Layers of Student Understanding Based on Pirie Kieren's theory in Solving Story Problems in Terms of Cognitive Style
Abstract
Objective: Understanding lines and angles serves as the foundation for further mathematical topics such as trigonometry, geometry, calculus, etc. Students may struggle with advanced mathematical reasoning and problem-solving without a firm grasp of these basic concepts. This study aims to investigate how students' mathematical understanding processes are based on the folding back theory. Method: The research utilizes a qualitative approach with descriptive eksploratif design. Two subjects were selected from 28 seventh-grade students, each representing the field-dependent and field-independent cognitive style. Data was collected through mathematical comprehension tests, GEFT tests, and interviews. Data were analyzed through data reduction, data presentation, and verification stages, with each subject being interviewed to verify the processes. Results: Based on the research results, students in the field-independent cognitive style were much more active and better understood the problem-solving process than those in the field-dependent. However, both subjects still required learning assistance. Novelty: This research explores the folding back theory in the mathematical understanding process based on cognitive styles, whereas previous studies have mainly focused on mathematical comprehension abilities. Therefore, further research would benefit from using instructional media to better engage students in understanding the material.
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Amin, S. M., & Sulaiman, R. (2021). Students’ growing understanding in solving mathematics problems based on gender: elaborating folding back. Journal on Mathematics Education, 12(3), 507–530. https://doi.org/10.22342/jme.12.3.14267.507-530
Anggraeni, D., Purnomo, D., & Nugroho, A. A. (2021). Analisis pemahaman konsep matematis siswa berdasarkan teori van hiele ditinjau dari gaya kognitif field independent dan field dependent. Imajiner: Jurnal Matematika dan Pendidikan Matematika, 3(5), 428–438. https://doi.org/10.26877/imajiner.v3i5.8084
Asih, A., Rohman, N., & Utami, A. D. (2020). Profil lapisan pemahaman konsep barisan dan deret berdasar teori piere kieren pada siswa kelas VIII SMP muhammadiyah 2 bojonegoro. Jurnal Inovasi Pembelajaran Matematika (JIPM), 2(1), 12–34. https://doi.org/10.36379/jipm.v2i1.125
Ayuningtyas, I. N., Amir, M. F., & Wardana, M. D. K. (2024). Elementary school students’ layers of understanding in solving literacy problems based on Sidoarjo context. Infinity Journal, 13(1), 157–174. https://doi.org/10.22460/infinity.v13i1.p157-174
Chen, C. H. (2020). AR videos as scaffolding to foster students’ learning achievements and motivation in EFL learning. British Journal of Educational Technology, 51(3), 657–672. https://doi.org/10.1111/bjet.12902
DiNapoli, J., & Miller, E. K. (2022). Recognizing, supporting, and improving student perseverance in mathematical problem-solving: The role of conceptual thinking scaffolds. The Journal of Mathematical Behavior, 66, 1-12. https://doi.org/10.1016/j.jmathb.2022.100965
Fauzi, I., & Chano, J. (2022). Online learning: How does it impact on students’ mathematical literacy in elementary school? Journal of Education and Learning, 11(4), 220-235. https://doi.org/10.5539/jel.v11n4p220
George, L., & Voutsina, C. (2023). Children engaging with partitive quotient tasks: elucidating qualitative heterogeneity within the image having layer of the Pirie–Kieren model. Mathematics Education Research Journal, 1-19. https://doi.org/10.1007/s13394-023-00461-1
Gulkilik, H., Moyer-Packenham, P. S., Ugurlu, H. H., & Yuruk, N. (2020). Characterizing the growth of one student’s mathematical understanding in a multi-representational learning environment. The Journal of Mathematical Behavior, 58, 1-29. http://dx.doi.org/10.1016/j.jmathb.2020.100756
Hähkiöniemi, M., Francisco, J., Lehtinen, A., Nieminen, P., & Pehkonen, S. (2023). The interplay between the guidance from the digital learning environment and the teacher in supporting folding back. Educational Studies in Mathematics, 112(3), 461–479. https://doi.org/10.1007/s10649-022-10193-x
Hernama, H., & Maharani, A. (2023). Pengaruh perhatian orang tua, motivasi belajar, dan lingkungan sosial terhadap prestasi belajar matematika pada siswa SMP. J-KIP (Jurnal Keguruan dan Ilmu Pendidikan), 4(1), 164–173. http://dx.doi.org/10.21831/jrpm.v1i2.2674
Hikmah, S. N., & Saputra, V. H. (2023). Korelasi motivasi belajar dan pemahaman matematis terhadap hasil belajar matematika. Mathema: Jurnal Pendidikan Matematika, 5(1), 42–57. https://doi.org/10.33365/jm.v5i1.2552
Hou, H. T., & Keng, S. H. (2020). A dual-scaffolding framework integrating peer-scaffolding and cognitive-scaffolding for an augmented reality-based educational board game: An analysis of learners’ collective flow state and collaborative learning behavioral patterns. Journal of Educational Computing Research, 59(3), 547–573. https://doi.org/10.1177/0735633120969409
Ihechukwu, N. B. (2020). Impact of instructional scaffolding approach on secondary school students achievement in mathematics. Malikussaleh Journal of Mathematics Learning (MJML), 3(2), 46-52. https://doi.org/10.29103/mjml.v3i2.3168
Ivars, P., Fernández, C., & Llinares, S. (2020). A learning trajectory as a scaffold for pre-service teachers’ noticing of students’ mathematical understanding. International Journal of Science and Mathematics Education, 18(3), 529–548. https://doi.org/10.1007/s10763-019-09973-4
Janson, A., Sӧllner, M., & Leimeister, J. M. (2019). Ladders for learning: Is scaffolding the key to teaching problem-solving in technology-mediated learning contexts? Academy of Management Learning & Education, 19(4), 439–468. https://doi.org/10.5465/amle.2018.0078
Jarvis, M. A., & Baloyi, O. B. (2020). Scaffolding in reflective journaling: A means to develop higher order thinking skills in undergraduate learners. International Journal of Africa Nursing Sciences, 12, 1-23. https://doi.org/10.1016/j.ijans.2020.100195
Kholid, M. N., Imawati, A., Swastika, A., Maharani, S., & Pradana, L. N. (2021). How are students’ conceptual understanding for solving mathematical problem? Journal of Physics: Conference Series, 1776(1), 1-5. https://doi.org/10.1088/1742-6596/1776/1/012018
Kim, N. J., Vicentini, C. R., & Belland, B. R. (2022). Influence of scaffolding on information literacy and argumentation skills in virtual field trips and problem-based learning for scientific problem solving. International Journal of Science and Mathematics Education, 20(2), 215–236. https://doi.org/10.1007/s10763-020-10145-y
Lestari, L., & Surya, E. (2017). The effectiveness of realistic mathematics education approach on ability of students’ mathematical concept understanding. International Journal of Sciences: Basic and Applied Research (IJSBAR), 34(1), 91–100.
Lynch, M., Kamovich, U., Longva, K. K., & Steinert, M. (2021). Combining technology and entrepreneurial education through design thinking: Students’ reflections on the learning process. Technological Forecasting and Social Change, 164, 1-23. https://doi.org/10.1016/j.techfore.2019.06.015
MacLeod, M., & van der Veen, J. T. (2020). Scaffolding interdisciplinary project-based learning: a case study. European Journal of Engineering Education, 45(3), 363–377. https://doi.org/10.1080/03043797.2019.1646210
Mahfiroh, N., Mustangin, M., & Wulandari, T. C. (2021). Kemampuan pemecahan masalah matematis ditinjau dari gaya kognitif. Laplace: Jurnal Pendidikan Matematika, 4(1), 63–74. https://doi.org/10.31537/laplace.v4i1.464
Mangaroska, K., Sharma, K., Gašević, D., & Giannakos, M. (2022). Exploring students’ cognitive and affective states during problem solving through multimodal data: Lessons learned from a programming activity. Journal of Computer Assisted Learning, 38(1), 40–59. https://doi.org/10.1111/jcal.12590
Marufi, M., Ilyas, M., Ikram, M., Rosidah, R., & Kaewhanam, P. (2022). Exploration of high school students’ reasoning in solving trigonometric function problems. Al-Jabar : Jurnal Pendidikan Matematika, 13(2), 231–249. https://doi.org/10.24042/ajpm.v13i2.12972
Muliawati, N. E. (2020). Lapisan pemahaman mahasiswa calon guru matematika dengan tipe middle ability dalam menyelesaikan soal pembuktian grup berdasarkan teori Pirie-Kieren. JEMS: Jurnal Edukasi Matematika dan Sains, 8(2), 157–164.
Mustikaningtyas, R., & Susiswo, S. (2020). Analysis of folding back of a Kepanjen Islamic senior high school student in solving the function problems and their intervention. AIP Conference Proceedings, 2215(1), 1-8. http://dx.doi.org/10.1063/5.0000523
Purnomo, D., Bekti, S., Sulistyorini, Y., & Napfiah, S. (2021). The analysis of students’ ability in thinking based on cognitive learning style. Anatolian Journal of Education, 6(2), 13–26. http://dx.doi.org/10.29333/aje.2021.622a
Rahayuningsih, S., Sa’dijah, C., Sukoriyanto, S., & Qohar, A. (2022). Exploring students’ understanding layers in solving arithmagon problems. Cakrawala Pendidikan: Jurnal Ilmiah Pendidikan, 41(1), 170–185. http://dx.doi.org/10.21831/cp.v41i1.33837
Sengul, S., & Argat, A. (2015). The analysis of understanding factorial concept processes of 7th grade students who have low academic achievements with Pirie Kieren theory. Procedia-Social and Behavioral Sciences, 197, 1263–1270.
Shabrina, P., Mostafavi, B., Abdelshiheed, M., Chi, M., & Barnes, T. (2023). Investigating the impact of backward strategy learning in a logic tutor: aiding subgoal learning towards improved problem solving. International Journal of Artificial Intelligence in Education, 1-12. https://doi.org/10.1007/s40593-023-00338-1
Sinha, T., Kapur, M., West, R., Catasta, M., Hauswirth, M., & Trninic, D. (2021). Differential benefits of explicit failure-driven and success-driven scaffolding in problem-solving prior to instruction. Journal of Educational Psychology, 113(3), 530–555. https://doi.org/10.1037/edu0000483
Susiswo, S., Parameswari, P., Putri, O. R. U., Lanya, H., Utami, A. D., & Murniasih, T. R. (2023). The growth of students’ function limit concepts understanding in solving controversial problems based on pirie kieren’s theory. JTAM (Jurnal Teori Dan Aplikasi Matematika), 7(4), 1204–1220.
Susiswo, S., Rosyadi, A. A. P., Utami, O. R. P., Sudirman, S., Lestyanto, L. M., & Azizah, A. (2022). Eksplorasi persepsi calon guru dalam menyelesaikan masalah kontroversial matematika. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 11(4), 2977–2984. http://dx.doi.org/10.24127/ajpm.v11i4.6163
Tegeh, I. M., Astawan, I. G., Sudiana, I. K., & Kristiantari, M. G. R. (2021). Murder learning model assisted by metacognitive scaffolding to improve students’ scientific literacy and numeracy skills through science studies in elementary schools. Jurnal Pendidikan IPA Indonesia, 10(4), 618–626. https://doi.org/10.15294/jpii.v10i4.32926
Vogel, F., Kollar, I., Fischer, F., Reiss, K., & Ufer, S. (2022). Adaptable scaffolding of mathematical argumentation skills: The role of self-regulation when scaffolded with CSCL scripts and heuristic worked examples. International Journal of Computer-Supported Collaborative Learning, 17(1), 39–64. https://doi.org/10.1007/s11412-022-09363-z
Widyastuti, W., Juandi, D., & Hasanah, A. (2023). Proses folding back siswa dengan resiliensi matematis sangat tinggi pada masalah open-ended. JUMLAHKU: Jurnal Matematika Ilmiah STKIP Muhammadiyah Kuningan, 9(1), 62–73. http://dx.doi.org/10.33222/jumlahku.v9i1.2644
Wilson, P. H., Mojica, G. F., & Confrey, J. (2013). Learning trajectories in teacher education: Supporting teachers’ understandings of students’ mathematical thinking. The Journal of Mathematical Behavior, 32(2), 103–121. https://doi.org/10.1016/j.jmathb.2012.12.003
Zhai, X. (2021). Practices and theories: How can machine learning assist in innovative assessment practices in science education. Journal of Science Education and Technology, 30(2), 139–149. https://doi.org/10.1007/s10956-021-09901-8
Zhang, J. H., Meng, B., Zou, L. C., Zhu, Y., & Hwang, G. J. (2023). Progressive flowchart development scaffolding to improve university students’ computational thinking and programming self-efficacy. Interactive Learning Environments, 31(6), 3792–3809. https://doi.org/10.1080/10494820.2021.1943687
Zhong, B., & Si, Q. (2020). Troubleshooting to learn via scaffolds: Effect on students’ ability and cognitive load in a robotics course. Journal of Educational Computing Research, 59(1), 95–118. https://doi.org/10.1177/0735633120951871
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