AN ANALYSIS OF THE COMPONENTS OF METACOGNITION IN MATHEMATICAL KNOWLEDGE CONSTRUCTION
DOI:
https://doi.org/10.18173/2354-1075.2026-0015Keywords:
metacognition, metacognitive knowledge, metacognitive strategies, mathematical knowledge constructionAbstract
Metacognition plays a critical role in guiding, regulating, and monitoring teaching and learning processes. Despite its acknowledged importance, research focusing on metacognition in the process of knowledge construction remains relatively limited, partly due to the diversity of conceptualizations and the challenges associated with measuring metacognition. This study aims to analyze and clarify the metacognitive components inherent in the construction of mathematical knowledge. Adopting qualitative research, the study synthesizes relevant literature and incorporates classroom observations of constructivist-oriented mathematics instruction at the primary level. The collected data were analyzed to identify students’ metacognitive manifestations during the construction of mathematical knowledge. Based on these findings, the study proposes a framework of metacognitive components in mathematical knowledge construction, comprising metacognitive knowledge and metacognitive strategies. These components are illustrated through a constructivist teaching situation involving the derivation of the area formula for a trapezoid in Grade 5.
Downloads
References
[1] De Corte E, (2000). Marrying theory building and the improvement of school practice: A permanent challenge for instructional psychology. Learning and Instruction, 10, 249-266.
[2] Resnick LB, (1989). Introduction. In Resnick LB (Ed.). Knowing, learning, and instruction (p.1-25). Hillsdale NJ, Lawrence Erlbaum.
[3] Steffe LP & Kieren T, (1994). Radical constructivism and mathematics education. Journal for Research in Mathematics Education, 25(6), 71-733.
[4] Laz HA & Shafei KE, (2014). The effectiveness of constructivist learning model in the teaching of mathematics. Journal of Applied and Industrial Sciences, 2(3), 106-109.
[5] Vasuki M, Celestin M & Kumar AD, (2016). Constructivism in the math classroom: theory, practice, and challenges. Practice, 2(2).
[6] Flavell JH, (1976). Metacognitive aspects of problem solving. In Resnick LB (ed.), The nature of intelligence, chapter 12, p. 231-235, Lawrence Erlbaum Associates, Hillsdale, New Jersey.
[7] Brown AL, Bransford JD, Ferrara RA, & Campion JC, (1983). Learning, Remembering, and Understanding, Handbook of Child Psychology (4th ed.), Cognitive development, Vol. 3, 420-494, New York: Wiley.
[8] Flavell JH, (1979). Metacognition and cognitive monitoring: A new area of cognitive developmental inquiry. American Psychology, 34(10), 906-911.
[9] Rozencwajg P, (2003). Metacognitive factors in scientific problem-solving strategies. European Journal of Psychology of Education, 18, 281-294. Doi: 10.1007/BF03173249.
[10] Van der Stel M & Veenman MVJ, (2010). Development of metacognitive skillfulness: A longitudinal study. Learning and Individual Differences, 20, 220-224.
[11] HT Nga, VT Binh & NT Trung, (2024). Metacognition in mathematics education: From academic chronicle to future research scenario–A bibliometric analysis with the Scopus database. Eurasia Journal of Mathematics, Science and Technology Education, 20(4), em2427.
[12] Flavell JH, (1985). Conitive Development. London: Prentice Hall.
[13] Schoenfeld AH, (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In Grouws DA (Ed.), Handbook of research on mathematics teaching and learning. A project of the National Council of Teachers of Mathematics, p. 334-370. New York: Macmillan.
[14] Schwartz BL & Metcalfe J, (1994). Methodological problems and pitfalls in the study of human metacognition. In Metcalfe J & Shimamura AP (Eds.), Metacognition: Knowing about knowing, p. 93-113. Cambridge: MIT Press.
[15] Desoete A & Roeyers H, (2006). Metacognitive macroevaluations in mathematical problem solving. Learning and Instruction, 16, 12-25.
[16] Stillman G, (2011). Applying metacognitive knowledge and strategies in applications and modeling tasks at secondary school. In Kaiser G, Blum W, Borromeo Ferri R & Stillman G (Eds.), Trends in teaching and learning of mathematical modeling. ICTMA14. International Conference on the Teaching of Mathematical Modeling and Applications, p. 165-180. Dordrecht: Springer.
[17] Vorhölter K & Kaiser G, (2016). Theoretical and pedagogical considerations in promoting students’ metacognitive modeling competencies. In Hirsch C (Ed.), Annual perspectives in mathematics education 2016: Mathematical modeling and modeling mathematics, p. 273-280. Reston, VA: National Council of Teachers of Mathematics.
[18] Vorhölter K, (2017). Measuring metacognitive modeling competencies. In Stillman G, Blum W & Kaiser G (Eds.), Mathematical modeling and applications: Crossing and researching boundaries in mathematics education, p. 175-185. Springer.
[19] Vorhölter K, (2018). Conceptualization and measurement of metacognitive modeling competencies – empirical verification of theoretical assumptions. ZDM - The International Journal on Mathematics Education, 16(3). https://doi.org/10.1007/s11858-017-0909-x.
[20] Carr M & Biddlecomb B, (1998). Metacognition in mathematics from a constructivist perspective. In Metacognition in educational theory and practice, p. 69-91. Routledge.
[21] Nadim D, (2022). The interplay between constructivism and metacognitive regulation: An experimental study on mathematics students. Towards Excellence, 14(4).
[22] Amin I & Mariani S. (2017). PME learning model: The conceptual theoretical study of metacognition learning in mathematics problem solving based on constructivism. International Electronic Journal of Mathematics Education, 12(3), 333-352.
[23] Flavell JH, (1981). Cognitive monitoring. In Dickson WP (Ed.), Children's oral communication skills, p. 35-60. New York: Academic Press.
[24] Brown AL, (1987). Metacognition, executive control, self regulation, and other more mysterious mechanisms. In Weinert FE & Kluwe RH (Eds.). Metacognition, motivation, and understanding, p. 65-116. Hillsdale, NJ: Lawrence Erlbaum.
[25] Brown AL & Palinscar AS, (1982). Inducing strategic learning from texts by means of informed, self-control training. Topics in Learning and Learning Disabilities, 2(1), 1-17.
[26] Cross DR & Paris SG, (1988). Developmental and instructional analyses of children’s metacognition and reading comprehension. Journal of Educational Psychology, 80(2), 131-142.
[27] Schraw G & Moshman D, (1995). Metacognitive theories. Educational Psychology Review, 7(4), 351-371.
[28] Whitebread D, Coltman P, Pasternak DP, Sangster C, Grau V, Bingham S, Almeqdad Q & Demetriou D, (2009). The development of two observational tools for assessing metacognition and self-regulated learning in young children. Metacognition and Learning, 4(1), 63-85.
[29] Jacobs JE & Paris SG, (1987). Children’s metacognition about reading: Issues in the definition, measurement, and instruction. Educational Psychologist, 22 (3-4), 255-278. Doi: 10.1080/00461520.1987.9653052.
[30] Cross DR & Paris SG, (1988). Developmental and instructional analyses of children’s metacognition and reading comprehension. Journal of Educational Psychology, 80(2), 131-142.
[31] Kuhn D, (2000). Metacognitive development. Current Directions in Psychological Science, 9(5), 178-181.
[32] Schraw G, (1994). The effect of metacognitive knowledge on local and global monitoring. Contemporary Educational Psychology. 19, 143-154.
[33] NT Trung, (2013). Thiết kế tình huống dạy học hình học ở trường trung học phổ thông theo hướng giúp học sinh kiến tạo tri thức. Luận án tiến sĩ Giáo dục học, Trường Đại học Sư phạm Hà Nội.
[34] HT Ngà, (2021). Rèn luyện kĩ năng siêu nhận thức cho sinh viên ngành Giáo dục Tiểu học thông qua dạy học các học phần về phương pháp dạy học toán. Luận án tiến sĩ Khoa học Giáo dục, Trường Đại học Sư phạm Hà Nội.
[35] BV Nghị, (2017). Vận dụng lí luận vào thực tiễn dạy học môn Toán ở trường phổ thông. NXB Đại học Sư phạm.
