Designing a PMRI-Based Learning Trajectory for Algebraic Forms Using the Iftar Context
DOI:
https://doi.org/10.22437/edumatica.v15i2.44218Keywords:
algebraic form, design research, iftar, PMRI, realistic mathematics educationAbstract
Algebra is an essential part of mathematics and is still challenging for students to understand, including algebraic forms. Difficulties concern mathematization, understanding algebraic expressions, applying arithmetic operations in numerical and algebraic expressions, understanding the concept of variables, and formulating mathematical models. The design of a Hypothetical Learning Trajectory (HLT) with PMRI learning principles that integrate the context of Iftar can assist students in understanding this algebraic form. This study aims to describe the design and implementation of HLT for learning algebraic form using the context of Iftar. The method used was design research with validation studies, consisting of three main phases: preparing for the experiment, experimenting in the classroom (pilot and teaching experiment), and conducting retrospective analysis. The subjects were 18 7th-grade students of MTs Laboratorium UIN Sultan Thaha Saifuddin Jambi. Data were collected through observation, interviews, and documentation. The results showed that learning using the context of Iftar could promote students' understanding of algebraic form, students stated a situation in algebraic form, used algebraic operations in problem solving, and provided real experience solving problems with algebra.
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Agasi, G. R., Wahyuono, Y. D., & Rudhito, M. A. (2017). Junior High School Students’ Ability to Apply Algebra in Real-World Problems. IJIET (International Journal of Indonesian Education and Teaching), 1(2), 206–215. https://doi.org/10.24071/IJIET.V1I2.662
Agustina, A., & Zulkardi. (2020). Designing Reasoning Problem of Linear Equations with Two Variables Through Compare and Exchange Activities. Journal of Physics: Conference Series, 1470(1), 012062. https://doi.org/10.1088/1742-6596/1470/1/012062
Ali, C. A. (2022). The Didactical Phenomenology in Learning the Circle Equation. International Electronic Journal of Mathematics Education, 17(4), em0713. https://doi.org/10.29333/IEJME/12472
Andzin, N. S., Sari, P. Y. P., Widodo, R. C., Sukowati, D. I., Indriastuti, S., & Nursyahidah, F. (2024). Arithmetic Sequences and Series Learning Using Realistic Mathematics Education Assisted by Augmented Reality. Mathematics Education Journal, 18(1), 139–148. https://doi.org/10.22342/JPM.V18I1.PP139-148
Beeh, H., Rosjanuardi, R., & Jupri, A. (2018). Investigating the Misconception of Students in Initial Algebra. International Conference on Mathematics and Science Education.
Bouck, E. C., Cox, S., Long, H., & Reiley, S. (2025). Schemas, Rounding, and Comparison, Oh My!: Supporting Students With Money Word Problems. School Science and Mathematics, 125(1), 62–74. https://doi.org/10.1111/SSM.12664
BSKAP. (2024). Capaian Pembelajaran pada Pendidikan Anak Usia Dini, Jenjang Pendidikan Dasar, dan Jenjang Pendidikan Menengah Pada Kurikulum Merdeka, Pub. L. No. 032/H/KR/2024.
Cai, J., Ng, S. F., & Moyer, J. C. (2011). Developing Students’ Algebraic Thinking in Earlier Grades: Lessons from China and Singapore. https://doi.org/10.1007/978-3-642-17735-4_3
Chasanah, N., Zulkardi, Z., & Darmawijoyo, D. (2015). Area Model to Support Students to Sense During the Transition from Binomials Multiplication to Factorization.
Dawkins, P. C., & Cook, J. P. (2017). Guiding Reinvention of Conventional Tools of Mathematical Logic: Students’ Reasoning About Mathematical Disjunctions. Educational Studies in Mathematics, 94(3), 241–256. https://doi.org/10.1007/S10649-016-9722-7/METRICS
Dhlamini, Z. B. (2023). The Structural and Operational Complementarity: Grade Nine Learners’ Pitfalls and Gains of Simplifying Algebraic Expressions. Eurasia Journal of Mathematics, Science and Technology Education, 19(10), em2344. https://doi.org/10.29333/EJMSTE/13653
Domu, I., & Mangelep, N. O. (2020). The Development of Students’ Learning Material on Arithmatic Sequence Using PMRI Approach. 426–432. https://doi.org/10.2991/AER.K.201124.076
Doorman, M., Bakker, A., Drijvers, P., & Wijaya, A. (2016). Design-Based Research in Mathematics Education. Sriwijaya University Learning and Education International Conference, 2(1).
Eriyenti Putri, D. (2019). Preliminary Research of Development Learning Design of System of Two Linear Equations Based on Realistic Mathematics Education. Journal of Physics: Conference Series, 1317(1). https://doi.org/10.1088/1742-6596/1317/1/012130
Flores, A., & Park, J. (2016). Students’ Guided Reinvention of Definition of Limit of a Sequence with Interactive Technology. Contemporary Issues in Technology and Teacher Education (CITE Journal), 16(2).
Gravemeijer, K. (1999). How Emergent Models May Foster the Constitution of Formal Mathematics. Mathematical Thinking and Learning, 1(2), 155–177. https://doi.org/10.1207/S15327833MTL0102_4
Gravemeijer, K. (2020). A Socio-Constructivist Elaboration of Realistic Mathematics Education. https://doi.org/10.1007/978-3-030-33824-4_12
Gravemeijer, K., & Cobb, P. (2006). Design Research from a Learning Design Perspective. In Educational Design Research. https://doi.org/10.4324/9780203088364-12
Jupri, A., & Drijvers, P. (2016). Student Difficulties in Mathematizing Word Problems in Algebra. Eurasia Journal of Mathematics, Science and Technology Education, 12(9), 2481–2502. https://doi.org/10.12973/EURASIA.2016.1299A
Jupri, A., Drijvers, P., & van den Heuvel-Panhuizen, M. (2014). Difficulties in Initial Algebra Learning in Indonesia. Mathematics Education Research Journal, 26(4), 683–710. https://doi.org/10.1007/S13394-013-0097-0
Kenney, S., & Ntow, F. D. (2024). Unveiling the Errors Learners Make When Solving Word Problems Involving Algebraic Task. SAGE Open, 14(4). https://doi.org/10.1177/21582440241299245
Khairunnisak, C., Johar, R., Yuhasriati, Zubainur, C. M., Suhartati, & Sasalia, P. (2021). Learning Trajectory of Algebraic Expression: Supporting Students’ Mathematical Representation Ability. Mathematics Teaching Research Journal, 13(4), 27–41. https://commons.hostos.cuny.edu/mtrj/
Kieran, C. (2018). The Early Learning of Algebra: A Structural Perspective. In Research Issues in the Learning and Teaching of Algebra: the Research Agenda for Mathematics Education, Volume 4. https://doi.org/10.4324/9781315044378-4
Kinanti, M. A. H., Sujadi, I., Indriati, D., & Kuncoro, K. S. (2023). Examining Students’ Cognitive Processes in Solving Algebraic Numeracy Problems: A Phenomenology Study. Jurnal Elemen, 9(2), 494–508. https://doi.org/10.29408/JEL.V9I2.13266
Kwabena Tuffour, G. (2014). Enhancing Students’ Understanding in Translating Word Problems into Algebraic Equations: A Case Study at Navrongo Community Vocational Training Institute in The Ghana. http://ir.uew.edu.gh
Macgregor, M., & Stacey, K. (1997). Students’ Understanding of Algebraic Notation: 11-15. Educational Studies in Mathematics, 33(1), 1–19. https://doi.org/10.1023/A:1002970913563/METRICS
Mcguffey, W. (2018). Insights from College Algebra Students’ Reinvention of Limit at Infinity [Columbia University]. https://core.ac.uk/download/pdf/161459137.pdf
Nansiana, M. N., Usodo, B., & Fitriana, L. (2024). Analysis of Epistemological Obstacles Experienced by Indonesian Junior High School Students in Solving Mathematical Literacy Problems viewed from Algebraic Thinking Skills. Jurnal Pendidikan Progresif, 14(2), 1334–1354. https://doi.org/10.23960/JPP.V14.I2.202495
Nataraj, M. S., & Thomas, M. (2016). Teaching and Learning Middle School Algebra: Valuable Lessons from the History of Mathematics. In And the Rest is Just Algebra. https://doi.org/10.1007/978-3-319-45053-7_8
Nieveen, N., McKenney, S., & van den Akker, J. (2006). Educational Design Research: The Value of Variety. In Educational Design Research. https://doi.org/10.4324/9780203088364-21
Noto, M. S., Pramuditya, S. A., & Handayani, V. D. (2020). Exploration of Learning Obstacle Based on Mathematical Understanding of Algebra in Junior High School. Eduma : Mathematics Education Learning and Teaching, 9(1). https://doi.org/10.24235/eduma.v9i1.5946
Peraturan Menteri Pendidikan, Kebudayaan, Riset, dan Teknologi Republik Indonesia Nomor 12 Tahun 2024 Tentang Kurikulum Pada Pendidikan Anak Usia Dini, Jenjang Pendidikan Dasar, Dan Jenjang Pendidikan Menengah (2024).
Pitriani, P. (2016). Kemampuan Pemodelan Matematika dalam Realistic Mathematics Education (RME). Jurnal Edukasi Dan Sains Matematika (JES-MAT), 2(1). https://doi.org/10.25134/JES-MAT.V2I1.282
Purwitaningrum, R., & Prahmana, R. C. I. (2021). Developing Instructional Materials on Mathematics Logical Thinking Through the Indonesian Realistic Mathematics Education Approach. International Journal of Education and Learning, 3(1). https://doi.org/10.31763/ijele.v3i1.178
Putri, A. M. J., Cholily, Y. M., & Kusgiarohmah, P. A. (2020). Students’ Critical Thinking in Determining Coefficients of Algebraic Forms. Kalamatika: Jurnal Pendidikan Matematika, 5(1), 61–68. https://doi.org/10.22236/KALAMATIKA.VOL5NO1.2020PP61-68
Putri, R. I. I., Dolk, M., & Zulkardi. (2015). Professional Development of PMRI Teachers for Introducing Social Norms. Journal on Mathematics Education, 6(1). https://doi.org/10.22342/jme.6.1.1900.11-19
Rodríguez, O. H., & Fernández, J. M. L. (2017). A Commentary on Freudenthal’s Didactic Phenomenology of the Mathematical Structures Associated with the Notion of Measurement. The Mathematics Enthusiast, 14(1), 3–14. https://doi.org/10.54870/1551-3440.1385
Saputra, Y. A., & Cesaria, A. (2023). Students’ Errors in Algebraic form Operations Based on Newman’s Criteria. Jurnal Inovasi Pembelajaran Matematika: PowerMathEdu, 2(3), 301–308. https://doi.org/10.31980/PME.V2I3.1766
Solomon, Y., Hough, S., & Gough, S. (2021). The Role of Appropriation in Guided Reinvention: Establishing and Preserving Devolved Authority with Low-Attaining Students. Educational Studies in Mathematics, 106(2), 171–188. https://doi.org/10.1007/S10649-020-09998-5/FIGURES/3
Utami, M. R. P., Zulkardi, Z., Susanti, E., & Meryansumayeka, M. (2024). Designing Learning Materials for Systems of Linear Equations in Two Variables in the Context of Jakabaring Tourism in Palembang. Edumatica : Jurnal Pendidikan Matematika, 14(3), 242–258. https://doi.org/10.22437/EDUMATICA.V14I3.38806
Utami, N. S., Prabawanto, S., & Priatna, N. (2022). A Didactical Design for Introducing the Concepts in Algebraic Forms Using the Theory of Praxeology. Beta: Jurnal Tadris Matematika, 15(1), 53–71. https://doi.org/10.20414/BETAJTM.V15I1.508
Veith, J. M., Beste, M. L., Kindervater, M., Krause, M., Straulino, M., Greinert, F., & Bitzenbauer, P. (2023). Mathematics Education Research on Algebra Over the Last Two Decades: Quo Vadis? In Frontiers in Education (Vol. 8). https://doi.org/10.3389/feduc.2023.1211920
Wahyuni, R., Herman, T., & Fatimah, S. (2023). Letters in Algebra as the Transition from Arithmetic Thinking to Algebraic Thinking. Mosharafa: Jurnal Pendidikan Matematika, 12(3). https://doi.org/10.31980/mosharafa.v12i3.2369
Yulia, Y., Musdi, E., Afriadi, J., -, al, Yerizon, Y., Yolanda -, R. N., Fauzan, A., & Diana, F. (2020). Learning Trajectory for Teaching Number Patterns Using RME Approach in Junior High Schools. Journal of Physics: Conference Series, 1470(1), 012019. https://doi.org/10.1088/1742-6596/1470/1/012019
Yuliani, S. B., Lus, E., Palupi, W., & Fiangga, S. (2024). Pengembangan Hypothetical Learning Trajectory Materi Perkalian Bentuk Aljabar Kelas VII dengan Pendekatan Realistic Mathematics Education. MATHEdunesa, 13(2), 550–575. https://doi.org/10.26740/MATHEDUNESA.V13N2.P550-575
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