Depicting Epistemological Obstacles in Understanding the Concept of Sequence and Series
Keywords:Epistemological obstacle Sequence, and sequence
This study aimed to discover epistemological obstacle on secondary students to solve sequence and series problems based on three indicators, there are a conceptual obstacle, procedural obstacle, and operational technique obstacle. This study was descriptive with qualitative research approaches. Data were collected with the test and interview method. The subjects in this study are students of SMP Negeri 86 Jakarta class VIII based on the errors seen from the diagnostic tests that had been tested. The analysis was done by giving written tests which are essay and interview formatted. Results on analysis showed that: (1) Conceptual obstacle, obstacle that was experienced by students are: students considered that a pattern was said as a numeral pattern because they own odd numeral pattern and own 2,2,2 of difference; were not able to find exact pattern within the problem; considering that Fibonacci numeral sequence was a pattern that form prime numeral pattern; were not able to differ the concept of arithmetics and geometry sequence; were not able to understand the concept of first quarter on arithmetics sequence; error when interpreted the meaning of problems; were not able to intepret what was given on mathematics model; interpreting sum of the first 20 quarters with sequences which own the 20th quarter; and interpreting sum of the first 20 quarters with the 20th quarter; (2) While on procedural obstacle, obstacle that was experienced are: interpreting numeral pattern if they own their pair; error on determining multiplication or difference; and applying formulas incorrectly; (3) Last on operasional technique obstacle, obstacle that was experienced are error on calculation and using sign and symbol mathematics incorrectly.
Brousseau, G. (2006). Epistemological Obstacles, Problems, and Didactical Engineering. In Theory of Didactical Situations in Mathematics (pp. 79â€“117). https://doi.org/10.1007/0-306-47211-2_6
Brousseau, Guy. (2002). Theory of Didactical Situations in Mathematics (N. Balacheff, M. Cooper, R. Sutherland, & V. Warfield (eds.); 1st ed., Vol. 19). Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47211-2
Cornu, B. (1991). Limits. In D. Tall (Ed.), Advanced Mathematical Thinking (pp. 153â€“166). Springer Netherlands. https://doi.org/10.1007/0-306-47203-1
Creswell, J. W. (2012). Research Design Qualitative, Quantitative, and Mixed Second Edition. Sage Publication.
Elfiah, N. S., Maharani, H. R., & Aminudin, M. (2020). Hambatan epistemologi siswa dalam menyelesaikan masalah bangun ruang sisi datar. Delta: Jurnal Ilmiah Pendidikan Matematika, 8(1), 11â€“22.
Hardiyanti, A. (2017). Analisis Kesulitan Siswa Kelas IX SMP Dalam Menyelesaikan Soal Pada Materi Barisan Dan Deret. Prosiding Konferensi Nasional Penelitian Matematika dan Pembelajaran I.
Herscovics, N. (1989). Cognitive Obstacles Encountered in the Learning of Algebra. In S. Wagner & C. Kieran (Eds.), Research Issues in the Learning and Teaching of Algebra (pp. 60â€“86). Routledge. https://doi.org/10.4324/9781315044378-6
Kadarisma, G., & Amelia, R. (2018). Epistemological Obstacles in Solving Equation of Straight Line Problems. International Conference on Mathematics and Science Education of Universitas Pendidikan Indonesia, 905â€“910.
Kharisma, E. N. (2016). Analisis Kemampuan Berpikir Kritis Matematis Siswa SMK Pada Materi Barisan dan Deret. Jurnal Review Pembelajaran Matematika, 3(1), 62-75
Maarif, S, Perbowo, K. S., Noto, M. S., & Harisman, Y. (2019). Obstacles in Constructing Geometrical Proofs of Mathematics-Teacher-Students Based on Boeroâ€™s Proving Model. Journal of Physics: Conference Series, 1315, 012043. https://doi.org/10.1088/1742-6596/1315/1/012043
Maarif, Samsul, Setiarini, R. N., & Nurafni, N. (2020). Hambatan Epistimologis Siswa dalam Menyelesaikan Masalah Sistem Persamaan Linear Dua Variabel. Jurnal Didaktik Matematika, 7(1). https://doi.org/10.24815/jdm.v7i1.15234
Masjudin, M. (2018). Pembelajaran Kooperatif Investigatif Untuk Meningkatkan Pemahaman Siswa Materi Barisan Dan Deret. Jurnal Edukasi Matematika Dan Sains, 4(2), 76.
Modestou, M., & Gagatsis, A. (2007). Studentsâ€™ Improper Proportional Reasoning: A result of the epistemological obstacle of â€œlinearity.â€ Educational Psychology, 27(1), 75â€“92. https://doi.org/10.1080/01443410601061462
Moru, E. K. (2007). Talking With the Literature on Epistemological Obstacles. For the Learning of Mathematics, 27(3), 34â€“37.
Moru, E. K. (2010). Epistemological Obstacle in Coming to Understand the Limit Concept at Undergraduate Level: A Case of the National University of Lesotho.
Ningrum, L. S. (2013). Analisis Kemampuan Siswa Menyelesaikan Soal Matematika Dalam Bentuk Cerita Pokok Bahasan Barisan dan Deret Pada Siswa Kelas XII SMA Al-Islam 3 Surakarta.
Nopriana, T., Firmasari, S., & Tonah. (2016). Desain Bahan Ajar Aktivitas Pemecahan Masalah Pada Pokok Bahasan Barisan dan Deret. Jurnal Euclid, Vol.2, No.4, p.251, 2(4), 251â€“263.
Nurfadhilah, Suharto, & Setiawan, S. (2016). Profil Siswa Memahami Konsep Barisan Dan Deret Berdasarkan Tahap Belajar Dienes di Kelas IX-C SMP Nuris Jember. Kadikma, 7(1), 34-45.
Nyikahadzoyi, M. R., Mapuwei, T., & Chinyoka, M. (2013). Some Cognitive Obstacles Faced By â€œAâ€ Level Mathematics Students in Understanding Inequalities: A Case Study of Bindura Urban High Schools. International Journal of Academic Research in Progressive Education and Development, 2(2), 206â€“221.
Permendikbud Nomor 24 Tahun 2016 Tentang Kompetensi Inti dan Kompetensi Dasar Pelajaran Pada Kurikulum 2013, (2016).
Putri, N. S., Hartoyo, A., & Jamiah, Y. (2018). Desain Didaktis Melalui NaÃ¯ve Geometri Untuk Mengatasi Hambatan Epistemologis Dalam Persamaan Kuadrat di SMA. Jurnal Pendidikan Dan Pembelajaran Khatulistiwa, 7(9), 1â€“11.
Rasmania, R., Sugiatno, S., & Suratman, D. (2018). Hambatan Epistimologis Siswa Dalam Menentukan Domain Dan Range Fungsi Kuadrat Di Sekolah Menengah Atas. Jurnal Pendidikan Dan Pembelajaran Khatulistiwa, 7(7), 1â€“9.
Setiawan, D. I., & Widodo, S. A. (2019). Analisis Kesalahan dalam Menyelesaikan Masalah Segi empat Ditinjau dari Perkembangan Kognitif. Jurnal Edukasi Matematika Dan Sains, 7(2). https://doi.org/10.25273/jems.v7i2.5291
Sugiyono. (2016). Metode Penelitian Pendidikan Pendekatan Kuantitatif, Kualitatif, dan R&D. Alfabeta.
Suryadi, D. (2019). Landasan Filosofis Penelitian Desain Didaktis (DDR). Gapura Press.
Syah, M. (2010). Psikologi Belajar. Pt RajaGrafindo Persada Jakarta.
Widodo, S. A., Irfan, M., Trisniawati, T., Hidayat, W., Perbowo, K. S., Noto, M. S., & Prahmana, R. C. I. (2020). Process of algebra problem-solving in formal student. Journal of Physics: Conference Series, 1657(1). https://doi.org/10.1088/1742-6596/1657/1/012092
Widodo, S. A., Pangesti, A. D., Kuncoro, K. S., & Arigiyati, T. A. (2020). Thinking Process of Concrete Student in Solving Two-Dimensional Problems. Jurnal Pendidikan Matematika, 14(2), 117â€“128.
Widodo, S. A., Turmudi, T., & Dahlan, J. A. (2019). An Error Students In Mathematical Problems Solves Based On Cognitive Development. International Journal Of Scientific & Technology Research, 8(07), 433â€“439.
Widyatari, R. (2017). Analisis Kesalahan Siswa Dalam Menyelesaikan Soal Barisan dan Deret Ditinjau Dari Komunikasi Matematika. Naskah Publikasi, hlm, 1-14.
Yusuf, Y., Titat, N., & Yuliawati, T. (2017). Analisis hambatan belajar (learning obstacle) siswa SMP pada materi statistika. AKSIOMA: Jurnal Matematika dan Pendidikan Matematika, 8(1), 76-86.
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