Causes of Student Errors in Solving Numeration Problems : A Case Study on Students with a Strongly Field Independent Cognitive Style

Salman Alfarisi, Abdur Rahman As’ari, Sukoriyanto Sukoriyanto

Abstract


This research aims to uncover the causes of errors in solving numeracy problems related to trigonometry among students with a strongly field-independent cognitive style. The research method employs a case study with a qualitative approach. The subjects of this study are students of class XI MA Ibadurrochman Malang. The instrument in this study consists of the main instrument, namely the researcher himself and supporting instruments consisting of GEFT (Group Embedded Figure Test) sheets and Numeration Problem Solving Test Sheets (TPMN) and interview guidelines. This data analysis technique used interactive model analysis. The research findings indicate that the causes of student errors in solving numeracy problems are primarily rooted in their previous knowledge, which results in these errors. In other words, their previous knowledge is unable to serve as a foundational material for generating ideas in solving new problems encountered. These new problems related to trigonometry are used not only to apply previously acquired knowledge to the issues at hand but also to learn new mathematical concepts. Consequently, numeracy problems become a solution for students to study mathematics coherently.


Keywords


Field Independent; Thinking Process; Numeration; Student Errors.

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References


Allinson, C. W., & Hayes, J. (1996). The cognitive style index: A measure of intuition-analysis for organizational research. Journal of Management Studies, 33(1), 119–135. https://doi.org/10.1111/j.1467-6486.1996.tb00801.x

Amir, A. (2013). Pembelajaran Matematika dengan Menggunakan Kecerdasan Majemuk (Multiple Intelligences). Logaritma: Jurnal Ilmu-Ilmu Pendidikan Dan Sains, 1(01).

Ariefia, H. E., As’ari, A. R., & Susanto, H. (2016). Proses Berpikir Siswa dalam Menyelesaikan Permasalahan pada Materi Trigonometri. Jurnal Pembelajaran Matematika, 3(1), 28–32. http://journal.um.ac.id/index.php/pembelajaran-matematika/article/view/5565%0A

Arifani, N. H., As’ari, A. R., & Abadyo. (2017). Proses Berpikir Siswa Kelas VIII dalam Menyelesaikan Soal Matematika TIMSS Materi Besar Sudut dalam Bentuk Geometris. Jurnal Pendidikan: Teori, Penelitian, Dan Pengembangan, 2(7), 946–954. http://dx.doi.org/10.17977/jptpp.v2i7.9677

As’ari, A. R., Kurniati, D., & Subanji. (2019). Teachers Expectation of Students’ Thinking Processes in Written Works: A Survey of Teachers’ Readiness in Making Thinking Visible. Journal on Mathematics Education, 10(3), 409–424. https://doi.org/10.22342/jme.10.3.7978.409-424

Baroody, A. J., & Coslick, R. T. (1993). Problem Solving, Reasoning, and Communicating, K-8: Helping Children Think Mathematically. Merrill.

Creswell, J. W. (2012). Educational Research (FOURTH EDI). Matthew Buchholtz. https://www.ptonline.com/articles/how-to-get-better-mfi-results

Farida, N. (2015). Analisis kesalahan siswa SMP kelas VIII dalam menyelesaikan masalah soal cerita matematika. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 4(2).

Handayaningsih, R., & Nusantara, T. (2021). Profil Multiple Intelligences dalam Kemampuan Pemecahan Masalah Matematika. Edu Sains: Jurnal Pendidikan Sains Dan Matematika, 9(1), 20–32.

Hardianto, H. (2017). Deskripsi Proses Berpikir Siswa dalam Menyelesaikan Soal Pisa Berdasarkan Gaya Kognitif. Prosiding, 3(1), 371–470.

Hayuningrat, S., & Listiawan, T. (2018). Proses Berpikir Siswa dengan Gaya Kognitif Reflektif dalam Memecahkan Masalah Matematika Generalisasi Pola. Jurnal Elemen, 4(2), 183–196.

Hidayah, S. (2016). Analisis Kesalahan Siswa dalam Menyelesaikan Soal Cerita SPLDV Berdasarkan Langkah Penyelesaian Polya. Prosiding Seminar Nasional Pendidikan Matematika, 1(29), 182–190.

Hidayanto, E. (2013). Proses Berpikir Aritmetika dan Berpikir Aljabar Siswa dalam Menyelesaikan Soal Cerita. Prosiding Seminar Nasional Aljabar Dan Pembelajarannya, 173–177.

Hudojo, H. (2005). Pengembangan Kurikulum dan Pembelajaran Matematika. Malang: UM Press.

Kevin A. Artuz, J., & B. Roble, D. (2021). Developing Students’ Critical Thinking Skills in Mathematics Using Online-Process Oriented Guided Inquiry Learning (O-POGIL). American Journal of Educational Research, 9(7), 404–409. https://doi.org/10.12691/education-9-7-2

Kristofora, M., & Sujadi, A. A. (2017). Analisis Kesalahan Dalam Menyelesaikan Masalah Matematika dengan Menggunakan Langkah Polya Siswa Kelas VII SMP. Prisma, 6(1), 9–16.

Kurniawan, E., Mulyati, S., & Rahardjo, S. (2017). Proses Asimilasi dan Akomodasi dalam Memecahkan Masalah Matematika Berdasarkan Kecerdasan Emosional. Jurnal Pendidikan, 2(5), 592–598. http://journal.um.ac.id/index.php/jptpp/

Liljedahl, P., Santos-Trigo, M., Malaspina, U., & Bruder, R. (2016). Problem Solving in Mathematics Education. Springer Nature.

Lin, X., & Powell, S. R. (2022). The Roles of Initial Mathematics, Reading, and Cognitive Skills in Subsequent Mathematics Performance: A Meta-analytic Structural Equation Modeling Approach. Review of Educational Research, 92(2), 288–325.

Maharani, D., Dasari, D., & Prabawanto, S. (2019). Analysis of Students’ Thinking Process in Mathematical ProblemSolving Viewed From Adversity Quotient. 1st International Seminar STEMEIF (Science, Technology, Engineering and Mathematics Learning International Forum). http://digital.library.ump.ac.id/377/

Marasabessy, R., Hasanah, A., & Juandi, D. (2021). Bangun Ruang Sisi Lengkung dan Permasalahannya dalam Pembelajaran Matematika. EQUALS: Jurnal Ilmiah Pendidikan Matematika, 4(1), 1–20.

Miles, M. B., & Huberman, A. M. (1994). Qualitative data Analysis: An Expanded Sourcebook. sage.

Mirlanda, E. P., Nindiasari, H., & Syamsuri, S. (2020). Pengaruh Pembelajaran Flipped Classroom Terhadap Kemampuan Penalaran Matematis Ditinjau Dari Gaya Kognitif Siswa. Prima: Jurnal Pendidikan Matematika, 4(1), 11–21.

Moleong, L. J. (2016). Metedologi penelitian kualitatif (Vol. 2448). Kakek nenek.

Muliawati, N. E. (2016). Proses Berpikir Lateral Siswa dalam Memecahkan Masalah Matematika Berdasarkan Langkah Polya ditinjau dari Gaya Kognitif Field Independent-Field Dependent dan Perbedaan Gender. JP2M (Jurnal Pendidikan Dan Pembelajaran Matematika) (2017) 2(1) 55.

Nadhifa, N., Maimunah, M., & Roza, Y. (2019). Analisis Kemampuan Pemecahan Masalah Siswa pada Materi Bangun Ruang Sisi Datar. Numerical: Jurnal Matematika Dan Pendidikan Matematika, 63–76.

Ngilawajan, D. A. (2013). Proses Berpikir Siswa SMA dalam Memecahkan Masalah Matematika Materi Turunan Ditinjau Dari Gaya Kognitif Field Independent dan Field Dependent. Pedagogia, 2(1), 71–83.

Oh, E., & Lim, D. (2005). Cross Relationship Between Cognitive Style and Learner Variables in Online Learning Envirobment. Journal of Interactive Online Learning, 4(1), 53–66.

Polya, G. (1973). How to Solve It A New Aspect of Mathematical Method. The Mathematical Gazette, 30, 181. http://www.jstor.org/stable/3609122?origin=crossref

Potter, J. (2012). Re‐reading Discourse and Social Psychology: Transforming Social Sychology. British Journal of Social Psychology, 51(3), 436–455.

Purwanto, W. R., Sukestiyarno, Y., & Junaedi, I. (2019). Proses Berpikir Siswa dalam Memecahkan Masalah Matematika Ditinjau dari Perspektif Gender. Prosiding Seminar Nasional Pascasarjana UNNES, 895–900.

Rofi’ah, N., Ansori, H., & Mawaddah, S. (2019). Analisis Kesalahan Siswa Dalam Menyelesaikan Soal Cerita Matematika Berdasarkan Langkah Penyelesaian Polya. EDU-MAT: Jurnal Pendidikan Matematika, 7(2).

Saparwadi, L. (2022). Kesalahan Siswa SMP dalam Memahami Masalah Matematika Bentuk Soal Cerita. MATHEMA: Jurnal Pendidikan Matematika, 4(1), 1–12.

Sapti, M., Purwanto, Irawan, E. B., As’ari, A. R., Sa’dijah, C., Susiswo, & Wijaya, A. (2019). Comparing Model-building Process: A Model Prospective Teachers Used in Interpreting Students’ Mathematical Thinking. Journal on Mathematics Education, 10(2), 171–184. https://doi.org/10.22342/jme.10.2.7351.171-184

Saraswati, P. M. S., & Agustika, G. N. S. (2020). Kemampuan Berpikir Tingkat Tinggi dalam Menyelesaikan Soal HOTS Mata Pelajaran Matematika. Jurnal Ilmiah Sekolah Dasar, 4(2), 257–269.

Schoenfeld, A. H. (1982). Measures of Problem-Solving Performance and of Problem-Solving Instruction. Journal for Research in Mathematics Education, 13(1), 31–49.

Setiawan, Y. E. (2020). Analisis Kesalahan Siswa Dalam Menggeneralisasi Pola Linier. JNPM (Jurnal Nasional Pendidikan Matematika), 4(2), 180–194.

Sternberg, R. J., & Sternberg, K. (2013). Cognitive Psychology. In Case-Based Reasoning (Sixth Edit). Ingram Publishing/Getty Images. https://doi.org/10.1007/978-3-031-01562-5_3

Subanji, R., & Supratman, A. M. (2015). The Pseudo-Covariational Reasoning Thought Processes in Constructing Graph Function of Reversible Event Dynamics Based on Assimilation and Accommodation Frameworks. Research in Mathematical Education, 19(1), 61–79. https://doi.org/10.7468/jksmed.2015.19.1.61

Sunarsi, A. (2009). Analisis Kesalahan Dalam Menyelesaikan Soal Pada Materi Luas Permukaan Serta Volume Prisma dan Limas Pada Siswa Kelas VIII Semester genap smp negeri 2 Karanganyar Tahun Ajaran 2008/2009.

Supriadi, D., Mardiyana, & Subanti, S. (2015). Analisis Proses Berpikir Siswa Dalam Memecahkan Masalah Matematika Berdasarkan Langkah Polya Ditinjau Dari Kecerdasan Emosional Siswa Kelas Viii Smp Al Azhar Syifa Budi Tahun Pelajaran 2013/2014. Jurnal Elektronik Pembelajaran Matematika, 3(2), 204–214.

Swartz, R. J., Fischer, S. D., & Parks, S. (1998). Infusing the Teaching of Critical and Creative Thinking into Secondary Science: A Lesson Design Handbook. ERIC.

Tumanggor, M. (2021). Berfikir Kritis: Cara Jitu Menghadapi Tantangan Pembelajaran Abad 21. Gracias Logis Kreatif.

Vitale, M. R., & Romance, N. R. (2012). Using in-Depth Science Instruction to Accelerate Student Achievement in Science and Reading Comprehension in Grades 1–2. International Journal of Science and Mathematics Education, 10, 457–472.

Wardhani, W.A., Subanji, D. (2016). Proses Berpikir Siswa Berdasarkan Kerangka Kerja Mason. Jurnal Pendidikan: Teori, Penelitian, Dan Pengembangan, 1(3), 297–313.

Witkin, H. A., Moore, C. A., Goodenough, D., & Cox, P. W. (1977). Field-Dependent and Field-Independent Cognitive Styles and Their Educational Implications. Review of Educational Research, 47(1), 1–64. https://doi.org/10.3102/00346543047001001

Wulan, E. R., & Anggraini, R. E. (2019). Gaya Kognitif Field-Dependent dan Field-Independent sebagai Jendela Profil Pemecahan Masalah Polya dari Siswa SMP. Journal Focus Action of Research Mathematic (Factor M), 1(2), 123–142. https://doi.org/10.30762/factor_m.v1i2.1503

Yoğurtçu, K. (2013). The Impact of Self-efficacy Perception on Reading Comprehension on Academic Achievement. Procedia-Social and Behavioral Sciences, 70, 375–386.




DOI: https://doi.org/10.33394/jk.v9i3.8673

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