Measuring the Difficulty Level of Mathematical Problems Based on Polya Criteria
DOI:
https://doi.org/10.23887/jere.v6i4.46316Keywords:
Student Errors, Math Problems, Polya CriteriaAbstract
Mathematics learning needs to be directed in understanding mathematical concepts and principles because it will be necessary for solving mathematical problems, problems in other disciplines, and problems in everyday life. But sometimes, we make mistakes both intentional and unintentional so that they will have an impact on the results of the mathematical problems we work on. Today many studies discuss the difficulty of students in solving math problems but there has been no research that discusses further the level of difficulty. This study aims to analyze the level of error students solve math problems according to Polya criteria, student errors based on education level, based on focus areas, and student errors based on other moderator variables. The method in this study uses meta-analysis. Data must meet the inclusion and exclusion criteria of indexing databases such as Scopus, DOAJ, WorldCat, Google Scholar, and Garuda Portal. The data was analyzed using JASP software. The results showed that of the 53 data that met the eligibility criteria obtained error rate information on criteria (1) understanding of problems by 37%, (2) devising a plan by 36%, (3) carrying out the plan by 36%, and (4) looking back by 44%. Based on the focus field focus obtained the RE Model for the highest error is in the case of number patterns when compared to algebraic and geometric cases.
References
Agustina, I., Subanji, & Irawati, S. (2019). Constraints of students in drawing logarithmic graphs based on polya steps and scaffolding implementation. Journal of Physics: Conference Series. https://doi.org/10.1088/1742-6596/1200/1/012005.
Antara, I. G. W. S., Sudarma, I. K., & Dibia, I. K. (2020). The Assessment Instrument of Mathematics Learning Outcomes Based on HOTS Toward Two-Dimensional Geometry Topic. Indonesian Journal Of Educational Research and Review, 3(2), 19–24. https://doi.org/10.23887/ijerr.v3i2.25869.
Apriani, F. (2018). Kesalahan Mahasiswa Calon Guru SD Dalam Menyelesaikan Soal Pemecahan Masalah Matematika. Journal of Mathematics Science and Education, 1(1), 102–117. https://doi.org/10.31540/jmse.v1i1.167.
Apriliyanto, B. (2019). Analisis Kesalahan Siswa dalam Pemecahan Masalah Turunan Fungsi Aljabar. Jurnal Komunikasi Pendidikan, 3(2), 117–125. https://doi.org/10.32585/jkp.v3i2.300.
Awantagusnik, A., Susiswo, S., & Irawati, S. (2021). Mathematical representation process analysis of students in solving contextual problem based on Polya ’ s strategy. AIP Conference Proceedings, 2330. https://doi.org/10.1063/5.0043422.
Bani, Y., & Ate, D. (2020). Analisis Kesalahan Siswa SMAN 1 Kota Tambolaka Dalam Menyelesaikan Soal Matematika Pada Pokok Bahasan Induksi Matematika Dengan Panduan Criteria Polya. Jurnal Penelitian Pendidikan Matematika Sumba, 2(1), 196–205. https://doi.org/10.53395/jppms.v2i1.102.
Baskorowati, H., & Wijatanti, P. (2020). Studi Kasus: Analisis Kesalahan Siswa Dalam Menyelesaikan Soal Cerita Matematika Materi Sistem Persamaan Linear Tiga Variabel Di Sma Negeri 1 Cerme. MATHEdunesa, 9(3), 529–539. https://doi.org/10.26740/mathedunesa.v9n3.p529-539.
Erwin, Rustaman, N., Firman, H., & Ramalis, T. (2019). Instrumen Asesmen Pedagogical Content Knowledge dalam Konteks Pengembangan Keterampilan Komunikasi Saintifik pada Pembelajaran Fisika. Titian Ilmu: Jurnal Ilmiah Multi Sciences, 11(2), 102–110. https://doi.org/10.30599/jti.v11i2.494.
Fajri, N., & Iwan, I. (2018). Analisis Kesalahan Siswa Kelas VII SMP Negeri 8 Banda Aceh dalam Menyelesaikan Soal Matematika pada Pokok Bahasan Segiempat Berdasarkan Kriteria Polya. Numeracy, 5(2), 257–269. https://doi.org/10.46244/numeracy.v5i2.399.
Faseha, H., Evendi, E., & Nugraha, Y. (2021). Analisis Kesalahan Siswa Dalam Memecahkan Masalah Perbandingan Berdasarkan Langkah Polya. Journal of Math Tadris, 1(01), 40–54. https://doi.org/10.55099/jmt.v1i01.7.
Fathonah, N., Juwita, R., & Jana, P. (2018). Analisis Kesalahan Mahasiswa dalam Menyelesikan Soal Program Linear dengan Menerapkan Teori Polya Ditinjau dari Perbedaan Gender. Universitas PGRI Yogyakarta.
Fauziyah, R. S., Pujiastuti, HeniMatematika, P., Sultan, U., Tirtayasa, A., & Serang, K. (2020). Analisis Kesalahan Siswa dalam Menyelesaikan Soal Cerita Program Linear Berdasarkan Prosedur Polya. UNION: Jurnal Pendidikan Matematika, 8(2), 253–264. https://core.ac.uk/download/pdf/328101584.pdf.
Gradini, E., Yustinaningrum, B., & Safitri, D. (2022). Kesalahan Siswa Dalam Memecahkan Masalah Trigonometri Ditinjau dari Indikator Polya. Mosharafa: Jurnal Pendidikan Matematika, 11(1), 49–60. https://doi.org/10.31980/mosharafa.v11i1.1226.
Hasanah, A. U., & Murtiyasa, B. (2020). Analisis Kesalahan Siswa Dalam Mengerjakan Soal Cerita Materi Program Linear Kelas Xi Sma Negeri 1 Sukodono. Universitas Muhammadiyah Surakarta.
Hidayah, S. (2016). Analisis kesalahan siswa dalam menyelesaikan soal cerita spldv berdasarkan langkah penyelesaian polya. Prosiding Seminar Nasional Pendidikan Matematika, 1(2), 182–190.
Jamilah, S. N. (2017). Analisis Kesalahan dalam Menyelesaikan Soal Cerita Menurut Polya Pokok Bahasan Keliling dan Luas Daerah Persegi, Persegi Panjang, dan Segitiga pada Siswa Kelas V SDN Bintoro 02 Jember. Universitas Negeri Jember.
Jana, P. (2018). Analisis Kesalahan Mahasiswa Dalam Menyelesaikan Soal Matematika Pada Pokok Bahasan Vektor. Jurnal Mercumatika: Jurnal Penelitian Matematika Dan Pendidikan Matematika, 2(2), 8–14. https://doi.org/10.26486/jm.v2i2.398 W.
Jedaus, M. D., Farida, N., & Suwanti, V. (2019). Analisis kesalahan siswa dalam menyelesaikan soal cerita pokok bahasan perbandingan tahapan Polya. Semnas SENASTEK Unikama 2019, 2, 306–315. https://conference.unikama.ac.id/artikel/index.php/senastek/article/view/102.
Katon, K. S., & Arigiyati, T. A. (2018). Analisis Kesalahan Siswa Menurut Polya Materi Persamaan Dan Pertidaksamaan Linear Satu Variabel. Prosiding Seminar Nasional Etnomatnesia, 576–580. https://jurnal.ustjogja.ac.id/index.php/etnomatnesia/article/view/2386.
Khusniawati, E., Marsitin, R., & Murniasih, T. R. (2019). Analisis kesalahan peserta didik pada pemecahan masalah polya dalam menyelesaikan soal aljabar. Seminar Nasional FST 2019 Universitas Kanjuruan Malang, 2, 583–588. https://conference.unikama.ac.id/artikel/index.php/senastek/article/view/161.
Komarudin, K. (2016). Analisis kesalahan siswa dalam pemecahan masalah matematika pada materi peluang berdasarkan high order thinking dan pemberian scaffolding. Jurnal Darussalam: Jurnal Pendidikan, Komunikasi Dan Pemikiran Hukum Islam, 8(1), 202–217. https://doi.org/10.30739/darussalam.v8i1.96.
Kurniawan, A., Ihwayudin, I., & Permata, R. A. (2021). Analisis Kesalahan Siswa Dalam Menyelesaikan Soal Cerita Segitiga Berdasarkan Prosedur Polya. Jurnal Ilmiah IKIP Mataram, 8(1), 127–136. https://e-journal.undikma.ac.id/index.php/jiim/article/view/4093.
Logachev, M. S., Orekhovskaya, N. A., Seregina, T. N., Shishov, S., & Volvak, S. F. (2021). Information system for monitoring and managing the quality of educational programs. Journal of Open Innovation: Technology, Market, and Complexity, 7(1), 93–102. https://doi.org/10.3390/JOITMC7010093.
Lukas, I. S., Salajang, S. M., Manurung, O., & Sulistyaningsih, M. (2021). Analisis Kesalahan Siswa dalam Menyelesaikan Soal Cerita Sistem Persamaan Linier Dua Variabel Menggunakan Prosedur Polya. MARISEKOLA: Jurnal Matematika Riset Edukasi Dan Kolaborasi, 2(2), 53–58. https://doi.org/10.53682/marisekola.v2i2.1072.
Lukum, A. (2015). Evaluasi Program Pembelajaran Ipa Smp Menggunakan Model Countenance Stake. Jurnal Penelitian Dan Evaluasi Pendidikan, 19(1), 25–37. https://doi.org/10.21831/pep.v19i1.4552.
Mandailina, V., Syaharuddin, S., Pramita, D., Ibrahim, I., & Haifaturrahmah, H. (2021). Pembelajaran Daring Dalam Meningkatkan Motivasi dan Hasil Belajar Peserta Didik Selama Pandemi Covid-19: Sebuah Meta-Analisis. Indonesian Journal of Educational Science (IJES), 3(2), 120–129. https://doi.org/10.31605/ijes.v3i2.955.
Muharram, M. R. W. (2021). Model Pembelajaran SPADE: Solusi Kesulitan Belajar Matematika Pada Materi Geometri di Sekolah Dasar (Tinjauan Sistematis). De Fermat: Jurnal Pendidikan Matematika, 4(2), 112–124. http://jurnal.pmat.uniba-bpn.ac.id/index.php/DEFERMAT/article/view/188.
Mustika, E., Winarko, W., Ika, Y., Pranyata, P., & Mustika, E. (2018). Analisis kesalahan siswa saat mengerjakan soal matematika ukk ditinjau dari langkah polya. Seminar Nasional FST 2018, 1, 570–579.
Ngura, E. R., Rahayuningsih, S., & Khasanah, F. (2020). Analisis Kesalahan Siswa dalam Menyelesaikan Soal Aljabar Siswa Kelas X SMK Shalahuddin 1 Malang. Jurnal Penelitian Dan Pengkajian Ilmiah Mahasiswa (JPPIM), 1(1), 33–40. http://jppim.wisnuwardhana.ac.id/index.php/jppim/article/view/7.
Nikmah, I. L., Juandi, D., & Prabawanto, S. (2019). Students’ difficulties on solving mathematical problem based on ESD objectives. Journal of Physics: Conference Series, 1157(3). https://doi.org/10.1088/1742-6596/1157/3/032116.
Nova, F., Hayono, Y., & Yunita, A. (2021). Analisis Kesalahan Siswa Dalam Menyelesaikan Soal Pemecahan Masalah Matematika Berdasarkan Kriteria Polya. Jurnal Horizon Pendidikan, 1(2), 324–333. https://doi.org/10.36269/hjrme.v4i2.499.
Nurdiana Hidayanti, E., Setia wardana, M. Y., & Prima Artharina, F. (2022). Analisis Kemampuan Pemecahan Masalah Matematis Dalam Menyelesaikan Soal Cerita Berdasarkan Langkah- Langkah Polya Pada Siswa Kelas III SD Negeri Muntung Temanggung. Praniti: Jurnal Pendidikan, Bahasa, Dan Sastra, 2(1), 36–42. http://jurnal.unw.ac.id:1254/index.php/praniti/article/view/1476.
Nurhalin, Y., & Ramlah. (2021). Analisis Kemampuan Pemecahan Masalah Matematis Siswa Kelas VII SMP Pada Materi Himpunan. AlphaMath : Journal of Mathematics Education, 8(2), 185–194. https://doi.org/10.30595/alphamath.v7i1.9936.
Pitriani, Y., & Ocktaviaini, N. N. (2020). Kesalahan Siswa dalam Menyelesaikan Soal Cerita pada Materi Aritmatika Sosial Menurut Polya. Mosharafa: Jurnal Pendidikan Matematika, 9(2), 287–298. https://doi.org/10.31980/mosharafa.v9i2.656.
Pramesti, S. L. D. (2020). Evaluasi Pembelajaran Matematika Pada Boarding School Berdasarkan Model Cipp. Integral: Pendidikan Matematika, 11(1), 17–32. https://ojs3.umc.ac.id/index.php/JNR/article/view/1139.
Pratiwi, S. A. (2019). Analisis Kesalahan Siswa Dalam Menyelesaikan Soal Persamaan Linear Satu Variabel Berdasarkan Teori Polya Kelas VII SMP Muhammadiyah 4 Surakarta. Universitas Muhammadiyah Surakarta.
Retnawati, H., Apino, E., Kartianom, Djidu, H., & D.anazifa, R. (2018). Pengantar Analisis Meta (E. Apino (ed.); Pertama). Parama Publishing.
Rismadani, R. A., Aetharina, F. P., & Cahyadi, F. (2021). Kesulitan Siswa Menyelesaikan Soal Cerita Matematika Pada Materi Pecahan Kelas V Sdn Jomblang 03 Semarang Berdasarkan Langkah – Langkah Pemecahan Masalah Menurut Polya. Dwijaloka Jurnal Pendidikan Dasar & Menengah, 2(3), 266–274. https://doi.org/10.35473/dwijaloka.v2i3.1207.
Rizaq, M. A., & Sulikan, S. (2020). Analisis Kesalahan Siswa Dalam Menyelesaikan Soal Cerita Kedalam Model Matematika Materi Bangun Datar Berdasarkan Pemecahan Masalah Dikelas IV MI KH. Romly Tamim Poncokusumo. Prosiding Seminar Nasional IKIP Budi Utomo, 1, 26–35. https://doi.org/10.33503/prosiding.v1i01.1092.
Sastri, N. D., Sujatmiko, P., & Fitriana, L. (2019). Analisis kesalahan siswa dalam memecahkan masalah matematika pokok bahasan aplikasi barisan dan deret berdasarkan langkah polya ditinjau dari kemampuan awal siswa. Jurnal Pendidikan Matematika Dan Matematika (JPMM), 3(6), 601–610. https://doi.org/10.20961/jpmm%20solusi.v3i6.39276.
Suciati, I., & Wahyuni, D. S. (2018). Analisis kesalahan siswa dalam menyelesaikan soal matematika pada operasi hitung pecahan pada siswa kelas v sdn pengawu. Jurnal Penelitian Dan Pembelajaran Matematika, 11(2). https://doi.org/10.30870/jppm.v11i2.3760.
Suharti, S., Nur, F., & Alim, B. (2021). Polya Steps for Analyzing Errors in Mathematical Problem Solving. AL-ISHLAH: Jurnal Pendidikan, 13(1), 741–748. https://doi.org/10.35445/alishlah.v13i1.570.
Sukmarini, M. A., & Hasanah, I. A. (2022). Analisis Kesalahan Siswa Terhadap Soal Cerita SPLDV dengan Langkah Penyelesaian Polya Kelas VIII di SMP Plus Darul Hikmah. Prosiding SI MaNIs (Seminar Nasional Integrasi Matematika Dan Nilai-Nilai Islami), 4(1), 106–109. http://conferences.uin-malang.ac.id/index.php/SIMANIS/article/view/1507.
Sukoriyanto, S., Nusantara, T., Subanji, S., & Chandra, T. D. (2016). Students ’ Errors in Solving the Permutation and Combination Problems Based on Problem Solving Steps of Polya. International Education Studies, 9(2), 11–16. https://doi.org/10.5539/ies.v9n2p11.
Sulistyaningsih, A., & Rakhmawati, E. (2017). Analisis Kesalahan Siswa Menurut Kastolan Dalam Pemecahan Masalah Matematika. Seminar Matematika Dan Pendidikan Matematika Uny, 19(2), 123–130. http://seminar.uny.ac.id/semnasmatematika/sites/seminar.uny.ac.id.semnasmatematika/files/full/M-19.pdf.
Sulistyorini, Y. (2017). Error Analysis in Solving Geometry Problem on Pseudo-Thinking’s Students. University of Muhammadiyah Malang’s 1st International Conference of Mathematics Education (INCOMED 2017), 160, 103–107. https://doi.org/10.2991/incomed-17.2018.22.
Suparman, S., Tamur, M., Yunita, Y., Wijaya, T. T., & Syaharuddin, S. (2021). Using Problem-Based Learning to Enhance Mathematical Abilities of Primary School Students: A Systematic Review and Meta-Analysis. JTAM (Jurnal Teori Dan Aplikasi Matematika), 5(1), 144. https://doi.org/10.31764/jtam.v5i1.3806.
Syaharuddin, Mulyono, S., Retno Utami, R., Ghazali, M., Yustitia, V., Nurhayati, & Merdekawaty, A. (2021). Penelitian Meta Analisis Menggunakan Software JASP: Pengumpulan Data Sampai Publikasinya (Pertama). CV. Pena Persada.
Syahda, U., Yuhana, Y., Pujiastuti, H., Sultan, U., & Tirtayasa, A. (2021). Analisis Kesalahan dalam Menyelesaikan Soal Cerita Persamaan dan Pertidaksamaan Linear Satu Variabel Berdasarkan Teori Polya Ditinjau dari Gaya Kognitif. Didaktis Jurnal Pendidikan Dan Ilmu Pengetahuan, 21(3), 336–349. https://doi.org/10.30651/didaktis.v21i3.9838.
Utami, G., Saputro, B. A., Fita, M., & Untari, A. (2020). Error Analysis In Solving FPB And KPK Story Questions Based On Polya Procedures For Fourth Grade Elementary School Students. International Journal of Elementary Education, 4(4), 642–654. https://doi.org/10.23887/jisd.v4i4.27464.
Widodo, S. A., & Sujadi, A. . (2017). Analisis Kesalahan Mahasiswa Dalam Memecahkan Masalah Trigonometri. SOSIOHUMANIORA: Jurnal Ilmiah Ilmu Sosial Dan Humaniora, 1(1), 1–14. https://doi.org/10.30738/sosio.v1i1.518.
Winarso, W., Wahid, S., & Rizkiah, R. (2022). Type of Error in Completing Mathematical Problem Based on Newman’s Error Analysis (NEA) And Polya Theory. Jurnal Pendidikan Matematika Dan IPA, 13(1), 51–67. https://doi.org/10.26418/jpmipa.v13i1.44765.
Wiyah, R. B., & Nurjanah. (2021). Error analysis in solving the linear equation system of three variables using Polya’s problem-solving steps. Journal of Physics: Conference Series, 1882(1). https://doi.org/10.1088/1742-6596/1882/1/012084.
Wulandari, W., & Dadi, O. (2021). Analisis Kesalahan Siswa pada Materi Bentuk Aljabar Berdasarkan Tahapan Polya. Jurnal Inovasi Pembelajaran Matematika (JIPM), 3(1), 8–15. http://e-jurnal.stkippgrisumenep.ac.id/index.php/JIPM/article/view/166.
Yuliani, S. R., Setiawan, W., & Hendriana, H. (2018). Analisis kesalahan siswa smp pada materi perbandingan ditinjau dari indikator kemampuan pemecahan masalah matematis. 1(2), 77–82. https://doi.org/10.31004/joe.v1i2.26.
Yulita, Y., & Ishartono, N. (2021). Kesalahan siswa kelas unggulan dalam menyelesaikan soal materi pecahan berdasarkan langkah-langkah Polya. Delta-Pi: Jurnal Matematika Dan Pendidikan Matematika, 10(2), 240–253. https://doi.org/10.33387/dpi.v10i2.3208.
Zainal, N. F. (2020). Pengukuran, Assessment dan Evaluasi dalam Pembelajaran Matematika. Jurnal Pendidikan Matematika, 3(1), 8–26. https://doi.org/10.31537/laplace.v3i1.310.
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