Designing a Project-Based Learning Worksheet: Validity and Feasibility Evidence from the Geometrocity Project
DOI:
https://doi.org/10.22437/edumatica.v16i1.49315Keywords:
External Representation, Geometrocity, Mathematics, Project-based Learning, Student WorksheetAbstract
Students often struggle to express mathematical ideas through multiple external representations, particularly when learning polyhedral geometry that requires coordination of visual, verbal, and symbolic forms. This study aims to design a project-based learning worksheet and examine its validity and feasibility through the Geometrocity project. In this activity, students construct a miniature city as a contextual medium to explore geometric concepts while engaging with structured representational tasks. The study follows the ADDIE development framework and is limited to the development stage. The focus lies on producing a valid and feasible learning tool rather than measuring classroom effectiveness. Two material experts and one media expert evaluated the worksheet using validation instruments that assess content accuracy, language clarity, instructional presentation, and graphical design. Quantitative ratings were analyzed using descriptive statistics, while qualitative feedback supported iterative product revisions. The results indicate that the Geometrocity worksheet achieved high validity scores across all assessed aspects and met the criteria for feasibility. These findings suggest that the worksheet is suitable for use in further implementation studies. This study contributes a project-based worksheet that integrates structured representational activities within contextual geometry tasks.
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Abrahamson, D., Nathan, M. J., Williams-Pierce, C., Walkington, C., Ottmar, E. R., Soto, H., & Alibali, M. W. (2020). The future of embodied design for mathematics teaching and learning. Frontiers in Education, 5. doi:10.3389/feduc.2020.00147
Ahmad, Akhsani, L., & Mohamed, Z. (2023). The profile of students’ mathematical representation competence, self-confidence, and habits of mind through problem-based learning models. Infinity Journal, 12(2), 323–338. doi:10.22460/infinity.v12i2.p323-338
Ahmar, S., & Soro, S. (2023). Pengaruh penggunaan E-LKPD dalam pembelajaran matematika terhadap kemampuan penalaran peserta didik kelas VIII SMP. Edumatica: Jurnal Pendidikan Matematika, 13(2). doi:10.22437/edumatica.v13i02.26352
Akbar, S. (2013). Instrumen Perangkat Pembelajaran. Bandung: Remaja Rosdakarya.
Astuti, N., Jana, P., & Marsyiam. (2022). Pengembangan LKS berbasis etnomatematika untuk memfasilitasi kemampuan representasi matematis. Edumatica: Jurnal Pendidikan Matematika, 12(2). doi:10.22437/edumatica.v12i02.15814
Branch, R. M. (2009). Instructional Design: The ADDIE Approach. Springer Science & Business Media.
Cai, H., & Gu, X. (2022). Factors that influence the different levels of individuals’ understanding after collaborative problem solving: the effects of shared representational guidance and prior knowledge. Interactive Learning Environments, 30(4), 695–706. doi:10.1080/10494820.2019.1679841
Chang, Y., Choi, J., & Şen-Akbulut, M. (2024). Undergraduate students’ engagement in project-based learning with an authentic context. Education Sciences, 14(2). doi:10.3390/educsci14020168
Creswell, J. W., & Creswell, J. D. (2018). Research Design: Qualitative, Quantitative, and Mixed Methods Approaches (5th Edition). SAGE Publications, Inc.
Desai, S., Bush, S. B., & Safi, F. (2021). Mathematical representations in the teaching and learning of geometry: A review of the literature from the United States. Electronic Journal for Research in Science & Mathematics Education, 25(4), 6–22.
Dewi, M. P., & Darussyamsu, R. (2024). Meta analisis validitas dan praktikalitas pengembangan LKPD sebagai media pembelajaran. Jurnal Pendidikan Tambusai, 8(2). doi:10.31004/jptam.v8i2.14929
Dreher, A., Wang, T. Y., Feltes, P., Hsieh, F. J., & Lindmeier, A. (2024). High-quality use of representations in the mathematics classroom – a matter of the cultural perspective? ZDM - Mathematics Education, 56(5), 965–980. doi:10.1007/s11858-024-01597-5
Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1–2), 103–131. doi:10.1007/s10649-006-0400-z
González-Ramírez, T., & García-Hernández, A. (2022). Design and validation of a questionnaire to assess student satisfaction with mathematics study materials. International Journal of Instruction, 15(1), 1–20. doi:10.29333/iji.2022.1511a
Gradini, E., & Susanti. (2022). Pengembangan perangkat pembelajaran berbasis model learning cycle 5E untuk memfasilitasi perubahan konseptual siswa dalam pembelajaran matematika. Edumatica: Jurnal Pendidikan Matematika, 12(2). doi:10.22437/edumatica.v12i02.16933
Hatisaru, V. (2020). Exploring evidence of mathematical tasks and representations in the drawings of middle school students. International Electronic Journal of Mathematics Education, 15(3), 1–21. doi:10.29333/iejme/8482
Hidayat, L. D., & Mawaddah, S. (2023). Effectiveness of realistic mathematics approach to increasing mathematical representation ability at SMP N 9 Purwokerto. International Journal of Research in Mathematics Education, 1(2), 121–130. doi:10.24090/ijrme.v1i2.9139
Himmi, N., Armanto, D., & Amry, Z. (2025). Implementation of project-based learning (PjBL) in mathematics education: A systematic analysis of international practices and theoretical foundations. Science Insights Education Frontiers, 26(2), 4305–4321. doi:10.15354/sief.25.or699
Hughes, E. M., Riccomini, P. J., & Lee, J. Y. (2020). Investigating written expressions of mathematical reasoning for students with learning disabilities. Journal of Mathematical Behavior, 58. doi:10.1016/j.jmathb.2020.100775
Kablan, Z., & Uğur, S. S. (2020). The relationship between routine and non-routine problem solving and learning styles. Educational Studies, 47(3), 328–343. doi:10.1080/03055698.2019.1701993
Kamid, K., Rohati, R., Hobri, H., Triani, E., Rohana, S., & Pratama, W. A. (2022). Process skill and student’s interest for mathematics learning: Playing a traditional games. International Journal of Instruction, 15(3), 967–988. doi:10.29333/iji.2022.15352a
Kemdikbudristek. (2023). Panduan Implementasi Pembelajaran Berpusat Pada Mahasiswa. Jakarta: Dirjen Dikti.
Kohen, Z., & Orenstein, D. (2021). Mathematical modeling of tech-related real-world problems for secondary school-level mathematics. Educational Studies in Mathematics, 107(1), 71–91. doi:10.1007/s10649-020-10020-1
Kokotsaki, D., Menzies, V., & Wiggins, A. (2016). Project-based learning: A review of the literature. Improving Schools, 19(3), 267–277. doi:10.1177/1365480216659733
Kolar, V. M., & Hodnik, T. (2021). Mathematical literacy from the perspective of solving contextual problems. European Journal of Educational Research, 10(1), 467–483. doi:10.12973/EU-JER.10.1.467
Latifa, U., Indrasari, P., Pramuditya, S. A., & Asnawati, S. (2025). Connecting concepts and representations in mathematics: A sistematic literature review. International Journal of Contemporary Studies in Education (IJ-CSE), 4(2), 100–113. doi:10.56855/ijcse.v4i2.1483
Leow, F. T., & Neo, M. (2023). Critical factors for enhancing students’ collaborative learning experiences in a project-based connectivism learning environment. International Journal of Learning, Teaching and Educational Research, 22(7), 388–410. doi:10.26803/ijlter.22.7.21
Lockwood, E., & Ellis, A. B. (2022). Two students’ mathematical thinking and activity across representational registers in a combinatorial setting. ZDM - Mathematics Education, 54(4), 829–845. doi:10.1007/s11858-022-01352-8
López, J. A., & Palacios, F. J. P. (2024). Effects of a project-based learning methodology on environmental awareness of secondary school students. International Journal of Instruction, 17(1), 1–22. doi:10.29333/iji.2024.1711a
Loyens, S. M. M., van Meerten, J. E., Schaap, L., & Wijnia, L. (2023). Situating higher-order, critical, and critical-analytic thinking in problem- and project-based learning environments: A systematic review. Educational Psychology Review, 35(39). doi:10.1007/s10648-023-09757-x
Magana, A. J., Arigye, J., Udosen, A., Lyon, J. A., Joshi, P., & Pienaar, E. (2024). Scaffolded team-based computational modeling and simulation projects for promoting representational competence and regulatory skills. International Journal of STEM Education, 11(1). doi:10.1186/s40594-024-00494-3
Marhamah, M., Zulkardi, Putri, R. I. I., Susanti, E., & Nusantara, D. S. (2024). Design experiment pada pembelajaran bangun datar dengan pendekatan PMRI bagi siswa autis. Indiktika: Jurnal Inovasi Pendidikan Matematika, 6(2), 348–360. doi:10.31851/indiktika.v6i2.15085
Markula, A., & Aksela, M. (2022). The key characteristics of project-based learning: how teachers implement projects in K-12 science education. Disciplinary and Interdisciplinary Science Education Research, 4(1). doi:10.1186/s43031-021-00042-x
Maros, M., Korenkova, M., Fila, M., Levicky, M., & Schoberova, M. (2023). Project-based learning and its effectiveness: evidence from Slovakia. Interactive Learning Environments, 31(7), 4147–4155. doi:10.1080/10494820.2021.1954036
Najah, K. (2024). The influence of mathematical beliefs on the mathematical representation ability of students in Class VII. International Journal of Research in Mathematics Education, 2(1), 27–34. doi:10.24090/ijrme.v2i1.9328
Nurhayati, Suwartono, T., Saripudin, A., & Juwita, N. (2022). Applying web-based technology in developing student worksheets on writing local culture content drama script. Theory and Practice in Language Studies, 12(2), 263–273. doi:10.17507/tpls.1202.07
Nusantara, D. S., Ibarra, F. P., Pasaribu, F. T., & Lusinda, U. (2025). Designing JUMPISA: A PISA-based jumping task to support students’ statistical literacy using jambi context. Journal of Instructional Mathematics, 6(2). doi:10.37640/jim.v6i2.2518
Nusantara, D. S., Pasaribu, F. T., Gustiningsi, T., & Abdullah, A. H. (2025). Developing mind mapping-based pocketbook with augmented reality to support creative thinking skills in pre-service mathematics teachers. SJME (Supremum Journal of Mathematics Education), 9(2), 297–317. doi:10.35706/sjme.v9i2.204
Nusantara, D. S., & Putri, R. I. I. (2025). Investigating students’ mathematical argumentation ability in solving pisa-like mathematics tasks on change and relationships. Mathematics Education Journal, 19. doi:10.22342/mej.v19i4.pp807-826
Plomp, Tj., & Nieveen, Nienke. (2014). Educational design research. Netherlands Institute for Curriculum Development (SLO). Enschede: Netherlands Institue for Curriculum Development (SLO).
Pramasdyahsari, A. S., Setyawati, R. D., Wardani, T. I., Fenyvesi, K., & Jusni, E. (2025). Exploring pre-service mathematics teachers’ numeracy development through art-integrated STEAM geometry: Balancing creativity and mathematical precision. Journal on Mathematics Education, 16(4), 1365–1388. doi:10.22342/jme.v16i4.pp1365-1388
Qodaria, R., Rohati, R., & Marlina, M. (2025). Bibliometric mapping of research on mathematical representation ability in Indonesia (2020–2025). Journal of General Education and Humanities, 4(4), 2287–2296. doi:10.58421/gehu.v4i4.770
Ruamba, M. Y., Sukestiyarno, Y. L., Rochmad, R., & Asih, T. S. N. (2025). The impact of visual and multimodal representations in mathematics on cognitive load and problem-solving skills. International Journal of Advanced and Applied Sciences, 12(4), 164–172. doi:10.21833/ijaas.2025.04.018
Sari, E. M., Misdalina, M., & Septiati, E. (2024). Pengembangan LKPD berbasis project-based learning (pjbl)materi bangun ruang sisi datar untuk siswa kelas VIII. Jurnal Cendekia: Jurnal Pendidikan Matematika, 8(1), 634–645. doi:10.31004/cendekia.v8i1.2196
Shakeel, S. I., Al Mamun, M. A., & Haolader, M. F. A. (2023). Instructional design with ADDIE and rapid prototyping for blended learning: validation and its acceptance in the context of TVET Bangladesh. Education and Information Technologies, 28(6), 7601–7630. doi:10.1007/s10639-022-11471-0
Sinclair, N., & Bruce, C. D. (2015). New opportunities in geometry education at the primary school. ZDM Mathematics Education, 47(3), 319–329. doi:10.1007/s11858-015-0693-4
Siswantari, Sabon, S. S., Listiawati, N., Wirda, Y., Zulkardi, & Riyanto, B. (2025). Bridging mathematics and communication: Implementing realistic mathematics education principles for skill development. Journal on Mathematics Education, 16(2), 729–752. doi:10.22342/jme.v16i2.pp729-752
Song, X., Razali, A. B., Sulaiman, T., & Jeyaraj, J. J. (2024). Impact of project-based learning on critical thinking skills and language skills in EFL context：A review of literature. World Journal of English Language, 14(5), 402–412. doi:10.5430/wjel.v14n5p402
Sudianto, Laelasari, & Julia, R. (2023). Enhancing pre-service mathematics teachers’ mathematical literacy through project-based learning. International Journal of Advance Research in Mathematics Education, 1(1), 36–45. doi:10.56916/ijr.v1i1.319
Sukmaningthias, N., Sari, N., Susanti, E., & Safitri, D. (2022). LKS berbasis RME menggunakan cabri 3d untuk koneksi matematis siswa pada bangun ruang bidang lengkung. Edumatica: Jurnal Pendidikan Matematika, 12(03). doi:10.22437/edumatica.v12i03.21364
Susanti, N., Putri, R. I. I., Susanti, E., & Nusantara, D. S. (2024). Learning trajectory flat building material using batik besemah context for elementary school students. Numerical: Jurnal Matematika Dan Pendidikan Matematika, 8(1), 105–114. doi:10.25217/numerical.v8i1
Uegatani, Y., Otani, H., Shirakawa, S., & Ito, R. (2024). Real and illusionary difficulties in conceptual learning in mathematics: comparison between constructivist and inferentialist perspectives. Mathematics Education Research Journal, 36(4), 895–915. doi:10.1007/s13394-023-00478-6
Weinhandl, R., Mayerhofer, M., Houghton, T., Lavicza, Z., Kleinferchner, L. M., Anđić, B., … Hohenwarter, M. (2024). Enhancing user-centred educational design: Developing personas of mathematics school students. Heliyon, 10(2). doi:10.1016/j.heliyon.2024.e24173
Winarni, S., Hanim, M., Kumalasari, A., Marlina, M., & Rohati, R. (2023). Pengembangan buku saku berbasis augmented reality pada materi bangun ruang untuk meningkatkan kemampuan spasial siswa. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 12(4), 3561. doi:10.24127/ajpm.v12i4.8193
Winarni, S., Kumalasari, A., Marlina, M., & Rohati, R. (2021). Efektivitas video pembelajaran matematika untuk mendukung kemampuan literasi numerasi dan digital siswa. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 10(2), 574. doi:10.24127/ajpm.v10i2.3345
Winarni, S., Simanjuntak, R. P., Marlina, M., Rohati, R., & Kumalasari, A. (2024). Pengembangan e-modul interaktif untuk mendukung algebraic thinking pada materi turunan fungsi aljabar. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 13(3), 791. doi:10.24127/ajpm.v13i3.8540
Wu, X. Y. (2024). Unveiling the dynamics of self-regulated learning in project-based learning environments. Heliyon, 10(5). doi:10.1016/j.heliyon.2024.e27335
Yang, D., Chen, P., Wang, H., Wang, K., & Huang, R. (2022). Teachers’ autonomy support and student engagement: A systematic literature review of longitudinal studies. Frontiers in Psychology, 13. doi:10.3389/fpsyg.2022.925955
Yanto, Y., Zulkardi, Putri, R. I. I., & Nusantara, D. S. (2020). Learning geometry transformations using batik motifs: systematic literature review. Histogram: Jurnal Pendidikan Matematika, 8(1), 160–168. doi:10.31100/histogram.v8i1.3337
Žakelj, A., & Klančar, A. (2022). The role of visual representations in geometry learning. European Journal of Educational Research, 11(3), 1393–1411. doi:10.12973/eu-jer.11.3.1393
Zardari, B. A., Hussain, Z., Arain, A. A., Rizvi, W. H., & Vighio, M. S. (2021). Development and validation of user experience-based e-learning acceptance model for sustainable higher education. Sustainability, 13(11). doi:10.3390/su13116201
Zhao, L., Zhao, B., & Li, C. (2023). Alignment analysis of teaching–learning-assessment within the classroom: how teachers implement project-based learning under the curriculum standards. Disciplinary and Interdisciplinary Science Education Research, 5(1). doi:10.1186/s43031-023-00078-1
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