Implementation of Inquiry Learning Model in Collaboration with PBL to Improve Student Understanding in Number Theory Course
DOI:
https://doi.org/10.31764/jtam.v8i1.17421Keywords:
Understanding of Proof, Mathematical Arguments, Infusion Learning, PBL.Abstract
The purpose of this study was to describe the presence or absence of the influence of the infusion learning model collaboration with Problem-Based Learning (PBL)Â to develop students' understanding of proof and mathematical argumentation in number theory courses. This research is an experimental study with a randomized control group pretest-posttest design, two groups namely the experimental group and the control group. The experimental group is the group that uses the infusion learning model in collaboration with PBL, while the control group is the group that uses conventional learning. The subjects of this study consisted of 40 students at a university in Jombang, Indonesia. Data collection techniques through observation sheets, proof understanding tests and observation sheets of students' mathematical argumentation abilities. The results of the research show that the significant difference between the average proof of understanding of students in the experimental group and the control group. The difference between the average proof of understanding in the experimental group and the average proof of understanding of students in the control group was 21.75. Furthermore, the significant difference between the average argumentation ability of students in the experimental group and the control group. The difference between the average argumentation ability of students in the experimental group and the average argumentation ability of students in the control group is 5.25. Therefore, the implementasion of infusion learning in collaboration with PBL is more effective than conventional learning models for developing students' ability to understand mathematical proof and argumentation. This learning model promotes the development of critical thinking skills, problem-solving, conceptual and different understanding needed to construct a formal proof, and strong and valid arguments.References
Affandi, Y., Darmuki, A., & Hariyadi, A. (2022). The Evaluation of JIDI (Jigsaw Discovery) Learning Model in the Course of Qur’an Tafsir. International Journal of Instruction, 15(1), 799–820. https://doi.org/https://doi.org/10.29333/iji.2022.15146a
Afifah, E. P., Wahyudi, W., & Setiawan, Y. (2019). Efektivitas Problem Based Learning Dan Problem Solving Terhadap Kemampuan Berpikir Kritis Siswa Kelas V Dalam Pembelajaran Matematika. MUST: Journal Of Mathematics Education, Science And Technology, 4(1), 95–107. https://doi.org/https://doi.org/10.30651/must.v4i1.2822
Arends, R. I. (2012). Learning to Teach (Ninth Edit). McGraw Hill Book. https://hasanahummi.files.wordpress.com/2017/04/connect-learn-succeed-richard-arends-learning-to-teach-mcgraw-hill-2012.pdf
Boero, P., Garuti, R., & Mariotti, M. A. (1996). Some Dynamic Mental Processes Underlying Producing And Proving Conjectures. Proceedings Of The 20th PME Conference (Vol. 2), 121–128. https://usiena-air.unisi.it/handle/11365/43769
Campbell, T. G., Boyle, J. D., & King, S. (2020). Proof and Argumentation in K-12 Mathematics: A Review of Conceptions, Content, and Support. International Journal of Mathematical Education in Science and Technology, 51(5), 754–774. https://doi.org/10.1080/0020739X.2019.1626503
Darmuki, A., Andayani, Nurkamto, J., & Saddhono, K. (2017). Evaluating Information-Processing-Based Learning Cooperative Model on Speaking Skill Course. Journal of Language Teaching and Reasearch, 8(1), 44–51. https://doi.org/http://dx.doi.org/10.17507/jltr.0801.06
Douek, N. (1999). Some Remarks about Argumentation and Mathematical Proof and Their Educational Implications. Proceedings of the First Conference of the European Society for Research in Mathematics Education Vol. 1, 125–139. https://www.academia.edu/48801273/Some_remarks_about_argumentation_and_mathematical_proof_and_their_educational_implications
Duch, B. J., Groh, S. E., & Allen, D. E. (2001). The Power of Problem-Based Learning: a Practical “how to†for Teaching Undergraduate Courses in Any Discipline. Stylus Publishing, LLC. https://books.google.co.id/books/about/The_Power_of_Problem_based_Learning.html?id=-78ZnGLRacAC&redir_esc=y
Duval, R. (1989). Langage Et Représentation Dans L’apprentissage D’une Démarche Déductive. Proceedings Of The 13th PME International Conference Vol 1, 228–235.
Edwards, L. D. (1998). Odds And Evens: Mathematical Reasoning And Informal Proof Among High School Students. The Journal Of Mathematical Behavior, 17(4), 489–504. https://doi.org/10.1016/S0732-3123(99)00002-4
Griffiths, P. A. (2000). Mathematics at the turn of the millennium. The American Mathematical Monthly, 107(1), 1–14. https://doi.org/http://dx.doi.org/10.2307/2589372
Gunawan, G. (2019). Increasing Students’ Critical Thinking Skills In Physics Using A Guided Inquiry Model Combined With An Advanced Organizer. Journal Of Advanced Research In Dynamical And Control Systems (JARDCS), 11(7), 313–320. https://doi.org/http://eprints.unram.ac.id/id/eprint/23939
Indrawatiningsih, N., Purwanto, P., As’ari, A. R., & Sa’dijah, C. (2020). Argument Mapping to Improve Student’s Mathematical Argumentation Skills. TEM Journal, 9(3). https://www.temjournal.com/content/93/TEMJournalAugust_1208_1212.pdf
Knuth, E. J. (2002). Teachers’ Conceptions ff Proof in The Context of Secondary School Mathematics. Journal Of Mathematics Teacher Education, 5(1), 61–88. https://www.researchgate.net/publication/226457717_Teachers’_Conceptions_of_Proof_in_the_Context_of_Secondary_School_Mathematics
Krummheuer, G. (1995). The Ethnography Of Argumentation. In P. Cobb & H. Bauersfeld (Eds.), The Emergence Of M (pp. 229–269). Hillsdale, NJ: Lawrence Erlbaum. https://www.taylorfrancis.com/chapters/edit/10.4324/9780203053140-7/ethnography-argumentation-g%C3%B6tz-krummheuer
Kurniasih, I., & Sani, B. (2016). Model Pembelajaran. Yogyakarta: Kata Pena.
Leitgeb, H. (2009). On Formal And Informal Provability. In In New Waves In Philosophy Of Mathematics (pp. 263–299). London: Palgrave Macmillan UK. https://link.springer.com/chapter/10.1057/9780230245198_13
Maya, R., & Sumarmo, U. (2011). Mathematical Understanding And Proving Abilities: Experiment With Undergraduate Student By Using Modified Moore Learning Approach. Journal On Mathematics Education, 2(2), 231–250. https://doi.org/http://dx.doi.org/10.22342/jme.2.2.751.231-250
Mejia-Ramos, J. P., Fuller, E., Weber, K., Rhoads, K., & Samkoff, A. (2012). An Assessment Model for Proof Comprehension in Undergraduate Mathematics. Educational Studies in Mathematics, 79, 3–18. https://www.researchgate.net/publication/257557197_An_assessment_model_for_proof_comprehension_in_undergraduate_mathematics
Osborne, J. (2005). The Role Of Argument In Science Education. In Research and the Quality of Science Education (pp. 367–380). Springer, Dordrecht. https://link.springer.com/chapter/10.1007/1-4020-3673-6_29
Palupi, B. S., Subiyantoro, S., Rukayah, & Triyanto. (2020). The Effectiveness of Guided Inquiry Learning (GIL) and Problem-Based Learning (PBL) for Explanatory Writing Skill. International Journal of Instruction, 13(1), 713–730. https://doi.org/https://doi.org/10.29333/iji.2020.13146a
Panza, M. (2003). Mathematical Proofs. Synthese, 134(1/2), 119–158. https://doi.org/https://doi.org/10.1023/A:1022187631022
Rahman, N. A. A., Razak, F. A., & Dzul-Kifli, S. C. (2020). The Effect Of Peer Tutoring On The Process Of Learning Mathematical Proofs. Adv. Math. Sci. J, 9, 7375–7384. https://doi.org/https://doi.org/10.37418/amsj.9.9.84
Santyasa, I. W., Rapi, N. K., & Sara, I. (2020). Project Based Learning and Academic Procrastination of Students in Learning hysics. International Journal of Instruction, 13(1), 489–508. https://doi.org/https://doi.org/10.29333/iji.2020.13132a
Sari, C. K., Waluyo, M., Ainur, C. M., & Darmaningsih, E. N. (2018). Logical Errors On Proving Theorem. Journal Of Physics: Conference Series Vol. 948, No. 1, 012059. https://doi.org/https://iopscience.iop.org/article/10.1088/1742-6596/948/1/012059/pdf
Soekisno, R. B. A. (2015). Pembelajaran Berbasis Masalah Untuk Meningkatkan Kemampuan Argumentasi Matematis Mahasiswa. Infinity Journal, 4(2), 120–139. http://e-journal.stkipsiliwangi.ac.id/index.php/infinity/article/view/77
Stylianides, A. J., Bieda, K. N., & Morselli, F. (2016). Proof And Argumentation In Mathematics Education Research. In The Second Handbook Of Research On The Psychology Of Mathematics Education (pp. 315–351). Brill.
Sugiyono. (2011). Metode Penelitian Kuantitatif, Kualitatif, dan R&D. Bandung: Alfabeta. http://repository.unjani.ac.id/repository/bb3c79a5b289950bb62ef247eb2d473a.pdf
Toulmin, S. (2003). The uses of argument. Cambridge University Press. https://doi.org/10.2307/2183556
Tristanti, L. B. (2017). Pengaruh Model Pembelajaran Kooperatif Tipe TAI dan Problem Based Learning (PBL) Terhadap Pemahaman Konsep Bangun Ruang Siswa. Jurnal Pendidikan Matematika FKIP Univ. Muhammadiyah Metro, 6(3), 338–349. https://doi.org/http://dx.doi.org/10.24127/ajpm.v6i3.1131
Tristanti, L. B., & Nusantara, T. (2021). Improving Students’ Mathematical Argumentation Skill through Infusion Learning Strategy. Journal of Physics: Conference Series, 1783(1), 012103. https://doi.org/10.1088/1742-6596/1783/1/012103
Tristanti, L. B., & Nusantara, T. (2022a). The Advantage and Impact of CIRC-Typed and Problem-Based Cooperative Learning Models on Students’ Mathematical Argument. 2nd International Conference on Education and Technology (ICETECH 2021), 172–178. https://www.atlantis-press.com/proceedings/icetech-21/125968176
Tristanti, L. B., & Nusantara, T. (2022b). The Influence of Infusion Learning Strategy on Students’ Mathematical Argumentation Skill. International Journal of Instruction, 15(2), 277–292.
Tristanti, L. B., Sutawidjaja, A., As’ari, A. R., & Muksar, M. (2015). Modelling Student Mathematical ArgumentationWith Structural-Intuitive and Deductive Warrantto Solve Mathematics Problem. Proceeding of International Conference on Educational Research and Development (ICERD, 2015), 130–139.
Tristanti, L. B., Sutawidjaja, A., As’ari, A. R., & Muksar, M. (2017). Types of Warrant in Mathematical Argumentations of Prospective-Teacher. International Journal of Science and Engineering Investigations, 6(68), 96–101.
Tristanti, L. B., Sutawidjaja, A., Asâ, A. R., & Muksar, M. (2016). The Construction of Deductive Warrant Derived from Inductive Warrant in Preservice-Teacher Mathematical Argumentations. Educational Research and Reviews, 11(17), 1696–1708. https://doi.org/https://doi.org/10.5897/ERR2016.2872
Tristanti, L., & Nusantara, T. (2023). The Effectiveness of Infusion Learning Model in Linear Algebra Course. Education Research International, 2023(9004072), 1–10. https://doi.org/https://doi.org/10.1155/2023/9004072
Utami, R. A., & Giarti, S. (2020). Efektivitas Model Pembelajaran Problem Based Learning (PBL) dan Discovery Learning Ditinjau dari Keterampilan Berpikir Kritis Siswa Kelas 5 SD. PeTeKa, 3(1), 1–8. https://doi.org/http://dx.doi.org/10.31604/ptk.v3i1.1-8
Vahlia, I., Rahmawati, D., Mustika, M., Yunarti, T., & Nurhanurawati, N. (2001). Analisis kebutuhan pengembangan bahan ajar aljabar linear bagi mahasiswa pendidikan matematika. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 10(2), 1182–1189. https://doi.org/http://dx.doi.org/10.24127/ajpm.v10i2.3671
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