Student metacognition levels for solving PISA-like problems: A hierarchy
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Abstract
The metacognitive process is frequently presented in a fragmented manner, and a limited number of integrated learning models are designed to enhance these skills. These gaps underscore the necessity for research that defines metacognitive level hierarchies, clarifies process integration, and develops effective learning models to improve metacognitive abilities in PISA-like problem solving. This study aims to identify and describe the hierarchy of students' metacognitive levels as they solve PISA-like mathematical problems, mapping the stages of metacognition demonstrated throughout the problem-solving process. This qualitative study employed a phenomenological design, involving 76 students from three islands in Indonesia. Data were collected through tests, observations, and in-depth interviews, and were validated by implementing triangulation methods by comparing student answer sheets, observations, and interview results. The data were analyzed using thematic analysis. Then, five metacognition levels were identified: understanding the problem, thinking about the answer, comprehending how to answer, finding the answer, and being confident. Future research may focus on efforts to defragment and explore higher levels of metacognition and develop integrated learning models.
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Amini, D., Anhari, M. H., & Ghasemzadeh, A. (2020). Modeling the relationship between metacognitive strategy awareness, self-regulation and reading proficiency of Iranian EFL learners. Cogent Education, 7(1), 1787018. https://doi.org/10.1080/2331186x.2020.1787018
Anggo, M. (2011). Pelibatan metakognisi dalam pemecahan masalah matematika [Involvement of metacognition in mathematical problem solving]. Edumatica: Jurnal Pendidikan Matematika, 1(1), 25–32.
Annevirta, T., & Vauras, M. (2006). Developmental changes of metacognitive skill in elementary school children. The journal of experimental education, 74(3), 195–226. https://doi.org/10.3200/jexe.74.3.195-226
Bae, H., & Kwon, K. (2019). Developing metacognitive skills through class activities: what makes students use metacognitive skills? Educational Studies, 47(4), 456–471. https://doi.org/10.1080/03055698.2019.1707068
Bakar, M. A. A., & Ismail, N. (2019). Metacognitive learning strategies in mathematics classroom intervention: A review of implementation and operational design aspect. International Electronic Journal of Mathematics Education, 15(1), em0555. https://doi.org/10.29333/iejme/5937
Braun, V., & Clarke, V. (2019). Reflecting on reflexive thematic analysis. Qualitative Research in Sport, Exercise and Health, 11(4), 589–597. https://doi.org/10.1080/2159676x.2019.1628806
Callan, G. L., Marchant, G. J., Finch, W. H., & German, R. L. (2016). Metacognition, strategies, achievement, and demographics: Relationships across countries. Educational Sciences: Theory and Practice, 16(5), 1485–1502.
Chatzipanteli, A., Grammatikopoulos, V., & Gregoriadis, A. (2014). Development and evaluation of metacognition in early childhood education. Early Child Development and Care, 184(8), 1223–1232. https://doi.org/10.1080/03004430.2013.861456
Christ, L., & Dreesmann, D. C. (2022). Protect + prevent = preserve? Exploring students’ arguments for and attitudes toward conservation. Environmental Education Research, 29(1), 45–62. https://doi.org/10.1080/13504622.2022.2128059
Creswell, J. W. (2014). Research design: Qualitative, quantitative, and mixed methods approaches (4th ed.). Sage.
Desoete, A., & De Craene, B. (2019). Metacognition and mathematics education: an overview. Zdm, 51(4), 565–575. https://doi.org/10.1007/s11858-019-01060-w
Dragan, M., Dragan, W. Ł., Kononowicz, T., & Wells, A. (2012). On the relationship between temperament, metacognition, and anxiety: independent and mediated effects. Anxiety, Stress & Coping, 25(6), 697–709. https://doi.org/10.1080/10615806.2011.630071
Fisher, R. (1998). Thinking about thinking: Developing metacognition in children. Early Child Development and Care, 141(1), 1–15. https://doi.org/10.1080/0300443981410101
Flavell, J. H. (1979). Metacognition and cognitive monitoring: A new area of cognitive–developmental inquiry. American psychologist, 34(10), 906–911. https://doi.org/10.1037/0003-066x.34.10.906
Fleur, D. S., Bredeweg, B., & van den Bos, W. (2021). Metacognition: ideas and insights from neuro- and educational sciences. npj Science of Learning, 6(13), 1–11. https://doi.org/10.1038/s41539-021-00089-5
Guest, G., Namey, E., & Chen, M. (2020). A simple method to assess and report thematic saturation in qualitative research. PLoS One, 15(5), e0232076. https://doi.org/10.1371/journal.pone.0232076
Händel, M., Artelt, C., & Weinert, S. (2013). Assessing metacognitive knowledge: Development and evaluation of a test instrument. Journal for educational research online, 5(2), 162–188. https://doi.org/10.25656/01:8429
Hargrove, R. A., & Nietfeld, J. L. (2015). The impact of metacognitive instruction on creative problem solving. The journal of experimental education, 83(3), 291–318. https://doi.org/10.1080/00220973.2013.876604
Jayapraba, G. (2013). Metacognitive instruction and cooperative learning-strategies for promoting insightful learning in science. International Journal on New Trends in Education & their Implications (IJONTE), 4(1), 165–172.
Jiang, R., Liu, R. d., Star, J., Zhen, R., Wang, J., Hong, W., Jiang, S., Sun, Y., & Fu, X. (2020). How mathematics anxiety affects students' inflexible perseverance in mathematics problem‐solving: Examining the mediating role of cognitive reflection. British Journal of Educational Psychology, 91(1), 237–260. https://doi.org/10.1111/bjep.12364
Katsantonis, I. G. (2024). Typologies of teaching strategies in classrooms and students’ metacognition and motivation: a latent profile analysis of the Greek PISA 2018 data. Metacognition and Learning, 20(1), 4. https://doi.org/10.1007/s11409-024-09410-0
Kholid, M. N., & Ahadiyati, A. (2022). Students' metacognition in solving non-routine problems. Al-Jabar : Jurnal Pendidikan Matematika, 13(1), 125–138. https://doi.org/10.24042/ajpm.v13i1.11776
Kholid, M. N., & Lestari, N. P. (2019). Metakognisi siswa dalam menyelesaikan soal matematika berbasis PISA pada konten space and shape [Students' metacognition in solving PISA-based mathematics problems on space and shape content]. In Prosiding Seminar Nasional MIPA Kolaborasi, (Vol. 1, pp. 208–215).
Kholid, M. N., Putri, Y. P., Swastika, A., Maharani, S., & Ikram, M. (2022). What are the pupils’ challenges in implementing reflective thinking for problem-solving? AIP Conference Proceedings, 2479(1), 020012. https://doi.org/10.1063/5.0099600
Kholid, M. N., & Yuhana, N. D. (2019). Metakognisi mahasiswa dalam memecahkan masalah geometri analatik ruang ditinjau dari adversity quotient [Students' metacognition in solving analytical geometry problems in space as viewed from the adversity quotient]. In Seminar & Conference Proceedings of UMT, (pp. 32–39).
Kuzle, A. (2013). Patterns of metacognitive behavior during mathematics problem-solving in a dynamic geometry environment. International Electronic Journal of Mathematics Education, 8(1), 20–40. https://doi.org/10.29333/iejme/272
Laamena, C. M., & Laurens, T. (2021). Mathematical literacy ability and metacognitive characteristics of mathematics pre-service teacher. Infinity Journal, 10(2), 259–270. https://doi.org/10.22460/infinity.v10i2.p259-270
Landis, J. R., & Koch, G. G. (1977). An application of hierarchical Kappa-type statistics in the assessment of majority agreement among multiple observers. biometrics, 33(2), 363. https://doi.org/10.2307/2529786
Lingel, K., Lenhart, J., & Schneider, W. (2019). Metacognition in mathematics: do different metacognitive monitoring measures make a difference? Zdm, 51(4), 587–600. https://doi.org/10.1007/s11858-019-01062-8
Magiera, M. T., & Zawojewski, J. S. (2011). Characterizations of social-based and self-based contexts associated with students' awareness, evaluation, and regulation of their thinking during small-group mathematical modeling. Journal for Research in Mathematics Education JRME, 42(5), 486–520. https://doi.org/10.5951/jresematheduc.42.5.0486
Masduki, M., Kholid, M. N., & Khotimah, R. P. (2020). Exploring students' problem-solving ability and response towards metacognitive strategy in mathematics learning. Universal Journal of Educational Research, 8(8), 3698–3703. https://doi.org/10.13189/ujer.2020.080849
Mevarech, Z. R., & Fan, L. (2018). Cognition, metacognition, and mathematics literacy. In Y. J. Dori, Z. R. Mevarech, & D. R. Baker (Eds.), Cognition, Metacognition, and Culture in STEM Education: Learning, Teaching and Assessment (pp. 261–278). Springer International Publishing. https://doi.org/10.1007/978-3-319-66659-4_12
OECD. (2022). Programme for international student assessment (PISA) 2022 : Insights and interpretations. OECD Publishing.
Patton, M. Q. (2014). Qualitative research & evaluation methods: Integrating theory and practice. Sage publications.
Pennequin, V., Sorel, O., Nanty, I., & Fontaine, R. (2010). Metacognition and low achievement in mathematics: The effect of training in the use of metacognitive skills to solve mathematical word problems. Thinking & Reasoning, 16(3), 198–220. https://doi.org/10.1080/13546783.2010.509052
Puente-Díaz, R., Cavazos-Arroyo, J., & Vargas-Barrera, F. (2021). Metacognitive feelings as a source of information in the evaluation and selection of creative ideas. Thinking Skills and Creativity, 39. https://doi.org/10.1016/j.tsc.2020.100767
Purnomo, D., Nusantara, T., Subanji, S., & Rahardjo, S. (2017). The characteristic of the process of students’ metacognition in solving calculus problems. International Education Studies, 10(5), 13. https://doi.org/10.5539/ies.v10n5p13
Purnomo, R. C., Sunardi, S., Yuliati, N., Yudianto, E., Mahfut, M., & Sa’dijah, C. (2020). Anxiety: How was the process of the undergraduate students who were in visualization level in constructing the definition? Journal of Physics: Conference Series, 1465(1), 012049. https://doi.org/10.1088/1742-6596/1465/1/012049
Ramlah, R., Siswono, T. Y. E., & Lukito, A. (2024). Revealing the uniqueness of variations in prospective teachers' metacognitive activities in solving mathematical problems based on gender. Infinity Journal, 13(2), 477–500. https://doi.org/10.22460/infinity.v13i2.p477-500
Sa'dijah, C., Kholid, M. N., Hidayanto, E., & Permadi, H. (2020). Reflective thinking characteristics: A study in the proficient mathematics prospective teachers. Infinity Journal, 9(2), 159–172. https://doi.org/10.22460/infinity.v9i2.p159-172
Sahin, A., & Kulm, G. (2008). Sixth grade mathematics teachers’ intentions and use of probing, guiding, and factual questions. Journal of Mathematics Teacher Education, 11(3), 221–241. https://doi.org/10.1007/s10857-008-9071-2
Salwadila, T., & Hapizah, H. (2024). Computational thinking ability in mathematics learning of exponents in grade IX. Infinity Journal, 13(2), 441–456. https://doi.org/10.22460/infinity.v13i2.p441-456
Sari, Y. M., & Valentino, E. (2017). An analysis of students error in solving PISA 2012 and its scaffolding. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 1(2), 90–98. https://doi.org/10.23917/jramathedu.v1i2.3380
Schneider, W., & Artelt, C. (2010). Metacognition and mathematics education. Zdm, 42(2), 149–161. https://doi.org/10.1007/s11858-010-0240-2
Schraw, G., & Dennison, R. S. (1994). Assessing metacognitive awareness. Contemporary Educational Psychology, 19(4), 460–475. https://doi.org/10.1006/ceps.1994.1033
Semerari, A., Cucchi, M., Dimaggio, G., Cavadini, D., Carcione, A., Battelli, V., Nicolò, G., Pedone, R., Siccardi, T., D′Angerio, S., Ronchi, P., Maffei, C., & Smeraldi, E. (2012). The development of the metacognition assessment interview: Instrument description, factor structure and reliability in a non-clinical sample. Psychiatry Research, 200(2-3), 890–895. https://doi.org/10.1016/j.psychres.2012.07.015
Sengul, S., & Katranci, Y. (2015). Meta-cognitive aspects of solving indefinite integral problems. Procedia - Social and Behavioral Sciences, 197, 622–629. https://doi.org/10.1016/j.sbspro.2015.07.205
Shute, R. H. (2019). Schools, mindfulness, and metacognition: A view from developmental psychology. International Journal of School & Educational Psychology, 7(1), 123–136. https://doi.org/10.1080/21683603.2018.1435322
Sistyawati, R. I., Zulkardi, Z., Putri, R. I. I., Samsuriyadi, S., Alwi, Z., Sepriliani, S. P., Tanjung, A. L., Pratiwi, R. P., Aprilisa, S., Nusantara, D. S., Meryansumayeka, M., & Jayanti, J. (2023). Development of PISA types of questions and activities content shape and space context pandemic period. Infinity Journal, 12(1), 1–12. https://doi.org/10.22460/infinity.v12i1.p1-12
Sutama, S., Anif, S., Prayitno, H. J., Narimo, S., Fuadi, D., Sari, D. P., & Adnan, M. (2021). Metacognition of junior high school students in mathematics problem solving based on cognitive style. Asian Journal of University Education, 17(1), 134–144. https://doi.org/10.24191/ajue.v17i1.12604
Sutama, S., Prayitno, H., Anif, S., Faiziyah, N., Novitasari, M., & Fadhilah, M. (2019). A PISA-based student worksheet for better understanding of mathematical concept Proceedings of the Proceedings of the 4th Progressive and Fun Education International Conference, Makassar, Indonesia.
Sutarni, S., Sutama, S., Prayitno, H. J., Sutopo, A., & Laksmiwati, P. A. (2024). The development of realistic mathematics education-based student worksheets to enhance higher-order thinking skills and mathematical ability. Infinity Journal, 13(2), 285–300. https://doi.org/10.22460/infinity.v13i2.p285-300
Toit, S. D., & Kotze, G. (2009). Metacognitive strategies in the teaching and learning of mathematics. Pythagoras, 2009(70), 57–67. https://doi.org/10.10520/EJC20916
Vorhölter, K. (2021). Metacognition in mathematical modeling: The connection between metacognitive individual strategies, metacognitive group strategies and modeling competencies. Mathematical thinking and learning, 25(3), 317–334. https://doi.org/10.1080/10986065.2021.2012740
Vygotsky, L. S. (1978). Mind in society: Development of higher psychological processes. Harvard university press.
Weiland, I. S., Hudson, R. A., & Amador, J. M. (2014). Preservice Formative Assessment Interviews: The Development of Competent Questioning. International Journal of Science and Mathematics Education, 12(2), 329–352. https://doi.org/10.1007/s10763-013-9402-3
Wijaya, T. T., Hidayat, W., Hermita, N., Alim, J. A., & Talib, C. A. (2024). Exploring contributing factors to PISA 2022 mathematics achievement: Insights from Indonesian teachers. Infinity Journal, 13(1), 139–156. https://doi.org/10.22460/infinity.v13i1.p139-156
Wilson, J., & Clarke, D. (2004). Towards the modelling of mathematical metacognition. Mathematics Education Research Journal, 16(2), 25–48. https://doi.org/10.1007/bf03217394
Wong, P. (1992). Metacognition in mathematical problem solving. Singapore Journal of Education, 12(2), 48–58. https://doi.org/10.1080/02188799208547691
Yorulmaz, A., Uysal, H., & Çokçalışkan, H. (2021). Pre-service primary school teachers’ metacognitive awareness and beliefs about mathematical problem solving. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 6(3), 239–259. https://doi.org/10.23917/jramathedu.v6i3.14349
Zhang, L. f. (2010). Do thinking styles contribute to metacognition beyond self‐rated abilities? Educational Psychology, 30(4), 481–494. https://doi.org/10.1080/01443411003659986
Zhang, W., & Lian, R. (2024). The impact of reading metacognitive strategies on mathematics learning efficiency and performance: An analysis using PISA 2018 data in China. Acta Psychologica, 246, 104247. https://doi.org/10.1016/j.actpsy.2024.104247
Zimmerman, B. J. (1990). Self-regulated learning and academic achievement: An overview. Educational Psychologist, 25(1), 3–17. https://doi.org/10.1207/s15326985ep2501_2
Zohar, A., & Barzilai, S. (2013). A review of research on metacognition in science education: current and future directions. Studies in Science Education, 49(2), 121–169. https://doi.org/10.1080/03057267.2013.847261