Eksplorasi Kemampuan Abstraksi Matematis Siswa SMP Negeri 2 Kajen dalam Materi Geometri Serta Implikasinya dalam Pembelajaran

Nadia Risqi Sabita; Santika Lya Diah Pramesti

doi:10.26877/imajiner.v8i4.27938

Eksplorasi Kemampuan Abstraksi Matematis Siswa SMP Negeri 2 Kajen dalam Materi Geometri Serta Implikasinya dalam Pembelajaran

Nadia Risqi Sabita, Santika Lya Diah Pramesti

Abstract

This study aimed to explore the mathematical abstraction abilities of eighth-grade students at SMP Negeri 2 Kajen in the context of solid geometry, and to identify implications for instructional practice. A descriptive qualitative approach was employed, with three students selected through purposive sampling to represent a range of mathematical proficiency levels: high (S1), high-to-moderate (S2), and moderate (S3). Data were gathered through classroom observation and in-depth interviews, analysed using the Miles and Huberman framework, and validated through method triangulation. Abstraction ability was examined across four indicators adapted from Dreyfus (1991): representation, identification of geometric properties and elements, classification, and generalisation. Findings revealed a consistent gradient aligned with the cognitive hierarchy of the indicators: representation and property identification were relatively more developed than classification and generalisation. S1 demonstrated proficiency across all four indicators independently; S2 handled representation well but required prompting for abstract classification and generalisation; S3 could only operate at the visual level for representation and identification, while classification and generalisation had yet to emerge. Teacher-centred instruction and limited use of hands-on manipulatives were found to constrain the development of higher-order abstraction abilities. The study recommends incorporating open-ended questioning, integrating digital geometry tools, and applying adaptive scaffolding as strategies to progressively support the growth of mathematical abstraction in junior high school students.

Keywords

classification; generalization; mathematical abstraction; representation; solid geometry.

Full Text:

PDF

References

Amalliyah, N., Dewi, N. R., & Dwijanto, D. (2021). Tahap berpikir geometri siswa SMA berdasarkan teori Van Hiele ditinjau dari perbedaan gender. JNPM (Jurnal Nasional Pendidikan Matematika), 5(2), 352–361. https://doi.org/10.33603/jnpm.v5i2.4550

Clark, J. M., & Paivio, A. (1991). Dual Coding Theory and Education. Educational Psychology Review, 3(3), 149–210. https://doi.org/10.1007/BF01320076

Creswell, J. W. (2014). Research Design: Qualitative, Quantitative, and Mixed Methods Approaches (4th ed.). SAGE Publications.

Creswell, J. W., & Poth, C. N. (2018). Qualitative inquiry and research design: Choosing among five approaches (4th ed.). SAGE Publications.

Dreyfus, T. (1991). Advanced Mathematical Thinking Processes (D. B. T.-A. M. T. Tall (ed.); pp. 25–41). Kluwer Academic Publishers.

Edimuslim, E. (2022). Analisis kemampuan abstraksi matematis siswa sekolah menengah pertama ditinjau dari gaya belajar tipe Kolb. Suska Journal of Mathematics Education, 8(1), 39–46. https://doi.org/10.24014/sjme.v8i1.16831

Ferrari, P. L. (2003). Abstraction in Mathematics. Philosophical Transactions of the Royal Society B: Biological Sciences, 358(1435), 1225–1230. https://doi.org/10.1098/rstb.2003.1316

Firdaus, A., Maryono, I., & Solehudin, S. (2024). Analisis kemampuan abstraksi matematis berdasarkan teori Van Hiele pada siswa sekolah menengah atas. Jurnal Perspektif, 8(1), 106–116. https://doi.org/10.15575/jp.v8i1.273

Fitriani, N., Hidayah, I. S., & Nurfauziah, P. (2021). Live worksheet realistic mathematics education berbantuan GeoGebra: Meningkatkan abstraksi matematis siswa SMP pada materi segiempat. JNPM (Jurnal Nasional Pendidikan Matematika), 5(1), 37–52. https://doi.org/10.33603/jnpm.v5i1.4526

Fitriani, N., Suryadi, D., & Darhim, D. (2018). Analysis of mathematical abstraction on concept of a three-dimensional figure with curved surfaces of junior high school students. Journal of Physics: Conference Series, 1132(1), 12037. https://doi.org/10.1088/1742-6596/1132/1/012037

Fitriyah, A., & Retnawati, H. (2022). Kemampuan Abstraksi Matematis Siswa SMP pada Materi Geometri Ditinjau dari Gaya Berpikir. Jurnal Imajiner: Jurnal Matematika Dan Pendidikan Matematika, 4(5), 387–397. https://doi.org/10.26877/imajiner.v4i5.11523

Hafizh, F. A., & Kusno. (2025). Analisis kesulitan berpikir abstrak siswa dalam materi transformasi geometri: Studi kualitatif pada siswa SMP. Jurnal Ilmiah Pendidikan Citra Bakti, 12(2), 570–584. https://doi.org/10.38048/jipcb.v12i2.5367

Hershkowitz, R., Schwarz, B. B., & Dreyfus, T. (2001). Abstraction in Context: Epistemic Actions. Journal for Research in Mathematics Education, 32(2), 195–222. https://doi.org/10.2307/749673

Jannah, M. J., Sihombing, T. V. B., Pandiangan, I. S., Annekarela, A., Buulolo, J. C., & Mailani, E. (2026). MATEMATIKA SEKOLAH DASAR. IMEIJ: Indo-MathEdu Intellectuals Journal, 7(3), 4159–4169. https://doi.org/http://doi.org/10.54373/imeij.v7i3.6348

Kustiani, D., & Prahmana, R. C. I. (2021). Penggunaan Alat Peraga Model Bangun Ruang terhadap Kemampuan Identifikasi Unsur-unsur Bangun Ruang Siswa SMP. Jurnal Imajiner: Jurnal Matematika Dan Pendidikan Matematika, 3(6), 479–489. https://doi.org/10.26877/imajiner.v3i6.9112

Lenaini, I. (2021). Teknik Pengambilan Sampel Purposive Dan Snowball Sampling. HISTORIS: Jurnal Kajian, Penelitian & Pengembangan Pendidikan Sejarah, 6(1), 33–39. https://doi.org/https://doi.org/10.31764/historis.v6i1.4075

Miles, M. B., Huberman, A. M., & Saldana, J. (2014). Qualitative Data Analysis: A Methods Sourcebook (Third Edit). SAGE Publications, Inc.

Nihayah, A. L. (2021). Analisis kemampuan abstraksi matematis siswa dalam menyelesaikan soal pada materi segiempat kelas VII SMP. JPM: Jurnal Pendidikan Matematika, 4(1), 1–8. https://doi.org/10.33474/jpm.v4i1.2610

Nurhayati, E., & Sari, A. P. (2020). Profil Kemampuan Berpikir Klasifikasi Siswa SMP dalam Menyelesaikan Masalah Geometri Berdasarkan Teori Van Hiele. Jurnal Imajiner: Jurnal Matematika Dan Pendidikan Matematika, 2(4), 311–321. https://doi.org/10.26877/imajiner.v2i4.6173

Ocy, D. R., & Sarifah, I. (2025). EFA and CFA analysis: Development and validation of a test instrument for mathematical abstraction skills. Journal of Research and Advances in Mathematics Education, 10(2), 101–119. https://doi.org/10.23917/jramathedu.v10i2.4127

Permata, L. D., & Wijaya, A. (2021). Kemampuan Representasi Matematis Siswa SMP pada Materi Bangun Ruang Sisi Datar melalui Pendekatan Kontekstual. Jurnal Pendidikan Matematika, 15(2), 181–196. https://doi.org/10.22342/jpm.15.2.13524.181-196

Prasetya, D. A., & Setyaningrum, W. (2022). Efektivitas Penggunaan GeoGebra 3D terhadap Kemampuan Representasi Spasial dan Identifikasi Sifat Bangun Ruang Siswa SMP. Jurnal Imajiner: Jurnal Matematika Dan Pendidikan Matematika, 4(6), 507–519. https://doi.org/10.26877/imajiner.v4i6.12314

Presmeg, N. C. (2006). Research on Visualization in Learning and Teaching Mathematics (A. Gutiérrez & P. B. T.-H. of R. on the P. of M. E. Boero (eds.); pp. 205–235). Sense Publishers.

Rahmawati, D., & Firmansyah, D. (2023). Analisis Kemampuan Generalisasi Matematis Siswa SMP dalam Pembelajaran Berbasis Masalah pada Materi Geometri Ruang. Jurnal Imajiner: Jurnal Matematika Dan Pendidikan Matematika, 5(3), 241–254. https://doi.org/10.26877/imajiner.v5i3.14785

Rubiyanti, D. P., Wijayanti, P., & Surabaya, U. N. (2023). Profil kemampuan berpikir abstrak siswa SMP dalam memecahkan masalah matematika ditinjau dari adversity quotient. MATHEdunesa: Jurnal Ilmiah Pendidikan Matematika, 12(2), 569–587. https://doi.org/10.26740/mathedunesa.v12n2.p569-587

Sfard, A. (1991). On the Dual Nature of Mathematical Conceptions: Reflections on Processes and Objects as Different Sides of the Same Coin. Educational Studies in Mathematics, 22(1), 1–36. https://doi.org/10.1007/BF00302715

Sugiyono. (2019). Metode Penelitian Kuantitatif, Kualitatif, dan R&D. Alfabeta.

Sugiyono. (2022). Metode Penelitian Kualitatif. Alfabeta.

Suryadi, D. (2010). Menciptakan Proses Belajar Aktif: Kajian dari Sudut Pandang Teori Belajar dan Teori Didaktik BT - Seminar Nasional Pendidikan Matematika.

Susanto, H. A., Waluya, S. B., & Rochmad. (2020). Efektivitas Pembelajaran Berbasis Concept Mapping dalam Meningkatkan Kemampuan Klasifikasi Bangun Geometri Siswa SMP. Unnes Journal of Mathematics Education, 9(2), 121–130. https://doi.org/10.15294/ujme.v9i2.38912

Susanto, S., & Mahmudi, A. (2021). Tahap berpikir geometri siswa SMP berdasarkan teori Van Hiele ditinjau dari keterampilan geometri. Jurnal Riset Pendidikan Matematika, 8(1), 106–116. https://doi.org/10.21831/jrpm.v8i1.17044

Sweller, J. (1988). Cognitive Load During Problem Solving: Effects on Learning. Cognitive Science, 12(2), 257–285. https://doi.org/10.1207/s15516709cog1202_4

Van Hiele, P. M. (1986). Structure and Insight: A Theory of Mathematics Education. Academic Press.

Wahyuni, R., & Rohaeti, E. E. (2023). Kemampuan Abstraksi Matematis Siswa SMP pada Pembelajaran Geometri Ditinjau dari Perbedaan Kemampuan Awal dan Preferensi Media Belajar. Jurnal Imajiner: Jurnal Matematika Dan Pendidikan Matematika, 5(4), 331–344. https://doi.org/10.26877/imajiner.v5i4.16291

Woolfolk, A. (2016). Educational Psychology (13th ed.). Pearson.

DOI: https://doi.org/10.26877/imajiner.v8i4.27938