Development of Combinatorial Optimization Models with Discrete Mathematics Methods in Mathematical Physics Courses
Abstract
Purpose of the study: This research aims to develop a combinatorial optimization model based on discrete mathematical methods that can be applied to mathematical physics problems in complex systems, such as molecular energy configurations and viscoelastic system simulations.
Methodology: The study used a development approach with ADDIE design (Analysis, Design, Development, Implementation, Evaluation). Data were obtained through interviews, simulations, and instrument validation involving lecturers and students of mathematical physics.
Main Findings: The results of the study showed that the developed model had an average accuracy of 85% and a time efficiency of 2.5 seconds per iteration. This model also received positive feedback from users, with an average satisfaction score of 4.6 out of 5.
Novelty/Originality of this study: The novelty of the research lies in the integration of discrete mathematical methods with combinatorial optimization to solve complex mathematical physics problems.
References
Ü. B. Cebesoy and B. Yeniterzi, “7th Grade Students’ Mathematical Difficulties in Force and Motion Unit,” Turkish J. Educ., vol. 5, no. 1, p. 18, 2016, doi: 10.19128/turje.51242.
N.S. Mumthas and Shyma Usman Abdulla, “Substandard Performance In Mathematical Problem Solving In Physics Among Higher Secondary School Students In Kerala - An Investigation On Teacher Perceptions And Student Difficulties,” Issues Ideas Educ., vol. 7, no. 1, pp. 35–43, 2019, doi: 10.15415/iie.2019.71005.
Y. Nakakoji and R. Wilson, “First-year mathematics and its application to science: Evidence of transfer of learning to physics and engineering,” Educ. Sci., vol. 8, no. 1, 2018, doi: 10.3390/educsci8010008.
Y. Karaca, “Computational Complexity-based Fractional-Order Neural Network Models for the Diagnostic Treatments and Predictive Transdifferentiability of Heterogeneous Cancer Cell Propensity,” Chaos Theory Appl., vol. 5, no. 1, pp. 34–51, 2023, doi: 10.51537/chaos.1249532.
M. C. Butter, E. M. Aguilera, M. G. B. Quintana, L. J. Pérez, and E. S. Valenzuela, “Quality assurance for postgraduate programs: Design of a model applied on a university in Chile,” Int. Rev. Res. Open Distrib. Learn., vol. 18, no. 1, pp. 266–292, 2017, doi: 10.19173/irrodl.v18i1.2670.
K. Vakili and Z. Pourrazavy, “CORRESPONDENCE Khatoon Vakili,” vol. 12, no. 4, pp. 755–761, 2017.
J. Jufrida, W. Kurniawan, A. Astalini, D. Darmaji, D. A. Kurniawan, and W. A. Maya, “Students’ attitude and motivation in mathematical physics,” Int. J. Eval. Res. Educ., vol. 8, no. 3, pp. 401–408, 2019, doi: 10.11591/ijere.v8i3.20253.
E. B. Kırıkkaya and B. Başaran, “Investigation of the effect of the integration of arduino to electrical experiments on students’ attitudes towards technology and ICT by the mixed method,” Eur. J. Educ. Res., vol. 8, no. 1, pp. 31–48, 2019, doi: 10.12973/eu-jer.8.1.31.
H. KOĞAR, “Which scale short form development method is better? A Comparison of ACO, TS, and SCOFA,” Int. J. Assess. Tools Educ., vol. 9, no. 3, pp. 583–592, 2022, doi: 10.21449/ijate.946231.
L. S. Ling and S. Krishnasamy, “Information Technology Capability (ITC) Framework to Improve Learning Experience and Academic Achievement of Mathematics in Malaysia,” Electron. J. e-Learning, vol. 21, no. 1, pp. 36–51, 2023, doi: 10.34190/ejel.21.1.2169.
J. Hinojosa, F. L. Martínez-Viviente, V. Garcerán-Hernández, and R. Ruiz-Merino, “Teaching-learning model for the science of electronics,” J. Technol. Sci. Educ., vol. 10, no. 1, pp. 87–100, 2020, doi: 10.3926/jotse.604.
P. Emanovský and D. Gonda, “Mathematical calculations within physics lessons and their popularity among learners,” J. Effic. Responsib. Educ. Sci., vol. 13, no. 4, pp. 204–211, 2020, doi: 10.7160/ERIESJ.2020.130404.
J. A. Bawalsah et al., “Students With and Without Handwriting Difficulties,” vol. 17, no. 7, pp. 2447–2461, 2022.
A. M. Alzoebi, M. A. Ghunaimat, and E. A. Alawneh, “The Effects of Flipped Classroom Strategy Based on ‘Addie Model’ for Algebraic Skill Development,” Anatol. J. Educ., vol. 8, no. 1, pp. 141–158, 2023, doi: 10.29333/aje.2023.8110a.
A. Spatioti, I. Kazanidis, and J. Pange, “Educational Design and Evaluation Models of the Learning Effectiveness in E-Learning Process: a Systematic Review,” Turkish Online J. Distance Educ., vol. 24, no. 4, pp. 318–347, 2023, doi: 10.17718/tojde.1177297.
P. M. Seloane, S. Ramaila, and M. Ndlovu, “Developing undergraduate engineering mathematics students’ conceptual and procedural knowledge of complex numbers using GeoGebra,” Pythagoras, vol. 44, no. 1, pp. 1–14, 2023, doi: 10.4102/PYTHAGORAS.V44I1.763.
S. Gultom, A. F. Hutauruk, and A. M. Ginting, “Teaching Skills of Teacher in Increasing Student Learning Interest,” Budapest Int. Res. Critics Inst. Humanit. Soc. Sci., vol. 3, no. 3, pp. 1564–1569, 2020, doi: 10.33258/birci.v3i3.1086.
P. Cantor, D. Osher, J. Berg, L. Steyer, and T. Rose, “Malleability, plasticity, and individuality: How children learn and develop in context1,” Appl. Dev. Sci., vol. 23, no. 4, pp. 307–337, 2019, doi: 10.1080/10888691.2017.1398649.
T. Vervust, G. Buyle, F. Bossuyt, and J. Vanfleteren, “Integration of stretchable and washable electronic modules for smart textile applications,” J. Text. Inst., vol. 103, no. 10, pp. 1127–1138, 2012, doi: 10.1080/00405000.2012.664866.
T. Broderick, A. Gelman, R. Meager, A. L. Smith, and T. Zheng, “Our Focus Where trust can break down,” pp. 1–19, 2022.
J. G. Tupouniua, “What challenges emerge when students engage with algorithmatizing tasks?,” J. Pedagog. Res., vol. 7, no. 2, pp. 93–107, 2023, doi: 10.33902/JPR.202318518.
A. Alvarez-Marin and J. A. Velazquez-Iturbide, “Augmented Reality and Engineering Education: A Systematic Review,” IEEE Trans. Learn. Technol., vol. 14, no. 6, pp. 817–831, 2021, doi: 10.1109/TLT.2022.3144356.
A. Barana, M. Marchisio, and F. Roman, “Fostering Problem Solving and Critical Thinking in Mathematics Through Generative Artificial Intelligence,” 20th Int. Conf. Cogn. Explor. Learn. Digit. Age, CELDA 2023, no. Celda, pp. 377–385, 2023, doi: 10.33965/celda2023_202306l046.
T. Pajk, K. Van Isacker, B. Aberšek, and A. Flogie, “Stem education in eco-farming supported by ict and mobile applications,” J. Balt. Sci. Educ., vol. 20, no. 2, pp. 277–288, 2021, doi: 10.33225/jbse/21.20.277.
H. Yilmaz and P. H. Çavaş, “Reliability and Validity Study of the Students ’ Motivation toward Science Learning ( SMTSL ) Questionnaire Fen Ö renimine Yönelik Motivasyon Ölçeğinin Geçerlik ve Güvenirlik Çalışması,” Elem. Educ. Online, vol. 6, no. 3, pp. 430–440, 2007.
Tanti, Astalini, Darmaji, D. A. Kurniawan, and R. Fitriani, “Student Perception Review from Gender : Electronic Moduls of Mathematical Physics,” J. Pendidik. Indones., vol. 11, no. 1, pp. 125–132, 2022.
G. E. Karniadakis, I. G. Kevrekidis, L. Lu, P. Perdikaris, S. Wang, and L. Yang, “Physics-informed machine learning,” Nat. Rev. Phys., vol. 3, no. 6, pp. 422–440, 2021, doi: 10.1038/s42254-021-00314-5.
Syaiful, Kamid, D. A. Kurniawan, and P. A. Rivani, “The impact of project-based learning on students’ achievement in mathematics,” J. Educ. Res. Eval., vol. 5, no. 4, pp. 558–567, 2021, doi: 10.48081/kxbi5168.
I. Dalaila, P. Widiyaningrum, and S. Saptono, “Developing E-Module Based on Socio-Scientific Issues to Improve Students Scientific Literacy,” J. Innov. Sci. Educ., vol. 11, no. 3, pp. 285–294, 2022, doi: 10.15294/jise.v10i1.54500.
S. Rahayu, A. R. Hakim, P. D. Yuliana, and I. Ladamay, “Integrated Thematic Oriented ‘Pop Up Book’ Development on Thematic Learning for Lower Grade Elementary School,” Int. J. Elem. Educ., vol. 5, no. 4, p. 666, 2021, doi: 10.23887/ijee.v5i4.41096.
Matsun, V. S. Andrini, T. W. Maduretno, and A. C. Yusro, “Development of physics learning e-module based on local culture wisdom in Pontianak,West Kalimantan,” J. Phys. Conf. Ser., vol. 1381, no. 1, 2019, doi: 10.1088/1742-6596/1381/1/012045.
D. Setiawan, “The development of authentic assessment instrument to expand the character values of citizenship education at primary school No 104202 and No 106811 Bandar Setia, Medan, Indonesia,” Budapest Int. Res. Critics Linguist. Educ. J., vol. 2, no. 1, pp. 79–90, Feb. 2019, doi: 10.33258/birle.v2i1.188.
S. Mundarti and F. T. Aldila, “Affective Assessment Instrument Based on Krathwohl-Anderson Taxonomy in Senior High School,” J. Eval. Educ., vol. 4, no. 2, pp. 74–79, 2023, doi: 10.37251/jee.v4i2.323.
A. A. Zamista, H. Rahmi, and Juni, “Development of Physics Module based on Process Oriented Guided Inquiry Learning as a Tool to Increase Student Science Process Skills,” J. Phys. Conf. Ser., vol. 1233, no. 1, 2019, doi: 10.1088/1742-6596/1233/1/012067.
W. H. Woo, “Applying ADDIE model to ideate precision medicine in a polytechnic biomedical science programme,” J. Biomed. Educ., vol. 2018, pp. 1–5, Jun. 2018, doi: 10.1155/2018/4268517.
L. S. Putri, Y. Setiani, and C. A. H. F. Santosa, “E-Modul Matematika Berbasis Problem Based Learning Bermuatan Pengetahuan Budaya Lokal untuk Meningkatkan Kemampuan Pemecahan Masalah,” J. Educ. FKIP UNMA, vol. 9, no. 2, pp. 880–890, 2023, doi: 10.31949/educatio.v9i2.5002.
Nurul Fadila, “Pengembangan Modul Matematika Berbasis Accelerated Learning pada Materi Himpunan di SMPN 1 Kota Jambi,” J. Eval. Educ., vol. 3, no. 1, pp. 19–23, 2022, doi: 10.37251/jee.v3i1.217.
V. Phan, L. Wright, and B. Decent, “Addressing Competing Objectives in Allocating Funds to Scholarships and Need-based Financial Aid,” Proc. 15th Int. Conf. Educ. Data Mining, EDM 2022, no. July, pp. 110–121, 2022, doi: 10.5281/zenodo.6853028.
S. Schallert, Z. Lavicza, and E. Vandervieren, “Merging flipped classroom approaches with the 5E inquiry model: a design heuristic,” Int. J. Math. Educ. Sci. Technol., vol. 53, no. 6, pp. 1528–1545, 2022, doi: 10.1080/0020739X.2020.1831092.
N. Kesorn, P. Junpeng, M. Marwiang, K. Pongboriboon, K. N. Tang, and M. Wilson, “Development of an assessment tool for mathematical reading, analytical thinking and mathematical writing,” Int. J. Eval. Res. Educ., vol. 9, no. 4, p. 955, Dec. 2020, doi: 10.11591/ijere.v9i4.20505.
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