Dissecting thought patterns: Analyzing how cognitive fragmentation affects conceptualization and problem-solving abilities in junior high school students
Abstract
Background: This research is rooted in the exploration of a nuanced understanding of the effect of cognitive fragmentation on the conceptual grasp and problem-solving competencies among junior high school students.
Aim: The principal aim of this investigation is to delve into the way cognitive fragmentation influences the conceptualization and problem-solving faculties of pupils aged 12-14, from varied academic milieus.
Method: Employing a qualitative research blueprint, specifically phenomenological inquiry, the study probes into the subjective experiences and cognitions of the participants. Purposefully chosen for this research, the participants consist of junior high school students. The multi-faceted data collection approach includes task-centered, in-depth individual interviews with students and Focus Group Discussions with educators. The amassed data are then meticulously examined through thematic analysis.
Result: Findings of the research reveal diverse manifestations of cognitive fragmentation among the learners. A phenomenon termed 'Pseudo construction' emerges when learners articulate correct responses without wholly comprehending the foundational concepts. 'Mis analogical construction' is recognized when incorrect analogies are deployed in problem-solving, culminating in fallacious solutions. 'Construction holes' are detected when learners exhibit inconsistent responses owing to an absence of alignment with scientific principles.
Conclusion: In summation, this inquiry furnishes invaluable insights and evidence-supported strategies to foster efficacious learning and surmount cognitive impediments within the sphere of junior high school education. The conclusions drawn herein contribute to a broader understanding of cognitive dynamics in mathematics education, offering a fresh perspective on enhancing educational practices.
Keywords
Full Text:
PDFReferences
Amir-Mofidi, S., Amiripour, P., & Bijan-Zadeh, M. H. (2012). Instruction of mathematical concepts through analogical reasoning skills. Indian Journal of Science and Technology, 5(6), 2916–2922. https://doi.org/10.17485/ijst/2012/v5i6.12
Blanton, M., Stephens, A., Knuth, E., Gardiner, A. M., Isler, I., & Kim, J.-S. (2015). The development of children’s algebraic thinking: The impact of a comprehensive early algebra intervention in third grade. Journal for Research in Mathematics Education, 46(1), 39–87. https://doi.org/10.5951/jresematheduc.46.1.0039
Brodie, K. (2009). Teaching mathematical reasoning in secondary school classrooms (Vol. 775). Springer Science & Business Media. https://doi.org/10.1007/978-0-387-09742-8
Clements, D. H., & Sarama, J. (2020). Learning and teaching early math: The learning trajectories approach. Routledge. https://doi.org/10.4324/9781003083528
Davidov, J., & Russo-Netzer, P. (2022). Exploring the phenomenological structure of existential anxiety as lived through transformative life experiences. Anxiety, Stress, & Coping, 35(2), 232–247. https://doi.org/10.1080/10615806.2021.1921162
Ghani, A., & Maat, S. N. (2018). Misconception of fraction among middle grade year four pupils at primary school. Research on Education and Psychology (REP), 2(1), 111–125.
Glatzeder, Goel, & Müller, V. (2010). Towards a theory of thinking. In Problem Solving. Dalam B.M. Glatzeder, et al. (Eds.),. Springer. https://doi.org/10.1007/978-3-642-03129-8
Gök, M. (2020). Mathematical Mystery in a Cultural Game. World Journal of Education, 10(6), 64-73. https://doi.org/10.5430/wje.v10n6p64
Hidayanto, T., & Subanji. (2015). Pemberian Contoh Untuk Mengatasi Miskonsepsi Siswa. J-TEQIP, VI(2), 156–162.
Hidayanto, T., Subanji, & Hidayanto, E. (2017). Deskripsi Kesalahan Struktur Berpikir Siswa SMP Dalam Menyelesaikan Masalah Geometri Serta Defragmentingnya: Suatu Studi Kasus. Jurnal Kajian Pembelajaran Matematika, 25(April), 72–81.
Hiebert, J. (2013). Conceptual and procedural knowledge: The case of mathematics. Routledge. https://doi.org/10.4324/9780203063538
Hwa, S. P. (2018). Pedagogical change in mathematics learning: Harnessing the power of digital game-based learning. Journal of Educational Technology & Society, 21(4), 259–276.
Isnawan, M. G., Suryadi, D., & Turmudi, T. (2022). How secondary students develop the meaning of fractions? A hermeneutic phenomenological study. Beta: Jurnal Tadris Matematika, 15(1), 1–19. https://doi.org/10.20414/betajtm.v15i1.496
Jiménez-Fernández, G. (2016). How can I help my students with learning disabilities in Mathematics? Journal of Research in Mathematics Education, 5(1), 56–73. https://doi.org/10.17583/redimat.2016.1469
Koutselini, M. (2008). Teacher Misconceptions and Understanding of Cooperative Learning: An Intervention Study. The Journal of Classroom Interaction, 43(2), 34–44.
Mejía-Ramos, J. P., & Weber, K. (2020). Using task-based interviews to generate hypotheses about mathematical practice: Mathematics education research on mathematicians’ use of examples in proof-related activities. ZDM, 52, 1099–1112. https://doi.org/10.1007/s11858-020-01170-w
Muhaimin, L. H., & Kholid, M. N. (2023). Pupils ’ Mathematical Literacy Hierarchy Dimension for solving the minimum competency assessment. AIP Conference Proceedings, 2727(020091), 1–15. https://doi.org/10.1063/5.0141406
Neubauer, B. E., Witkop, C. T., & Varpio, L. (2019). How phenomenology can help us learn from the experiences of others. Perspectives on Medical Education, 8, 90–97. https://doi.org/10.1007/S40037-019-0509-2
Permadi, W. E., & Irawan, E. B. (2016). Memahamkan Konsep Pecahan pada Siswa Kelas IV SDN Sumberejo 03 Kabupaten Malang. Jurnal Pendidikan: Teori, Penelitian, Dan Pengembangan, 1(9), 1735–1738.
Ruppert, M. (2013). Ways of Analogical Reasoning – Thought Processes in an Example Based Learning Environment. Eight Congress of European Research in Mathematics Education (CERME 8), 6–10.
Sharp, J., & Adams, B. (2002). Children’s constructions of knowledge for fraction division after solving realistic problems. The Journal of Educational Research, 95(6), 333–347. https://doi.org/10.1080/00220670209596608
Smith III, J. P., diSessa, A. A., & Roschelle, J. (1994). Misconceptions Reconceived: A Constructivist Analysis of Knowledge in Transition. Journal of the Learning Sciences, 3(2), 115–163. https://doi.org/10.1207/s15327809jls0302_1
Subanji. (2016). Teori Defragmentasi Struktur Berpikir Dalam Mendiagnosis Konstruksi Konsep dan Pemecahan Masalah Matematika. UNM Press.
Subanji, & Nusantara, T. (2013). Karakterisasi kesalahan berpikir siswa dalam mengonstruksi konsep matematika. Jurnal Ilmu Pendidikan, 19(2), 208–2017. https://doi.org/10.36312/e-saintika.v2i1.80
Subanji, & Nusantara, T. (2016). Thinking Process of Pseudo Construction in Mathematics Concepts. International Education Studies, 9(2), 17. https://doi.org/10.5539/ies.v9n2p17
Subanji, R., & Supratman, A. M. (2015). The Pseudo-Covariational Reasoning Thought Processes in Constructing Graph Function of Reversible Event Dynamics Based on Assimilation and Accommodation Frameworks. J. Korean Soc. Math. Educ., Ser. D, Res. Math. Educ., 19(1), 61–79. https://doi.org/10.7468/jksmed.2015.19.1.61
Suprapto, N. (2020). Do We Experience Misconceptions?: An Ontological Review of Misconceptions in Science. Studies in Philosophy of Science and Education, 1(2), 50–55. https://doi.org/10.46627/sipose.v1i2.24
Swidan, A., Hermans, F., & Smit, M. (2018). Programming misconceptions for school students. ICER 2018 - Proceedings of the 2018 ACM Conference on International Computing Education Research, 8(1), 151–159. https://doi.org/10.1145/3230977.3230995
Vinner, S. (1997). The pseudo-conceptual and the pseudo-analytical thought processes in mathematics learning. Educational Studies in Mathematics, 34(2), 97–129. https://doi.org/10.1023/A:1002998529016
DOI: http://dx.doi.org/10.24042/ajpm.v14i2.17064
Refbacks
- There are currently no refbacks.
Al-Jabar : Jurnal Pendidikan Matematika is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.