From complex to simple: Analyzing prospective teachers' analogy reasoning in creating accessible geometry problems
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Abstract
Students often struggle to identify relevant analog problems when solving new tasks, highlighting the need for teachers to design simple analog problems that serve as scaffolding. This study aims to analyze prospective teachers’ analogical reasoning processes in simplifying complex geometry problems using the Analogical Reasoning in Mathematics (ARM) framework. This qualitative research involved 34 prospective mathematics teachers from a public university in Surabaya, Indonesia. Participants were selected through purposive sampling based on their academic performance and prior coursework in geometry and problem solving. Data were collected through task-based interviews, written work, and observations during problem-simplification activities. The collected data were analyzed thematically, guided by the components of the ARM framework. The results indicate that prospective teachers with varying ability levels employed different analogical reasoning strategies to simplify complex problems through ARM activities. High-ability prospective teachers identified a broader range of student difficulties and adapted the problems into two-step analog problems featuring variations in visual representations, number of circles, and geometric shapes. Conversely, low-ability prospective teachers focused on difficulties related to verbal representation and the need for concrete numerical information, adapting the problems into single, highly simplified analog problems with specific images and numbers. Overall, prospective teachers actively utilized analogical reasoning to design analog problems that addressed student difficulties. Differences in ability were associated with the complexity of adaptation strategies and the depth of difficulty identification, underscoring the importance of training prospective teachers to integrate both approaches to effectively support student understanding.
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Rosyidi, A. H., Sa’dijah, C., Purnomo, H., & Abdullah, A. H. (2025). From complex to simple: Analyzing prospective teachers’ analogy reasoning in creating accessible geometry problems. Kalamatika: Jurnal Pendidikan Matematika, 10(2), 73-93. https://doi.org/10.22236/KALAMATIKA.vol10no2.2025pp73-93
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Peled, I. (2007). The role of analogical thinking in designing tasks for mathematics teacher education: An example of a pedagogical ad hoc task. Journal of Mathematics Teacher Education, 10, 369–379. https://doi.org/10.1007/s10857-007-9048-6
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Sun, L., & Lin, C. (2025). Cases on informal learning for science and mathematics education. IGI Global Scientific Publishing. https://doi.org/10.4018/979-8-3693-1894-2
Susanto, S., & Mahmudi, A. (2021). Tahap berpikir geometri siswa SMP berdasarkan teori Van Hiele ditinjau dari keterampilan geometri [Junior High School Students’ Geometric Thinking Stages Based on the Van Hiele Theory in Terms of Geometric Skills]. Jurnal Riset Pendidikan Matematika, 8(1), 106-116. https://doi.org/10.21831/jrpm.v8i1.17044
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Amalliyah, N., Dewi, N. R., & Dwijanto, D. (2021). Tahap Berpikir Geometri Siswa SMA Berdasarkan Teori Van Hiele Ditinjau dari Perbedaan Gender. JNPM (Jurnal Nasional Pendidikan Matematika), 5(2), 352-361. http://doi.org/10.33603/jnpm.v5i2.4550
Branca, N. A. (1980). Problem Solving as a Goal, Process, and Basic Skill. Reston, VA: NCTM.
Cai, J., Ran, H., Hwang, S., Ma, Y., Han, J., & Muirhead, F. (2023). Impact of prompts on students’ mathematical problem posing. Journal of Mathematical Behavior, 72(September). https://doi.org/10.1016/j.jmathb.2023.101087
Calabrese, J.E., Capraro, M.M., Viruru, R. (2024). Semantic structure and problem posing: Preservice teachers' experience. School Science and Mathematics, 124(4), 266-278. https://doi.org/10.1111/ssm.12648
Clement, C. A., & Gentner, D. (1991). Systematicity as a selection constraint in analogical mapping. Cognitive science, 15(1), 89-132. https://doi.org/10.1016/0364-0213(91)80014-V
Dai, Y., Lin, Z., Liu, A., Dai, D., & Wang, W. (2023). Effect of an Analogy-Based Approach of Artificial Intelligence Pedagogy in Upper Primary Schools. Journal of Educational Computing Research, 61(8), 1695-1722. https://doi.org/10.1177/07356331231201342
Danlami, K.B., Zakariya, Y.F., Balarabe, B., Alotaibi, S.B. & Alrosaa, T.M. (2025). Improving students’ performance in geometry: an empirical evidence of the eectiveness of brainstorming learning strategy. Frontiers in Psychology. 16, 1577912. https://doi.org/10.3389/fpsyg.2025.1577912
Hasan, B., Juniati, D., & Masriyah. (2024). Gender and Analogical Reasoning in Mathematics Problem Solving. In AIP Conference Proceedings (Vol. 3046, No. 1, p. 020015). AIP Publishing LLC. https://doi.org/10.1063/5.0195145
Hicks, M. D. (2022). Fostering productive ways of thinking associated with analogical reasoning in advanced mathematics. For the Learning of Mathematics, 42(3), 10–15. https://www.jstor.org/stable/27239244
Hicks, M. D. (2024). “I’ll just try to mimic that”: an exploration of students’ analogical structure creation in abstract algebra. Educational Studies in Mathematics, 117(2), 303–327. https://doi.org/10.1007/s10649-024-10345-1
Hicks, M. D., & Flanagan, K. (2024). Analogical structure sense: A case study of students’ analogical reasoning between groups and rings. Journal of Mathematical Behavior, 73, 101136. https://doi.org/10.1016/j.jmathb.2024.101136
Kirisci, N., Sak, U., & Karabacak, F. (2020). The effectiveness of the selective problem solving model on students’ mathematical creativity: A Solomon four-group research. Thinking Skills and Creativity, 38, 100719. https://doi.org/10.1016/j.tsc.2020.100719
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, 20(88), 87-104. https://doi.org/10.14689/ejer.2020.88.4
Kroczek, B., Ciechanowska, I., & Chuderski, A. (2022). Uncovering the course of analogical mapping using eye tracking. Cognition, 225, 105140. https://doi.org/10.1016/j.cognition.2022.105140
Lee, K. H., & Sriraman, B. (2011). Conjecturing via reconceived classical analogy. Educational Studies in Mathematics, 76(2), 123–140. https://doi.org/10.1007/s10649-010-9274-1
Lester Jr, F. K. (2013). Thoughts about research on mathematical problem-solving instruction. The mathematics enthusiast, 10(1), 245-278. https://doi.org/10.54870/1551-3440.1267
Lester, F. K. (1980). Research in mathematical problem solving. In R. J. Shumway (Ed.), Research in mathematics education (pp. 286-323). Reston, VA: NCTM.
Lobato, J. (2012). The actor-oriented transfer perspective and its contributions to educational research and practice. Educational Psychologist, 47(3), 232–247. https://doi.org/10.1080/00461520.2012.693353
Lupiáñez, J.L., Olivares, D. & Segovia, I. (2024). Examining the role played by resources, goals and orientations in primary teachers’ decision-making for problem-solving lesson plans. ZDM–Mathematics Education, 56(6), 1153-1167. https://doi.org/10.1007/s11858-024-01614-7
Milles, Matthew B & Huberman, A. Michael. (2014). Analisis Data Kualitatif. Buku Sumber Tentang Metode-Metode Baru [Qualitative Data Analysis: A Sourcebook of New Methods]. Jakarta: Penerbit Unversitas Indonesia Press.
Moursund, D. G. (2005). Improving math education in elementary schools: A short book for teachers. Oregon: University of Oregon.
Mutia, Kartono, Dwijanto, & Wijayanti, K. (2023). Students’ Analogical Reasoning in Solving Trigonometric Target Problem. Malaysian Journal of Mathematical Sciences, 17(3), 425-440. https://doi.org/10.47836/MJMS.17.3.11
Peled, I. (2007). The role of analogical thinking in designing tasks for mathematics teacher education: An example of a pedagogical ad hoc task. Journal of Mathematics Teacher Education, 10, 369–379. https://doi.org/10.1007/s10857-007-9048-6
Polya, G. (1957). How to solve it: A new aspect of mathematical method (Second Edition). Princeton university press.
Richland, L. E., Holyoak, K. J., & Stigler, J. W. (2004). Analogy use in eighth-grade mathematics classrooms. Cognition and instruction, 22(1), 37-60. https://doi.org/10.1207/s1532690Xci2201_2
Riegel, K. (2021). Frustration in mathematical problem-solving: A systematic review of research. Stem Education, 1(3), 157-169. https://doi.org/10.3934/steme.2021012
Schoenfeld, A. H. (2014). Mathematical problem solving. Academic Press, Inc. Orlando.
Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19-28. https://www.jstor.org/stable/40248099
Silwana, A., Sa’dijah,C., Sukoriyanto. (2023). Analogical reasoning of students with logical-mathematical intelligence tendency in solving trigonometry problem. AIP Conference Proceedings, 2614(1), 040029. https://doi.org/10.1063/5.0125757
Steele, M. D. (2013). Exploring the mathematical knowledge for teaching geometry and measurement through the design and use of rich assessment tasks. Journal of Mathematics Teacher Education, 16, 245-268. https://doi.org/10.1007/s10857-012-9230-3
Sun, L., & Lin, C. (2025). Cases on informal learning for science and mathematics education. IGI Global Scientific Publishing. https://doi.org/10.4018/979-8-3693-1894-2
Susanto, S., & Mahmudi, A. (2021). Tahap berpikir geometri siswa SMP berdasarkan teori Van Hiele ditinjau dari keterampilan geometri [Junior High School Students’ Geometric Thinking Stages Based on the Van Hiele Theory in Terms of Geometric Skills]. Jurnal Riset Pendidikan Matematika, 8(1), 106-116. https://doi.org/10.21831/jrpm.v8i1.17044
Takona, J.P. (2024). Research design: qualitative, quantitative, and mixed methods approaches / sixth edition. Quality and Quantity, 58(1), 1011-1013, ISSN 0033-5177, https://doi.org/10.1007/s11135-023-01798-2
Tzuriel, D. (2024). Analogical thinking modifiability and math processing strategy. Frontiers in Psychology, 15, ISSN 1664-1078, https://doi.org/10.3389/fpsyg.2024.1339591
Vygotsky, L. S., & Cole, M. (1978). Mind in society: Development of higher psychological processes. Harvard university press.
Woods, P.J & Y. Copur-Gencturk. (2024). Examining the role of student-centered versus teacher-centered pedagogical approaches to self-directed learning through teaching. Teaching and Teacher Education, 138, 104415. https://doi.org/10.1016/j.tate.2023.104415
Yi, M., Flores, R., & Wang, J. (2020). Examining the influence of van Hiele theory-based instructional activities on elementary preservice teachers’ geometry knowledge for teaching 2-D shapes. Teaching and Teacher Education, 91, 103038. https://doi.org/10.1016/j.tate.2020.103038
Zhu, C., Klapwijk, R., Silva-Ordaz, M. et al. (2024). Investigating the role of spatial thinking in children’s design ideation through an open-ended design-by-analogy challenge. International Journal of Technology and Design Education, 34, 1733–1762. https://doi.org/10.1007/s10798-024-09877-7