Exploring psychological, conceptual, and instrumental ontogenetic learning obstacles in elementary geometry: Evidence from students’ solutions to composite plane figure area tasks
DOI:
https://doi.org/10.58524/jasme.v6i3.1414Keywords:
Elementary Geometry, Learning Obstacles, Mathematics Education, Ontogenetic Learning Obstacles, Qualitative StudyAbstract
Background: Geometry is a fundamental component of elementary mathematics that supports the development of logical reasoning, spatial visualization, and problem-solving skills. However, many students continue to experience persistent learning difficulties that extend beyond procedural errors and reflect deeper ontogenetic learning obstacles associated with cognitive readiness and conceptual development. Despite increasing attention to learning obstacles in mathematics education, empirical studies examining the psychological, conceptual, and instrumental dimensions of ontogenetic obstacles in elementary geometry remain limited.
Aims: This study aimed to explore students’ psychological, conceptual, and instrumental ontogenetic learning obstacles when solving composite plane figure area tasks.
Methods: A qualitative descriptive approach was employed as the prospective analysis stage of Didactical Design Research (DDR). Twenty sixth-grade elementary school students participated in the study. Data were collected through a validated Learning Obstacle Diagnostic Test consisting of three open-ended tasks and analyzed descriptively based on the ontogenetic learning obstacle framework.
Results: The findings revealed that conceptual ontogenetic obstacles were the most dominant, followed by instrumental obstacles, while psychological obstacles emerged primarily as a consequence of unresolved conceptual and procedural difficulties.
Conclusion: The three types of ontogenetic learning obstacles were interconnected and significantly influenced students’ understanding of composite plane figure area concepts. These findings provide an empirical foundation for designing adaptive instructional strategies that better accommodate students’ cognitive development and learning needs.
References
Abrahamson, D., Nathan, M. J., Williams-Pierce, C., Walkington, C., Ottmar, E. R., Soto, H., & Alibali, M. W. (2020). The future of embodied design for mathematics teaching and learning. Frontiers in Education, 5. https://doi.org/10.3389/feduc.2020.00147
Adeleke, J. O., Balogun, H. A., & Ayanwale, M. A. (2025). Assessment of content and cognitive dimensions of learners’ mathematics performance. STEM Education, 5(3), 383–400. https://doi.org/10.3934/steme.2025019
Adeniji, S. M., & Baker, P. (2022). Worked-examples instruction versus Van Hiele teaching phases: A demonstration of students’ procedural and conceptual understanding. Journal on Mathematics Education, 13(2), 337–356. https://doi.org/10.22342/jme.v13i2.pp337-356
Aguilar, J. J. (2021). High school students’ reasons for disliking mathematics: The intersection between teacher’s role and student’s emotions, belief and self-efficacy. International Electronic Journal of Mathematics Education, 16(3), em0658. https://doi.org/10.29333/iejme/11294
Aljura, A. N., Retnawati, H., Dewanti, S. R., Kassymova, G. K., Sotlikova, R., & Septiana, A. R. (2025). Mathematical reasoning and communication word problems with mathematical problem-solving orientation: A relation between the skills. Journal on Mathematics Education, 16(2), 529–558. https://doi.org/10.22342/jme.v16i2.pp529-558
Aucejo, E., & James, J. (2021). The path to college education: The role of math and verbal skills. Journal of Political Economy, 129(10), 2905–2946. https://doi.org/10.1086/715417
Bojorque, R., Moscoso, F., Arcos-Argudo, M., & Pesántez, F. (2025). A data-driven analysis of cognitive learning and illusion effects in university mathematics. Data, 10(11). https://doi.org/10.3390/data10110192
Büchele, S., & Feudel, F. (2023). Changes in students’ mathematical competencies at the beginning of higher education within the last decade at a German university. International Journal of Science and Mathematics Education, 21(8), 2325–2347. https://doi.org/10.1007/s10763-022-10350-x
Capone, R. (2022). Blended learning and student-centered active learning environment: A case study with STEM undergraduate students. Canadian Journal of Science, Mathematics and Technology Education, 22(1), 210–236. https://doi.org/10.1007/s42330-022-00195-5
Caviedes Barrera, S., de Gamboa, G., & Badillo Jiménez, E. R. (2023). Mathematical objects that configure the partial area meanings mobilized in task-solving. International Journal of Mathematical Education in Science and Technology, 54(6), 1092–1111. https://doi.org/10.1080/0020739X.2021.1991019
Ceballos, H., van den Bogaart, T., van Ginkel, S., Spandaw, J., & Drijvers, P. (2026). How collaborative problem solving promotes higher-order thinking skills: A systematic review of design features and processes. Thinking Skills and Creativity, 59, 102001. https://doi.org/10.1016/j.tsc.2025.102001
Chiphambo, S. M., & Mtsi, N. (2021). Exploring grade 8 students’ errors when learning about the surface area of prisms. Eurasia Journal of Mathematics, Science and Technology Education, 17(8), em1985. https://doi.org/10.29333/ejmste/10994
Di Martino, P., Gregorio, F., & Iannone, P. (2023). The transition from school to university mathematics in different contexts: Affective and sociocultural issues in students’ crisis. Educational Studies in Mathematics, 113(1), 79–106. https://doi.org/10.1007/s10649-022-10179-9
Ding, Y. (2024). Analysis of students’ conceptual change in learning Newton’s third law with an integrated framework of model analysis and knowledge integration. Physical Review Physics Education Research, 20(2). https://doi.org/10.1103/PhysRevPhysEducRes.20.020141
Dorel, L. (2023). The relationship between visual and abstract comprehension in spatial geometry, and its importance to developing spatial perception and vision. International Journal for Technology in Mathematics Education, 30(4), 219–226. https://doi.org/10.1564/tme_v30.4.3
Durmaz, A., & Işiksal Bostan, M. (2022). Pre-service teachers’ knowledge regarding the area of triangle. European Journal of Science and Mathematics Education, 10(2). https://doi.org/10.30935/scimath/11716
Flavin, E., Chung, M., Hwang, S., & Flavin, M. T. (2025). Augmented reality for area measurement reasoning of elementary students. Educational Technology Research and Development, 73(4), 2663–2697. https://doi.org/10.1007/s11423-025-10502-0
Galitskaya, V., & Drigas, A. S. (2023). Mobiles and ICT based interventions for learning difficulties in geometry. International Journal of Engineering Pedagogy, 13(4), 21. https://doi.org/10.3991/ijep.v13i4.36309
Gao, J. (2020). Sources of mathematics self-efficacy in Chinese students: A mixed-method study with Q-sorting procedure. International Journal of Science and Mathematics Education, 18(4), 713–732. https://doi.org/10.1007/s10763-019-09984-1
Harbison, L., Nic Fhinn, T., Scully, C., Nic Con Ultaigh, N., & Wyndham, B.-T. (2026). Exploring concept images and misconceptions in geometry through creative mathematical story writing. Investigations in Mathematics Learning, 0(0), 1–22. https://doi.org/10.1080/19477503.2026.2692318
Hendriyanto, A., Suryadi, D., Juandi, D., Dahlan, J. A., Hidayat, R., Wardat, Y., Sahara, S., & Muhaimin, L. H. (2024). The didactic phenomenon: Deciphering students’ learning obstacles in set theory. Journal on Mathematics Education, 15(2), 517–544. https://doi.org/10.22342/jme.v15i2.pp517-544
Hofer, S. I., Reinhold, F., & Koch, M. (2023). Students home alone: Profiles of internal and external conditions associated with mathematics learning from home. European Journal of Psychology of Education, 38(1), 333–366. https://doi.org/10.1007/s10212-021-00590-w
Hsu, H.-Y., & Silver, E. A. (2026). Cognitive complexity of geometric proof and geometric calculation: A problem-solving perspective. Educational Studies in Mathematics, 121(1), 29–50. https://doi.org/10.1007/s10649-025-10434-9
Hwang, W.-Y., Zhao, L., Shadiev, R., Lin, L.-K., Shih, T. K., & Chen, H.-R. (2020). Exploring the effects of ubiquitous geometry learning in real situations. Educational Technology Research and Development, 68(3), 1121–1147. https://doi.org/10.1007/s11423-019-09730-y
Idrus, H., Rahim, S. S. A., & Zulnaidi, H. (2022). Conceptual knowledge in area measurement for primary school students: A systematic review. STEM Education, 2(1), 47. https://doi.org/10.3934/steme.2022003
Jablonski, S., & Ludwig, M. (2023). Teaching and learning of geometry: A literature review on current developments in theory and practice. Education Sciences, 13(7). https://doi.org/10.3390/educsci13070682
Jiang, R., Liu, R., Star, J., Zhen, R., Wang, J., Hong, W., Jiang, S., Sun, Y., & Fu, X. (2021). How mathematics anxiety affects students’ inflexible perseverance in mathematics problem-solving: Examining the mediating role of cognitive reflection. British Journal of Educational Psychology, 91(1), e12364. https://doi.org/10.1111/bjep.12364
Kokkonen, T., & Schalk, L. (2021). One instructional sequence fits all? A conceptual analysis of the applicability of concreteness fading in mathematics, physics, chemistry, and biology education. Educational Psychology Review, 33(3), 797–821. https://doi.org/10.1007/s10648-020-09581-7
Lee, C.-Y., Lei, K. H., Chen, M.-J., Lee, C.-R., & Chen, C.-C. (2023). Helping low-achieving students to comprehend the area of basic geometric shapes using an enclosing-rectangle scaffold via computer-assisted instruction. Cogent Education, 10(2), 2277576. https://doi.org/10.1080/2331186X.2023.2277576
Lee, M. Y., & Lee, J.-E. (2021). Spotlight on area models: Pre-service teachers’ ability to link fractions and geometric measurement. International Journal of Science and Mathematics Education, 19(5), 1079. https://doi.org/10.1007/s10763-020-10098-2
Lehmann, T. H. (2023). Learning to measure the area of composite shapes. Educational Studies in Mathematics, 112(3), 531–565. https://doi.org/10.1007/s10649-022-10191-z
Liu, M., Bryant, D. P., Kiru, E., & Nozari, M. (2021). Geometry interventions for students with learning disabilities: A research synthesis. Learning Disability Quarterly, 44(1), 23–34. https://doi.org/10.1177/0731948719892021
Lowrie, T., & Logan, T. (2023). Spatial visualization supports students’ math: Mechanisms for spatial transfer. Journal of Intelligence, 11(6). https://doi.org/10.3390/jintelligence11060127
Maifa, T. S., Suryadi, D., & Fatimah, S. (2025). Identifying learning obstacles in proof construction for geometric transformations: Conceptual, procedural, and visualization errors. Infinity Journal, 14(3), 673–694. https://doi.org/10.22460/infinity.v14i3.p673-694
Mogan, A. D., Guang, C., Bishop, C., Zajas, M., Alvarez, S., Whitsitt, C., Wilkey, E. D., & McNeil, N. M. (2026). Bridging the divide: Comparing the efficiency and transparency of two division algorithms. Journal of Educational Psychology. https://doi.org/10.1037/edu0001046
Nilimaa, J. (2023). New examination approach for real-world creativity and problem-solving skills in mathematics. Trends in Higher Education, 2(3), 477–495. https://doi.org/10.3390/higheredu2030028
Osei, P. C., & Bjorklund, D. F. (2024). Motivating the learning process: Integrating self-determination theory into a dynamical systems framework. Educational Psychology Review, 36(3), 89. https://doi.org/10.1007/s10648-024-09934-6
Payadnya, I. P. A. A., Prahmana, R. C. I., Lo, J.-J., Noviyanti, P. L., & Atmaja, I. M. D. (2023). Designing area of circle learning trajectory based on “what-if” questions to support students’ higher-order thinking skills. Journal on Mathematics Education, 14(4), 757–780. https://doi.org/10.22342/jme.v14i4.pp757-780
Prabowo, A., Suryadi, D., Dasari, D., Juandi, D., & Junaedi, I. (2022). Learning obstacles in the making of lesson plans by prospective mathematics teacher students. Education Research International, 2022(1), 2896860. https://doi.org/10.1155/2022/2896860
Price, S., Yiannoutsou, N., & Vezzoli, Y. (2020). Making the body tangible: Elementary geometry learning through VR. Digital Experiences in Mathematics Education, 6(2), 213–232. https://doi.org/10.1007/s40751-020-00071-7
Pyke, W., Lunau, J., & Javadi, A.-H. (2025). Does difficulty moderate learning? A comparative analysis of the desirable difficulties framework and cognitive load theory. Quarterly Journal of Experimental Psychology, 78(10), 2181–2195. https://doi.org/10.1177/17470218241308143
Runnalls, C., & Hong, D. S. (2020). “Well, they understand the concept of area”: Pre-service teachers’ responses to student area misconceptions. Mathematics Education Research Journal, 32(4), 629–651. https://doi.org/10.1007/s13394-019-00274-1
Saha, M., Islam, S., Akhi, A. A., & Saha, G. (2024). Factors affecting success and failure in higher education mathematics: Students’ and teachers’ perspectives. Heliyon, 10(7). https://doi.org/10.1016/j.heliyon.2024.e29173
Sánchez, E., García-Ríos, V. N., & Sepúlveda, F. (2024). Development of high school students’ conceptions of sampling distribution in the context of learning significance tests with technology. Educational Studies in Mathematics, 117(2), 215–238. https://doi.org/10.1007/s10649-024-10330-8
Sari, Y. M., Fiangga, S., El Milla, Y. I., & Puspaningtyas, N. D. (2023). Exploring students’ proportional reasoning in solving guided-unguided area conservation problem: A case of Indonesian students. Journal on Mathematics Education, 14(2), 375–394. https://doi.org/10.22342/jme.v14i2.pp375-394
Schulz, A. (2024). Assessing student teachers’ procedural fluency and strategic competence in operating and mathematizing with natural and rational numbers. Journal of Mathematics Teacher Education, 27(6), 981–1008. https://doi.org/10.1007/s10857-023-09590-7
Seah, R., & Horne, M. (2021). Developing reasoning within a geometric learning progression: Implications for curriculum development and classroom practices. Australian Journal of Education, 65(3), 248–264. https://doi.org/10.1177/00049441211036532
Semper, J. V. O., & Iriso, I. L. (2026). Learning model based on early psychological development and the constitutive role of relationship. Education Sciences, 16(1). https://doi.org/10.3390/educsci16010116
Shekhar, P., Borrego, M., DeMonbrun, M., Finelli, C., Crockett, C., & Nguyen, K. (2020). Negative student response to active learning in STEM classrooms: A systematic review of underlying reasons. Journal of College Science Teaching, 49(6), 45–54. https://doi.org/10.1080/0047231X.2020.12290664
Skilling, K., Bobis, J., & Martin, A. J. (2020). The “ins and outs” of student engagement in mathematics: Shifts in engagement factors among high and low achievers. Mathematics Education Research Journal, 33. https://ora.ox.ac.uk/objects/uuid:a86cafb5-ec71-4bd1-a40e-fc9a5bdb11ce
Sortwell, A., Gkintoni, E., Díaz-García, J., Ellerton, P., Ferraz, R., & Hine, G. (2026). Beyond cognitive load theory: Why learning needs more than memory management. Brain Sciences, 16(1). https://doi.org/10.3390/brainsci16010109
Sugiarni, R., Herman, T., Suryadi, D., Prabawanto, S., & Maskar, S. (2025). Digital didactical design alternatif based on learning obstacles in topic of proportion: A study of pre-service mathematics teachers. Acta Scientiae, 27(3). https://doi.org/10.17648/acta.scientiae.8155
Sutarni, S., Sutama, S., 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
Szabo, Z. K., Körtesi, P., Guncaga, J., Szabo, D., & Neag, R. (2020). Examples of problem-solving strategies in mathematics education supporting the sustainability of 21st-century skills. Sustainability, 12(23). https://doi.org/10.3390/su122310113
Thurn, C. M., Hänger, B., & Kokkonen, T. (2020). Concept mapping in magnetism and electrostatics: Core concepts and development over time. Education Sciences, 10(5). https://doi.org/10.3390/educsci10050129
Torres-Peña, R. C., Peña-González, D., Lara-Orozco, J. L., Ariza, E. A., & Vergara, D. (2025). Enhancing numerical thinking through problem solving: A teaching experience for third-grade mathematics. Education Sciences, 15(6). https://doi.org/10.3390/educsci15060667
van Nooijen, C. C. A., de Koning, B. B., Bramer, W. M., Isahakyan, A., Asoodar, M., Kok, E., van Merrienboer, J. J. G., & Paas, F. (2024). A cognitive load theory approach to understanding expert scaffolding of visual problem-solving tasks: A scoping review. Educational Psychology Review, 36(1), 12. https://doi.org/10.1007/s10648-024-09848-3
Wang, Y., Zhang, J., & Pellicioni, M. S. (2025). Math anxiety is associated with skipping problems and less help-seeking behavior after error commission. Learning and Individual Differences, 120, 102681. https://doi.org/10.1016/j.lindif.2025.102681
Wijaya, A., Elmaini, & Doorman, M. (2021). A learning trajectory for probability: A case of game-based learning. Journal on Mathematics Education, 12(1), 1–16. https://doi.org/10.22342/jme.12.1.12836.1-16
Wu, Y. (2025). Unlocking mathematics success: Global lessons on student achievement, teacher satisfaction, and school environments. International Electronic Journal of Mathematics Education, 20(2). https://doi.org/10.29333/iejme/15900
Yang, K.-L., Krawitz, J., Schukajlow, S., Yang, C.-C., & Chang, Y.-P. (2024). German and Taiwanese secondary students’ mathematical modelling task value profiles and their relation to mathematical knowledge and modelling performance. European Journal of Psychology of Education, 39(3), 2969–2989. https://doi.org/10.1007/s10212-024-00866-x
Yunianto, W., Jarvis, D., Lavicza, Z., Putra, Z. H., & El-Bedewy, S. (2025). Primary school students’ problem-solving strategies in creating artworks with GeoGebra: Integrating computational thinking skills into mathematics and visual arts lessons. LUMAT: International Journal on Math, Science and Technology Education, 13(2), 1–1. https://doi.org/10.31129/LUMAT.13.2.2547
Yunianto, W., Rully Charitas Indra, P., & Crisan, C. (2021). Indonesian mathematics teachers’ knowledge of content of area and perimeter of rectangle. Journal on Mathematics Education, 12(2), 223–238. https://doi.org/10.22342/jme.12.2.13537.223-238
Zhang, D. (2021). Teaching geometry to students with learning disabilities: Introduction to the special series. Learning Disability Quarterly, 44(1), 4–10. https://doi.org/10.1177/0731948720959769
Zhang, Q. (2021). Opportunities to learn three-dimensional shapes in primary mathematics: The case of content analysis of primary mathematics textbooks in Hong Kong. Eurasia Journal of Mathematics, Science and Technology Education, 17(6). https://doi.org/10.29333/ejmste/10884
Zhang, X., Räsänen, P., Koponen, T., Aunola, K., Lerkkanen, M.-K., & Nurmi, J.-E. (2020). Early cognitive precursors of children’s mathematics learning disability and persistent low achievement: A 5-year longitudinal study. Child Development, 91(1), 7–27. https://doi.org/10.1111/cdev.13123
Zhou, Y.-J., Wang, X.-T., Chen, J., Xu, D., Cui, Y., & Wang, T. (2025). Estimation of lateral drifts of RC wall structural system by monitored coupling beams. Earthquake Engineering & Structural Dynamics, 54(9), 2325–2338. https://doi.org/10.1002/eqe.4364
Zhu, Y., Liu, X., Xiao, Y., & Sindakis, S. (2024). Mathematics anxiety and problem-solving proficiency among high school students: Unraveling the complex interplay in the knowledge economy. Journal of the Knowledge Economy, 15(4), 20516–20546. https://doi.org/10.1007/s13132-023-01688-w
Ziatdinov, R., & James R. Valles, J. (2022). Synthesis of modeling, visualization, and programming in GeoGebra as an effective approach for teaching and learning STEM topics. Mathematics, 10(3). https://doi.org/10.3390/math10030398
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