Students’ Cognitive Barrier in Problem Solving: Picture-based Problem-solving

A.Wilda Indra Nanna, Enditiyas Pratiwi

Abstract


Pre-service teachers in primary education often have difficulty in solving mathematical problems, specifically fractions that are presented with a picture. In solving problems, some thought processes are needed by the teacher to reduce students' cognitive barriers. Therefore, this study aimed to reveal the cognitive barriers experienced by students in solving fraction problems. The cognitive barriers referred to in this study are ways of thinking about structures or mathematical objects that are appropriate in one situation and not appropriate in another situation. This study employed a descriptive-qualitative method. Furthermore, participants were followed up with in-depth semi-structured interviews to find out the cognitive barriers that occurred in solving fraction problems. This study discovers that the participants, in solving fraction problems, experienced all indicators of cognitive barrier and two cognitive obstacles are found as new findings that tend to involve mathematical calculations and violates the rules in dividing images into equal parts in the problem-solving procedure.

 


Keywords


Cognitive Barrier; Fraction;Mathematics; Problem-Solving.

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References


Abdullah, A. H., Abidin, N. L. Z., & Ali, M. (2015). Analysis of students’ errors in solving Higher Order Thinking Skills (HOTS) problems for the topic of fraction. Asian Social Science, 11(21), 133–142. https://doi.org/10.5539/ass.v11n21p133

Alghazo, Y. M., & Alghazo, R. (2017). Exploring Common Misconceptions and Errors about Fractions among College Students in Saudi Arabia. International Education Studies, 10(4), 133. https://doi.org/10.5539/ies.v10n4p133

Amerika, D. R. (n.d.). USAID PRIORITAS: Mengutamakan Pembaharuan, Inovasi, dan Kesempatan bagi Guru, Tenaga Kependidikan, dan Siswa.

Antonijević, R. (2016). Cognitive activities in solving mathematical tasks: The role of a cognitive obstacle. Eurasia Journal of Mathematics, Science and Technology Education, 12(9), 2503–2515. https://doi.org/10.12973/eurasia.2016.1306a

Beghetto, R. A. (2017). Lesson unplanning: toward transforming routine tasks into non-routine problems. ZDM - Mathematics Education, 49(7), 987–993. https://doi.org/10.1007/s11858-017-0885-1

Bentley, B., & Bossé, M. J. (2018). College Students’ Understanding of Fraction Operations. International Electronic Journal of Mathematics Education, 13(3), 233–247. https://doi.org/10.12973/iejme/3881

Brown, S. A. (2008). Exploring epistemological obstacles to the development of mathematics induction. The 11th Conference for Research on Undergraduate Mathematics Education, 1–19.

Faradiba, R., Susiswo, S., & As’ari, A. R. (2019). Representasi Visual Dalam Menyelesaikan Masalah Pecahan. Jurnal Pendidikan: Teori, Penelitian, & Pengembangan Journal Of Education, 4(7), 885–891. https://doi.org/http://dx.doi.org/10.17977/jptpp.v4i7.12629

Fuadiah, N. F. (2015). Me-43 Epistemological Obstacles on Mathematic’S Learning in Junior High School Students: a Study on the Operations of Integer Material. May, 17–19. https://eprints.uny.ac.id/23197/1/ME - 43.pdf

Herman, J., Ilucova, L., Kremsova, V., Pribyl, J., Ruppeldtova, J., Simpson, A., Stehlikova, N., Sulista, M., & Ulrychova, M. (2004). Images of Fractions As Processes and Images of Fractions in Processes. Psychology, 4, 249–256.

Herscovics, N. (2019). Cognitive Obstacles Encountered in the Learning of Algebra. In Research Issues in the Learning and Teaching of Algebra. https://doi.org/10.4324/9781315044378-6

Idris, N., & Narayanan, L. M. (2011). Error Patterns in Addition and Subtraction of Fractions among Form Two Students. Journal of Mathematics Education, 4(2), 35–54. http://educationforatoz.com/images/Idris.pdf

Jäder, J., Sidenvall, J., & Sumpter, L. (2017). Students’ Mathematical Reasoning and Beliefs in Non-routine Task Solving. International Journal of Science and Mathematics Education, 15(4), 759–776. https://doi.org/10.1007/s10763-016-9712-3

Nyikahadzoyi, M. R., Mapuwei, T., & Chinyoka, M. (2013). Some Cognitive Obstacles Faced By “A” Level Mathematics Students in Understanding Inequalities: A Case Study of Bindura Urban High Schools. International Journal of Academic Research in Progressive Education and Development.

Osana, H. P., & Royea, D. A. (2011). Obstacles and challenges in preservice teachers’ explorations with fractions: A view from a small-scale intervention study. Journal of Mathematical Behavior, 30(4), 333–352. https://doi.org/10.1016/j.jmathb.2011.07.001

Perbowo, K. S., & Anjarwati, R. (2017). Analysis of Students’ Learning Obstacles on Learning Invers Function Material. Infinity Journal, 6(2), 169. https://doi.org/10.22460/infinity.v6i2.p169-176

Prakitipong, N., & Nakamura, S. (2006). Analysis of mathematics performance of grade five students in Thailand using Newman procedure. Journal of International Cooperation …, 9(1), 111–122.

Siegler, R. S., Fazio, L. K., Bailey, D. H., & Zhou, X. (2013). Fractions: The new frontier for theories of numerical development. Trends in Cognitive Sciences, 17(1), 13–19. https://doi.org/10.1016/j.tics.2012.11.004

Sukmana, A. (2011). Profil berpikir intuitif matematik. Profil Berpikir Intuitif Matematik, 1–55.

Suyitno, H. (2008). Hubungan Antara Bahasa Dengan Logika Dan Matematika Menurut Pemikiran Wittgenstein. Humaniora, 20(1), 26–37. https://doi.org/10.22146/jh.v20i1.917

Swanson, D., & Williams, J. (2014). Making abstract mathematics concrete in and out of school. Educational Studies in Mathematics, 86(2), 193–209. https://doi.org/10.1007/s10649-014-9536-4

Tall, D. (1989). New Cognitive Obstacles in a Technological Paradigm. 92, 87–92.

Tall, D. (2002). The Psychology of Advanced Mathematical Thinking. In Advanced Mathematical Thinking. https://doi.org/10.1007/0-306-47203-1_1

Tian, J., & Siegler, R. S. (2017). Fractions Learning in Children With Mathematics Difficulties. Journal of Learning Disabilities, 50(6), 614–620. https://doi.org/10.1177/0022219416662032

Yoshida, H., & Sawano, K. (2002). Overcoming cognitive obstacles in learning fractions: Equal-partitioning and equal-whole. Japanese Psychological Research, 44(4), 183–195.




DOI: http://dx.doi.org/10.24042/ajpm.v11i1.5652

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