Designing Learning Trajectory of Curved 3D Shapes using RME with The Context of Sesaji Rewanda Semarang
Abstract
Curved 3D shapes are one of the essential materials in geometry, but students have difficulty learning the material. Thus, this study aimed to describe a learning trajectory to aid students in comprehending curved 3D shapes in the context of the Sesaji Rewanda tradition. The method used is design research with the RME learning approach as developed by McKenney and Akker. The subject in this research is the 9th grade of SMP Negeri 6 Semarang. The resulting learning trajectory comprised 5 sets of activities, namely: (1) identifying the types and characteristics of curved 3D shapes, (2) determining the beginning of the formulas for cylinder surface area and volume, (3) determining the beginning of the formulas for cone surface area and volume, (4) determining the beginning of the formulas for sphere surface area and volume, and (5) resolve contextual problems associated to curved shapes. The 5 activities produced in this study are hopefully to encourage students to learn and become an inspiration for teachers in implementing learning.
Downloads
Download data is not yet available.
References
Afdila, N. F., & Roza, Y. (2018). Analisis Kesalahan Siswa dalam menyelesaikan Masalah Kontekstual Materi Bangun Ruang Sisi Datar berdasarkan Tahapan Kastolan. Letters of Mathematics Education, 5(1), 65–72. Retrieved from https://doi.org/10.22202/jl.v5i1.3383
Agustien, R., Umamah, N., & Sumarno, S. (2018). Pengembangan Media Pembelajaran Video Animasi Dua Dimensi Situs Pekauman di Bondowoso Dengan Model Addie Mata Pelajaran Sejarah Kelas X IPS. Jurnal Edukasi, 5(1), 19. Retrieved from https://doi.org/10.19184/jukasi.v5i1.8010
Bustang, Zulkardi, Darmawijoyo, Dolk, M., & van Eerde, D. (2013). Developing a local instruction theory for learning the concept of angle through visual field activities and spatial representations. International Education Studies, 6(8), 58–70. Retrieved from https://doi.org/10.5539/ies.v6n8p58
Fahrurozi, A., Maesaroh, S., Suwanto, I., & Nursyahidah, F. (2018). Developing Learning Trajectory Based Instruction of the Congruence for Ninth Grade Using Central Java Historical Building. JRAMathEdu, 3(2), 78–85. 10.23917/jramathedu.v3i2.6616
Farnika, N., Ikhsan, M., & Sofyan, H. (2015). Peningkatan Kemampuan Pemahaman dan Pemecahan Masalah Matematis Siswa Sekolah Menengah Atas dengan Model Pembelajaran Kooperatif Tipe Team Assisted Individualization. Jurnal Elemen, 1(2), 144. Retrieved from https://doi.org/10.29408/jel.v1i2.146
Febrian, Astuti, P., & Antika, R. (2019). PELATIHAN PENGEMBANGAN MEDIA VIDEOSCRIBE DENGAN KONTEKS LOKAL BINTAN 1Universitas Maritim Raja Ali Haji . Email?: febrian@umrah.ac.id Maritim Raja Ali Haji . Email?: pujiastuti@umrah.ac.id 3 Universitas Maritim Raja Ali Haji . Email?: rindiantika@umrah.ac, 3(2), 101–110.
Gravemeijer, K. P. . (1994). Developing realistic mathematics education. ESoE.
Haris, D., & Ilma, R. (2011). The role of context in third graders’ learning of area measurement. Journal on Mathematics Education, 2(1), 55–66. Retrieved from https://doi.org/10.22342/jme.2.1.778.55-66
Khoiri, M. (2014). Pemahaman Siswa pada Konsep Segiempat Berdasarkan Teori Van Hiele. Pemahaman Siswa Pada Konsep Segiempat Berdasarkan Teori van Hiele, 1 (1)(Universitas Jember), 262–267.
Kurniasih, R. (2017). Penerapan Strategi Pembelajaran Fase Belajar Model Van Hiele Pada Materi Bangun Ruang Sisi Datar di SMP Islam Al-Azhaar Tulungagung. Jurnal Silogisme, 2(2), 61–68. 10.24269/js.v2i2.626
Kusumaningsih, W., Hartono, & Nursyahidah, F. (2022). Designing hypothetical learning trajectory for lines and angles using Central Java traditional house context. AIP Conference Proceedings, 2577(July). Retrieved from https://doi.org/10.1063/5.0096084
Mariyana, F. A., Rosady, I. A., & Latifah, N. (2018). Pemahaman Konsep Melalui Pendekatan Pendidikan Matematika Realistik Indonesia pada Materi Pengukuran Sudut di Kelas IV Sekolah Dasar. Sekolah Dasar: Kajian Teori Dan Praktik Pendidikan, 27(2), 98–107. Retrieved from https://doi.org/10.17977/um009v27i22018p098
Mulyani, A., Indah, E. kurnia N. I., & Satria, A. P. (2018). Analisis Kemampuan Pemahaman Matematis Siswa SMP pada Materi Bentuk Aljabar Mosharafa?: Jurnal Pendidikan Matematika Mosharafa?: Jurnal Pendidikan Matematika. Mosharafa: Jurnal Pendidikan Matematika, 7(2), 251–262. http://journal.institutpendidikan.ac.id/index.php/mosharafa
Muna, H., Nizaruddin, N., & Murtianto, Y. H. (2017). Pengembangan Video Pembelajaran Matematika Berbantuan Macromedia Flash 8 Dengan Pendekatan Kontekstual Pada Materi Program Linier Kelas Xi. Aksioma, 8(2), 9. Retrieved from https://doi.org/10.26877/aks.v8i2.1686
Najwa, W. A. (2018). Pendekatan PMRI sebagai Gerakan Literasi Sekolah dalam Pembelajaran Matematika. Prisma, Prosicing Seminar Nasional Matematika, 1, 575–581.
Nasrullah, & Zulkardi. (2011). Building counting by traditional game: A mathematics program for young children. Journal on Mathematics Education, 2(1), 41–54. Retrieved from https://doi.org/10.22342/jme.2.1.781.41-54
Nurainah, N., Maryanasari, R., & Nurfauziah, P. (2018). Analisis Kesulitan Kemampuan Koneksi Matematis Siwa Smp Kelas Viii Pada Materi Bangun Datar. JPMI (Jurnal Pembelajaran Matematika Inovatif), 1(1), 61. Retrieved from https://doi.org/10.22460/jpmi.v1i1.p61-68
Nursyahidah, F., & Albab, I. U. (2021). Learning Design on Surface Area and Volume of Cylinder Using Indonesian Ethno-mathematics of Traditional Cookie maker Assisted by GeoGebra, 13(4).
Nursyahidah, F., Ilma, R., & Putri, I. (2014). 2014 Instructional Design of Subtraction Using Pmri Approach, (978), 132–141.
Nursyahidah, F., Putri, R. I. I., & Somakim. (2013). Supporting first grade students’ understanding of addition up to 20 using traditional game. Journal on Mathematics Education, 4(2), 212–223. Retrieved from https://doi.org/10.22342/jme.4.2.557.212-223
Nursyahidah, F., Saputro, B. A., Albab, I. U., & Aisyah, F. (2020). Pengembangan Learning Trajectory Based Instruction Materi Kerucut Menggunakan Konteks Megono Gunungan. Mosharafa: Jurnal Pendidikan Matematika, 9(1), 47–58. Retrieved from https://doi.org/10.31980/mosharafa.v9i1.560
Nursyahidah, F., Saputro, B. A., & Rubowo, M. R. (2018). A Secondary Student’s Problem Solving Ability in Learning Based on Realistic Mathematics with Ethnomathematics. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 3(1), 13. Retrieved from https://doi.org/10.23917/jramathedu.v3i1.5607
Özerem, A. (2012). Misconceptions In Geometry And Suggested Solutions For Seventh Grade Students. Procedia - Social and Behavioral Sciences, 55, 720–729. Retrieved from https://doi.org/10.1016/j.sbspro.2012.09.557
Puspasari, L., Zulkardi, Z., & Somakim, S. (2015). Desain Pembelajaran Luas Segi Banyak Menggunakan Tangram Berpetak di Kelas IV. JINoP (Jurnal Inovasi Pembelajaran), 1(2), 150. Retrieved from https://doi.org/10.22219/jinop.v1i2.2566
Risdiyanti, I., & Indra Prahmana, R. C. (2020). The learning trajectory of number pattern learning using barathayudha war stories and uno stacko. Journal on Mathematics Education, 11(1), 157–166. Retrieved from https://doi.org/10.22342/jme.11.1.10225.157-166
Rofii, A., Sunardi, S., & Irvan, M. (2018). Characteristics of Students’ Metacognition Process At Informal Deduction Thinking Level in Geometry Problems. International Journal on Emerging Mathematics Education, 2(1), 89. Retrieved from https://doi.org/10.12928/ijeme.v2i1.7684
Rosyida, E. M., Riyadi, & Mardiyana. (2016). Analisis Kesalahan Siswa Dalam Pemecahan Masalah Berdasarkan Pendapat John W. Santrock Pada Pokok Bahasan Bangun Ruang Sisi Lengkung Ditinjau Dari Gaya Belajar Dan Gaya Berpikir Siswa. Jurnal Elektronik Pembelajaran Matematika, 4(10), 973–981.
Widiawati, Marzal, D., & Juwita, H. (2018). Desain Pembelajaran Garis Dan Sudut Dengan Konteks Pagar Buluh Di Kelas Vii. Journal of Mathematics Science and Education, 1(1), 118–130. Retrieved from https://doi.org/10.31540/jmse.v1i1.186
Yani, C. F., Maimunah, M., Roza, Y., Murni, A., & Daim, Z. (2019). Analisis Kemampuan Pemahaman Matematis Siswa pada Materi Bangun Ruang Sisi Lengkung. Mosharafa: Jurnal Pendidikan Matematika, 8(2), 203–214. Retrieved from https://doi.org/10.31980/mosharafa.v8i2.481
Agustien, R., Umamah, N., & Sumarno, S. (2018). Pengembangan Media Pembelajaran Video Animasi Dua Dimensi Situs Pekauman di Bondowoso Dengan Model Addie Mata Pelajaran Sejarah Kelas X IPS. Jurnal Edukasi, 5(1), 19. Retrieved from https://doi.org/10.19184/jukasi.v5i1.8010
Bustang, Zulkardi, Darmawijoyo, Dolk, M., & van Eerde, D. (2013). Developing a local instruction theory for learning the concept of angle through visual field activities and spatial representations. International Education Studies, 6(8), 58–70. Retrieved from https://doi.org/10.5539/ies.v6n8p58
Fahrurozi, A., Maesaroh, S., Suwanto, I., & Nursyahidah, F. (2018). Developing Learning Trajectory Based Instruction of the Congruence for Ninth Grade Using Central Java Historical Building. JRAMathEdu, 3(2), 78–85. 10.23917/jramathedu.v3i2.6616
Farnika, N., Ikhsan, M., & Sofyan, H. (2015). Peningkatan Kemampuan Pemahaman dan Pemecahan Masalah Matematis Siswa Sekolah Menengah Atas dengan Model Pembelajaran Kooperatif Tipe Team Assisted Individualization. Jurnal Elemen, 1(2), 144. Retrieved from https://doi.org/10.29408/jel.v1i2.146
Febrian, Astuti, P., & Antika, R. (2019). PELATIHAN PENGEMBANGAN MEDIA VIDEOSCRIBE DENGAN KONTEKS LOKAL BINTAN 1Universitas Maritim Raja Ali Haji . Email?: febrian@umrah.ac.id Maritim Raja Ali Haji . Email?: pujiastuti@umrah.ac.id 3 Universitas Maritim Raja Ali Haji . Email?: rindiantika@umrah.ac, 3(2), 101–110.
Gravemeijer, K. P. . (1994). Developing realistic mathematics education. ESoE.
Haris, D., & Ilma, R. (2011). The role of context in third graders’ learning of area measurement. Journal on Mathematics Education, 2(1), 55–66. Retrieved from https://doi.org/10.22342/jme.2.1.778.55-66
Khoiri, M. (2014). Pemahaman Siswa pada Konsep Segiempat Berdasarkan Teori Van Hiele. Pemahaman Siswa Pada Konsep Segiempat Berdasarkan Teori van Hiele, 1 (1)(Universitas Jember), 262–267.
Kurniasih, R. (2017). Penerapan Strategi Pembelajaran Fase Belajar Model Van Hiele Pada Materi Bangun Ruang Sisi Datar di SMP Islam Al-Azhaar Tulungagung. Jurnal Silogisme, 2(2), 61–68. 10.24269/js.v2i2.626
Kusumaningsih, W., Hartono, & Nursyahidah, F. (2022). Designing hypothetical learning trajectory for lines and angles using Central Java traditional house context. AIP Conference Proceedings, 2577(July). Retrieved from https://doi.org/10.1063/5.0096084
Mariyana, F. A., Rosady, I. A., & Latifah, N. (2018). Pemahaman Konsep Melalui Pendekatan Pendidikan Matematika Realistik Indonesia pada Materi Pengukuran Sudut di Kelas IV Sekolah Dasar. Sekolah Dasar: Kajian Teori Dan Praktik Pendidikan, 27(2), 98–107. Retrieved from https://doi.org/10.17977/um009v27i22018p098
Mulyani, A., Indah, E. kurnia N. I., & Satria, A. P. (2018). Analisis Kemampuan Pemahaman Matematis Siswa SMP pada Materi Bentuk Aljabar Mosharafa?: Jurnal Pendidikan Matematika Mosharafa?: Jurnal Pendidikan Matematika. Mosharafa: Jurnal Pendidikan Matematika, 7(2), 251–262. http://journal.institutpendidikan.ac.id/index.php/mosharafa
Muna, H., Nizaruddin, N., & Murtianto, Y. H. (2017). Pengembangan Video Pembelajaran Matematika Berbantuan Macromedia Flash 8 Dengan Pendekatan Kontekstual Pada Materi Program Linier Kelas Xi. Aksioma, 8(2), 9. Retrieved from https://doi.org/10.26877/aks.v8i2.1686
Najwa, W. A. (2018). Pendekatan PMRI sebagai Gerakan Literasi Sekolah dalam Pembelajaran Matematika. Prisma, Prosicing Seminar Nasional Matematika, 1, 575–581.
Nasrullah, & Zulkardi. (2011). Building counting by traditional game: A mathematics program for young children. Journal on Mathematics Education, 2(1), 41–54. Retrieved from https://doi.org/10.22342/jme.2.1.781.41-54
Nurainah, N., Maryanasari, R., & Nurfauziah, P. (2018). Analisis Kesulitan Kemampuan Koneksi Matematis Siwa Smp Kelas Viii Pada Materi Bangun Datar. JPMI (Jurnal Pembelajaran Matematika Inovatif), 1(1), 61. Retrieved from https://doi.org/10.22460/jpmi.v1i1.p61-68
Nursyahidah, F., & Albab, I. U. (2021). Learning Design on Surface Area and Volume of Cylinder Using Indonesian Ethno-mathematics of Traditional Cookie maker Assisted by GeoGebra, 13(4).
Nursyahidah, F., Ilma, R., & Putri, I. (2014). 2014 Instructional Design of Subtraction Using Pmri Approach, (978), 132–141.
Nursyahidah, F., Putri, R. I. I., & Somakim. (2013). Supporting first grade students’ understanding of addition up to 20 using traditional game. Journal on Mathematics Education, 4(2), 212–223. Retrieved from https://doi.org/10.22342/jme.4.2.557.212-223
Nursyahidah, F., Saputro, B. A., Albab, I. U., & Aisyah, F. (2020). Pengembangan Learning Trajectory Based Instruction Materi Kerucut Menggunakan Konteks Megono Gunungan. Mosharafa: Jurnal Pendidikan Matematika, 9(1), 47–58. Retrieved from https://doi.org/10.31980/mosharafa.v9i1.560
Nursyahidah, F., Saputro, B. A., & Rubowo, M. R. (2018). A Secondary Student’s Problem Solving Ability in Learning Based on Realistic Mathematics with Ethnomathematics. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 3(1), 13. Retrieved from https://doi.org/10.23917/jramathedu.v3i1.5607
Özerem, A. (2012). Misconceptions In Geometry And Suggested Solutions For Seventh Grade Students. Procedia - Social and Behavioral Sciences, 55, 720–729. Retrieved from https://doi.org/10.1016/j.sbspro.2012.09.557
Puspasari, L., Zulkardi, Z., & Somakim, S. (2015). Desain Pembelajaran Luas Segi Banyak Menggunakan Tangram Berpetak di Kelas IV. JINoP (Jurnal Inovasi Pembelajaran), 1(2), 150. Retrieved from https://doi.org/10.22219/jinop.v1i2.2566
Risdiyanti, I., & Indra Prahmana, R. C. (2020). The learning trajectory of number pattern learning using barathayudha war stories and uno stacko. Journal on Mathematics Education, 11(1), 157–166. Retrieved from https://doi.org/10.22342/jme.11.1.10225.157-166
Rofii, A., Sunardi, S., & Irvan, M. (2018). Characteristics of Students’ Metacognition Process At Informal Deduction Thinking Level in Geometry Problems. International Journal on Emerging Mathematics Education, 2(1), 89. Retrieved from https://doi.org/10.12928/ijeme.v2i1.7684
Rosyida, E. M., Riyadi, & Mardiyana. (2016). Analisis Kesalahan Siswa Dalam Pemecahan Masalah Berdasarkan Pendapat John W. Santrock Pada Pokok Bahasan Bangun Ruang Sisi Lengkung Ditinjau Dari Gaya Belajar Dan Gaya Berpikir Siswa. Jurnal Elektronik Pembelajaran Matematika, 4(10), 973–981.
Widiawati, Marzal, D., & Juwita, H. (2018). Desain Pembelajaran Garis Dan Sudut Dengan Konteks Pagar Buluh Di Kelas Vii. Journal of Mathematics Science and Education, 1(1), 118–130. Retrieved from https://doi.org/10.31540/jmse.v1i1.186
Yani, C. F., Maimunah, M., Roza, Y., Murni, A., & Daim, Z. (2019). Analisis Kemampuan Pemahaman Matematis Siswa pada Materi Bangun Ruang Sisi Lengkung. Mosharafa: Jurnal Pendidikan Matematika, 8(2), 203–214. Retrieved from https://doi.org/10.31980/mosharafa.v8i2.481
Published
2024-09-23
How to Cite
TUNI'MAH, Lattifah et al.
Designing Learning Trajectory of Curved 3D Shapes using RME with The Context of Sesaji Rewanda Semarang.
Journal of Medives : Journal of Mathematics Education IKIP Veteran Semarang, [S.l.], v. 8, n. 3, p. 449-460, sep. 2024.
ISSN 2549-5070.
Available at: <https://www.e-journal.ivet.ac.id/index.php/matematika/article/view/3097>. Date accessed: 07 july 2025.
doi: https://doi.org/10.31331/medivesveteran.v8i3.3097.
Issue
Section
Articles
This work is licensed under a Creative Commons Attribution 4.0 International License.
The copyright for all articles belongs to the authors. All other copyright is held by the journal.
