Exploring the Student Critical Thinking in Mathematical Problem Solving
DOI:
https://doi.org/10.18502/kss.v10i11.18733Keywords:
research qualitative, critical thinking, problem solving, arithmetic seriesAbstract
This research qualitative aims to describe students’ critical thinking in solving sequences and series. The research participants were 3 students from grade VIII, selected based on the results of their math tests. Data were collected by giving the task of solving problems and interviews. The student’s critical thinking is described using the approach focus, reason, inference, clarity, and overview (FRISCO). The results showed that participants with high math skills can identify the main problem, analyzing questions and statements, reasoning of inductive and assessing the difference was the same, concluding the value of the difference and the solution, making pattern of sequence, and determining the sum of the first 12 terms using the arithmetic series formula, explaining the terms and symbols used in the formula, solving the problem again by adding up each term and comparing the results with the previous results. Participant with moderate mathematical ability wrote down relevant information, using inductive reasoning and mathematical principles and did not use arithmetic series formula, concluding the value of the difference and the solution, making sequence pattern, determining the sum of the first 12 terms by add up each, explaining the term and the difference symbol. Participant with low math ability, only wrote down and mentioned what is known and asked and gave reasons using question marks for question sentences. The description of critical thinking can be considered by teachers in formulating learning strategies for critical thinking.
References
Bradshaw Z, Hazell A. Developing problem-solving skills in mathematics: a lesson study. International Journal for Lesson and Learning Studies. 2017;6(1):32–44. DOI: https://doi.org/10.1108/IJLLS-09-2016-0032
Vijayan V, Joshith V. Reflection of Problem Solving Skill in Life and Mathematics Education Through Modeling and Applying. I-Manager’s. J Educ Psychol. 2018;12(2):1. DOI: https://doi.org/10.26634/jpsy.12.2.15141
Gattuso J. Problem Solving Strategies: Helping Students Develop a Conceptual Understanding of Word Problems. Student Research Submissions; 2015. p. 182.
Albay EM. Analyzing the effects of the problem solving approach to the performance and attitude of first year university students. Soc Sci Humanit Open. 2019;1(1):100006. DOI: https://doi.org/10.1016/j.ssaho.2019.100006
Căprioară D. Problem Solving - Purpose and Means of Learning Mathematics in School. Procedia Soc Behav Sci. 2015;191:1859–64. DOI: https://doi.org/10.1016/j.sbspro.2015.04.332
Osman S, Che Yang CN, Abu MS, Ismail N, Jambari H, Kumar JA. Enhancing Students’ Mathematical Problem-Solving Skills through Bar Model Visualisation Technique. International Electronic Journal of Mathematics Education. 2018;13(3):273–9. DOI: https://doi.org/10.12973/iejme/3919
Doorman M, Drijvers P, Dekker T, van den Heuvel-Panhuizen M, de Lange J, Wijers M. Problem solving as a challenge for mathematics education in The Netherlands. ZDM - International Journal on Mathematics Education. 2007;39(5– 6):405–18. https://doi.org/10.1007/s11858-007-0043-2. DOI: https://doi.org/10.1007/s11858-007-0043-2
Nasution PN, Herman T, Jupri A. Problem Solving Analysis in Early Adult Period. In: STEMEIF (Science, Technology, Engineering and Mathematics Learning International Forum), Purwokerto, April 25th 2019. 2019. p. 540–50.
Fitriani HT, Fatimah S. Considering the Mathematical Resilience in Analyzing Students’ Problem-Solving Ability through Learning Model Experimentation. Int J Instr. 2023;16(1):219–40. DOI: https://doi.org/10.29333/iji.2023.16113a
Khalid M, Saad S, Abdul Hamid SR, Ridhuan Abdullah M, Ibrahim H, Shahrill M. Enhancing creativity and problem solving skills through creative problem solving in teaching mathematics. Creativity Studies. 2020;13(2):270–91. DOI: https://doi.org/10.3846/cs.2020.11027
Urban K, Urban M. How can we measure metacognition in creative problem-solving? Standardization of the MCPS scale. Think Skills Creativity. 2023;49:101345. DOI: https://doi.org/10.1016/j.tsc.2023.101345
Williams G. Optimistic problem-solving activity: enacting confidence, persistence, and perseverance. ZDM - International Journal on Mathematics Education. 2014;46(3):407–22. https://doi.org/10.1007/s11858-014-0586-y. DOI: https://doi.org/10.1007/s11858-014-0586-y
Beyer BK. Critical Thinking. Fastback 385; 1995.
Da Silva Almeida L, Rodrigues Franco AH. Critical thinking : its relevance for education in a shifting society [PUCP]. Rev Psicol. 2011;29(1):175–95.
Butterworth J, Thwaites G. Thinking skills: Critical thinking and problem solving. Cambridge University Press; 2013.
Pratama MA. Mathematical critical thinking ability and students’ confidence in mathematical literacy. J Phys Conf Ser. 2020;1663(1):012028. DOI: https://doi.org/10.1088/1742-6596/1663/1/012028
Firdaus KI. Bakar MdN Bin, Bakry. Limiting Behavior of Random Continued Fractions. Journal of Education and Learning. 2015;9(3):226–36. DOI: https://doi.org/10.11591/edulearn.v9i3.1830
Peter EE. Critical thinking: essence for teaching mathematics and mathematics problem solving skills. Afr J Math Comput Sci Res. 2012;5(3):39–43. DOI: https://doi.org/10.5897/AJMCSR11.161
Yildirim B, Ozkahraman S. Critical thinking in nursing process and education. Int J Humanit Soc Sci. 2011;1(13):257–62.
Turan U, Fidan Y, Yιldιran C. Critical Thinking as a Qualified Decision Making Tool. Tar Kültür Sanat Arast Derg. 2019;8(4):1–18. DOI: https://doi.org/10.7596/taksad.v8i4.2316
Ennis RH. Critical Thinking. New Jersey: Prentice-Hall; 1996.
Mahanal S, Zubaidah S, Sumiati ID, Sari TM, Ismirawati N. RICOSRE: A learning model to develop critical thinking skills for students with different academic abilities. Int J Instr. 2019;12(2):417–34. DOI: https://doi.org/10.29333/iji.2019.12227a
Siriwat R, Katwibun D. Exploring Critical Thinking in a Mathematics Problem- Based Learning Classroom. In: Proceedings of the 40th Annual Conference of the Mathematics Education Research Group of Australasia. 2017. p. 474–81.
Cahya E, Juandi D. Students’ critical thinking skills in solving mathematical problems; a systematic procedure of grounded theory study. Int J Instr. 2021;14(4):529–48. DOI: https://doi.org/10.29333/iji.2021.14431a
Amanda FF, Sumitro SB, Lestari SR, Ibrohim I. Analysis of the Relationship Between Concept Mastery and Problem-Solving Skills of Pre-Service Biology Teachers in Human Physiology Courses. Jurnal Pendidikan Sains Indonesia. 2021;9(3):421–32. DOI: https://doi.org/10.24815/jpsi.v9i3.19956
Al-Mutawah MA, Thomas R, Eid A, Mahmoud EY, Fateel MJ. Conceptual understanding, procedural knowledge and problem-solving skills in mathematics: high school graduates work analysis and standpoints. International Journal of Education and Practice. 2019;7(3):258–73. DOI: https://doi.org/10.18488/journal.61.2019.73.258.273
Nurfaizah N, Putro KZ, Tejaningrum D. Students’ critical thinking skills in the learning strategy course. Jurnal Penelitian Ilmu Pendidikan. 2022;15(1):46–54. DOI: https://doi.org/10.21831/jpipfip.v15i1.41689
Almulla MA. Constructivism learning theory: A paradigm for students’ critical thinking, creativity, and problem solving to affect academic performance in higher education. Vol. 10. Cogent Educ. 2023;10(1):2172929. DOI: https://doi.org/10.1080/2331186X.2023.2172929
English L, Sriraman B. Problem Solving for the 21st Century. Theories of Mathematics Education. Berlin, Heidelberg: Springer Berlin Heidelberg; 2009. pp. 263–90. DOI: https://doi.org/10.1007/978-3-642-00742-2_27
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Sutji Rochaminah, Irmawati, Muh. Rizal
This work is licensed under a Creative Commons Attribution 4.0 International License.
