The Impact of Metacognitive Strategy Training on Higher-Order Thinking Skills (HOTS) in High School Mathematics: A Quasi-Experimental Study
Article Sidebar
Main Article Content
Abstract
Difficulties developing higher-order thinking skills (HOTS) in mathematics education represent a persistent and significant challenge in educational practice. These skills, such as analysis, evaluation, and creation, are essential for students to succeed in complex problem-solving and adapt to the evolving demands of the 21st century. This study assesses how effectively structured metacognitive training improves high school students' mathematical HOTS. The research employed a quasi-experimental pretest-posttest design involving 72 students from a senior high school in Indonesia, divided into two groups: an experimental group (n=36) that received metacognitive training over one semester, and a control group (n=36) that did not receive any intervention. The primary outcome measure was HOTS scores, assessed through standardized pre-test and post-test instruments designed to evaluate students' higher-order thinking in mathematics. ANCOVA results revealed a significant effect of the metacognitive intervention on HOTS post-test scores (F=44.36; p<0.001; ηp²=0.391), even after controlling for pre-test performance. The experimental group exhibited substantially greater HOTS improvements than the control group. These results prove that structured metacognitive training is an effective pedagogical strategy for fostering advanced mathematical thinking. The findings hold significant implications for curriculum designers, educators, and policymakers aiming to improve mathematics instruction, particularly within the Indonesian context. Future studies involving larger sample sizes, diverse school settings, and longitudinal follow-up are recommended to validate and extend the impact of this intervention.
Downloads
Article Details
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Copyright of the published article belongs to the authors and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution-ShareAlike 4.0 (CC BY SA) International License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See the Effect of Open Access).
References
[1] R. Collins, “Skills for the 21st Century: teaching higher-order thinking,” Curric. Leadersh. J., vol. 12, no. 14, pp. 1–8, 2014.
[2] W. Conklin, Higher-Order Thinking Skills to Develop 21st Century Learners. Huntington Beach, CA: Teacher Created Materials, 2012.
[3] S. M. Brookhart, How to assess higher-order thinking skills in your classroom. Ascd, 2010.
[4] A. Zohar and S. Barzilai, “A review of research on metacognition in science education: current and future directions,” Stud. Sci. Educ., vol. 49, no. 2, pp. 121–169, 2013, doi: 10.1080/03057267.2013.847261.
[5] OECD, “PISA 2022 Results (Volume I): The State of Learning and Equity in Education,” OECD Publishing, Paris, 2023. doi: 10.1787/53f23881-en.
[6] A. Schleicher, “PISA 2018: Insights and interpretations.,” 2019.
[7] C. Saavedra and W. W. Budd, “Climate change and environmental planning: Working to build community resilience and adaptive capacity in Washington State, USA,” Habitat Int., vol. 33, no. 3, pp. 246–252, 2009, doi: 10.1016/j.habitatint.2008.10.004.
[8] J. H. Flavell, “Metacognition and cognitive monitoring: A new area of cognitive-developmental inquiry,” Am. Psychol., vol. 34, no. 10, pp. 906–911, 1979, doi: 10.1037/0003-066X.34.10.906.
[9] G. M. Harrison and L. M. Vallin, “Evaluating the metacognitive awareness inventory using empirical factor-structure evidence,” Metacognition Learn., vol. 13, no. 1, pp. 15–38, 2018, doi: 10.1007/s11409-017-9176-z.
[10] G. Schraw and R. S. Dennison, “Assessing metacognitive awareness,” Contemp. Educ. Psychol., vol. 19, no. 4, pp. 460–475, 1994, doi: 10.1006/ceps.1994.1033.
[11] A. Efklides, “Metacognition: Defining its facets and levels of functioning in relation to self-regulation and co-regulation,” Eur. Psychol., vol. 13, no. 4, pp. 277–287, 2008, doi: 10.1027/1016-9040.13.4.277.
[12] X. Wang, X. Liu, L. Chen, K. Feng, Q. Ye, and H. Zhu, “The Forward Effect of Delayed Judgments of Learning Is Influenced by Difficulty in Memory and Category Learning,” J. Intell., vol. 11, no. 6, pp. 1–18, 2023, doi: 10.3390/jintelligence11060101.
[13] E. Panadero, “A review of self-regulated learning: Six models and four directions for research,” Front. Psychol., vol. 8, no. APR, p. 422, 2017, doi: 10.3389/fpsyg.2017.00422.
[14] C. D. Zepeda, J. Elizabeth Richey, P. Ronevich, and T. J. Nokes-Malach, “Direct instruction of metacognition benefits adolescent science learning, transfer, and motivation: An in vivo study,” J. Educ. Psychol., vol. 107, no. 4, pp. 954–970, 2015, doi: 10.1037/edu0000022.
[15] S. L. Wismath and D. Orr, “Collaborative Learning in Problem Solving: A Case Study in Metacognitive Learning,” Can. J. Scholarsh. Teach. Learn., vol. 6, no. 3, p. 10, 2015, doi: 10.5206/cjsotl-rcacea.2015.3.10.
[16] I. G. A. L. Parwata, I. N. L. Jayanta, and I. W. Widiana, “Improving Metacognitive Ability and Learning Outcomes with Problem-Based Revised Bloom’s Taxonomy Oriented Learning Activities,” Emerg. Sci. J., vol. 7, no. 2, pp. 569–577, 2023, doi: 10.28991/ESJ-2023-07-02-019.
[17] B. Kramarski and Z. R. Mevarech, “Enhancing mathematical reasoning in the classroom: The effects of cooperative learning and metacognitive training,” Am. Educ. Res. J., vol. 40, no. 1, pp. 281–310, 2003, doi: 10.3102/00028312040001281.
[18] S. Fowler, J. P. Kennedy, C. Cutting, F. Gabriel, and S. N. Leonard, “Self-determined learning in a virtual makerspace: a pathway to improving spatial reasoning for upper primary students,” Int. J. Technol. Des. Educ., vol. 34, no. 2, pp. 563–584, 2024, doi: 10.1007/s10798-023-09840-y.
[19] D. H. Jonassen and L. Rohrer-Murphy, “Activity theory as a framework for designing constructivist learning environments,” Educ. Technol. Res. Dev., vol. 47, no. 1, pp. 61–79, 1999, doi: 10.1007/BF02299477.
[20] B. R. Belland, C. M. Kim, and M. J. Hannafin, “A Framework for Designing Scaffolds That Improve Motivation and Cognition,” Educ. Psychol., vol. 48, no. 4, pp. 243–270, 2013, doi: 10.1080/00461520.2013.838920.
[21] B. Kwon and O. K. Yang, “The effects of autonomy support and psychological capital on readiness for independent living through personal growth initiative among youth in out-of-home care,” Asian Soc. Work Policy Rev., vol. 14, no. 2, pp. 85–98, 2020, doi: 10.1111/aswp.12196.
[22] T. Lehtimäki, R. Monahan, A. Mooney, K. Casey, and T. J. Naughton, “A Computational Thinking Obstacle Course Based on Bebras Tasks for K-12 Schools,” Annu. Conf. Innov. Technol. Comput. Sci. Educ. ITiCSE, vol. 1, pp. 478–484, 2023, doi: 10.1145/3587102.3588775.
[23] S. Grover and R. Pea, “Computational Thinking: A Competency Whose Time Has Come,” Comput. Sci. Educ., vol. 19, no. 1, pp. 19–38, 2023, doi: 10.5040/9781350296947.ch-005.
[24] K. Brennan and M. Resnick, “New frameworks for studying and assessing the development of computational thinking,” in annual American Educational Research Association meeting, Vancouver, BC, Canada, 2012, vol. 1, pp. 1–25, [Online]. Available: http://web.media.mit.edu/~kbrennan/files/Brennan_Resnick_AERA2012_CT.pdf.
[25] K. Fricke and B. Reinisch, “Evaluation of Nature of Science Representations in Biology School Textbooks Based on a Differentiated Family Resemblance Approach,” Sci. Educ., vol. 32, no. 5, pp. 1583–1611, 2023, doi: 10.1007/s11191-023-00444-5.
[26] A. J. Stylianides and G. J. Stylianides, “Impacting positively on students’ mathematical problem solving beliefs: An instructional intervention of short duration,” J. Math. Behav., vol. 33, no. 1, pp. 8–29, 2014, doi: 10.1016/j.jmathb.2013.08.005.
[27] J. K. J. Khadka, D. R. Joshi, K. P. Adhikari, and B. Khanal, “Teachers’ Humanistic Role in Teaching Mathematics Online During the COVID-19 Pandemic in Nepal,” Int. J. Distance Educ. Technol., vol. 21, no. 1, pp. 1–19, 2023, doi: 10.4018/ijdet.324951.
[28] M. Nind and J. Grace, “The emotional wellbeing of students with profound intellectual disabilities and those who work with them: a relational reading,” Disabil. Soc., vol. 40, no. 7, pp. 1757–1778, 2024, doi: 10.1080/09687599.2024.2407819.
[29] B. J. Zimmerman, “Becoming a self-regulated learner: An overview,” Theory Pract., vol. 41, no. 2, pp. 64–70, 2002, doi: 10.1207/s15430421tip4102_2.
[30] R. Fogarty, The Mindful School: How To Teach for Metacognitive Reflection. ERIC, 1994.
[31] L. Qiao, W. Zhao, F. Liu, X. Xu, and J. Tao, “Effects of multilevel metacognition on group performance and regulation in collaborative learning,” Front. Psychol., vol. 15, p. 1419408, 2024, doi: 10.3389/fpsyg.2024.1419408.
[32] A. L. Brown, “Metacognition, executive control, self-regulation, and other more mysterious mechanisms,” Metacognition, Motiv. Underst., pp. 65–116, 1987.
[33] M. V. J. Veenman, B. H. A. M. Van Hout-Wolters, and P. Afflerbach, “Metacognition and learning: Conceptual and methodological considerations,” Metacognition Learn., vol. 1, no. 1, pp. 3–14, 2006, doi: 10.1007/s11409-006-6893-0.
[34] S. Kusaka and K. Ndihokubwayo, “Metacognitive strategies in solving mathematical word problems: a case of Rwandan primary school learners,” SN Soc. Sci., vol. 2, no. 9, p. 186, 2022, doi: 10.1007/s43545-022-00495-5.
[35] G. Polya, “How to Solve It,” How to Solve It, 2019, doi: 10.2307/j.ctvc773pk.
[36] M. Montague, “Self-regulation strategies to improve mathematical problem solving for students with learning disabilities,” Learn. Disabil. Q., vol. 31, no. 1, pp. 37–44, 2008, doi: 10.2307/30035524.
[37] C. Dignath and G. Büttner, “Components of fostering self-regulated learning among students. A meta-analysis on intervention studies at primary and secondary school level,” Metacognition Learn., vol. 3, no. 3, pp. 231–264, 2008, doi: 10.1007/s11409-008-9029-x.
[38] A. Zohar and B. Peled, “The effects of explicit teaching of metastrategic knowledge on low- and high-achieving students,” Learn. Instr., vol. 18, no. 4, pp. 337–353, 2008, doi: 10.1016/j.learninstruc.2007.07.001.
[39] D. Kuhn and D. Dean, “Metacognition: A bridge between cognitive psychology and educational practice,” Theory Pract., vol. 43, no. 4, pp. 268–273, 2004, doi: 10.1353/tip.2004.0047.
[40] R. Azevedo and A. F. Hadwin, “Scaffolding self-regulated learning and metacognition - Implications for the design of computer-based scaffolds,” Instr. Sci., vol. 33, no. 5–6, pp. 367–379, 2005, doi: 10.1007/s11251-005-1272-9.
[41] S. Sujatmika, Sutarno, M. Masykuri, and B. A. Prayitno, “Applying the Rasch model to measure students’ critical thinking skills on the science topic of the human circulatory system,” Eurasia J. Math. Sci. Technol. Educ., vol. 21, no. 4, p. em2622, 2025, doi: 10.29333/ejmste/16221.
[42] S. Olstad, S. Solem, O. Hjemdal, and R. Hagen, “Metacognition in eating disorders: Comparison of women with eating disorders, self-reported history of eating disorders or psychiatric problems, and healthy controls,” Eat. Behav., vol. 16, pp. 17–22, 2015, doi: 10.1016/j.eatbeh.2014.10.019.
[43] A. M. Grant, “Rethinking psychological mindedness: Metacognition, self-reflection, and insight,” Behav. Chang., vol. 18, no. 1, pp. 8–17, 2001, doi: 10.1375/bech.18.1.8.
[44] Y. Wang, H. Zhang, J. Wang, and X. Ma, “The Impact of Prompts and Feedback on the Performance during Multi-Session Self-Regulated Learning in the Hypermedia Environment,” J. Intell., vol. 11, no. 7, 2023, doi: 10.3390/jintelligence11070131.
[45] K. Mulholland, W. Gray, C. Counihan, and D. Nichol, “Stepping Stones: Adopting a Fading Programme Design to Promote Teachers’ Use of Metacognitive Strategies for Mathematical Problem Solving,” Educ. Sci., vol. 15, no. 7, p. 892, 2025, doi: 10.3390/educsci15070892.
[46] A. Bandura, “Self-efficacy: toward a unifying theory of behavioral change.,” Psychol. Rev., vol. 84, no. 2, p. 191, 1977.
[47] J. Hattie, Visible learning: A synthesis of over 800 meta-analyses relating to achievement. routledge, 2008.
[48] L. S. Shulman, “Those who understand: Knowledge growth in teaching,” J. Educ., vol. 193, no. 3, pp. 1–11, 2013, doi: 10.1177/002205741319300302.
[49] D. R. Krathwohl, “A revision of bloom’s taxonomy: An overview,” Theory Pract., vol. 41, no. 4, pp. 212–218, 2002, doi: 10.1207/s15430421tip4104_2.
[50] L. W. Anderson, D. R. Krathwohl, and B. S. Bloom, A taxonomy for learning, teaching, and assessing: a revision of Bloom’s taxonomy of educational objectives. Addison Wesley Longman, Inc., 2001.
[51] N. Kania and Y. S. Kusumah, “the Measurement of Higher-Order Thinking Skills: a Systematic Literature Review,” Malaysian J. Learn. Instr., vol. 22, no. 1, pp. 97–116, 2025, doi: 10.32890/mjli2025.22.1.6.
[52] W. J. Boone, M. S. Yale, and J. R. Staver, Rasch analysis in the human sciences, vol. 10. Springer, 2014.
[53] T. G. Bond, Z. Yan, and M. Heene, Applying the rasch model: Fundamental measurement in the human sciences. Psychology Press, 2020.
[54] A. Zohar and Y. J. Dori, “Higher order thinking skills and low-achieving students: Are they mutually exclusive?,” J. Learn. Sci., vol. 12, no. 2, pp. 145–181, 2003, doi: 10.1207/S15327809JLS1202_1.
[55] T. M. Haladyna and M. C. Rodriguez, Developing and validating test items. Routledge, 2013.
[56] S. G. Paris and P. Winograd, “Promoting Metacognition and Motivation of Exceptional Children,” Remedial Spec. Educ., vol. 11, no. 6, pp. 7–15, 1990, doi: 10.1177/074193259001100604.
[57] D. Moshman, “Metacognitive Theories Revisited,” Educ. Psychol. Rev., vol. 30, no. 2, pp. 599–606, 2018, doi: 10.1007/s10648-017-9413-7.
[58] A. Efklides, “Metacognition and affect: What can metacognitive experiences tell us about the learning process?,” Educ. Res. Rev., vol. 1, no. 1, pp. 3–14, 2006, doi: 10.1016/j.edurev.2005.11.001.
[59] B. J. Zimmerman, “Self-Efficacy: An Essential Motive to Learn,” Contemp. Educ. Psychol., vol. 25, no. 1, pp. 82–91, 2000, doi: 10.1006/ceps.1999.1016.
[60] P. R. Pintrich, “The role of metacognitive knowledge in learning, teaching, and assessing,” Theory Pract., vol. 41, no. 4, pp. 219–225, 2002, doi: 10.1207/s15430421tip4104_3.
[61] P. Nenniger, “Commentary on self-regulation in the classroom: A perspective on assessment and intervention,” Appl. Psychol., vol. 54, no. 2, pp. 239–244, 2005, doi: 10.1111/j.1464-0597.2005.00207.x.
[62] M. Boekaerts and L. Corno, “Self‐regulation in the classroom: A perspective on assessment and intervention,” Appl. Psychol., vol. 54, no. 2, pp. 199–231, 2005, doi: 10.1111/j.1464-0597.2005.00205.x.
[63] D. L. C. Cornoldi, “Mathematics and Metacognition: What Is the Nature of the Relationship?,” Math. Cogn., vol. 3, no. 2, pp. 121–139, 1997, doi: 10.1080/135467997387443.
[64] V. Pennequin, O. Sorel, I. Nanty, and R. Fontaine, “Metacognition and low achievement in mathematics: The effect of training in the use of metacognitive skills to solve mathematical word problems,” Think. Reason., vol. 16, no. 3, pp. 198–220, 2010, doi: 10.1080/13546783.2010.509052.
[65] A. Desoete, H. Roeyers, and A. Huylebroeck, “Metacognitive skills in Belgian third grade children (age 8 to 9) with and without mathematical learning disabilities,” Metacognition Learn., vol. 1, no. 2, pp. 119–135, 2006, doi: 10.1007/s11409-006-8152-9.
[66] A. Desoete and H. Roeyers, “Off-line metacognition - A domain-specific retardation in young children with learning disabilities?,” Learn. Disabil. Q., vol. 25, no. 2, pp. 123–139, 2002, doi: 10.2307/1511279.
[67] R. Azevedo, “Reflections on the field of metacognition: issues, challenges, and opportunities,” Metacognition Learn., vol. 15, no. 2, pp. 91–98, 2020, doi: 10.1007/s11409-020-09231-x.
[68] J. Dunlosky and J. Metcalfe, Metacognition. Sage Publications, 2008.
[69] R. P. Balzan, M. Gilder, M. Thompson, and T. D. Wade, “A randomized controled feasibility trial of metacognitive training with adolescents receiving treatment for anorexia nervosa.,” Int. J. Eat. Disord., 2023, doi: 10.1002/eat.24009.
[70] C. B. McCormick, C. Dimmitt, and F. R. Sullivan, “Metacognition, Learning, and Instruction,” in Handbook of psychology: Educational psychology, 2nd ed., 4: John Wiley & Sons, Inc.., 2013.
[71] D. August, C. D. Barr, and C. D. Carlson, “A promising intervention designed to improve EAL learners’ mathematics skills and associated academic language,” Biling. Res. J., pp. 1–25, 2023, doi: 10.1080/15235882.2023.2225459.
[72] P. R. Pintrich, “A conceptual framework for assessing motivation and self-regulated learning in college students,” Educ. Psychol. Rev., vol. 16, no. 4, pp. 385–407, 2004, doi: 10.1007/s10648-004-0006-x.
[73] A. Desoete and B. De Craene, “Metacognition and mathematics education: an overview,” ZDM - Math. Educ., vol. 51, no. 4, pp. 565–575, 2019, doi: 10.1007/s11858-019-01060-w.
[74] W. Schneider and C. Artelt, “Metacognition and mathematics education,” ZDM, vol. 42, no. 2, pp. 149–161, 2010.