development of learning materials based on realistic mathematics education to improve problem solving ability and student learning independence. International Electronic Journal of Mathematics Education, 14(1), 243-252. https://doi.org/10.29333/iejme/4000.
- Hendrowati, T. Y. (2015). Formation of knowledge circles through assimilation and accommodation learning Piaget's constructivism theory [in Bahasa]. Jurnal E-DuMath, 1(1).
- Herman, T. (2000). Problem-solving strategies in mathematics learning [in Bahasa]. Retrieved from file.upi.edu/Direktori/FPMIPA/JUR._PEND._MATEMATIKA/196210111991011- TATANG_HERMAN/Artikel/Artikel14.pdf
- Hertiavi, M. A., Langlang, H., & Khanafiyah, S. (2010). Application of cooperative learning model with Jigsaw type to improve the problem solving ability of junior high school students [in Bahasa]. Jurnal Pendidikan Fisika Indonesia, 6(1). https://doi.org/10.15294/jpfi.v6i1.1104.
- Ibda, F. (2015). Cognitive development: Jean Piaget's theory [in Bahasa]. Jurnal Intelektualita, 3(1), 27–38. https://doi.org/10.3109/02841851.2010.495350.
- Inhelder, B., & Piaget, J. (1964). The early growth of logic in the child, clasification and seriation.Harper & Row.
- Kiosses, D. N., Ravdin, L. D., Gross, J. J., Raue, P., Kotbi, N., & Alexopoulos, G. S. (2015). Problem adaptation therapy for older adults with major depression and cognitive impairment: A randomized clinical trial. JAMA Psychiatry, 72 (1), 22-30. https://doi.org/10.1001/jamapsychiatry.2014.1305.
- Kusmayadi, T. A., Sujadi, I., & Muhtarom. (2011). The thinking process of eleventh-grade students with high mathematics ability in solving mathematical problems [in Bahasa]. JMEE, 1(2), 60–71.
- Kusumawardani, L. (2017). Student thinking process in solving open-ended problem of the PISA model of space and shape contents based on Adversity Quotient (AQ). International Journal of Scientific Research and Management, 5(12), 7673-7680. https://doi.org/10.18535/ijsrm/v5i12.14.
- Labouvie-Vief, G. (2015). Equilibrium and disequilibrium in development. in Integrating emotions and cognition throughout the lifespan (pp. 17-28). Springer, Cham. https://doi.org/10.1007/978-3-319-09822-7_2.
- Lane, R. D., Ryan, L., Nadel, L., & Greenberg, L. (2015). Memory reconsolidation, emotional arousal, and the process of change in psychotherapy: New insights from brain science. In Behavioral and brain sciences, 38. https://doi.org/10.1017/S0140525X14000041.
- Lastiningsih, N., Mutohir, T. C., Riyanto, Y., & Siswono, T. Y. E. (2017). Management of the School Literacy Movement (SLM) programme in Indonesian junior secondary schools. World Transactions on Engineering and Technology Education, 15(4), 384–389.
- Leongson, J. A., & Limjap, A. A. (2003). Assessing the mathematics achievement of college freshmen using Piaget’s logical operation. The Hawaii International Conference on Education, 1–25.
- Masfingatin, T. (2013). The thinking process of secondary school students in solving mathematical problems in terms of Adversity Quotient [in Bahasa]. JIPM (Jurnal Ilmiah Pendidikan Matematika), 2(1). https://doi.org/10.25273/jipm.v2i1.491.
- McReynolds, P. (2015). Assimilation and anxiety. In Emotions and anxiety (PLE: Emotion): New concepts, methods, and applications. https://doi.org/10.4324/9781315744643.
- Miles, M. B., Huberman, M. A., & Saldaña, J. (2013). Qualitative data analysis. Sage Publications. Minarni, A., Napitupulu, E. E., & Husein, R. (2016). Mathematical understanding and representation ability of public junior high school in North Sumatra. Journal on Mathematics Education, 7(1), 45-58. https://doi.org/10.22342/jme.7.1.2816.43-56.
- Nadapdap, A. T. Y., & Istiyono, E. (2017). Developing physics problem-solving skill test for grade X students of senior high school. Research and Evaluation in Education, 3(2), 114-123. https://doi.org/10.21831/reid.v3i2.14982.
- Nagai, Y., & Asada, M. (2015). Predictive learning of sensorimotor information as a key for cognitive development. Proceedings of the IROS 2015 Workshop on Sensorimotor Contingencies for Robotics.
- Ngilawajan, D. A. (2013). The thinking process of senior high school students in solving mathematical problems on derivative material in term of the cognitive style of independent field and field dependent [in Bahasa]. Pedagogia, 2(1), 71–83. https://doi.org/10.21070/pedagogia.v2i1.48.
- Nuritasari, F., & Anjani, D. R. (2019). Learning With quantitative reasoning problem solving in numbers theory courses [in Bahasa]. IndoMath: Indonesia Mathematics Education, 2(1), 53–58. https://doi.org/10.30738/indomath.v2i1.3348.
- Ojose, B. (2008). Applying Piaget’ s theory of cognitive development to mathematics instruction. The Mathematics Educators, 18(1), 26–30.
- Peranginangin, S. A., Saragih, S., & Siagian, P. (2019). Development of learning materials through PBL with Karo culture context to improve students’ problem solving ability and self-efficacy. International Electronic Journal of Mathematics Education, 14(2), 265-274. https://doi.org/10.29333/iejme/5713.
- Piaget, J. (2003). The Psychology of Intelligence. Routledge.
- Polya, G. (1973). How Solve It: A new Aspect of Mathematical Method. Princeton University Press. Puadi, E. F. W., & Habibie, M. I. (2018). Implementation of PBL assisted by GSP software against the improvement of students mathematical problem solving ability [in Bahasa]. Indomath: Indonesia Mathematics Education, 1(1), 19–26. https://doi.org/10.30738/indomath.v1i1.2091.
- Purnomo, E. A., & Mawarsari, V. D. (2014). Improvement of problem solving ability through learning model of IDEAL problem solving based on project based learning [in Bahasa]. Jurnal Karya Pendidikan Matematika, 1(1). https://doi.org/10.26714/jkpm.1.1.2014.%25p.
- Robert S Siegler. (2016). Continuity and change in the field of cognitive development and in the perspectives of one cognitive developmentalist. Child Development Perspectives, 10(2), 128-133. https://doi.org/10.1111/cdep.12173.
- Selvianiresa, D., & Prabawanto, S. (2017). Contextual teaching and learning approach of mathematics in primary schools. Journal of Physics: Conference Series, 895(1). https://doi.org/10.1088/1742-6596/895/1/012171.
- Siagian, M. V., Saragih, S., & Sinaga, B. (2019). Development of learning materials oriented on problem-based learning model to improve students’ mathematical problem solving ability and metacognition ability. International Electronic Journal of Mathematics Education, 14(2), 331-340. https://doi.org/10.29333/iejme/5717.
- Siswono, T. Y. E. (2012). Implementation of character education in mathematics learning [in Bahasa]. Proceedings of the National Seminar on Mathematics Education at UIN Syarif Hidayatullah Jakarta (Issue 2, pp. 1–12).
- Someren, M. W. Van, Barnard, Y. F., & Sandberg, J. A. C. (1994). The think aloud method: A practical guide to mcognitive processes. In Information processing & management (Vol. 31, Issue 6). Academic Press.
- Sudarman. (2009). Climber students' thinking processes in solving mathematical problems [in Bahasa]. Jurnal Didaktita, 10(1), 1–10.
- Sumartini, T. S. (2015). Improving students' mathematical reasoning abilities through problem based learning [in Bahasa]. Mosharafa: Jurnal Pendidikan Matematika, 5(2), 148–158.
- Suratno. (2014). The learning effectiveness of TPS and JIGSAW types based on mathematics learning achievement in and character students [in Bahasa]. PYTHAGORAS: Jurnal Pendidikan Matematika Volume 9 – Nomor 1, Juni 2014, (70-78). https://doi.org/10.21831/pg.v9i1.9069.
- Surya, E., Putri, F. A., & Mukhtar. (2017). Improving mathematical problem-solving ability and self- confidence of high school students through contextual learning model. Journal on Mathematics Education, 8(1), 85-94. https://doi.org/10.22342/jme.8.1.3324.85-94.
- Suryana, A. (2015). Application of problem solving approach through problem story in fraction to improve student learning outcomes of fourth-grade students of Ciherang elementary school, Pamovery district, Sumedang regency [in Bahasa]. Jurnal Cakrawala Pendas, 1(2), 12–18.
- Ulya, H. (2015). Relationship of cognitive style with students' mathematical problem solving ability [in Bahasa]. Jurnal Konseling Gusjigang, 1(2). https://doi.org/10.24176/jkg.v1i2.410.
- Ulya, H. (2016). Profile of Problem solving ability of students with hight motivated to study based on Ideal problem solving [in Bahasa]. Jurnal Konseling Gusjigang, 2(1). https://doi.org/10.24176/jkg.v2i1.561.
- Utomo, D. P. (2012). Learning circle using Polya version problem solving approach in class VIII in SMP PGRI 01 Dau [in Bahasa]. Widya Warta, 36(1), 145–158.
- Wahyudi, & Budiyono, I. (2011). Mathematical problem solving [in Bahasa]. Widya Sari Press. Wahyudi, Waluya, S. B., Rochmad, & Suyitno, H. (2018). Assimilation and accommodation processes in improving mathematical creative thinking with scaffolding according to learning style. Journal of Physics: Conference Series. https://doi.org/10.1088/1742-6596/1097/1/012156.
- Ward, S., Pellett, H. H., & Perez, M. I. (2017). Cognitive Disequilibrium and service-learning in physical education teacher education: Perceptions of pre-service teachers in a study abroad experience. Journal of Teaching in Physical Education, 36 (1), 70-82. https://doi.org/10.1123/jtpe.2015-0006.
- Widodo, S. A., Istiqomah, Leonard, Nayazik, A., & Prahmana, R. C. I. (2019). Formal student thinking in mathematical problem-solving. Journal of Physics: Conference Series, 1188, 012087. https://doi.org/10.1088/1742-6596/1188/1/012087.
- Widodo, S. A., & Turmudi. (2017). Guardian student thinking process in resolving issues divergence. Journal of Education and Learning, 11(4), 431–437. https://doi.org/10.11591/edulearn.v11i4.5639.
- Widodo, S. A., Turmudi, & Dahlan, J. A. (2019). An error students in mathematical problems solves based on cognitive development. International Journal Of Scientific & Technology Research, 8(07), 433–439.
- Widyastuti, R. (2015). Students' thinking processes in solving mathematical problems based on Polya's theory in term of adversity quotient type climber [in Bahasa]. Al-Jabar : Jurnal Pendidikan Matematika, 6(2), 183–193.
- Wilkie, K. J. (2016). Rise or resist: Exploring senior secondary students’ reactions to challenging mathematics tasks incorporating multiple strategies. EURASIA Journal of Mathematics, Science and Technology Education, 12(8), 2061-2083. https://doi.org/10.12973/eurasia.2016.1260a.
- Worsley, M., & Blikstein, P. (2015). Using learning analytics to study cognitive disequilibrium in a complex learning environment. ACM International Conference Proceeding Series. https://doi.org/10.1145/2723576.2723659.
- Zhiqing, Z. (2015). Assimilation, accommodation, and equilibration: A schema-based perspective on translation as process and as product. International Forum of Teaching and Studies.
References
Abdullah, A. H., Abidin, N. L. Z., & Ali, M. (2015). Analysis of students’ errors in solving Higher Order Thinking Skills (HOTS) problems for the topic of fraction. Asian Social Science, 11(21), 996–1005. https://doi.org/10.5539/ass.v11n21p133.
Adi, I. M. S., Meter, I. G., & Kristiantari, M. G. R. (2014). The effect of RME learning model assisted by semi-concrete media on mathematics learning outcomes of elementary students in class V of cluster 8 in Gianyar district, Gianyar regency, academic year 2013/2014 [in Bahasa]. Jurnal Mimbar PGSD Universitas Pendidikan Ganesha, 2(1), 1–11.
Akbar, P., Hamid, A., Bernard, M., & Sugandi, A. I. (2017). Analysis of problem solving ability and mathematical disposition in eleventh-grade students of Putra Juang senior high school on opportunity material [in Bahasa]. Jurnal Cendekia : Jurnal Pendidikan Matematika, 2(1), 144–153. https://doi.org/10.31004/cendekia.v2i1.62.
Amir, A. (2014). Reasoning and communication ability in mathematics learning [in Bahasa]. Logaritma: Jurnal Ilmu-Ilmu Pendidikan dan Sains, 2(01). https://doi.org/10.24952/logaritma.v2i01.211.
Anisa, W. N. (2014). Improvement of problem solving ability and mathematical communication through learning realistic mathematics education for junior high school students in Garut [in Bahasa]. Jurnal Pendidikan Dan Keguruan, 1(1).
Annamma, S. A. (2015). Whiteness as property: Innocence and ability in teacher education. Urban Review, 47(2), 293-316. https://doi.org/10.1007/s11256-014-0293-6.
Barrouillet, P. (2015). Theories of cognitive development : From Piaget to today. Development Review, 38, 1–12. https://doi.org/10.1016/j.dr.2015.07.004.
Blake, B., & Pope, T. (2008). Developmental Psychology: Incorporating Piaget’s and Vygotsky’s Theories in classrooms. Journal of Cross-Disciplinary Perspectives in Education, 1(1), 59-67.
Bormanaki, H. B., & Khoshhal, Y. (2017). The Role of equilibration in piaget’s theory of cognitive development and its implication for receptive skills: A theoretical study. Journal of Language Teaching and Research, 8(5), 996-1005. https://doi.org/10.17507/jltr.0805.22.
Creswell, J. W. (2009). Research design: Qualitative, quantitative, and mixed methods approaches (3rd ed). Sage Publication
Creswell, J. W. (2012). Educational research: Planning, Conducting and evaluating quantitative and qualitative research. Pearson.
Effendi, L. A. (2012). Mathematics learning with guided discovery method to improve mathematical representation and problem solving ability of junior high school students [in Bahasa]. Jurnal Penelitian Pendidikan, 13(2), 1–10.
Elstad, E., & Christophersen, K.-A. (2017). Perceptions of digital competency among student teachers: Contributing to the development of student teachers’ instructional self-efficacy in technology-rich classrooms. Education Sciences, 7(1), 27. https://doi.org/10.3390/educsci7010027.
Fauziyah, I. N. L., Usodo, B., & Ekana, C. H. (2013). The tenth-grade students' creative thinking process in solving geometry problems based on wallas stages in terms of students' Adversity Quotient (AQ) [in Bahasa]. Jurnal Pendidikan Matematika Solusi, 1(1), 1–16.
Fitriyani, H., Widodo, S. A., & Hendroanto, A. (2018). Students’ geometric thinking based on Van Hiele’ S Theory. Infinity Journal, 7(1), 55–60. https://doi.org/10.22460/infinity.v7i1.p55-60.
Hasibuan, A. M., Saragih, S., & Amry, Z. (2018). Development of learning materials based on realistic mathematics education to improve problem solving ability and student learning independence. International Electronic Journal of Mathematics Education, 14(1), 243-252. https://doi.org/10.29333/iejme/4000.
Hendrowati, T. Y. (2015). Formation of knowledge circles through assimilation and accommodation learning Piaget's constructivism theory [in Bahasa]. Jurnal E-DuMath, 1(1).
Herman, T. (2000). Problem-solving strategies in mathematics learning [in Bahasa]. Retrieved from file.upi.edu/Direktori/FPMIPA/JUR._PEND._MATEMATIKA/196210111991011- TATANG_HERMAN/Artikel/Artikel14.pdf
Hertiavi, M. A., Langlang, H., & Khanafiyah, S. (2010). Application of cooperative learning model with Jigsaw type to improve the problem solving ability of junior high school students [in Bahasa]. Jurnal Pendidikan Fisika Indonesia, 6(1). https://doi.org/10.15294/jpfi.v6i1.1104.
Ibda, F. (2015). Cognitive development: Jean Piaget's theory [in Bahasa]. Jurnal Intelektualita, 3(1), 27–38. https://doi.org/10.3109/02841851.2010.495350.
Inhelder, B., & Piaget, J. (1964). The early growth of logic in the child, clasification and seriation.Harper & Row.
Kiosses, D. N., Ravdin, L. D., Gross, J. J., Raue, P., Kotbi, N., & Alexopoulos, G. S. (2015). Problem adaptation therapy for older adults with major depression and cognitive impairment: A randomized clinical trial. JAMA Psychiatry, 72 (1), 22-30. https://doi.org/10.1001/jamapsychiatry.2014.1305.
Kusmayadi, T. A., Sujadi, I., & Muhtarom. (2011). The thinking process of eleventh-grade students with high mathematics ability in solving mathematical problems [in Bahasa]. JMEE, 1(2), 60–71.
Kusumawardani, L. (2017). Student thinking process in solving open-ended problem of the PISA model of space and shape contents based on Adversity Quotient (AQ). International Journal of Scientific Research and Management, 5(12), 7673-7680. https://doi.org/10.18535/ijsrm/v5i12.14.
Labouvie-Vief, G. (2015). Equilibrium and disequilibrium in development. in Integrating emotions and cognition throughout the lifespan (pp. 17-28). Springer, Cham. https://doi.org/10.1007/978-3-319-09822-7_2.
Lane, R. D., Ryan, L., Nadel, L., & Greenberg, L. (2015). Memory reconsolidation, emotional arousal, and the process of change in psychotherapy: New insights from brain science. In Behavioral and brain sciences, 38. https://doi.org/10.1017/S0140525X14000041.
Lastiningsih, N., Mutohir, T. C., Riyanto, Y., & Siswono, T. Y. E. (2017). Management of the School Literacy Movement (SLM) programme in Indonesian junior secondary schools. World Transactions on Engineering and Technology Education, 15(4), 384–389.
Leongson, J. A., & Limjap, A. A. (2003). Assessing the mathematics achievement of college freshmen using Piaget’s logical operation. The Hawaii International Conference on Education, 1–25.
Masfingatin, T. (2013). The thinking process of secondary school students in solving mathematical problems in terms of Adversity Quotient [in Bahasa]. JIPM (Jurnal Ilmiah Pendidikan Matematika), 2(1). https://doi.org/10.25273/jipm.v2i1.491.
McReynolds, P. (2015). Assimilation and anxiety. In Emotions and anxiety (PLE: Emotion): New concepts, methods, and applications. https://doi.org/10.4324/9781315744643.
Miles, M. B., Huberman, M. A., & Saldaña, J. (2013). Qualitative data analysis. Sage Publications. Minarni, A., Napitupulu, E. E., & Husein, R. (2016). Mathematical understanding and representation ability of public junior high school in North Sumatra. Journal on Mathematics Education, 7(1), 45-58. https://doi.org/10.22342/jme.7.1.2816.43-56.
Nadapdap, A. T. Y., & Istiyono, E. (2017). Developing physics problem-solving skill test for grade X students of senior high school. Research and Evaluation in Education, 3(2), 114-123. https://doi.org/10.21831/reid.v3i2.14982.
Nagai, Y., & Asada, M. (2015). Predictive learning of sensorimotor information as a key for cognitive development. Proceedings of the IROS 2015 Workshop on Sensorimotor Contingencies for Robotics.
Ngilawajan, D. A. (2013). The thinking process of senior high school students in solving mathematical problems on derivative material in term of the cognitive style of independent field and field dependent [in Bahasa]. Pedagogia, 2(1), 71–83. https://doi.org/10.21070/pedagogia.v2i1.48.
Nuritasari, F., & Anjani, D. R. (2019). Learning With quantitative reasoning problem solving in numbers theory courses [in Bahasa]. IndoMath: Indonesia Mathematics Education, 2(1), 53–58. https://doi.org/10.30738/indomath.v2i1.3348.
Ojose, B. (2008). Applying Piaget’ s theory of cognitive development to mathematics instruction. The Mathematics Educators, 18(1), 26–30.
Peranginangin, S. A., Saragih, S., & Siagian, P. (2019). Development of learning materials through PBL with Karo culture context to improve students’ problem solving ability and self-efficacy. International Electronic Journal of Mathematics Education, 14(2), 265-274. https://doi.org/10.29333/iejme/5713.
Piaget, J. (2003). The Psychology of Intelligence. Routledge.
Polya, G. (1973). How Solve It: A new Aspect of Mathematical Method. Princeton University Press. Puadi, E. F. W., & Habibie, M. I. (2018). Implementation of PBL assisted by GSP software against the improvement of students mathematical problem solving ability [in Bahasa]. Indomath: Indonesia Mathematics Education, 1(1), 19–26. https://doi.org/10.30738/indomath.v1i1.2091.
Purnomo, E. A., & Mawarsari, V. D. (2014). Improvement of problem solving ability through learning model of IDEAL problem solving based on project based learning [in Bahasa]. Jurnal Karya Pendidikan Matematika, 1(1). https://doi.org/10.26714/jkpm.1.1.2014.%25p.
Robert S Siegler. (2016). Continuity and change in the field of cognitive development and in the perspectives of one cognitive developmentalist. Child Development Perspectives, 10(2), 128-133. https://doi.org/10.1111/cdep.12173.
Selvianiresa, D., & Prabawanto, S. (2017). Contextual teaching and learning approach of mathematics in primary schools. Journal of Physics: Conference Series, 895(1). https://doi.org/10.1088/1742-6596/895/1/012171.
Siagian, M. V., Saragih, S., & Sinaga, B. (2019). Development of learning materials oriented on problem-based learning model to improve students’ mathematical problem solving ability and metacognition ability. International Electronic Journal of Mathematics Education, 14(2), 331-340. https://doi.org/10.29333/iejme/5717.
Siswono, T. Y. E. (2012). Implementation of character education in mathematics learning [in Bahasa]. Proceedings of the National Seminar on Mathematics Education at UIN Syarif Hidayatullah Jakarta (Issue 2, pp. 1–12).
Someren, M. W. Van, Barnard, Y. F., & Sandberg, J. A. C. (1994). The think aloud method: A practical guide to mcognitive processes. In Information processing & management (Vol. 31, Issue 6). Academic Press.
Sudarman. (2009). Climber students' thinking processes in solving mathematical problems [in Bahasa]. Jurnal Didaktita, 10(1), 1–10.
Sumartini, T. S. (2015). Improving students' mathematical reasoning abilities through problem based learning [in Bahasa]. Mosharafa: Jurnal Pendidikan Matematika, 5(2), 148–158.
Suratno. (2014). The learning effectiveness of TPS and JIGSAW types based on mathematics learning achievement in and character students [in Bahasa]. PYTHAGORAS: Jurnal Pendidikan Matematika Volume 9 – Nomor 1, Juni 2014, (70-78). https://doi.org/10.21831/pg.v9i1.9069.
Surya, E., Putri, F. A., & Mukhtar. (2017). Improving mathematical problem-solving ability and self- confidence of high school students through contextual learning model. Journal on Mathematics Education, 8(1), 85-94. https://doi.org/10.22342/jme.8.1.3324.85-94.
Suryana, A. (2015). Application of problem solving approach through problem story in fraction to improve student learning outcomes of fourth-grade students of Ciherang elementary school, Pamovery district, Sumedang regency [in Bahasa]. Jurnal Cakrawala Pendas, 1(2), 12–18.
Ulya, H. (2015). Relationship of cognitive style with students' mathematical problem solving ability [in Bahasa]. Jurnal Konseling Gusjigang, 1(2). https://doi.org/10.24176/jkg.v1i2.410.
Ulya, H. (2016). Profile of Problem solving ability of students with hight motivated to study based on Ideal problem solving [in Bahasa]. Jurnal Konseling Gusjigang, 2(1). https://doi.org/10.24176/jkg.v2i1.561.
Utomo, D. P. (2012). Learning circle using Polya version problem solving approach in class VIII in SMP PGRI 01 Dau [in Bahasa]. Widya Warta, 36(1), 145–158.
Wahyudi, & Budiyono, I. (2011). Mathematical problem solving [in Bahasa]. Widya Sari Press. Wahyudi, Waluya, S. B., Rochmad, & Suyitno, H. (2018). Assimilation and accommodation processes in improving mathematical creative thinking with scaffolding according to learning style. Journal of Physics: Conference Series. https://doi.org/10.1088/1742-6596/1097/1/012156.
Ward, S., Pellett, H. H., & Perez, M. I. (2017). Cognitive Disequilibrium and service-learning in physical education teacher education: Perceptions of pre-service teachers in a study abroad experience. Journal of Teaching in Physical Education, 36 (1), 70-82. https://doi.org/10.1123/jtpe.2015-0006.
Widodo, S. A., Istiqomah, Leonard, Nayazik, A., & Prahmana, R. C. I. (2019). Formal student thinking in mathematical problem-solving. Journal of Physics: Conference Series, 1188, 012087. https://doi.org/10.1088/1742-6596/1188/1/012087.
Widodo, S. A., & Turmudi. (2017). Guardian student thinking process in resolving issues divergence. Journal of Education and Learning, 11(4), 431–437. https://doi.org/10.11591/edulearn.v11i4.5639.
Widodo, S. A., Turmudi, & Dahlan, J. A. (2019). An error students in mathematical problems solves based on cognitive development. International Journal Of Scientific & Technology Research, 8(07), 433–439.
Widyastuti, R. (2015). Students' thinking processes in solving mathematical problems based on Polya's theory in term of adversity quotient type climber [in Bahasa]. Al-Jabar : Jurnal Pendidikan Matematika, 6(2), 183–193.
Wilkie, K. J. (2016). Rise or resist: Exploring senior secondary students’ reactions to challenging mathematics tasks incorporating multiple strategies. EURASIA Journal of Mathematics, Science and Technology Education, 12(8), 2061-2083. https://doi.org/10.12973/eurasia.2016.1260a.
Worsley, M., & Blikstein, P. (2015). Using learning analytics to study cognitive disequilibrium in a complex learning environment. ACM International Conference Proceeding Series. https://doi.org/10.1145/2723576.2723659.
Zhiqing, Z. (2015). Assimilation, accommodation, and equilibration: A schema-based perspective on translation as process and as product. International Forum of Teaching and Studies.