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Abstract

Inductive thinking is a method of thinking that involves recognizing patterns, understanding relationships, and deconstructing general rules, which develops through a variety of factors that support complex problem-solving. Using mathematical problems that describe the inductive thinking process in the context of number problems helps investigate students' inductive thinking process. This research aims to develop a new classification framework for students' inductive thinking in the context of mathematical problem-solving. A qualitative descriptive research approach was used in this study. It was carried out in a structured manner on 21 fifth-semester mathematics students at one of the universities in Indonesia with number sequence material. Data collection is done through tests and observations in problem-solving, and analysis is carried out using constant comparative procedures (CCP). The instruments used in this research include mathematical problems and recording tools. The conclusion of this study is presented in the form of three different classifications of inductive thinking: the use of variables (variables as a symbolic tool to solve problems), visual (the application of visual representations to solve problems), and the use of formulas (the use of mathematical formulas for problem-solving). The study offers significant theoretical insights for future research and practical implications for applying inductive thinking in improving mathematical problem-solving.

Keywords

Classification Inductive Thinking Mathematical Problems Problem-Solving

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How to Cite
Kholid, M. N., & Syafif, I. A. (2025). Classification of Inductive Thinking in Mathematical Problem-Solving . Journal on Mathematics Education, 16(2), 633–650. https://doi.org/10.22342/jme.v16i2.pp633-650
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References

  1. Adawiyah, R., Muin, A., & Khairunnisa, K. (2017). Mathematical Inductive-Creative Reasoning, A Theoretical Study. Proceedings of the 2016 International Conference on Mathematics and Science Education. https://doi.org/10.2991/icmsed-16.2017.53
  2. Anggo, M., Masi, L., & Haryani, M. (2021). The Use of Metacognitive Strategies in Solving Mathematical Problems. Journal of Physics: Conference Series, 1752(1). https://doi.org/10.1088/1742-6596/1752/1/012078
  3. Awasthy, R. (2019). Nature of Qualitative Research. In Methodological Issues in Management Research: Advances, Challenges, and the Way Ahead (pp. 145–161). Emerald Group Publishing Ltd. https://doi.org/10.1108/978-1-78973-973-220191010
  4. Barete, M., & Taja-on, E. (2024). Students’ Perception in Learning the Course Mathematics in the Modern World: A Qualitative Study. East Asian Journal of Multidisciplinary Research, 3(7). https://doi.org/10.55927/eajmr.v3i7.10071
  5. Belcastro, F. P. (1966). Relative Effectiveness of the Inductive and Deductive Methods of Programming Algebra. The Journal of Experimental Education, 34(3), 77–82. https://doi.org/10.1080/00220973.1966.11010941
  6. Benitez-Correa, C., Gonzalez-Torres, P., Ochoa-Cueva, C., & Vargas-Saritama, A. (2019). A Comparison between Deductive and Inductive Approaches for Teaching EFL Grammar to High School Students. International Journal of Instruction, 12(1), 225–236. https://doi.org/10.29333/iji.2019.12115a
  7. Benson, I., Marriott, N., & McCandliss, B. D. (2023). Interventions to Improve Equational Reasoning: Replication and Extension of The Cuisenaire-Gattegno Curriculum Effect. Frontiers in Psychology, 14. https://doi.org/10.3389/fpsyg.2023.1116555
  8. Carden, J., & Cline, T. (2015). Problem-Solving in Mathematics: The Significance of Visualisation and Related Working Memory. Educational Psychology in Practice, 31(3), 235–246. https://doi.org/10.1080/02667363.2015.1051660
  9. Chan, J. Y. C., Ottmar, E. R., Smith, H., & Closser, A. H. (2022). Variables Versus Numbers: Effects of Symbols and Algebraic Knowledge On Students’ Problem-Solving Strategies. Contemporary Educational Psychology, 71. https://doi.org/10.1016/j.cedpsych.2022.102114
  10. Clements, M. A. (2014). Fifty Years of Thinking About Visualization and Visualizing in Mathematics Education: A Historical Overview. In Fifty Years of Thinking About Visualization and Visualizing (pp. 177–192). https://doi.org/10.1007/978-94-007-7473-5_11
  11. Creswell, J. W. (2012). Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research (4th ed.). Pearson Education.
  12. Delima, N., Rahmah, M. A., & Akbar, A. (2018). The Analysis of Students’ Mathematical Thinking based on Their Mathematics Self-Concept. Journal of Physics: Conference Series, 1108, 012104. https://doi.org/10.1088/1742-6596/1108/1/012104
  13. Hamda, H. (2018). Mathematical Problem-Solving Strategy based on Conceptual Thinking. Journal of Physics: Conference Series, 1028(1). https://doi.org/10.1088/1742-6596/1028/1/012163
  14. Haverty, L. A., Koedinger, K. R., Klahr, D., & Alibali, M. W. (2000). Solving Inductive Reasoning Problems in Mathematics: Not-So-Trivial Pursuit. Cognitive Science, 24(2), 249–298. https://doi.org/10.1207/s15516709cog2402_3
  15. Hegarty, M., & Kozhevnikov, M. (1999). Types of visual–spatial representations and mathematical problem solving. Journal of Educational Psychology, 91(4), 684–689. https://doi.org/10.1037/0022-0663.91.4.684
  16. Helviyana, G., Susanti, E., Indaryanti, Sari, N., & Simarmata, R. H. (2020). Students’ Mathematical Reasoning in Inquiry Learning Model. Journal of Physics: Conference Series, 1480(1). https://doi.org/10.1088/1742-6596/1480/1/012058
  17. Hewitt-Taylor, J. (2001). Use of Constant Comparative Analysis in Qualitative Research. Nursing Standard, 15(42), 39–42. https://doi.org/10.7748/ns2001.07.15.42.39.c3052
  18. Hosseini, M. J., Hajishirzi, H., Etzioni, O., & Kushman, N. (2014). Learning to Solve Arithmetic Word Problems with Verb Categorization. Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP), 523–533. https://doi.org/10.3115/v1/D14-1058
  19. Ishartono, N., Nurcahyo, A., Waluyo, M., Prayitno, H. J., & Hanifah, M. (2022). Integrating GeoGebra into the flipped learning approach to improve students’ self-regulated learning during the covid-19 pandemic. Journal on Mathematics Education, 13(1), 69–86. https://doi.org/10.22342/jme.v13i1.pp69-86
  20. Iwane, H., & Anai, H. (2017). Formula Simplification for Real Quantifier Elimination Using Geometric Invariance. Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC, Part F129312, 213–220. https://doi.org/10.1145/3087604.3087627
  21. Jobes, P. C., Aldea, A., Cernat, C., Icolisan, I.-M., Iordache, G., Lazeru, S., Stoica, C., Tibil, G., & Udangiu, E. (1997). Using the Constant Comparative Method in the Foreign Classroom: Shopping as a Social Problem in Romania. Source: Teaching Sociology, 25(4), 292–302. https://doi.org/10.2307/1319297
  22. Kapur, M. (2014). Productive Failure in Learning Math. Cognitive Science, 38(5), 1008–1022. https://doi.org/10.1111/cogs.12107
  23. Kasmer, L., & Kim, O. (2011). Using Prediction to Promote Mathematical Understanding and Reasoning. School Science and Mathematics, 111(1), 20–33. https://doi.org/10.1111/j.1949-8594.2010.00056.x
  24. Kauts, D. S., & Kauts, A. (2020). Effect of Taba’s Inductive Thinking Model on Achievement in Science and Creative Thinking in Relation to Intelligence of Students at Secondary School Stage. MIER Journal of Educational Studies, Trends & Practices, 10(2), 151–166. https://doi.org/10.52634/mier/2020/v10/i2/1347
  25. Khan, S. B. S., & Salman, R. (2020). Influence of Mathematics in Our Daily Lives. Arts & Humanities Open Access Journal, 4(2), 50–52. https://doi.org/10.15406/ahoaj.2020.04.00152
  26. Kholid, M. N., Agustin, R. L., & Pradana, L. N. (2019). Effect Of Tps Strategy With Portfolio Assessment And Learning Interest On Mathematical Learning Achievement. International Journal of Scientific & Technology Research, 8(09), 616–620.
  27. Kholid, M. N., Hamida, P. S., Pradana, L. N., & Maharani, S. (2020). Students’ Critical Thinking Depends On Their Cognitive Style. International Journal of Scientific & Technology Research, 9(1), 1045–1049.
  28. 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
  29. Kholid, M. N., Putri, Y. P., Swastika, A., Maharani, S., & Ikram, M. (2022). What are The Pupils’ Challenges in Implementing Reflective Thinking for Problem-Solving? The International Conference on Mathematics and Learning Research (ICOMER) 2021, 020012. https://doi.org/10.1063/5.0099600
  30. Kholid, M. N., Rofi’ah, F., Ishartono, N., Waluyo, M., Maharani, S., Swastika, A., Faiziyah, N., & Sari, C. K. (2022). What Are Students’ Difficulties in Implementing Mathematical Literacy Skills for Solving PISA-Like Problem? Journal of Higher Education Theory and Practice, 22(2), 180–199. https://doi.org/10.33423/jhetp.v22i2.5057
  31. 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
  32. Kholid, M. N., Swastika, A., Ishartono, N., Nurcahyo, A., Tin Lam, T., Maharani, S., Ikram, M., Murniasih, T. R., Majid, M., Wijaya, A. P., & Pratiwi, E. (2022). Hierarchy of Students’ Reflective Thinking Levels in Mathematical Problem Solving. Acta Scientiae, 24(6), 24–59. https://doi.org/10.17648/acta.scientiae.6883
  33. Klauer, K. J., Willmes, K., & Phye, G. D. (2002). Inducing Inductive Reasoning: Does It Transfer to Fluid Intelligence? Contemporary Educational Psychology, 27(1), 1–25. https://doi.org/10.1006/ceps.2001.1079
  34. Kohen, Z., Amram, M., Dagan, M., & Miranda, T. (2022). Self-efficacy and problem-solving skills in mathematics: the effect of instruction-based dynamic versus static visualization. Interactive Learning Environments, 30(4), 759–778. https://doi.org/10.1080/10494820.2019.1683588
  35. Kurniawati, L., Miftah, R., & Indriani, R. (2021). Improving students’ mathematical inductive reasoning ability through reflective learning Model. Journal of Physics: Conference Series, 1836(1). https://doi.org/10.1088/1742-6596/1836/1/012071
  36. Li, Y., Xu, W., Xu, Y., & Liu, B. (2022). Mathematics Learning and Teaching Directed to Process Construction: Reflection on The Application of Mathematical Induction. Annals of Mathematical Modeling, 2(2), 82–89. https://doi.org/10.33292/amm.v2i2.23
  37. Lingefjärd, T. (2023). A Cognitive Aspect On Substitution in Problem-Solving in Mathematics. Journal of Mathematics and Science Teacher, 3(1). https://doi.org/10.29333/mathsciteacher/13085
  38. 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
  39. Mistry, K. B. (2012). Research & statistic: Qualitative research methods. Pediatrics in Review, 33(11), 521–523. https://doi.org/10.1542/pir.33-11-521
  40. Miswanto, A., Susanti, E., Hapizah, H., Meryansumayeka, M., & Nurzalena, A. (2019). Analysis of Mathematical Thinking Types Reasoning Students in Completing The Problem-Solving Question. Journal of Physics: Conference Series, 1318(1). https://doi.org/10.1088/1742-6596/1318/1/012101
  41. Moguel, L. E. S., Landa, E. A., & Cabañas-Sánchez, G. (2020). Fases del Razonamiento Inductivo Que Presentan Profesores de Matematicás al Resolver Un Problema de Generalización. PNA Revista En Didactica de La Matematica, 14(2), 118–141. https://doi.org/10.30827/PNA.V14I2.9118
  42. Moss, D. L., Boyce, S., & Lamberg, T. (2019). Representations and Conceptions of Variables in Students’ Early Understandings of Functions. International Electronic Journal of Mathematics Education, 15(2). https://doi.org/10.29333/iejme/6257
  43. Ngu, B. H., & Phan, H. P. (2017). Will Learning to Solve One-step Equations Pose A Challenge to 8th Grade Students? International Journal of Mathematical Education in Science and Technology, 48(6), 876–894. https://doi.org/10.1080/0020739X.2017.1293856
  44. Perret, P. (2015). Children’s Inductive Reasoning: Developmental and Educational Perspectives. Journal of Cognitive Education and Psychology, 14(3), 389–408. https://doi.org/10.1891/1945-8959.14.3.389
  45. Prince, M. J., & Felder, R. M. (2006). Inductive Teaching and Learning Methods: Definitions, Comparisons, and Research Bases. Journal of Engineering Education, 95(2), 123–138. https://doi.org/10.1002/j.2168-9830.2006.tb00884.x
  46. Rahmah, M. A. (2017). Inductive-Deductive Approach to Improve Mathematical Problem Solving for Junior High School. Journal of Physics: Conference Series, 812(1). https://doi.org/10.1088/1742-6596/812/1/012089
  47. Ramirez, G., Shaw, S. T., & Maloney, E. A. (2018). Math Anxiety: Past Research, Promising Interventions, and a New Interpretation Framework. Educational Psychologist, 53(3), 145–164. https://doi.org/10.1080/00461520.2018.1447384
  48. Rani, G., Kumar, P., Devi, R., Kumar, R., Kumar, S., & Kumar, M. (2023). Mathematics as a Part of The Real Life. International Journal of Advanced Research in Science, Communication and Technology, 409–418. https://doi.org/10.48175/ijarsct-11665
  49. Rizzuto, M. F. (1970). Experimental Comparison of Inductive and Deductive Methods of Teaching Concepts of Language Structure. Journal of Educational Research, 63(6), 269–273. https://doi.org/10.1080/00220671.1970.10884008
  50. Sachdeva, S., & Eggen, P.-O. (2021). Learners’ Critical Thinking About Learning Mathematics. International Electronic Journal of Mathematics Education, 16(3), em0644. https://doi.org/10.29333/iejme/11003
  51. Sa’dijah, C., Kholid, M. N., Hidayanto, E., & Permadi, H. (2020). Reflective Thinking Characteristics: A Study in The Proficient Mathematics Prospective Teachers. Infinity Journal, 9(2), 159. https://doi.org/10.22460/infinity.v9i2.p159-172
  52. Sanjaya, A., Johar, R., Ikhsan, M., & Khairi, L. (2018). Students’ Thinking Process in Solving Mathematical Problems Based on The Levels of Mathematical Ability. Journal of Physics: Conference Series, 1088. https://doi.org/10.1088/1742-6596/1088/1/012116
  53. Schiemer, G. (2019). Mathematik in den Wissenschaften. In Einheit und Vielfalt in den Wissenschaften (pp. 38–68). De Gruyter. https://doi.org/10.1515/9783110614831-003
  54. Supandi, S., Suyitno, H., Sukestiyarno, Y. L., & Dwijanto, D. (2019). Adaptation and creativity in mathematics learning. Journal of Physics: Conference Series, 1321(2). https://doi.org/10.1088/1742-6596/1321/2/022132
  55. Sutarni, S., Sutama, Prayitno, H. J., Sutopo, A., & Laksmiwati, P. A. (2024). The Development of Realistic Mathematics Education-Based Student Worksheets to Enhance Higher-Order Thinking Skills and Mathematical Ability. Infinity Journal, 13(2), 285–300. https://doi.org/10.22460/infinity.v13i2.p285-300
  56. Tan, L. G. (2023). Real-Life Valuation And Re-Configuring Instructional Approach Of Learning Mathematics Among College Non-Math-Oriented Students. Journal of Namibian Studies : History Politics Culture, 33, 1745–1765. https://doi.org/10.59670/jns.v33i.3165
  57. Tóth, P., Horváth, K., & Kéri, K. (2021). Development Level of Engineering Students’ Inductive Thinking. Acta Polytechnica Hungarica, 18(5), 107–129. https://doi.org/10.12700/APH.18.5.2021.5.8
  58. Trigueros, R., Aguilar-Parra, J. M., Mercader, I., Fernández-Campoy, J. M., & Carrión, J. (2020). Set the Controls for the Heart of the Maths. The Protective Factor of Resilience in the Face of Mathematical Anxiety. Mathematics, 8(10), 1–11. https://doi.org/10.3390/math8101660
  59. Vo, D. Van, & Csapó, B. (2022). Measuring Inductive Reasoning in School Contexts: A Review of Instruments and Predictors. International Journal of Innovation and Learning, 31(4), 506. https://doi.org/10.1504/IJIL.2022.10046982
  60. Vos, P., Wiik, A., & Hernandez-Martinez, P. (2024). “Imagine, Maths is Used Anywhere, and We Don’t Get to Know This”—Upper Secondary Students and The Relevance of Advanced mathematics. Frontiers in Education, 9. https://doi.org/10.3389/feduc.2024.1338205
  61. Wardani, S., Kusuma, I. W., Liu, S. T., & Harjito. (2020). Comparison of Learning in Inductive and Deductive Approach to Increase Student’s Conceptual Understanding Based On International Standard Curriculum. Jurnal Pendidikan IPA Indonesia, 9(1), 70–78. https://doi.org/10.15294/jpii.v9i1.21155
  62. Wright, D. P. (1977). Interactions Between Instructional Methods and Styles of Concept Learning. Journal of Educational Research, 70(3), 150–156. https://doi.org/10.1080/00220671.1977.10884973
  63. Zulu, M. W., & Mudaly, V. (2023). Unveiling Problem-Solving Strategies of Pre-Service Mathematics Teachers: A Visual and Discursive Exploration. Eurasia Journal of Mathematics, Science and Technology Education, 19(7). https://doi.org/10.29333/ejmste/13344

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