Metacognitive Self-management in Developing Students' Rigorous Mathematical Thinking Skills
Abstract
This study aims to describe the metacognitive self-management of students in developing rigorous mathematical thinking. This study uses a qualitative method with a case study approach. The participants were three students from the thirdlevel mathematics education department, who were selected and made a contract with for real analysis lectures. The first student experienced a significant change from the beginning of the meeting, resulting in the metacognitive self-management process being well-conditioned. He completed the task more confidently than the initial presentation, used several references and sources of information to complete the job, and represented each answer in the form of mathematical symbols. This studentscognitive function appears to be of level-1, with qualitative thinking. For the 2nd student, a change was observed in the learning process and the teacher’s motivation and guidance. The results of the interviews showed that the student applied strategies in completing assignments. He answered them systematically, based on experience, and mastered the prerequisite material. This student showed improved thinking skills related to mastery of concepts from new material, analyzing the problems given, being critical and focused when answering, and looking hard to get maximum evaluation results. This 2nd student entered the level of quantitative thinking with precision. Lastly, in the 3rd student, self-management seems stable, but was still lacking in adjusting the understanding of prerequisites with understanding concepts from new material. The development during the learning process shows that he can activate his mathematical knowledge, compose logical proofs of Real Analysis material problems, and build relationships between prerequisite concepts and new material. This type of student enters the level of abstract relational. The results of the study can be a reference for teachers to determine the learning model and the related instruments, so that they can grow the level of mathematical thinking before, during, and after the learning process.
Keywords: Metacognitive, self-management, Mathematical thinking skill
References
[1] Tandean D, Sharon M, Scool C. “Metacognitive strategies, reading comprehension, young learners.” Beyond Words. vol. 8, no. 2, pp. 124–139, 2020.
[2] Henrietta C, Corresponding M. “Ict and the teaching of reading comprehension in english as a second language in secondary schools: problems and prospects.” International Journal of Education and Literacy Studies. vol. 4, no. 3, p. 2016.
[3] Ramadhanti D, Ghazali AS, Hasanah M, Harsiati T. Students’ metacognitive weaknesses in academic writing: a preliminary research. Int J Emerg Technol Learn. 2019;14(11):41–57.
[4] Lawanto O, Johnson S. “Students’ cognitive self-appraisal, self-management, and the level of difficulty of an engineering design project: are they related?” In: ASEE Annual Conference and Exposition, Conference Proceedings. pp. 14–1089 (2009).
[5] Gurat MG, Medula CT. Metacognitive strategy knowledge use through mathematical problem solving amongst pre-service teachers. Am J Educ Res. 2016;4(2):170–89.
[6] Karim IH. “Enhancing the speaking skill using metacognitive strategy.” J-ELLiT ( Journal of English Language, Literature, and Teaching). vol. 3, no. 1, p. 12, 2019.
[7] Adicondro N, Purnamasari A. Efikasi diri, dukungan sosial keluarga dan self regulated learning pada siswa kelas viii. Humanitas (Universitas Ahmad Dahlan Fak Psikol). 2011;8(1):17.
[8] Lawanto O. The self-management of cognition in a team-based engineering design project: a case study., 2005.
[9] Feist J, Feist GJ. Teori kepribadian. Jakarta: Salemba Humanika; 2010.
[10] Kinard JT, Kozulin A. Rigorous mathematical thinking: conceptual formation in the mathematics classroom. New York: Cambridge University Press; 2008. https://doi.org/10.1017/CBO9780511814655.
[11] Schoenfeld AH. Uses of video in understanding and improving mathematical thinking and teaching. J Math Teach Educ. 2017;20(5):415–32.
[12] Masrukan AJ, Junaedi I. The ability of mathematical creative thinking viewed from student learning interest of class viii in learning cps contextual approach. Unnes Journal of Mathematics Education. 2019;8(1):58–64.
[13] Cancio EJ, West RP, Young KR. Improving mathematics homework completion and accuracy of students with ebd through self-management and parent participation. J Emot Behav Disord. 2004;12(1):9–22.
[14] Crowe S, Cresswell K, Robertson A, Huby G, Avery A, Sheikh A. The case study approach. BMC Med Res Methodol. 2011 Jun;11:100.
[15] Chetty L. Innovative interpretive qualitative case study research method aligned with systems theory for physiotherapy and rehabilitation research: a review of the methodology. African Journal of Physiotherapy and Rehabilitation Sciences. 2014;5(1–2):40.
[16] Lucas P, Fleming J, Bhosale J. The utility of case study as a methodology for work-integrated learning research. International Journal of Work-Integrated Learning. 2018;19(3):215–22.
[17] King-Sears ME. Self-management for students with disabilities: the importance of teacher follow-up. Int J Spec Educ. 2006;21(2):94–108.