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Abstract

Analogical thinking is a crucial strategy for mathematical problem-solving, enabling the discovery of solutions by identifying similarities between different problems. However, existing research needs a comprehensive classification of students' use of analogical thinking in this context. This study aims to develop a new classification framework for analogical thinking in mathematical problem-solving, emphasizing the identification and utilization of analogous methods between source and target problems. The research adopts a descriptive qualitative approach involving a purposive sample of 15 high school students from Surakarta, Central Java, who demonstrated analogical thinking in solving both source and target problems. Data collection was conducted through tests, observations, and interviews, with analysis performed using the constant comparative procedure (CCP). The findings reveal three distinct classifications of analogical thinking: pattern recognition (identifying common patterns to solve both source and target problems), variable utilization (using variables as symbolic tools for problem-solving), and visualization (applying graphical representations to address the issues). This study offers significant theoretical insights for future research and practical implications for applying analogical thinking in enhancing mathematical problem-solving.

Keywords

Analogical Thinking Classification Constant Comparative Procedure Mathematical Problem-Solving

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Kholid, M. N., Fadhilah, H., Loc, N. P., & Magdas, I. C. (2024). Classifying analogical thinking for mathematical problem-solving. Journal on Mathematics Education, 15(3), 793–814. https://doi.org/10.22342/jme.v15i3.pp793-814
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References

  1. Azmi, M. P. (2017). Mengembangkan kemampuan analogi matematis. Journal Cendekia: Jurnal Pendidikan Matematika, 1(1), 100–111. https://doi.org/10.31004/cendekia.v1i1.12
  2. Cai, J. (2003). Singaporean students’ mathematical thinking in problem solving and problem posing: An exploratory study. International Journal of Mathematical Education in Science and Technology, 34(5), 719–737. https://doi.org/10.1080/00207390310001595401
  3. Creswell, J. W. (2014). Research design; Qualitative, quantitative, and mixed methods approaches (4th ed., Issue 4th Ed.). SAGE Publications Ltd..
  4. Creswell, J. W., & Poth, C. N. (2007). Qualitative inquiry and research design: Choosing among five approaches (2nd ed.). Sage Publications.
  5. Dwirahayu, G., Mubasyiroh, S. M., & Mas’ud, A. (2018). The Effectiveness of teaching with analogy on students’ mathematical representation of derivative concept. Advances in Social Science, Education and Humanities Research, 115(3rd ICEMS 2017), 57–60. https://doi.org/10.2991/icems-17.2018.12
  6. English, L. D. (1999). Reasoning by analogy: Developing mathematical reasoning in grades K-12. National Council of Teacher of Mathematics, Inc.
  7. Etikan, I., Musa, S. A., & Alkassim, R. S. (2016). Comparison of convenience sampling and purposive sampling. American Journal of Theoretical and Applied Statistics, 5(1), 1–4. https://doi.org/10.11648/j.ajtas.20160501.11
  8. Eveleth, D. M. (1999). Analogical reasoning: When a non-expert reasons like an expert. 28–40.
  9. Fauzi, A., Rahmatih, A. N., Indraswati, D., & Husniati. (2020). Penalaran analogi mahasiswa PGSD dalam menyelesaikan masalah matematika berdasarkan gaya berpikir. AKSIOMA: Jurnal Matematika dan Pendidikan Matematika, 11(2), 323–334. https://doi.org/10.26877/aks.v11i2.6944
  10. Garderen, D. Van, & Montague, M. (2003). Visual-spatial representation, mathematical problem solving, and students of varying abilities. Learning Disabilities Research & Practice, 18(4), 246–254. https://doi.org/10.1111/1540-5826.00079
  11. Gentner, D. (1983). Structure mapping: A theoretical framework for analogy. Cognitive Science, 7(2), 155–170. https://doi.org/10.1016/S0364-0213(83)80009-3
  12. Gentner, D. (2010). Bootstrapping the mind : Analogical processes and symbol systems. Cognitive Science, 34, 752–775. https://doi.org/10.1111/j.1551-6709.2010.01114.x
  13. Gentner, D. (2016). Language as cognitive tool kit: How Language supports relational thought. American Psychologist, 71(8), 650–657. https://doi.org/10.1037/amp0000082
  14. Gentner, D., Holyoak, K. J., & Kokinov, B. K. (2001). The analogical mind: Perspectives from cognitive science. In Angewandte Chemie International Edition, 6(11), 951–952. (Issue Mi). MIT Press.
  15. Gentner, D., & Loewenstein, J. (2002). Language, literacy, and cognitive development: The development and consequences of symbolic communication. In E. Amsel & J. P. Byrnes (Eds.), Language, lteracy, and cognitive development: The development and consequences of symbolic communication. Lawrence Erlbaum Associates, Inc.
  16. Glaser, B. G. (1992). Emergence vs forcing: Basics of grounded theory analysis. Sociology Press.
  17. Gust, H., Krumnack, U., Kühnberger, K. U., & Schwering, A. (2008). Analogical reasoning: A core of cognition. KI - Künstliche Intelligenz, 22(1), 8–12.
  18. Handayani, U. F., Sa’Dijah, C., Sisworo, Sa’Diyah, M., & Anwar, L. (2020). Mathematical creative thinking skill of middle-ability students in solving contextual problems. AIP Conference Proceedings, 2215(April), 1–7. https://doi.org/10.1063/5.0000645
  19. Hardiani, N., & Kristayulita. (2023). Analogical reasoning in mathematical theorems. JTAM (Jurnal Teori dan Aplikasi Matematika), 7(1), 185–195. https://doi.org/10.31764/jtam.v7i1.11783
  20. Hendriana, H., Putra, H. D., & Ristiana, M. G. (2018). Scientific approach in developing mathematical analogy and communication ability of junior high school students in remote areas. International Conference on Mathematics and Science Education of Universitas Pendidikan Indonesia, 3(103), 597–601.
  21. Hidayat, W., Rohaeti, E. E., Ginanjar, A., & Putri, R. I. I. (2022). An EPub learning module and students’ mathematical reasoning ability: A development study. Journal on Mathematics Education, 13(1), 103–118. https://doi.org/10.22342/jme.v13i1.pp103-118
  22. Hidayati, Y. M., Ngalim, A., Sutama, Arifin, Z., Abidin, Z., & Rahmawati, E. (2020). Level of combinatorial thinking in solving mathematical problems. Journal for the Education of Gifted Young Scientists, 8(3), 1231–1243.
  23. Hoon, T. S., Kee, K. L., & Singh, P. (2013). Learning mathematics using heuristic approach. Procedia - Social and Behavioral Sciences, 90, 862–869. https://doi.org/10.1016/j.sbspro.2013.07.162
  24. Imroatun, S., Sutriyono, & Prihatnani, E. (2014). Strategi pemecahan masalah matematika siswa kelas VII SMP Kristen 2 Salatiga ditinjau dari langkah Polya. In Program Studi Pendidikan Matematika FKIP-UKSW. Universitas Kristen Satya Wacana.
  25. Kholid, M. N., Hamida, P. S., Pradana, L. N., & Maharani, S. (2020). Students’ critical thinking depends on their cognitive style. International Journal of Scientific and Technology Research, 9(1), 1045–1049.
  26. Kholid, M. N., Imawati, A., Swastika, A., Maharani, S., & Pradana, L. N. (2021). How are students’ conceptual understanding for solving mathematical problem? Journal of Physics: Conference Series, 1776(1), 012018. https://doi.org/10.1088/1742-6596/1776/1/012018
  27. Kholid, M. N., Sa’dijah, C., Hidayanto, E., & Permadi, H. (2020). How are students’ reflective thinking for problem solving? Journal for the Education of Gifted Young Scientists, 8(3), 1135–1146. https://doi.org/10.17478/JEGYS.688210
  28. Kholid, M. N., Sa’dijah, C., Hidayanto, E., & Permadi, H. (2022). Students’ reflective thinking pattern changes and characteristics of problem solving. Reflective Practice, 23(3), 319–341. https://doi.org/10.1080/14623943.2021.2025353
  29. Kholid, M. N., Santosa, Y. T., Toh, T. L., Wijaya, A. P., & Hendriana, H. (2024). Defragmenting students’ reflective thinking levels for mathematical problem solving: Does it work? Reflective Practice: International and Multidisciplinary Perspectives. https://doi.org/10.1080/14623943.2024.2320140
  30. Krawec, J. L. (2014). Problem representation and mathematical problem solving of students of varying math ability. Journal of Learning Disabilities, 47(2), 103–115. https://doi.org/10.1177/0022219412436976
  31. Kristayulita, K. (2021). Indirect analogical reasoning components. Malikussaleh Journal of Mathematics Learning (MJML), 4(1), 13–19. https://doi.org/10.29103/mjml.v4i1.2939
  32. Kristayulita, K., Nusantara, T., As’ari, A. R., & Sa’dijah, C. (2018). Identification of students errors in solving indirect analogical problems based on analogical reasoning components. Journal of Physics: Conference Series, 1028(1), 012154. https://doi.org/10.1088/1742-6596/1028/1/012154
  33. Kristayulita, K., Nusantara, T., As’ari, A. R., & Sa’dijah, C. (2020). Schema of analogical reasoning-thinking process in example analogies problem. Eurasian Journal of Educational Research, 88, 87–104. https://doi.org/10.14689/ejer.2020.88.4
  34. Lailiyah, S., Kusaeri, K., Retnowati, E., & Erman, E. (2022). A Ruppert’s framework: How do prospective teachers develop analogical reasoning in solving algebraic problems? JRAMathEdu (Journal of Research and Advances in Mathematics Education), 7(3), 145–160. https://doi.org/10.23917/jramathedu.v7i3.17527
  35. Lailiyah, S., Nusantara, T., Sa’dijah, C., Irawan, E. B., Kusaeri, & Asyhar, A. H. (2018). Structuring students’ analogical reasoning in solving algebra problem. IOP Conference Series: Materials Science and Engineering, 296(1), 1–6. https://doi.org/10.1088/1757-899X/296/1/012029
  36. Lailiyah, S., Nusantara, T., Sadijah, C., & Irawan, E. B. (2017). Developing students’ analogical reasoning through algebraic problems. Jurnal Pendidikan Sains, 5(2), 38–45. http://journal.um.ac.id/index.php/jps/
  37. Laurillard, D. (2016). The educational problem that MOOCs could solve: Professional development for teachers of disadvantaged students. Research in Learning Technology Is the Journal of the Association for LearningTechnology (ALT), 24(july), 1–17. https://doi.org/10.3402/rlt.v24.29369
  38. Loc, N. P., & Uyen, B. P. (2014). Using analogy in teaching mathematics: An investigation of mathematics education students in school of education- Can Tho university. International Journal of Education and Research, 2(7), 91–98.
  39. Magdaş, I. (2015). Analogical reasoning in geometry education. Acta Didactica Napocensia, 8(1), 57–66.
  40. Masduki, Kholid, M. N., & Khotimah, R. P. (2020). Exploring students’ problem-solving ability and response towards metacognitive strategy in mathematics learning. Universal Journal of Educational Research, 8(8), 3698–3703. https://doi.org/10.13189/ujer.2020.080849
  41. Musser, G. L., Burger, W. F., & Peterson, B. E. (2008). Mathematics for elementary teachers a contamporary approach (8th ed.). Laurie Rosatone.
  42. Mutia, Kartono, Dwijanto, & Wijayanti, K. (2023). Analogical thinking of student in solving function problems based on mathematical disposition. AIP Conference Proceedings, 2540(May). https://doi.org/10.1063/5.0105935
  43. NCTM. (2020). NCTM standards ( 2020 ) – Secondary (Initial Preparation). In NCTM Standards - Positions.
  44. Newman, M. A. (1977). An analysis of sixth-grade pupils’ errors on written mathematical tasks (pp. 31–43). Victorian Institute for Educational Research Bulletin.
  45. Novick, L. R. (1988). Analogical transfer, problem similarity, and expertise. Journal of Experimental Psychology, 14(3), 510–520. https://doi.org/10.1037/0278-7393.14.3.510
  46. Novick, L. R., & Holyoak, K. J. (1991). Mathematical problem solving by analogy. Journal of Experimental Psychology: Learning, Memory, and Cognition, 17(3), 398–415. https://doi.org/10.1037/0278-7393.17.3.398
  47. Novotná, J., Eisenmann, P., Přibyl, J., Ondrušová, J., & Břehovský, J. (2014). Problem solving in school mathematics based on heuristic strategies. ERIES: Journal on Efficiency and Responsibility in Education and Science, 7(1), 1–6. https://doi.org/10.7160/eriesj.2013.070101
  48. Penn, D. C., Holyoak, K. J., & Povinelli, D. J. (2008). Darwin’s mistake : Explaining the discontinuity between human and nonhuman minds. Behavioral and Brain Sciences, 31, 109–178. https://doi.org/10.1017/S0140525X08003543
  49. Pradana, L. N., Sholikhah, O. H., Maharani, S., & Kholid, M. N. (2020). Virtual Mathematics Kits (VMK): Connecting digital media to mathematical literacy. International Journal of Emerging Technologies in Learning (IJET), 15(3), 234–241.
  50. Purwanti, R., Hartoyo, A., & Suratman, D. (2016). Kemampuan penalaran analogi matematis siswa SMP dalam materi bangun ruang. Jurnal Pendidikan dan Pembelajaran Khatulistiwa, 5(10), 1–13.
  51. Rahayuningsih, S., Sirajuddin, S., & Nasrun, N. (2021). Cognitive flexibility: Exploring students’ problem-solving in elementary school mathematics learning. Journal of Research and Advances in Mathematics Education, 6(1), 59–70. https://doi.org/10.23917/jramathedu.v6i1.11630
  52. Ruppert, M. (2013). Ways of analogical reasoning – Thought processes in an example based learning environment. Eight Congress of European Research in Mathematics Education (CERME 8), 6–10.
  53. Saleh, K., Yuwono, I., As’ari, A. R., & Sa’dijah, C. (2017). Errors analysis solving problems analogies by newman procedure using analogical reasoning. International Journal of Humanities and Social Sciences, 9(1), 17–26.
  54. Sholihah, U., & Maryono, M. (2020). Students’ visual thinking ability in solving the integral problem. JRAMathEdu: Journal of Research and Advances in Mathematics Education, 5(2), 175–186. https://doi.org/10.23917/jramathedu.v5i2.10286
  55. Sutama, S., Fuadi, D., Narimo, S., Hafida, S. H. N., Novitasari, M., Anif, S., Prayitno, H. J., Sunanih, S., & Adnan, M. (2022). Collaborative mathematics learning management: Critical thinking skills in problem solving. International Journal of Evaluation and Research in Education (IJERE), 11(3), 1015–1027. https://doi.org/10.11591/ijere.v11i3.22193
  56. Usiskin, Z. (1999). Conceptions of School Algebra and Uses of Variables. ” In Algebraic Thinking, Grades K–12: Readings from NCTM’s School-Based Journals and Other Publications, 7–13.
  57. Vybihal, J. P., & Shultz, T. R. (1989). Search in Analogical Reasoning. 11th Annual Conference Cognitive Science Society.