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PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

Keywords

Lintasan belajar, limas, kemampuan spasial, pendidikan matematika realistik, learning trajectory, pyramid, spatial ability, realistic mathematics education

Document Type

Article

Abstract

Penelitian ini bertujuan untuk menghasilkan lintasan belajar pada materi limas untuk menumbuhkan kemampuan spasial siswa melalui pendidikan matematika realistik. Penelitian ini merupakan design research yang memuat tiga tahap, yaitu preparing for the experiment, the teaching experiment, dan retrospective analysis. Subjek penelitian adalah siswa kelas VIII di salah satu SMP di Aceh Besar, Indonesia. Uji coba terhadap Hypothetical Learning Trajectory (HLT) siklus 1 dilakukan secara offline dengan melibatkan tiga siswa, sementara uji coba Hypothetical Learning Trajectory (HLT) siklus 2 dilakukan secara online dengan melibatkan 10 siswa. Instrumen pengumpulan data berupa lembar aktivitas siswa, lembar observasi, pedoman wawancara, catatan lapangan, dan rekaman video pembelajaran. Penelitian ini menghasilkan lintasan belajar limas yang diperoleh dari merevisi HLT dengan cara memperbanyak tampilan contoh-contoh limas dalam kehidupan sehari-hari, menggambar lebih banyak jaring-jaring limas, mengurutkan pola dalam menemukan rumus jumlah diagonal bidang, dan menayangkan animasi 3D melalui GeoGebra. Lintasan belajar limas dimulai dari melukis limas, menggambar jaring-jaring limas, menemukan rumus berkaitan dengan hubungan antar unsur-unsur limas, menemukan rumus luas permukaan limas, dan menemukan rumus volume limas. Lintasan belajar yang dikembangkan secara teoritis dapat menumbuhkan kemampuan spasial siswa melalui pendidikan matematika realistik pada materi limas.

Development of pyramid learning trajectory to promote students' spatial ability through realistic mathematics education assisted by GeoGebra

Abstract

This study aimed to produce a learning trajectory in pyramid material to foster students' spatial ability through realistic mathematics education. This is design research which consists of three stages, namely experimental preparation, teaching experiment, and retrospective analysis. The research subjects were students of class VIII in a junior high school in Aceh Besar, Indonesia. The trial of Hypothetical Learning Trajectory (HLT) for cycle 1 that was performed offline involved three students and the trial of Hypothetical Learning Trajectory (HLT) for cycle 2 that was performed online involved 10 students. The instruments for data collection were student activity sheet (worksheet), observation sheet, interview protocol, field note, and learning video recording. The research produced a pyramid learning trajectory obtained from revising HLT by presenting more pyramid models in everyday life, drawing more pyramid nets, recognizing patterns in determining the number of face diagonal, and displaying 3D animations through GeoGebra. The pyramid learning trajectory started from drawing a pyramid, drawing the net of a pyramid, finding formulas related to the relationship between pyramid elements, finding the formula for the surface area of a pyramid, and finding the formula for the volume of a pyramid. The developed learning trajectory, theoretically, could foster students' spatial ability through realistic mathematics education on the learning material about pyramid.

Page Range

1-18

Issue

1

Volume

16

Digital Object Identifier (DOI)

10.21831/pg.v16i1.36157

Source

https://journal.uny.ac.id/index.php/pythagoras/article/view/36157

References

Alimuddin, H., & Trisnowali, A. (2018). Profil kemampuan spasial dalam menyelesaikan masalah geometri siswa yang memiliki kecerdasan logis. Histogram: Jurnal Pendidikan Matematika, 2(2), 169-182.

Armstrong, T. (2009). Multiple intelligences in the classroom (3rd ed.). ASCD.

Budiman, H. (2011). Peningkatan kemampuan berpikir kritis dan kreatif matematis siswa melalui pendekatan berbasis masalah berbantuan software Cabri 3D. Prosiding Seminar Nasional FMIPA-UT 2011 (pp. 1-19). http://repository.ut.ac.id/2498/

Bustang, B., Zulkardi, Z., Darmawijoyo, D., Dolk, M. L. A. M., & Van Eerde, H. A. A. (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. https://doi.org/10.5539/ies.v6n8p58

Faradisa, M., Sulistio, M., Ayu, Y. A. (2018). Penggunaan aplikasi GeoGebra pada pembelajaran matematika materi poligon dan sudut sebagai sarana meningkatkan kemampuan siswa. Jurnal Equation: Teori dan Penelitian Pendidikan Matematika, 1(2), 166-172. http://dx.doi.org/10.29300/equation.v1i2.2294

Giaquinto, M. (2007). Visual thinking in mathematics: An epistemological study. Oxford University Press.

Gravemeijer, K. P. E. (1994). Developing realistic mathematics education. CD-β Press, Freudenthal Institute.

Gravemeijer, K., & Cobb, P. (2006). Design research from a learning design perspective. In J. van den Akker, K. Gravemeijer, S. McKenney, & N. Nieveen (Eds.), Educational design research (pp. 17-51). Routledge.

Gravemeijer, K., & van Eerde, D. (2009). Design research as a means for building a knowledge base for teachers and teaching in mathematics education. The Elementary School Journal, 109(5), 510-524. https://doi.org/10.1086/596999

Meirida, U., Johar, R., & Ahmad, A. (2019). Ability of junior high school students in drawing 3D pyramids. Journal of Physics: Conference Series, 1460(1), 1-8. https://doi.org/10.1088/1742-6596/1460/1/012008

Nasution, E. Y. P. (2017). Meningkatkan kemampuan spasial siswa melalui pembelajaran geometri berbantuan Cabri 3D. Mathline: Jurnal Matematika dan Pendidikan Matematika, 2(2), 179-194. https://doi.org/10.31943/mathline.v2i2.45

National Research Council. (2006). Learning to think spatially. The National Academies Press.

National Research Council. (2007). Taking science to school: Learning and teaching science in grades K-8. The National Academies Press. https://doi.org/10.17226/11625

NCTM. (2000). Principles and standards for school mathematics. Author.

Nopiyani, D., Turmudi, T., & Prabawanto, S. (2016). Penerapan pembelajaran matematika realistik berbantuan GeoGebra untuk meningkatkan kemampuan komunikasi matematis siswa SMP. Mosharafa: Jurnal Pendidikan Matematika, 5(2), 45-52. https://doi.org/10.31980/mosharafa.v5i2.259

Ocal, M. F. (2017). The effect of Geogebra on students' conceptual and procedural knowledge: The case of applications of derivative. Higher Education Studies, 7(2), 67-78. https://doi.org/10.5539/hes.v7n2p67

Özdemir, B. G. (2017). Mathematical practices in a learning environment designed by realistic mathematics edu-cation: Teaching experiment about cone and pyramid. European Journal of Education Studies, 3(5), 405-430. http://dx.doi.org/10.46827/ejes.v0i0.675

Prahmana, R. C. I. (2017). Design research (Teori dan implementasinya: Suatu pengantar). Rajawali Pers.

Prasetyo, N. A. (2019). Desain didaktis berpikir kreatif matematis pada materi bangun ruang sisi datar berbantuan Geogebra (Unpublished bachelor's thesis). Universitas Pendidikan Indonesia.

Prihandoko, A. C. (2005). Buku rujukan PGSD bidang matematika: Memahami konsep matematika secara benar dan menyajikannya dengan menarik. Departemen Pendidikan Nasional.

Saputra, H. (2018). Kemampuan spasial matematis. https://doi.org/10.17605/OSF.IO/JFWST

Sari, D. P. (2018). Analisis kemampuan spasial dan self-efficacy siswa pada pembelajaran kooperatif tipe Jigsaw di SMAS Muhammadiyah 8 Kisaran (Unpublished master's thesis). Program Pascasarjana, Universitas Negeri Medan.

Subroto, T. (2012). Kemampuan spasial (spatial ability). Prosiding Seminar Nasional Pendidikan Matematika STKIP Sebelas April Sumedang (pp. 252-359).

Sulistiawati, S. (2014). Analisis kesulitan belajar kemampuan penalaran matematis siswa SMP pada limas. Prosiding Seminar Nasional Pendidikan STKIP Surya (pp. 205-225).

Syahbana, A. (2013). Alternatif pemahaman konsep umum volume suatu bangun ruang. Edumatica, 3(2), 1-7. https://doi.org/10.22437/edumatica.v5i01.2662

Sztajn, P., Confrey, J., Wilson, P. H., & Edgington, C. (2012). Learning trajectory based instruction: Toward a theory of teaching. Educational Researcher, 41(5), 147-156. https://doi.org/10.3102%2F0013189X12442801

Treffers, A. (1991). Didactical background of a mathematics program for primary education. In L. Streefland (Ed.), Realistic Mathematics Education in primary school: On the occasion of the opening of the Freudenthal Institute (pp. 21-56). CD-β Press, Freudenthal Institute.

Ubuz, B., & Gökbulut, Y. (2015). Primary prospective teachers' knowledge on pyramid: Generating definitions and examples. KırÅŸehir EÄŸitim Fakültesi Dergisi, 16(2), 335-351.

Unlu, M., & Horzum, T. (2018). Mathematics teacher candidates' definitions of prism and pyramid. International Journal of Research in Education and Science, 4(2), 670-685. https://doi.org/10.21890/ijres.438373

van den Akker, J., Gravemeijer, K., McKenney, S., & Nieveen, N. (Eds.). (2006). Educational design research. Routledge.

van den Heuvel-Panhuizen, M. (1996). Assessment and Realistic Mathematics Education. CD-β Press, Freudenthal Institute.

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