Exploring Grade VIII Students' Procedural Skills in Solving Pythagorean Problems

Ade Riska Sanjani(1), Achmad Salido(2*), Akbar Nasrum(3), Chairuddin Chairuddin(4), Jahring Jahring(5), Dian Ulfa Sari(6),


(1) Universitas Sembilanbelas November Kolaka
(2) Universitas Sembilanbelas November Kolaka
(3) Universitas Sembilanbelas November Kolaka
(4) Universitas Sembilanbelas November Kolaka
(5) Universitas Sembilanbelas November Kolaka
(6) Universitas Sembilanbelas November Kolaka
(*) Corresponding Author

Abstract


This study explores the procedural skills of grade VIII students in solving Pythagorean Theorem problems, focusing on the diversity of problem-solving steps and error patterns that emerge. A descriptive qualitative method was used in this study, with three students selected as subjects based on high, medium, and low levels of mathematical ability. Data were collected through problem-solving tasks and semi-structured interviews to comprehensively understand the students' approaches and strategies. The results showed that students with high procedural skills implemented problem-solving steps in a structured manner, while those with moderate skills often needed to be more consistent in recording critical steps. Students with low skills tended to bypass procedural structures and proceed directly to solutions, leading to a higher rate of errors. Error patterns varied by students' mathematical ability levels: high-ability students made no errors, medium-ability students exhibited errors in illustrations and procedural consistency, and low-ability students struggled with writing expressions and fully implementing steps. These findings emphasize the need for instructional approaches tailored to students' skill levels, such as structured learning and scaffolding, to strengthen procedural skills. A follow-up study with a broader sample is recommended to validate these findings and assess the effectiveness of instructional strategies for enhancing students' procedural skills across various mathematical topics.

Keywords


Procedural skills; geometry; Pythagoras; mathematics; junior high school

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References


Al-Mutawah, M. A., Thomas, R., Eid, A., Mahmoud, E. Y., & Fateel, M. J. (2019). Conceptual understanding, procedural knowledge and problem-solving skills in mathematics: High school graduates work analysis and standpoints. International Journal of Education and Practice, 7(3), 258–273. https://doi.org/10.18488/journal.61.2019.73.258.273

Antari, L., Rizta, A., Na’imah, U., & Inda Kusumawati, N. (2022). Pemahaman konsep matematika dasar mahasiswa pendidikan matematika. Nabla Dewantara : J.Pendidik.Matematika, 7(2), 56–63. https://doi.org/10.51517/nabla.v7i2.158

Ayuningtyas, D., Wahyuningsih, E. D., & Paridjo, P. (2021). Analisis kesalahan siswa secara prosedural dalam menyelesaikan soal transformasi geometri. JIPMat, 6(1), 24–33. https://doi.org/10.26877/jipmat.v6i1.8125

Ballon, E. M. M., Gomez, F. L. R., Castro, A. E. L. F., & Linares, M. R. F. C. (2024). Evaluating problem-solving and procedural skills offirst-year students in a Peruvian higher education institution. Eurasia Journal of Mathematics, Science and Technology Education, 20(2). https://doi.org/10.29333/ejmste/14154

Buaddin Hasan. (2020). Kesulitan siswa dan scaffolding dalam menyelesaikan masalah geometri ruang. Numeracy, 7(1), 49–64. https://doi.org/10.46244/numeracy.v7i1.998

Cragg, L., Keeble, S., Richardson, S., Roome, H. E., & Gilmore, C. (2017). Direct and indirect influences of executive functions on mathematics achievement. Cognition, 162, 12–26. https://doi.org/10.1016/j.cognition.2017.01.014

Fatimah, A. T., & Zakiah, N. E. (2018). Kelancaran Prosedural Matematis Dalam Pemecahan Masalah Konteks Pemasaran. In Mathline Jurnal Matematika Dan Pendidikan Matematika. https://doi.org/10.31943/mathline.v3i2.92

Faulkner, F., Breen, C., Prendergast, M., & Carr, M. (2023). Profiling mathematical procedural and problem-solving skills of undergraduate students following a new mathematics curriculum. International Journal of Mathematical Education in Science and Technology, 54(2), 220–249. https://doi.org/10.1080/0020739X.2021.1953625

Friantini, R. N., Winata, R., & Annurwanda, P. (2021). Procedural fluency from the view of students of mathematical disposition level through Google Classroom assisted learning. Formatif: Jurnal Ilmiah Pendidikan MIPA, 11(2), 201–216. https://doi.org/10.30998/formatif.v11i2.9907

Gilmore, C., Keeble, S., Richardson, S., & Cragg, L. (2017). The interaction of procedural skill, conceptual understanding and working memory in early mathematics achievement. Journal of Numerical Cognition, 3(2), 400–416. https://doi.org/10.5964/jnc.v3i2.51

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. https://doi.org/10.29333/iejme/8482

Jatisunda, G. (2016). Peningkatan kemampuan pemecahan masalah matematis siswa SMP melalui pembelajaran dengan pendekatan kontekstual. Jurnal THEOREMS (The Original Research of Mathematics), 1(1), 58–74.

Lenamah, A. S., Abi, A. M., & Babys, U. (2022). Analisis kemampuan pemahaman konsep matematis siswa SMP negeri Siso. Didactical Mathematics, 4(2), 294–301. https://doi.org/10.31949/dm.v4i2.2334

Lian, J., Yu, X., Kang, Q., & Jia, S. (2023). A comparative study of secondary school mathematics teaching materials from the perspective of reasoning-taking “Pythagorean theorem†as an example. Asian Journal of Education and Social Studies, 49(4), 190–198. https://doi.org/10.9734/ajess/2023/v49i41198

Lutfiya, L., Sumardi, H., & Siagian, T. A. (2021). Analisis kemampuan pemecahan masalah matematika siswa SMP berdasarkan langkah penyelesaian Polya. LINEAR: Journal of Mathematics Education, 6, 44. https://doi.org/10.32332/linear.v2i2.3738

Mardaleni, D., Noviarni, N., & Nurdin, E. (2018). Efek strategi pembelajaran scaffolding terhadap kemampuan pemecahan masalah matematis berdasarkan kemampuan awal matematis siswa. JURING (Journal for Research in Mathematics Learning), 1(3), 236. https://doi.org/10.24014/juring.v1i3.5668

Miles, M. B., Huberman, A. M., & Saldana, J. (2014). Qualitative Data Analysis A Methods Sourcebook Edition 3. SAGE Publications, Inc.

Oktavianti, S., Farida, F., & Putra, F. G. (2018). Implementasi model Osborn dengan teknik mnemonic melalui teori konstruktivisme terhadap kemampuan pemecahan masalah matematis. MaPan, 6(1), 94–103. https://doi.org/10.24252/mapan.2018v6n1a9

Pai’pinan, M., & Kho, R. (2018). Analisis keterampilan geometris siswa SMP berdasarkan gaya kognitif dalam menyelesaikan masalah geometri tiga dimensi. JISIP (Jurnal Ilmu Sosial Dan Pendidikan), 2(3), 186–190. https://doi.org/10.58258/jisip.v2i3.560

Permatahati, I., Rahmawati, N. D., & Aini, A. N. (2022). Analisis kesalahan siswa dalam menyelesaikan soal matematika materi teorema Pythagoras ditinjau dari kemampuan berpikir kritis. Imajiner: Jurnal Matematika Dan Pendidikan Matematika, 4(5), 401–406. https://doi.org/10.26877/imajiner.v4i5.10996

Pratidiana, D., & Muhayatun, N. (2021). Analisis kelancaran prosedural matematis siswa dalam menyelesaikan soal program linear. UNION: Jurnal Ilmiah Pendidikan Matematika, 9(2), 189–201. https://doi.org/10.30738/union.v9i2.9369

Putra, I. S. (2020). Improve student’s learning using media for understanding and interest in Pythagorean theorem learning. Vygotsky, 2(2), 66. https://doi.org/10.30736/vj.v2i2.222

Rachmawati, I. (2019). Penggunaan teknik Scaffolding pada pembelajaran matematika untuk meningkatkan kemampuan pemahaman matematik pada siswa SMP. Jurnal Equation: Teori Dan Penelitian Pendidikan Matematika, 2(2), 94. https://doi.org/10.29300/equation.v2i2.2314

Rahmawaty, A., & Nurmeidina, R. (2023). Analisis kesalahan siswa dalam menyelesaikan soal ulangan harian matematika pada materi teorema phytagoras di masa new normal. In Emteka Jurnal Pendidikan Matematika. https://doi.org/10.24127/emteka.v4i1.2509

Ridwan, M. R., Retnawati, H., Hadi, S., & Jailani, J. (2021). The effectiveness of innovative learning on mathematical problem-solving ability: A meta-analysis. International Journal of Research in Education and Science, 7(3), 910–932. https://doi.org/10.46328/ijres.2287

Rosdianwinata, E., & Ridwan, M. (2018). Penerapan model pembelajaran probing prompting terhadap kemampuan pemahaman konsep matematika siswa. MENDIDIK: Jurnal Kajian Pendidikan Dan Pengajaran, 4(1), 77–82. https://doi.org/10.30653/003.201841.46

Sa’diah, L. S., & Nahdi, D. S. (2023). Model pembelajaran kontekstual untuk membantu pemecahan masalah matematis. Jurnal Ilmiah Pendidik Indonesia, 2(1), 1–7.

Sari, W. P., Purwasi, L. A., & Yanto, Y. (2020). Analisis kesalahan siswa dalam menyelesaikan soal cerita materi teorema Pythagoras. Transformasi: Jurnal Pendidikan Matematika Dan Matematika, 4(2), 387–401.

Sasangka, P. A., Nugroho, A. A., & Setyawati, R. D. (2022). Analisis kesalahan dalam menyelesaikan masalah matematika SMP. Imajiner: Jurnal Matematika Dan Pendidikan Matematika, 4(5), 407–418. https://doi.org/10.26877/imajiner.v4i5.11111

Ulva, E., Maimunah, M., & Murni, A. (2020). Pengaruh model problem based learning terhadap kemampuan pemecahan masalah matematis siswa kelas VII SMPN se-kabupaten Kuantan Singingi pada materi aritmetika sosial. Jurnal Cendekia : Jurnal Pendidikan Matematika, 4(2), 1230–1238. https://doi.org/10.31004/cendekia.v4i2.356

Wati, R., & Ningtyas, Y. D. W. K. (2020). Analisis kesalahan koneksi matematis siswa dalam menyelesaikan masalah kontekstual ditinjau dari kemampuan matematis siswa. Jurnal Gammath, 5(1), 44–52.

Yuliana, Y., Rahayu, R. R., & Firmansah, F. (2022). Kesalahan siswa dalam pemecahan masalah matematika pada teorema pythagoras. Edukatif : Jurnal Ilmu Pendidikan, 4(4), 5532–5543. https://doi.org/10.31004/edukatif.v4i4.3294

Yuliani, D., Andriani, L., & Fitri, I. (2020). Pengaruh penerapan pendekatan RME (realistic mathematic education) terhadap kemampuan komunikasi matematis berdasarkan self efficacy siswa SMPN 18 Pekanbaru. JURING (Journal for Research in Mathematics Learning), 3(2), 193. https://doi.org/10.24014/juring.v3i2.9386

Yuswan, S. A., & Maat, S. M. (2021). Pengetahuan konseptual dan prosedural dalam matematik: Satu sorotan literatur sistematik. Malaysian Journal of Social Sciences and Humanities (MJSSH), 6(12), 94–108. https://doi.org/10.47405/mjssh.v6i12.1178




DOI: 10.24235/eduma.v13i2.18719

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