Adaptive Reasoning, Mathematical Problem Solving and Cognitive Styles

Aning Wida Yanti, I Ketut Budayasa, Raden Sulaiman

Abstract


The purpose of this research finds a link between adaptive reasoning, mathematical problem solving, and cognitive style. This research is a literature study. This paper showed the relationship between adaptive reasoning, mathematical problem solving, and cognitive styles. In particular, field-independent (FI) and field-dependent (FD) cognitive styles. Adaptive reasoning in mathematical problems is the legitimacy of problem strategies. Whereas the cognitive style provides opportunities for students to give reasonable arguments according to the tendency of the cognitive style. Mathematical problem-solving in the FI and the FD can vary according to students' cognitive styles. It was found that adaptive reasoning, mathematical problems, cognitive styles (FI, FD) have a strong stylistic relationship where adaptive reasoning will be able to give direction to students in solving math problems. Therefore, the basis for researching the adaptive reasoning profile of students in solving mathematical problems in terms of FI and FD cognitive styles is our understanding of the relationship between adaptive reasoning, mathematical problem solving, and cognitive style

Keywords


Adaptive Reasoning; Mathematical Problem Solving; Cognitive Styles;

Full Text:

DOWNLOAD [PDF]

References


Ansari, B. I., Taufiq, T., & Saminan, S. (2020). The use of creative problem solving model to develop students’ adaptive reasoning ability: Inductive, deductive, and intuitive. International Journal on Teaching and Learning Mathematics, 3(1), 21–36. https://doi.org/10.18860/ijtlm.v3i1.9439

Collins, A., Brown, J. S., & Newman, S. E. (2018). Cognitive Apprenticeship: Teaching the Crafts of Reading, Writing, and Mathematics. In Knowing, Learning, and Instruction (pp. 453–494). New York : Routledge. https://doi.org/10.4324/9781315044408-14

Creswell, J. W. (2014). Research Design: Qualitative, Quantitative and Mixed Methods Approaches (4th Editio). New York : SAGE Publications, Inc.

Custers, E. J. F. M. (2019). Theories of truth and teaching clinical reasoning and problem solving. Advances in Health Sciences Education, 24(4), 839–848. https://doi.org/10.1007/s10459-018-09871-4

Eggen, P., & Kauchak, D. (2015). Educational Psychology: Windows on Classrooms, Global Edition. London : Pearson.

Evans, T., Thomas, M. O. J., & Klymchuk, S. (2020). Non-routine problem solving through the lens of self-efficacy. Higher Education Research & Development. https://doi.org/10.1080/07294360.2020.1818061

Harianja, J. K., Hernadi, S. L., & Indah, I. (2020). Learner’s Mathematical Conceptual Understanding and Its Relation to The Mathematical Communication Skills. JP3M (Jurnal Penelitian Pendidikan Dan Pengajaran Matematika), 6(1), 1–12. https://doi.org/10.37058/jp3m.v6i1.1207

Harris, A. (2019). Models of teaching. In Teaching and Learning in the Effective School. London : Taylor & Francis Ltd. https://doi.org/10.4324/9780429398117-5

Joyce, B., Weil, M., & Calhoun, E. (2017). Models of Teaching (9th Editio). London : Pearson.

Khalifaeva, O. A., Kolenkova, N. Y., Tyurina, I. Y., & Fadina, A. G. (2020). The relationship of thinking styles and academic performance of students. The Education and Science Journal, 22(7), 52–76. https://doi.org/10.17853/1994-5639-2020-7-52-76

Kuo, F. R., Hwang, G. J., Chen, S. C., & Chen, S. Y. (2012). A cognitive apprenticeship approach to facilitating web-based collaborative problem solving. Educational Technology and Society, 15(4), 319–331.

Kusuma Dewi, I. L., Waluya, S. B., Rachmad, & Firmasari, S. (2020). Adaptive reasoning and procedural fluency in three-dimensional. Journal of Physics: Conference Series, 1511(012101), 1–7. https://doi.org/10.1088/1742-6596/1511/1/012101

Matsuo, M., & Tsukube, T. (2020). A review on cognitive apprenticeship in educational research: Application for management education. International Journal of Management Education, 18(3), 100417. https://doi.org/10.1016/j.ijme.2020.100417

Mawardi, A. V., Yanti, A. W., & Arrifadah, Y. (2020). Analisis Proses Berpikir Siswa Dalam Menyelesaikan. JRPM (Jurnal Review Pembelajaran Matematika), 5(1), 40–52.

McCrory, R., & Stylianides, A. J. (2014). Reasoning-and-proving in mathematics textbooks for prospective elementary teachers. International Journal of Educational Research, 64, 119–131. https://doi.org/10.1016/j.ijer.2013.09.003

Mellone, M., Ribeiro, M., Jakobsen, A., Carotenuto, G., Romano, P., & Pacelli, T. (2020). Mathematics teachers’ interpretative knowledge of students’ errors and non-standard reasoning. Research in Mathematics Education, 22(2). https://doi.org/10.1080/14794802.2019.1710557

Mousavi, S., Radmehr, F., & Alamolhodaei, H. (2012). The role of mathematical homework and prior knowledge on the relationship between students’ mathematical performance, cognitive style and working memory capacity. Electronic Journal of Research in Educational Psychology, 10(3), 1223–1248. https://doi.org/10.25115/ejrep.v10i28.1532

Nicolaou, A. A., & Xistouri, X. (2011). Field dependence/independence cognitive style and problem posing: an investigation with sixth grade students. Educational Psychology, 31(5), 611–627. https://doi.org/10.1080/01443410.2011.586126

Nugroho, A. A., Nizaruddin, N., Dwijayanti, I., & Tristianti, A. (2020). Exploring students’ creative thinking in the use of representations in solving mathematical problems based on cognitive style. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 5(2), 202–217. https://doi.org/10.23917/jramathedu.v5i2.9983

Öztürk, M., Akkan, Y., & Kaplan, A. (2020). Reading comprehension, Mathematics self-efficacy perception, and Mathematics attitude as correlates of students’ non-routine Mathematics problem-solving skills in Turkey. International Journal of Mathematical Education in Science and Technology, 51(7), 1042–1058. https://doi.org/10.1080/0020739X.2019.1648893

Pratikno, H., & Retnowati, E. (2018). How Indonesian Students Use the Polya’s General Problem Solving Steps. Southeast Asian Mathematics Education Journal, 8(1), 39–48. https://doi.org/10.46517/seamej.v8i1.62

Purwaningsih, W. I., Astuti, E. P., Nugraheni, P., & Rizkyaningtyas, N. P. (2019). Characteristics of intuitive thinking in solve mathematical issue based on cognitive style. Journal of Physics: Conference Series, 1254(012081), 1–6. https://doi.org/10.1088/1742-6596/1254/1/012081

Sidenvall, J. (2019). Literature review of mathematics teaching design for problem solving and reasoning. Nordic Studies in Mathematics Education, 24(1), 51–74.

Syukriani, A., Juniati, D., & Siswono, T. Y. E. (2017). Investigating adaptive reasoning and strategic competence: Difference male and female. AIP Conference Proceedings, 020033. https://doi.org/10.1063/1.4994436

Udil, P. A., Kusmayadi, T. A., & Riyadi, R. (2017). Metacognition Process of Students with High Mathematics Anxiety in Mathematics Problem-Solving. International Journal of Science and Applied Science: Conference Series, 2(1), 261. https://doi.org/10.20961/ijsascs.v2i1.16724

Villeneuve, E. F., Hajovsky, D. B., Mason, B. A., & Lewno, B. M. (2019). Cognitive ability and math computation developmental relations with math problem solving: An integrated, multigroup approach. School Psychology Quarterly, 34(1), 96–108. https://doi.org/10.1037/spq0000267

Weiten, W. (2017). Psychology: Themes and Variations. Boston : Cengage Learning.

Yanti, A. W., Sutini, & Kurohman, T. (2020). Adaptive reasoning profile of students in solving mathematical problems viewed from field-dependent and field-independent cognitive style. AIP Conference Proceedings, 060035. https://doi.org/10.1063/5.0000699

Yazgan, Y., & Busra Sahin, H. (2018). Relationship between Brain Hemisphericity and Non-routine Problem Solving Skills of Prospective Teachers. Universal Journal of Educational Research, 6(9), 2001–2007. https://doi.org/10.13189/ujer.2018.060919

Yudhanegara, M. R., & Lestari, K. E. (2017). How to Develop Students’ Experience on Mathematical Proof in Group Theory Course by Conditioning-Reinforcement-Scaffolding. Proceedings of the 5th SEA-DR (South East Asia Development Research) International Conference 2017 (SEADRIC 2017), 186–189. https://doi.org/10.2991/seadric-17.2017.38




DOI: https://doi.org/10.31764/jtam.v5i2.4652

Refbacks

  • There are currently no refbacks.


Copyright (c) 2021 Aning Wida Yanti, I Ketut Budayasa, Raden Sulaiman

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

_______________________________________________

JTAM already indexing:

                     


_______________________________________________

 

Creative Commons License

JTAM (Jurnal Teori dan Aplikasi Matematika) 
is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License

______________________________________________

_______________________________________________

_______________________________________________ 

JTAM (Jurnal Teori dan Aplikasi Matematika) Editorial Office: