Students' Analogical Reasoning in Solving Trigonometric Problems in Terms of Cognitive Style: A Case Study

Ummah Qurrotul Azizah, Ekawati Rooselyna, Masriyah Masriyah

Abstract


This article discusses the analogical reasoning of students' types in solving trigonometric problems based on cognitive styles. This research was conducted at MAN I Probolinggo, eighteen students was asked to complete cognitive style tests and math ability tests. It was found that students' answers can be grouped into two types of cognitive styles, namely systematic and intuitive. From each group, one student was taken to be interviewed with the aim of getting a more detailed explanation of each type of analogical reasoning. The results show that the two types can be explained as follows, first, the type of systematic cognitive style, students can understand the problem given, mention in detail all the information that is known and asked, use all known information about the problem, read and understand the problem, map the structure relational problems, applying a structured way to solve problems that have been planned in advance. In the intuitive cognitive style type, students can understand the problem only by reading the problem once, mention some information that is known about the problem, use the information that is known in the problem, read and understand the problem, apply problem-solving methods. pre-planned but unstructured. Therefore, teachers must encourage and enable students to use analogical reasoning optimally in learning mathematics.

Keywords


Analogical Reasoning; Problem Solving; Cognitive Style; Systematic; Intuitive

Full Text:

PDF

References


Amir-Mofidi, S., Amiripour, P., & Bijan-Zadeh, M. H. (2012). Instruction of mathematical concepts through analogical reasoning skills. Indian Journal of Science and Technology, 5(6), 2916-2922. https://doi.org/10.17485/ijst/2012/v5i6.12.

Almolhodaei, H. (2002). Students’ Cognitive Style and Mathematical Word Problem Solving. Journal of the Korea Society of Mathematical Education Series D Research in Mathematical Education, 6(2), 171–182. https://www.koreascience.or.kr/article/JAKO200211921431195.page.

Altun, A., & Cakan, M. (2006). International Forum of Educational Technology & Society Undergraduate Students ’ Academic Achievement , Field Dependent / Independent Cognitive Styles and Attitude toward Computers Published by : International Forum of Educational Technology & Society Lin, 9(1).

Bassok, M. (2001). Semantic alignments in mathematical word problems. The analogical mind: Perspectives from cognitive science, 401-433. https://psycnet.apa.org/record/2001-00520-011

Bergqvist, E. (2007). Types of reasoning required in university exams in mathematics. The Journal of Mathematical Behavior, 26(4), 348-370. https://doi.org/10.1016/j.jmathb.2007.11.001

Bormanaki, H. B., & Khoshhal, Y. (2017). The role of equilibration in Piaget’s theory of cognitive development and its implication for receptive skills: A theoretical study. Journal of Language Teaching and Research, 8(5), 996-1005. http://dx.doi.org/10.17507/jltr.0805.22

Depdiknas, (2006). Permendiknas Nomor 22 Tahun 2006 Tentang Standar Isi Sekolah Menengah Atas. Jakarta: Depdiknas.

English, L. D. (Ed.). (2004). Mathematical and analogical reasoning of young learners. Routledge. https://psycnet.apa.org/record/2004-14903-000

Graham, K. J., & Fennell, F. (2001). Principles and standards for school mathematics and teacher education: Preparing and empowering teachers. School Science and Mathematics, 101(6), 319-327. https://doi.org/10.1111/j.1949-8594.2001.tb17963.x

Gentner, D., & Smith, L. (2012). Analogical reasoning. Encyclopedia of human behavior, 1, 130-136. https://doi.org/10.1016/B978-0-12-375000-6.00022-7

Hendrawata, D. (2018). ANALISIS ANALOGI SISWA DALAM MENYELESAIKAN SOAL BANGUN DATAR (Doctoral dissertation, University Of Muhammadiyah Malang).

Hill, H. C., & Ball, D. L. (2004). Learning mathematics for teaching: Results from California's mathematics professional development institutes. Journal for research in mathematics education, 330-351. https://doi.org/10.2307/30034819

Hasbi, M., Lukito, A., & Sulaiman, R. (2019). Mathematical Connection Middle-School Students 8th in Realistic Mathematics Education. In Journal of Physics: Conference Series (Vol. 1417, No. 1, p. 012047). IOP Publishing. https://doi.org/%2010.1088/1742-6596/1417/1/012047/meta

Holyoak, K. J., Gentner, D., & Kokinov, B. N. (2001). Introduction: The place of analogy in cognition. The analogical mind: Perspectives from cognitive science, 1-19.

Huitt, W., & Hummel, J. (2003). Piaget's theory of cognitive development. Educational psychology interactive, 3(2), 1-5.

Isoda, M., & Katagiri, S. (2012). Mathematical thinking: How to develop it in the classroom (Vol. 1). World Scientific. https://doi.org/10.1142/9789814350853_others03

Jeannotte, D., & Kieran, C. (2017). A conceptual model of mathematical reasoning for school mathematics. Educational Studies in Mathematics, 96(1), 1-16. https://doi.org/10.1007/s10649-017-9761-8

Lefa, B. (2014). The Piaget theory of cognitive development: an educational implications. Educational Psychology, 1(9), 1-8.

Lehrer, R., & Schauble, L. (2000). Developing model-based reasoning in mathematics and science. Journal of Applied Developmental Psychology, 21(1), 39-48. https://doi.org/10.1016/S0193-3973(99)00049-0

National Council of Teachers of Mathematics (NCTM). (2000). Principles And Standards Schools Mathematics. Reston, VA: NCTM.

Norris, P., & Epstein, S. (2011). An experiential thinking style: Its facets and relations with objective and subjective criterion measures. Journal of personality, 79(5), 1043-1080. https://doi.org/10.1111/j.1467-6494.2011.00718.x

Richland, L. E., Holyoak, K. J., & Stigler, J. W. (2004). Analogy use in eighth-grade mathematics classrooms. Cognition and instruction, 22(1), 37-60. https://doi.org/10.1207/s1532690Xci2201_2

Richland, L. E., & Simms, N. (2015). Analogy, higher order thinking, and education. Wiley Interdisciplinary Reviews: Cognitive Science, 6(2), 177-192. https://doi.org/10.1177/2372732216629795

Richland, L. E., & Begolli, K. N. (2016). Analogy and higher order thinking: Learning mathematics as an example. Policy Insights from the Behavioral and Brain Sciences, 3(2), 160-168. https://doi.org/10.1177/2372732216629795

Sadiq, R., Kleiner, Y., & Rajani, B. (2007). Water quality failures in distribution networks—risk analysis using fuzzy logic and evidential reasoning. Risk Analysis: An International Journal, 27(5), 1381-1394. https://doi.org/10.1111/j.1539-6924.2007.00972.x

Sagiv, L., Arieli, S., Goldenberg, J., & Goldschmidt, A. (2010). Structure and freedom in creativity: The interplay between externally imposed structure and personal cognitive style. Journal of Organizational Behavior, 31(8), 1086-1110. https://doi.org/10.1002/job.664

Scott, S. G., & Bruce, R. A. (1995). Decision-making style: The development and assessment of a new measure. Educational and psychological measurement, 55(5), 818-831. https://doi.org/10.1177/0013164495055005017

Shadiq, F. (2007). Penalaran atau Reasoning. Perlu Dipelajari Para Siswa di Sekolah. Jurnal Online. https://fadjarp3g. files. wordpress. com/2007/09/ok-penalaran_gerbang_. pdf.

Smith, E. R., & DeCoster, J. (2000). Dual-process models in social and cognitive psychology: Conceptual integration and links to underlying memory systems. Personality and social psychology review, 4(2), 108-131. https://doi.org/10.1207/S15327957PSPR0402_01

Sternberg, R. J. (Ed.). (1999). Handbook of creativity. Cambridge University Press.

Sternberg, R. J., & Williams, W. M. (2009). Educational Psychology. 2nd Edition. In by Routledge New York, (ebk) by Amazon (Vol. 24). https://doi.org/10.7202/1016404ar

Vahrum, F. N., & Rahaju, E. B. (2016). Proses Berpikir Siswa SMP dalam Memecahkan Masalah Matematika Kontekstual Pada Materi Himpunan Berdasarkan Gaya Kognitif Reflective da Reflective. Jurnal Ilmiah Pendidikan Matematika, 3(5), 147-155.

Van de Walle, A., Tiwary, P., De Jong, M., Olmsted, D. L., Asta, M., Dick, A., ... & Liu, Z. K. (2013). Efficient stochastic generation of special quasirandom structures. Calphad, 42, 13-18. https://doi.org/10.1016/j.calphad.2013.06.006




DOI: https://doi.org/10.29103/ijevs.v3i1.3398

Article Metrics

 Abstract Views : 290 times
 PDF Downloaded : 53 times

Refbacks

  • There are currently no refbacks.


Copyright (c) 2021 Ummah Qurrotul Azizah, Ekawati Rooselyna, and Masriyah


International Journal for Educational and Vocational Studies (IJEVS)

E-ISSN : 2684-6950