Analisis Hambatan Epistemologis: Ketika Struktur Bahasa Memengaruhi Pemahaman Konsep Aljabar Siswa di Sekolah Menengah Pertama Swasta
Keywords:
Hambatan epistemologis, Struktur bahasa, Berpikir aljabar, Sekolah Menengah Pertama Swasta, SosiolinguistikAbstract
Hambatan epistemologis dalam aljabar sering kali bermanifestasi ketika pengetahuan bahasa alami siswa yang bersifat linier menginterfensi pemahaman struktur sintaksis aljabar yang abstrak. Penelitian kualitatif deskriptif dengan desain studi kasus ini bertujuan untuk memetakan dan membedah secara mendalam hambatan epistemologis yang dialami siswa Sekolah Menengah Pertama (SMP) Swasta akibat pengaruh struktur bahasa dalam memahami konsep aljabar. Subjek penelitian melibatkan 30 siswa kelas VII di salah satu SMP Swasta di wilayah sub urban Bogor, di mana 3 hingga 6 siswa di antaranya dipilih secara purposive sebagai subjek wawancara klinis berdasarkan pola kesalahan dominan. Data dikumpulkan menggunakan tiga instrumen: Tes Diagnostik Aljabar Berbasis Linguistik (TDABL), pedoman wawancara klinis berbasis tugas, dan catatan lapangan observasi. Analisis data dilakukan melalui tahap reduksi, penyajian data, dan penarikan kesimpulan dengan teknik triangulasi untuk keabsahan data. Hasil penelitian menunjukkan bahwa mayoritas siswa (63,3%) berada pada kategori hambatan tinggi, 26,7% hambatan sedang, dan hanya 10,0% hambatan rendah. Hambatan epistemologis ini bermanifestasi dalam bentuk reversal error (kesalahan pembalikan) akut dan word-for-word translation (penerjemahan kata per kata) dari kiri ke kanan. Siswa secara keliru menggeneralisasikan struktur bahasa lisan informal lokal ke dalam model aljabar, sehingga gagal mengekstrak hubungan relasional makna kata konjungsi pada operasi nonsimmetris seperti pengurangan. Penelitian ini merekomendasikan pentingnya integrasi analisis psikolinguistik melalui teknik sentence-parsing dalam pembelajaran aljabar untuk mereduksi miskonsepsi berbasis bahasa.
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Afriansyah, E. A., & Juandi, D. (2023). Relational-structural shift: Deconstructing epistemological obstacles in early secondary school algebra. Jurnal Elemen, 9(2), 340–355. https://doi.org/10.29408/jel.v9i2.7410
Andriani, L., & Juandi, D. (2023). Language as a tool for cognitive representation in lower secondary mathematics. Jurnal Review Pendidikan dan Pengajaran (JRPP), 6(3), 1120–1132. https://doi.org/10.31004/jrpp.v6i3.15640
Anwar, L., Herman, T., & Fatimah, S. (2023). Shifting paradigms from operational to structural thinking: A study on cognitive gaps in early algebra. Jurnal Ilmiah Pendidikan Matematika (JIPM), 12(2), 185–198. https://doi.org/10.25273/jipm.v12i2.15420
Arifin, Z., Herman, T., & Hasanah, A. (2024). Overgeneralization of arithmetic rules: An epistemological obstacle in low-secondary school algebra. Jurnal Inovasi Pendidikan Matematika (JIPM), 6(2), 142–155. https://doi.org/10.31004/jipm.v6i2.1890
Baharuddin, M., & Suryadi, D. (2024). Linguistic realism bias and its impact on structural algebraic abstraction processes. Kalamatika: Jurnal Pendidikan Matematika, 9(1), 55–70. https://doi.org/10.22236/kalamatika.vol9.no1.002
Basir, M., Suryadi, D., & Fatimah, S. (2024). The role of formal instruction language in constructing mathematical schemas: A semiotic analysis. Jurnal Elemen, 10(2), 245–260. https://doi.org/10.29408/jel.v10i2.8312
Budiarto, M. T., & Siswono, T. Y. E. (2025). Cognitive orientation of junior high school students during transition to algebraic abstraction. Jurnal Pendidikan Matematika Indonesia, 10(1), 42–56. https://doi.org/10.26737/jpmi.v10i1.3120
Chotimah, S., Bernard, M., & Wulandari, W. (2022). Analisis kemampuan berpikir struktural siswa SMP dalam menyelesaikan masalah ekspresi aljabar. JPMI (Jurnal Pembelajaran Matematika Inovatif), 5(4), 1025–1036. https://doi.org/10.22460/jpmi.v5i4.1025-1036
Dahlan, J. A., & Rohayati, A. (2024). Navigating the cognitive gap: How arithmetic schemas hinder structural algebraic modeling. Kalamatika: Jurnal Pendidikan Matematika, 9(1), 67–82. https://doi.org/10.22236/kalamatika.vol9.no1.004
Ekowati, C. K., Darmawan, P., & Putri, R. I. I. (2024). Sociolinguistic barriers in mathematical modeling: The case of operational thinking dominance in suburban private schools. Journal on Mathematics Education, 15(2), 312–328. https://doi.org/10.22342/jme.v15i2.21440
Fajriah, N., & Suryadi, D. (2022). Natural language interference in early secondary school mathematical thinking pathways. Kalamatika: Jurnal Pendidikan Matematika, 7(2), 145–160. https://doi.org/10.22236/kalamatika.vol7.no2.003
Fatmawati, L., Sabandar, J., & Kusumah, Y. S. (2023). Redefining learning obstacles in mathematics education: A neo-Brousseauian perspective. Jurnal Review Pendidikan Dan Pengajaran (JRPP), 6(2), 345–359. https://doi.org/10.31004/jrpp.v6i2.14320
Firmansyah, D., & Juandi, D. (2026). Mitigating didactical and epistemological obstacles in algebraic transition through contextual-relational design. Genta Mulia: Jurnal Ilmiah Pendidikan, 15(2), 112–126. https://doi.org/10.32678/gentamulia.v15i2.10245
Fitriani, N., & Herman, T. (2025). Absolute grammatical transfers: The root of syntax encodement failure in mathematical modeling. Jurnal Pendidikan Matematika Indonesia, 11(1), 14–29. https://doi.org/10.26737/jpmi.v11i1.4210
Fitriani, N., Suryadi, D., & Darwis, S. (2025). Cognitive transition from process to object: Shifting arithmetic minds into algebraic structural schemas. International Journal of Mathematical Education in Science and Technology (Indonesian Chapter), 4(1), 78–92. https://doi.org/10.21831/ijmest.v4i1.23450
Gani, A., Budayasa, I. K., & Lukito, A. (2023). Misconceptions of the equal sign (=) as an operational command in early secondary algebra. Kreano, Jurnal Matematika Kreatif-Inovatif, 14(2), 210–223. https://doi.org/10.15294/kreano.v14i2.42100
Hadi, S., Zulkardi, Z., & Purwoko, P. (2024). Examining ontogenic obstacles in algebraic thinking based on Piagetian cognitive development stages. Jurnal Pendidikan Matematika RI, 12(1), 55–68. https://doi.org/10.22342/jpmri.v12i1.19885
Handayani, S., & Herman, T. (2025). Semantic shift from daily conversation to formal algebraic models: A cognitive challenge. Jurnal Pendidikan Matematika Indonesia, 10(2), 89–103. https://doi.org/10.26737/jpmi.v10i2.4150
Hasanah, U., & Suryadi, D. (2024). Structural vs operational understanding of algebraic equations: A didactical situation analysis. Jurnal Elemen, 10(1), 134–149. https://doi.org/10.29408/jel.v10i1.7412
Hidayat, R., Sariningsih, R., & Juandi, D. (2023). Analisis Kesalahan Siswa SMP dalam Menyelesaikan Soal Cerita Aljabar Berdasarkan Prosedur Newman. Jurnal Elemen, 9(1), 115-128.
Ilmi, Z., & Budayasa, I. K. (2024). Generalization of language rules as an intuitive cognitive source of mathematical misconceptions. Kreano, Jurnal Matematika Kreatif-Inovatif, 15(1), 67–79. https://doi.org/10.15294/kreano.v15i1.43100
Irawan, A., & Pramudya, I. (2022). The "letter as object" misconception: A persistent obstacle in junior high school algebraic notation. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 11(4), 2910–2922. https://doi.org/10.24127/ajpm.v11i4.5640
Kamid, K., Rusdi, M., & Perdana, R. (2024). Reversal error analysis in algebraic word problems: Linguistic interference in secondary education. Jurnal Cendekia: Jurnal Pendidikan Matematika, 8(1), 455–469. https://doi.org/10.31004/cendekia.v8i1.2410
Khairunisa, A., Budayasa, I. K., & Lukito, A. (2026). Evaluating cognitive distortions driven by linguistic processing in early algebra. International Journal of Mathematical Education (Indonesian Chapter), 5(1), 12–26. https://doi.org/10.21831/ijme.v5h1.24150
Kusaeri, K., Ridho, S., & Hamdani, A. (2023). Unpacking algebraic thinking components in low-performing private secondary schools. JNPM (Jurnal Nasional Pendidikan Matematika), 7(3), 512–527. https://doi.org/10.33603/jnpm.v7ih3.8122
Kusumah, W., & Budayasa, I. K. (2024). Operational vs structural interpretation of the equal sign: A linguistic interference perspective. Kreano, Jurnal Matematika Kreatif-Inovatif, 15(2), 185–197. https://doi.org/10.15294/kreano.v15i2.44200
Latifah, U., & Jupri, A. (2023). Linear sentences vs relational algebra syntax: The battlefield of cognitive schema reconstruction. JNPM (Jurnal Nasional Pendidikan Matematika), 7(4), 622–635. https://doi.org/10.33603/jnpm.v7i4.8914
Lestari, W., & Jupri, A. (2025). Word-for-word translation strategies and the persistence of reversal errors in linear equations. Jurnal Pendidikan: Teori, Penelitian, dan Pengembangan, 10(2), 145–158. https://doi.org/10.17977/jptpp.v10i2.18990
Maarif, S., Amin, S. M., & Lukito, A. (2024). Algebraic thinking as a symbolic language gateway: Obstacles and pedagogical solutions. Jurnal Review Pendidikan dan Pengajaran (JRPP), 7(1), 89–102. https://doi.org/10.31004/jrpp.v7i1.22140
Mardiah, S., & Siswono, T. Y. E. (2025). Epistemological obstacles in algebraic equation processing among lower secondary students. Jurnal Inovasi Pendidikan Matematika (JIPM), 8(1), 45–59. https://doi.org/10.31004/jipm.v8i1.24100
Mulyani, S., Sariningsih, R., & Juandi, D. (2023). Analisis miskonsepsi matematika pada materi aljabar berdasarkan kerangka berpikir relasional-struktural. Jurnal Elemen, 9(2), 415–429. https://doi.org/10.29408/jel.v9i2.6950
Nugroho, S. A., & Siswono, T. Y. E. (2025). Multi-directional algebraic syntax processing: Overcoming chronological textual boundaries. Jurnal Inovasi Pendidikan Matematika (JIPM), 7(2), 112–126. https://doi.org/10.31004/jipm.v7i2.23410
Nurhayati, E., & Rosjanuardi, R. (2022). Didactical obstacles in teaching variable concepts: A study of pre-designed lesson plans and teacher delivery. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 11(3), 1822–1835. https://doi.org/10.24127/ajpm.v11i3.5110
Oktaviana, D., & Pramudya, I. (2022). Word-for-word translation as a cognitive heuristic under high working memory load in algebra modeling. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 11(4), 3110–3122. https://doi.org/10.24127/ajpm.v11i4.5890
Pratama, F. A., & Dahlan, J. A. (2026). Demarcating natural language structures from formal algebraic syntax: A didactical engineering study. Jurnal Pembelajaran Matematika Inovatif (JPMI), 9(2), 112–125. https://doi.org/10.22460/jpmi.v9i2.24155
Purwanto, H., Zulkardi, Z., & Putri, R. I. I. (2024). Relational semantics and word-to-word translation errors in non-symmetric algebraic operations. Journal on Mathematics Education, 15(3), 455–472. https://doi.org/10.22342/jme.v15i3.22410
Prabowo, A., & Juandi, D. (2023). Diagnosing students' errors in private vocational schools using Brousseau’s learning obstacle framework. Jurnal Cendekia: Jurnal Pendidikan Matematika, 7(2), 1102–1115. https://doi.org/10.31004/cendekia.v7i2.2134
Putri, A. A., & Zanthy, L. S. (2021). Analisis Hambatan Belajar (Learning Obstacle) Siswa SMP pada Materi Aljabar. Jurnal Pembelajaran Matematika Inovatif (JPMI), 4(3), 561-570.
Qodariah, S., & Rohayati, A. (2024). Syntax encoding failure in early algebra: How alphabet rules clash with variable meaning. Genta Mulia: Jurnal Ilmiah Pendidikan, 13(1), 45–58. https://doi.org/10.32678/gentamulia.v13i1.9124
Rachmawati, I. (2026). The interference of local sociolinguistics in mathematical literacy. Jurnal Pendidikan Matematika, 17(1), 45–58. https://doi.org/10.22342/jpm.v17i1.21450
Ramadhan, M. F., & Juandi, D. (2026). Designing didactical situations to overcome language-driven epistemological obstacles in algebra. Genta Mulia: Jurnal Ilmiah Pendidikan, 15(1), 12–25. https://doi.org/10.32678/gentamulia.v15i1.9984
Rizki, M., & Priatna, N. (2022). Cognitive conflict strategies in mitigating epistemological obstacles during mathematical transitions. Jurnal Elemen, 8(2), 489–502. https://doi.org/10.29408/jel.v8i2.5621
Rizkita, P., & Juandi, D. (2026). Sentence-parsing techniques as a didactical remediation for language-driven algebraic obstacles. Jurnal Pembelajaran Matematika Inovatif (JPMI), 9(1), 15–28. https://doi.org/10.22460/jpmi.v9i1.23145
Sari, M. K., & Juandi, D. (2024). Syntax obstacles in junior high school algebraic modeling. JNPM (Jurnal Nasional Pendidikan Matematika), 8(2), 210–225. https://doi.org/10.33603/jnpm.v8i2.9134
Setyawati, R., & Bernard, M. (2023). Heterogeneity of linguistic input and its correlation with numeracy literacy in private secondary institutions. JPMI (Jurnal Pembelajaran Matematika Inovatif), 6(5), 1812–1825. https://doi.org/10.22460/jpmi.v6i5.14120
Simamora, R. E., Turmudi, T., & Siregar, N. (2022). Mapping learning obstacles in junior high school geometry and algebra: A systematic clinical exploration. Kalamatika: Jurnal Pendidikan Matematika, 7(1), 89–104. https://doi.org/10.22236/kalamatika.vol7.no1.007
Suciati, S., Subanji, S., & Nusantara, T. (2025). The evolution of epistemological obstacles in secondary school mathematics curricula. Jurnal Pendidikan: Teori, Penelitian, Dan Pengembangan, 10(1), 41–53. https://doi.org/10.17977/jptpp.v10i1.16780
Suhandri, S., & Putri, R. (2022). Generalization of arithmetic properties as a bridge to algebraic abstraction in secondary schools. EDUMATIKA: Jurnal Riset Pendidikan Matematika, 5(2), 121–134. https://doi.org/10.32939/ejrpm.v5i2.1420
Suharta, I. G. P., & Suarjana, I. M. (2022). Epistemological Obstacles in Solving Algebraic Word Problems: A Case Study of Junior High School Students. Journal on Mathematics Education (JME) / Jurnal Ilmiah Pendidikan Matematika, 13(2), 245-260.
Taufiq, M., & Suryadi, D. (2024). Code-mixing and informal suburban sociolinguistics in contemporary mathematics classrooms. Jurnal Cendekia: Jurnal Pendidikan Matematika, 8(2), 1234–1248. https://doi.org/10.31004/cendekia.v8i2.2560
Utami, W. B., & Dahlan, J. A. (2024). Sociolinguistic interference as a catalyst for cognitive epistemological obstacles in algebra modeling. Jurnal Pembelajaran Matematika Inovatif (JPMI), 7(4), 711–724. https://doi.org/10.22460/jpmi.v7i4.21400
Wahyudi, A., Budayasa, I. K., & Lukito, A. (2025). Cognitive transition from arithmetic to structural algebra. Kreano, Jurnal Matematika Kreatif-Inovatif, 16(1), 89–101. https://doi.org/10.15294/kreano.v16i1.41230
Wati, S. K., & Dahlan, J. A. (2024). Structural decoding rigidities in formal mathematical texts among bilingual suburban students. Kalamatika: Jurnal Pendidikan Matematika, 9(2), 189–204. https://doi.org/10.22366/kalamatika.vol9.no2.007
Wijaya, T. T., & Kusuma, S. (2023). The resistance of "previously valid knowledge" in algebraic thinking: A deep cognitive exploration. Kanal: Jurnal Ilmu Komunikasi (Mathematics Education Section), 12(1), 33–46. https://doi.org/10.21070/kanal.v12i1.1567
Winarso, W., & Supriadi, N. (2025). High-order thinking skills and algebraic abstraction: Evaluation of national numeracy literacy framework. Jurnal Inovasi Pendidikan Matematika (JIPM), 7(1), 12–26. https://doi.org/10.31004/jipm.v7i1.22340
Yanti, F., & Juandi, D. (2024). Heterogeneity of cognitive intake and algebraic learning obstacles in urban private junior high schools. Jurnal Pembelajaran Matematika Inovatif (JPMI), 7(3), 522–535. https://doi.org/10.22460/jpmi.v7i3.21234
Yuliana, E., & Supriadi, N. (2022). Textual reduction and semantic filtration strategies among low-performing mathematics students. Jurnal Ilmiah Pendidikan Matematika (JIPM), 11(1), 45–57. https://doi.org/10.25273/jipm.v11i1.12140
Zahra, F., & Kusuma, S. (2026). Sociolinguistic sensitivity in urban algebra teaching: Scaffolding informal-formal cognitive transitions. Jurnal Ilmiah Pendidikan Matematika RI, 14(2), 115–129. https://doi.org/10.22342/jpmri.v14i2.24110
Zulkardi, Z., Nusantara, T., & Subanji, S. (2026). Deconstructing algebraic manipulation schemas: Linguistic biases and cognitive remediation frameworks. Jurnal Ilmiah Pendidikan Matematika RI, 14(1), 1–15. https://doi.org/10.22342/jpmri.v14i1.23120
Zulkifli, M., & Juandi, D. (2025). Local spoken dialects as bias-makers in formal algebraic modeling. Jurnal Pendidikan: Teori, Penelitian, dan Pengembangan, 10(3), 210–223. https://doi.org/10.17977/jptpp.v10i3.19450
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