Designing a Hypothetical Learning Trajectory with Student Worksheets: Fostering Collaboration and Innovation in Probability Learning
Keywords:
Hypothetical Learning Trajectory, Student Worksheet (LKPD), Probability, Design-Based Research, Conceptual Understanding
Abstract
This study aims to develop a Hypothetical Learning Trajectory (HLT) based on student worksheets for teaching probability as an innovative approach to enhance students’ conceptual understanding. The development is driven by the need for instructional design that connects abstract mathematical concepts to real-life contexts. The research adopts a design-based research (DBR) approach through an in-depth case study of three eleventh-grade students. Data were collected through LKPD tasks, observations, semi-structured interviews, and diagnostic tests. Findings show that the HLT-based student worksheet effectively supported students’ progressive understanding of probability, fostering intuitive exploration and formal application. Students demonstrated active engagement, cognitive growth, and positive attitudes toward learning. The study concludes that implementing HLT through LKPD is a valid and promising strategy to improve the quality of mathematics instruction, particularly in the topic of probability.
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Adha, I., Zulkardi, Putri, R. I. I., & Somakim. (2024). A Learning Trajectory for Surface Area Concept with the Context of the Tourist Destination Bukit Sulap. Jurnal Pendidikan Matematika, 18(3), 409–430. https://doi.org/10.22342/jpm.v18i3.pp409-430
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. Jurnal Pendidikan Matematika, 18(1), 139–148. https://doi.org/10.22342/jpm.v18i1.pp139-148
Aripin, U., Rosmiati, T., Rohaeti, E. E., & Hidayat, W. (2025). Learning Trajectory for Teaching the Mean Concept Using Problem-Based Learning and Animated Video.
Fauzan, A. (2024). How Students Understand the Area under a Curve: A Hypothetical Learning Trajectory. 16(3).
Fitri, J. (2022). Lembar Kerja Peserta Didik Berbasis Realistic Mathematics Education pada Materi Teorema Pythagoras. Plusminus: Jurnal Pendidikan Matematika, 2(3). https://doi.org/10.31980/plusminus.v2i3.2176
Hadila, R., Sukirwan, & Alamsyah, T. P. (2020). Desain Pembelajaran Bangun Datar melalui Pendekatan Realistic Mathematics Education (RME). GAUSS: Jurnal Pendidikan Matematika, 3(1), 49–63. https://doi.org/10.30656/gauss.v3i1.2172
Juana, N. A., Kaswoto, J., Sugiman, S., & Hidayat, A. A. A. (2022a). The Learning Trajectory of Set Concept Using Realistic Mathematics Education (RME). Jurnal Pendidikan Matematika, 17(1), 89–102. https://doi.org/10.22342/jpm.17.1.19077.89-102
Juana, N. A., Kaswoto, J., Sugiman, S., & Hidayat, A. A. A. (2022b). The Learning Trajectory of Set Concept Using Realistic Mathematics Education (RME). Jurnal Pendidikan Matematika, 17(1), 89–102. https://doi.org/10.22342/jpm.17.1.19077.89-102
Mouli, M. F., Zulkardi, Z., & Putri, R. I. I. (2023). Development of PISA-Type Questions and Activities in a Smartphone Context. Jurnal Pendidikan Matematika, 17(1), 1–20. https://doi.org/10.22342/jpm.17.1.19386.1-20
Nilsson, P. (2023). Hypothetical Learning Trajectory On Informal Hypothesis Testing In A Probability Context. STATISTICS EDUCATION RESEARCH JOURNAL, 22(2), 11. https://doi.org/10.52041/serj.v22i2.425
Nova, E., Retta, A. M., & Nopriyanti, T. D. (2022a). Student Worksheet Development Using the PMRI Approach in the Classroom Context with an Orientation toward Students’ Conceptual Understanding. Jurnal Pendidikan Matematika, 16(2), 203–214. https://doi.org/10.22342/jpm.16.2.14854.203-214
Nova, E., Retta, A. M., & Nopriyanti, T. D. (2022b). Student Worksheet Development Using the PMRI Approach in the Classroom Context with an Orientation toward Students’ Conceptual Understanding. Jurnal Pendidikan Matematika, 16(2), 203–214. https://doi.org/10.22342/jpm.16.2.14854.203-214
Nuraida, E. M., & Putri, R. I. I. (2019). The Context Of Archipelago Traditional Cake To Explore Students’ Understanding In Integers Division Class VII. Jurnal Pendidikan Matematika, 14(1), 91–100. https://doi.org/10.22342/jpm.14.1.7400.91-100
Nursyahidah, F., Anindya, F. M., Yulianti, M. A., Prisanto, Z. I., & Rosario, M. A. R. (2025). Integrating Local Wisdom with Technology: Designing Learning Trajectory of Cylinder through Realistic Mathematics Education Approach.
Rahayu, C., Putri, R. I. I., Zulkardi, & Hartono, Y. (2022). Curiosity: A game-based early mathematics case. Journal on Mathematics Education, 13(2), 275–288. https://doi.org/10.22342/jme.v13i2.pp275-288
Sahara, S., Juandi, D., Turmudi, T., Hendriyanto, A., Hakim, L., & Bulus, M. D. (2024). Geometric Reasoning to Reinventing Quadratic Formula: The Learning Trajectory on Realistic Mathematics Education Principles. 16(3).
Sari, A., & Putri, R. I. I. (2021). Inductive Reasoning Ability of Students Using the Palembang Songket Fabric Context in Rotational Learning in Grade IX. Jurnal Pendidikan Matematika, 16(1), 57–72. https://doi.org/10.22342/jpm.16.1.14304.57-72
Utari, R. S., Putri, R. I. I., & Zulkardi. (2024). Designing a Hypothetical Learning Trajectory using the Local Wisdom of South Sumatera as a Context through Hybrid Learning. Jurnal Pendidikan Matematika, 18(1), 79–96. https://doi.org/10.22342/jpm.v18i1.pp79-96
Published
2025-12-01
How to Cite
Indraswari, A., & Shodikin, A. (2025). Designing a Hypothetical Learning Trajectory with Student Worksheets: Fostering Collaboration and Innovation in Probability Learning. Pedagogi: Jurnal Ilmu Pendidikan, 25(2), 264-277. https://doi.org/https://doi.org/10.24036/pedagogi.v25i2.2576
Section
Articles
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
