ONTOGENETIC, EPISTEMOLOGICAL, AND DIDACTIC BARRIERS IN LEARNING THE PYTHAGOREAN THEOREM IN SECONDARY SCHOOLS: A SYSTEMATIC LITERATURE REVIEW

Gesa Febrina Gesvania, Dedi Muhtadi, Sukirwan Sukirwan

Abstract


The Pythagorean Theorem is a fundamental concept in geometry; however, international assessments such as PISA and TIMSS continue to reveal persistent student difficulties stemming from conceptual, procedural, and contextual barriers. This study aims to identify these barriers, examine their interrelationships, and propose a comprehensive model through a Systematic Literature Review (SLR) following the PRISMA 2020 protocol. A total of 312 initially retrieved from Scopus, Web of Science, ERIC, Google Scholar, DOAJ, and SINTA, with 65 meeting the inclusion criteria and assessed using MMAT 2018, yielding high inter-rater reliability (Cohen's Kappa = 0.87). The results indicate that ontogenetic barriers (68%) are linked to weak prerequisite knowledge and limited visualization skills, epistemological barriers (72%) are characterized by reliance on procedural memorization, and didactic obstacles (54%) reflect insufficient contextualization in instruction. Co-occurrence analysis further demonstrates strong associations between ONT–EPI (0.82) and EPI–DID (0.74), highlighting the cyclical nature of learning barriers. To address this, the ONT–EPI–DID Model was developed, extending the frameworks of Brousseau and Duval while complementing the vicious cycle model of Hiebert. Theoretically, this study contributes a cross-national perspective on learning obstacles, and practically, it provides evidence-based recommendations for diagnostic assessment, visual scaffolding, and contextualized instruction. Overall, the findings underscore the importance of holistic pedagogical interventions to disrupt recurring cycles of difficulty and enhance students' conceptual understanding across diverse educational contexts

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References


Abrahamson, D., & Sánchez-García, R. (2016). Learning Is Moving in New Ways: The

Ecological Dynamics of Mathematics Education. Journal of the Learning Sciences,

(2), 203–239. https://doi.org/10.1080/10508406.2016.1143370

Adorni, G., Alzetta, C., Koceva, F., Passalacqua, S., & Torre, I. (2019). Towards the

Identification of Propaedeutic Relations in Textbooks (pp. 1–13).

https://doi.org/10.1007/978-3-030-23204-7_1

Adu‐Gyamfi, K., Chandler, K., & Thompson, A. (2025). Algebra story problem: The nature of

students’ obstacles. School Science and Mathematics, 125(2), 140–153.

https://doi.org/10.1111/ssm.12659

Albarracín, L., Ferrando, I., & Gorgorió, N. (2021). The Role of Context for Characterising

Students’ Strategies when Estimating Large Numbers of Elements on a Surface.

International Journal of Science and Mathematics Education, 19(6), 1209–1227.

https://doi.org/10.1007/s10763-020-10107-4

Aydın, U., & Özgeldi, M. (2019). The PISA Tasks: Unveiling Prospective Elementary

Mathematics Teachers’ Difficulties with Contextual, Conceptual, and Procedural

Knowledge. Scandinavian Journal of Educational Research, 63(1), 105–123.

https://doi.org/10.1080/00313831.2017.1324906

Bhalwankar, A., & Treur, J. (2021). An adaptive intelligent tutoring system based on

dynamic cognitive models. Computers & Education, 173, 104276.

https://doi.org/10.1016/j.compedu.2021.104276

Brousseau, G. (1997). Theory of Didactical Situations in Mathematics: Didactique des

Mathématiques. Kluwer Academic Publishers.

Buckley, J., Seery, N., & Canty, D. (2019). Investigating the use of spatial reasoning

strategies in geometric problem solving. International Journal of Technology and

Design Education, 29(2), 341–362. https://doi.org/10.1007/s10798-018-9446-3

Gesvania, Muhutadi, Sukirwan, Ontogenic, Epistemological, and Didactic…

Burte, H., Gardony, A. L., Hutton, A., & Taylor, H. A. (2017). Think3d!: Improving

mathematics learning through embodied spatial training. Cognitive Research:

Principles and Implications, 2(1), 13. https://doi.org/10.1186/s41235-017-0052-9

Chen, J., Li, L., & Zhang, D. (2021). Students With Specific Difficulties in Geometry: Exploring

the TIMSS 2011 Data With Plausible Values and Latent Profile Analysis. Learning

Disability Quarterly, 44(1), 11–22. https://doi.org/10.1177/0731948720905099

Coutat, S., Laborde, C., & Richard, P. R. (2016). L’apprentissage instrumenté de propriétés

en géométrie : propédeutique à l’acquisition d’une compétence de démonstration.

Educational Studies in Mathematics, 93(2), 195–221.

https://doi.org/10.1007/s10649-016-9684-9

Cui, X., & Guo, K. (2022). Supporting mathematics learning: a review of spatial abilities from

research to practice. Current Opinion in Behavioral Sciences, 46, 101176.

https://doi.org/10.1016/j.cobeha.2022.101176

Dagnino, F. M., Dimitriadis, Y. A., Pozzi, F., Asensio‐Pérez, J. I., & Rubia‐Avi, B. (2018).

Exploring teachers’ needs and the existing barriers to the adoption of Learning

Design methods and tools: A literature survey. British Journal of Educational

Technology, 49(6), 998–1013. https://doi.org/10.1111/bjet.12695

Dresel, M., Daumiller, M., Spear, J., Janke, S., Dickhäuser, O., & Steuer, G. (2025). Learning

from errors in mathematics classrooms: Development over 2 years in dependence of

perceived error climate. British Journal of Educational Psychology, 95(1), 180–196.

https://doi.org/10.1111/bjep.12697

Duval, R. (2017). Understanding the Mathematical Way of Thinking – The Registers of

Semiotic Representations. Springer International Publishing.

https://doi.org/10.1007/978-3-319-56910-9

Dwyer, C. P. (2023). An Evaluative Review of Barriers to Critical Thinking in Educational

and Real-World Settings. Journal of Intelligence, 11(6), 105.

https://doi.org/10.3390/jintelligence11060105

Elen, J. (2020). “Instructional disobedience”: a largely neglected phenomenon deserving

more systematic research attention. Educational Technology Research and

Development, 68(5), 2021–2032. https://doi.org/10.1007/s11423-020-09776-3

Fan, Y., Tan, Y., Raković, M., Wang, Y., Cai, Z., Shaffer, D. W., & Gašević, D. (2023). Dissecting

learning tactics in MOOC using ordered network analysis. Journal of

Computer Assisted Learning, 39(1), 154–166. https://doi.org/10.1111/jcal.12735

Ferrara, F., & Pozio, S. (2023). Entanglements of Mathematics Education Research and

Large-Scale Assessment: Rethinking Formulas as Relational. Cognition and

Instruction, 41(4), 472–493. https://doi.org/10.1080/07370008.2023.2222860

Gao, Y., Li, W., & Treur, J. (2023). Adaptive network-based models for personalized learning

support. Artificial Intelligence in Education, 36(2), 215–234.

https://doi.org/10.1007/s40593-022-00295-9

Gershman, S. J., & Daw, N. D. (2017). Reinforcement learning and episodic memory in

humans and machines. Current Opinion in Behavioral Sciences, 20, 19.

https://doi.org/10.1016/j.cobeha.2017.01.013

Volume 8, No 2, July 2026, pp. 1-18 15 JARME

Gilligan-Lee, K. A., Hawes, Z. C. K., & Mix, K. S. (2022). Spatial thinking as the missing piece

in mathematics curricula. Npj Science of Learning, 7(1), 10.

https://doi.org/10.1038/s41539-022-00128-9

Gómez-Chacón, I. M., Romero Albaladejo, I. M., & del Mar García López, M. (2016). Zigzagging in geometrical reasoning in technological collaborative environments: a

Mathematical Working Space-framed study concerning cognition and affect. ZDM,

(6), 909–924. https://doi.org/10.1007/s11858-016-0755-2

Herheim, R. (2023). On the origin, characteristics, and usefulness of instrumental and

relational understanding. Educational Studies in Mathematics, 113(3), 389–404.

https://doi.org/10.1007/s10649-023-10225-0

Hiebert, J. and G. D. A. (2007). The Effects of Classroom Mathematics Teaching on Students’

Learning (N. Balacheff, M. Cooper, R. Sutherland, & V. Warfield, Eds.; Vol. 19).

Information Age Publishing. https://doi.org/10.1007/0-306-47211-2

Kinnebrew, J. S., Segedy, J. R., & Biswas, G. (2017). Integrating Model-Driven and DataDriven Techniques for Analyzing Learning Behaviors in Open-Ended Learning

Environments. IEEE Transactions on Learning Technologies, 10(2), 140–153.

https://doi.org/10.1109/TLT.2015.2513387

Lambert, R., & Tan, P. (2020). Does disability matter in mathematics educational research?

A critical comparison of research on students with and without disabilities.

Mathematics Education Research Journal, 32(1), 5–35.

https://doi.org/10.1007/s13394-019-00299-6

Lee, H., & Bosch, N. (2024). Subtopic-specific heterogeneity in computer-based learning

behaviors. International Journal of STEM Education, 11(1), 61.

https://doi.org/10.1186/s40594-024-00519-x

Liu, A. S., & Schunn, C. D. (2017). Applying math onto mechanisms: mechanistic knowledge

is associated with the use of formal mathematical strategies. Cognitive Research:

Principles and Implications, 2(1), 6. https://doi.org/10.1186/s41235-016-0044-1

Liu, R., Patel, R., & Koedinger, K. R. (2016). Modeling common misconceptions in learning

process data. Proceedings of the Sixth International Conference on Learning

Analytics & Knowledge - LAK ’16, 369–377.

https://doi.org/10.1145/2883851.2883967

Loibl, K., Leuders, T., Glogger-Frey, I., & Rummel, N. (2024). CID: a framework for the

cognitive analysis of composite instructional designs. Instructional Science.

https://doi.org/10.1007/s11251-024-09665-9

Mareva, S., & Holmes, J. (2021). Cognitive and Academic Skills in Two Developmental

Cohorts of Different Ability Level: A Mutualistic Network Perspective. Journal of

Applied Research in Memory and Cognition.

https://doi.org/10.1016/j.jarmac.2021.08.005

Ngu, B. H., Yeung, A. S., Phan, H. P., Hong, K. S., & Usop, H. (2018). Learning to Solve

Challenging Percentage-Change Problems: A Cross-Cultural Study From a Cognitive

Load Perspective. The Journal of Experimental Education, 86(3), 362–385.

https://doi.org/10.1080/00220973.2017.1347774

Gesvania, Muhutadi, Sukirwan, Ontogenic, Epistemological, and Didactic…

Offerdahl, E. G., Arneson, J. B., & Byrne, N. (2017). Lighten the Load: Scaffolding Visual

Literacy in Biochemistry and Molecular Biology. CBE—Life Sciences Education,

(1), es1. https://doi.org/10.1187/cbe.16-06-0193

Page, M. J., McKenzie, J. E., Bossuyt, P. M., Boutron, I., Hoffmann, T. C., Mulrow, C. D.,

Shamseer, L., Tetzlaff, J. M., Akl, E. A., Brennan, S. E., Chou, R., Glanville, J., Grimshaw,

J. M., Hróbjartsson, A., Lalu, M. M., Li, T., Loder, E. W., Mayo-Wilson, E., McDonald, S.,

… Moher, D. (2021). The PRISMA 2020 statement: An updated guideline for reporting

systematic reviews. PLOS Medicine, 18(3), e1003583.

https://doi.org/10.1371/journal.pmed.1003583

Payadnya, I. P. A. A., Wulandari, I. G. A. P. A., Puspadewi, K. R., & Saelee, S. (2024). The

significance of ethnomathematics learning: a cross-cultural perspectives between

Indonesian and Thailand educators. Journal for Multicultural Education, 18(4), 508–

https://doi.org/10.1108/JME-05-2024-0049

Pettersen, A., & Nortvedt, G. A. (2018). Identifying Competency Demands in Mathematical

Tasks: Recognising What Matters. International Journal of Science and Mathematics

Education, 16(5), 949–965. https://doi.org/10.1007/s10763-017-9807-5

Rana, P., Dubey, M. K., Gupta, L. R., & Thakur, A. K. (2024). A model to combine qualitative

and quantitative measures in education for better assessment of learning outcomes.

Interactive Learning Environments, 32(10), 5947–5977.

https://doi.org/10.1080/10494820.2023.2243291

Rasimin, Semma, A. B., Zakiyuddin, Ali, M., & Helmy, M. I. (2024). Multi-dimensional

challenges in the Indonesian social science information technology-based learning:

A systematic literature review. Heliyon, 10(7), e28706.

https://doi.org/10.1016/j.heliyon.2024.e28706

Rau, M. A. (2017). Conditions for the Effectiveness of Multiple Visual Representations in

Enhancing STEM Learning. Educational Psychology Review, 29(4), 717–761.

https://doi.org/10.1007/s10648-016-9365-3

Reid O’Connor, B., & Norton, S. (2024). Exploring the challenges of learning quadratic

equations and reflecting upon curriculum structure and implementation.

Mathematics Education Research Journal, 36(1), 151–176.

https://doi.org/10.1007/s13394-022-00434-w

Salas, J. L., Wang, X. W., Tucker, M. C., & Son, J. Y. (2024). Memorization and Performance

During Pandemic Remote Instruction: Evidence of Shifts from an Interactive

Textbook. Online Learning, 28(2). https://doi.org/10.24059/olj.v28i2.3435

Sauer, P. C., & Seuring, S. (2023). How to conduct systematic literature reviews in

management research: a guide in 6 steps and 14 decisions. Review of Managerial

Science, 17(5), 1899–1933. https://doi.org/10.1007/s11846-023-00668-3

Schou, M. H., & Bikner-Ahsbahs, A. (2022). Unpacking hidden views: seven ways to treat

your formula. Educational Studies in Mathematics, 109(3), 639–659.

https://doi.org/10.1007/s10649-021-10092-7

Volume 8, No 2, July 2026, pp. 1-18 17 JARME

Selleri, P., & Carugati, F. (2018). Errare humanum est! A socio-psychological approach to a

“Climbing Mount Fuji” PISA question. European Journal of Psychology of Education,

(3), 489–504. https://doi.org/10.1007/s10212-018-0373-1

Shvarts, A., Bos, R., Doorman, M., & Drijvers, P. (2024). Reifying actions into artifacts:

process–object duality from an embodied perspective on mathematics learning.

Educational Studies in Mathematics, 117(2), 193–214.

https://doi.org/10.1007/s10649-024-10310-y

Singh, S. (2017). How to Conduct and Interpret Systematic Reviews and Meta-Analyses.

Clinical and Translational Gastroenterology, 8(5), e93.

https://doi.org/10.1038/ctg.2017.20

Starling-Alves, I., Peters, L., & Wilkey, E. D. (2025). Beyond the sum of their parts: A multidimensional approach to dyscalculia-dyslexia comorbidity integrating studies of the

brain, behavior, and genetics. Developmental Cognitive Neuroscience, 72, 101510.

https://doi.org/10.1016/j.dcn.2025.101510

Sweller, J. (2024). Cognitive load theory and individual differences. Learning and

Individual Differences, 110, 102423. https://doi.org/10.1016/j.lindif.2024.102423

Szucs, D., & Mammarella, I. C. (2024). A biopsychological–social view of mathematical

development. Current Opinion in Behavioral Sciences, 55, 101332.

https://doi.org/10.1016/j.cobeha.2023.101332

Uegatani, Y., Otani, H., Shirakawa, S., & Ito, R. (2024). Real and illusionary difficulties in

conceptual learning in mathematics: comparison between constructivist and

inferentialist perspectives. Mathematics Education Research Journal, 36(4), 895–

https://doi.org/10.1007/s13394-023-00478-6

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

Varghese, T. (2017). Proof, Proving and Mathematics Curriculum. In Transformations (Vol.

, Number 1). https://nsuworks.nova.edu/transformations

Venenciano, L. C. H., Yagi, S. L., & Zenigami, F. K. (2021). The development of relational

thinking: a study of Measure Up first-grade students’ thinking and their symbolic

understandings. Educational Studies in Mathematics, 106(3), 413–428.

https://doi.org/10.1007/s10649-020-10014-z

Villalonga Pons, J., & Deulofeu Piquet, J. (2017). La Base de Orientación en la Resolución de

Problemas: “cuando me Bloqueo o me Equivoco.” Journal of Research in Mathematics

Education, 6(3), 256–282. https://doi.org/10.17583/redimat.2017.2262

Zwanch, K., & Wilkins, J. L. M. (2021). Releasing the conceptual spring to construct

multiplicative reasoning. Educational Studies in Mathematics, 106(1), 151–170.

https://doi.org/10.1007/s10649-020-09999-4

Gesvania, Muhutadi, Sukirwan, Ontogenic, Epistemological, and Didactic…

Παπαδάμ, Μ., & Αγαλιώτης, Ι. (2021). Διερεύνηση γεωμετρικών γνώσεων μαθητών με

ήπιες εκπαιδευτικές ανάγκες. Psychology: The Journal of the Hellenic Psychological

Society, 26(1), 135. https://doi.org/10.12681/psy_hps.26234




DOI: https://doi.org/10.37058/jarme.v8i2.18349

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