Characteristics of Students' Metacognitive Ability in Solving Problems using Awareness, Regulation and Evaluation Components

Anita Adinda, Heri Purnomo, Desi Rahmatina, Nur Choiro Siregar

Abstract


The process of solving absolute value problems is not only associated with the simplification of equations or inequalities. Students also need to pay close attention, ask the right questions, carry out the right strategies, and acquire adequate information. This step is essential to prevent students with good metacognitive ability from drawing wrong conclusions. The research discusses the metacognitive characteristics of mathematics education students in solving absolute value problems from the awareness, regulation and evaluation components. Participants consisted of 101 students from four state universities in the city of Malang. Data were obtained through written answers, transcripts of think aloud, and interviews. The data collected were analyzed to determine their metacognitive abilities in terms of awareness, regulation and evaluation components. The result showed that the metacognitive ability of low-skilled students only exists in the awareness component, which is thinking about what is being asked. Furthermore, those medium capable of the awareness component still lack adequate thinking ability. In the regulation and evaluation components, students do not realize that there are still inappropriate steps in solving problems and fail to check the correctness of their answers. However, high-ability students can solve problems in different ways and easily distinguish accurate information using effective strategies. Learn how the metacognitive characteristics of students in solving non-routine absolute value application questions, provides space for educators to be able to create appropriate learning models.

Keywords


Absolute value, awareness, evaluation, metacognitive, regulation, evaluation

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Abdallah, L., Haddou, M., & Migot, T. (2018). Solving absolute value equation using complementarity and smoothing functions. Journal of Computational and Applied Mathematics, 327, 196–207. https://doi.org/10.1016/j.cam.2017.06.019

Adinda, A., Purwanto, P., Parta, I. N., & Chandra, T. D. (2021). Investigation of students’ metacognitive awareness failures about solving absolute value problems in mathematics education. Eurasian Journal of Educational Research, 2021(95), 17–35. https://doi.org/10.14689/ejer.2021.95.2

Akben, N. (2020). Effects of the problem-posing approach on students’ problem solving skills and metacognitive awareness in science education. Research in Science Education, 50(3), 1143–1165. https://doi.org/10.1007/s11165-018-9726-7

Almog, N., & Ilany, B. S. (2012). Absolute value inequalities: High school students’ solutions and misconceptions. Educational Studies in Mathematics, 81(3), 347–364. https://doi.org/10.1007/s10649-012-9404-z

Amram, M., Dagan, M., Satianov, P., & Yoshpe, M. (2019). The absolute value operation as an effective tool for enhancing students’ cognitive activities in Calculus courses. International Journal of Contemporary Mathematical Sciences, 14(1), 9–15. https://doi.org/10.12988/ijcms.2019.81235

Arends, R. I. (2012). Learning to Teach (Beth Mejia & M. Magaziner (eds.); Ninth Edit). The McGraw-Hill Companies.

As’ari, A. R., Mahmudi, A., & Nuerlaelah, E. (2017). Our prospective mathematic teachers are not critical thinkers yet. Journal on Mathematics Education, 8(2), 145–156. https://doi.org/10.22342/jme.8.2.3961.145-156

Aurah, C. M., Koloi-Keaikitse, S., Isaacs, C., & Finc, H. (2011). The role of metacognition in everyday problem solving among primary students in Kenya. Problems of Education in the 21st Century, 30, 9–21.

Boekaerts, M. (1999). Metacognitive experiences and motivational state as aspects of self-awareness: Review and discussion. European Journal of Psychology of Education, 14(4), 571–584. https://doi.org/10.1007/BF03172980

Creswell, J. W. (2009). Research design: Qualitative, quantitative, and mixed methods approaches. SAGE Publications Inc. https://doi.org/10.1080/14675980902922143

Demirel, M., Aşkın, İ., & Yağcı, E. (2015). An investigation of teacher candidates’ metacognitive skills. Procedia - Social and Behavioral Sciences, 174, 1521–1528. https://doi.org/10.1016/j.sbspro.2015.01.783

Efklides, A. (2006). Metacognition and affect: What can metacognitive experiences tell us about the learning process? Educational Research Review, 1(1), 3–14. https://doi.org/10.1016/j.edurev.2005.11.001

El-khateeb, M. M. A. (2016). Errors analysis of solving linear inequalities among the preparatory year students at king saud university . Journal of Education and Practice, 7(12), 124–133.

Elia, I., Özel, S., Gagatsis, A., Panaoura, A., & Özel, Z. E. Y. (2016). Students’ mathematical work on absolute value: Focusing on conceptions, errors and obstacles. ZDM - Mathematics Education, 48(6), 895–907. https://doi.org/10.1007/s11858-016-0780-1

Flavell, J. H. (1979). Metacognition and cognitive monitoring a new area of cognitive — developmental inquiry. American Psychologist, 34(10), 906–911.

Güner, P., & Erbay, H. N. (2021). Metacognitive skills and problem-solving. International Journal of Research in Education and Science, 7(3), 715–734. https://doi.org/10.46328/ijres.1594

Jia, X., Li, W., & Cao, L. (2019). The role of metacognitive components in creative thinking. Frontiers in Psychology, 10, 1-11. https://doi.org/10.3389/fpsyg.2019.02404

Karaali, G. (2015). Metacognition in the classroom: Motivation and self-awareness of mathematics learners. Primus, 25(5), 439–452. https://doi.org/10.1080/10511970.2015.1027837

Kazemi, F., Reza, M., & Bayat, S. (2010). A subtle view to metacognitive aspect of mathematical problems solving. Procedia-Social and Behavioral Sciences, 8, 420–426. https://doi.org/10.1016/j.sbspro.2010.12.058

Kelemen, W. L., Frost, P. J., & Weaver, C. A. (2000). Individual differences in metacognition: Evidence against a general metacognitive ability. Memory and Cognition, 28(1), 92–107. https://doi.org/10.3758/BF03211579

Kuzle, A. (2019). Second graders’ metacognitive actions in problem solving revealed through action cards. The Mathematics Educator, 28(1), 27–60.

Li, C., & Nietfeld, J. L. (2007). College students’ metacognitive awareness of difficulties in learning the class content does not automatically lead to adjustment of study strategies. Australian Journal of Educational and Developmental Psychology, 7(678), 31–46.

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, 42(5), 486-520. https://doi.org/10.5951/jresematheduc.42.5.0486

Memnun, D. S., & Akkaya, R. (2009). The levels of metacognitive awareness of primary teacher trainees. Procedia - Social and Behavioral Sciences, 1(1), 1919–1923. https://doi.org/10.1016/j.sbspro.2009.01.337

Misu, L., Budayasa, I. K., Lukito, A., Hasnawati, & Rahim, U. (2019). Profile of metacognition of mathematics education students in understanding the concept of integral in category classifying and summarizing. International Journal of Instruction, 12(3), 481–496. https://doi.org/10.29333/iji.2019.12329a

O’Neil, H. F., & Brown, R. S. (1998). Differential Effects of Question Formats in Math Assessment on Metacognition and Affect. Applied Measurement in Education, 11(4), 331–351. https://doi.org/10.1207/s15324818ame1104_3

Oz, H. (2016). The importance of personality traits in students perceptions of metacognitive awareness. Procedia - Social and Behavioral Sciences, 232, 655–667. https://doi.org/10.1016/j.sbspro.2016.10.090

Panaoura, A., Gagatsis, A., & Demetriou, A. (2009). An intervention to the metacognitive performance: Self-regulation in mathematics and mathematical modeling. Acta Didactica Universitatis Comenianae, 9(9), 63–79. https://www.researchgate.net/publication/228416735_An_intervention_to_the_metacognitive_performance_Self-regulation_in_mathematics_and_mathematical_modeling

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), 13-25. https://doi.org/10.5539/ies.v10n5p13

Santoso, F. E., Napitupulu, E. E., & Amry, Z. (2019). Metacognitive level analysis of high school students in mathematical problem-solving skill. American Journal of Educational Research, 7(12), 919–924. https://doi.org/10.12691/education-7-12-4

Schraw, G., & Dennison, R. S. (1994). Assessing metacognitive awareness. Contemporary Educational Psychology, 19(4), 460-475. https://doi.org/http://dx.doi.org/10.1006/ceps.1994.1033

Schraw, Gregory, & Moshman, D. (1995). Metacognitive theories. Educational Psychology Review, 7(4), 351–371. https://doi.org/10.1007/BF02212307

Setiawan, B., & Supiandi, M. I. (2019). The contribution of metacognitive skills and reasoning skills on problem solving ability based on problem based learning (PBL) model. Anatolian Journal of Education, 3(2), 75-86. https://doi.org/10.29333/aje.2018.327a

Sierpinska, A., Bobos, G., & Pruncut, A. (2015). Teaching absolute value inequalities to mature students. Educational Studies in Mathematics, 78(3), 275–305. https://doi.org/10.1007/s10649-011-9325-2.The

Suryaningtyas, S., & Setyaningrum, W. (2020). Analisis kemampuan metakognitif siswa SMA kelas XI program IPA dalam pemecahan masalah matematika. Jurnal Riset Pendidikan Matematika, 7(1), 74–87. https://doi.org/10.21831/jrpm.v7i1.16049

Swartz, R. J. T., & Perkins, D. N. (2017). Teaching Thinking: Issues and Approaches (24th ed.). Routledge Taylor & Francis Group. https://doi.org/10.4324/9781315626468

Syaiful, Huda, N., Mukminin, A., & Kamid. (2022). Using a metacognitive learning approach to enhance students’ critical thinking skills through mathematics education. SN Social Sciences, 2(4), 1–26. https://doi.org/10.1007/s43545-022-00325-8

Van de Walle, J. A. (2007). Elementary and middle school mathematics (6th ed.). Boston: Pearson.

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

Yong, L. (2015). Iteration method for absolute value equation and applications in two-point boundary value problem of linear differential equation. Journal of Interdisciplinary Mathematics, 18(4), 355–374. https://doi.org/10.1080/09720502.2014.996022

Young, A., & Fry, J. D. (2008). Metacognitive awareness and academic achievement in college students. Journal of the Scholarship of Teaching and Learning, 8(5), 1–10. https://doi.org/10.3109/0142159X.2010.487711

Zhang, L., & Seepho, S. (2013). Metacognitive strategy use and academic reading achievement: Insights from a Chinese context. Electronic Journal of Foreign Language Teaching, 10(1), 54–69.

Zhao, N., Wardeska, J., McGuire, S., & Cook, E. (2014). Metacognition: An effective tool to promote success in college science learning. Journal of College Science Teaching, 043(04), 48–54. https://doi.org/10.2505/4/jcst14_043_04_48




DOI: https://doi.org/10.24815/jdm.v10i1.29041

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Jurnal Didaktik Matematika

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