International Journal of

ADVANCED AND APPLIED SCIENCES

EISSN: 2313-3724, Print ISSN: 2313-626X

Frequency: 12

line decor
  
line decor

 Volume 13, Issue 1 (January 2026), Pages: 190-200

----------------------------------------------

 Original Research Paper

Integration of the TPACK approach and augmented reality technology in a hybrid learning model to improve the understanding of geometry concepts

 Author(s): 

 Heni Pujiastuti 1, *, Rudi Haryadi 2, Dhafid W. Utomo 3, Rohman Rohman 4

 Affiliation(s):

  1Department of Mathematics Education, Faculty of Training Teachers and Education, Universitas Sultan Ageng Tirtayasa, Serang, Indonesia
  2Department of Physics Education, Faculty of Training Teachers and Education, Universitas Sultan Ageng Tirtayasa, Serang, Indonesia
  3Department of English Education, Faculty of Training Teachers and Education, Universitas Sultan Ageng Tirtayasa, Serang, Indonesia
  4Department of English Education, Faculty of Training Teachers and Education, Universitas Islam Negeri Sultan Maulana Hasanuddin Banten, Serang, Indonesia

 Full text

    Full Text - PDF

 * Corresponding Author. 

   Corresponding author's ORCID profile:  https://orcid.org/0000-0002-2968-4990

 Digital Object Identifier (DOI)

  https://doi.org/10.21833/ijaas.2026.01.020

 Abstract

This study develops and evaluates the effectiveness of a hybrid learning model based on Technological Pedagogical Content Knowledge (TPACK) and Augmented Reality (AR) to improve junior high school students’ understanding of geometry concepts. The study addresses low student achievement in geometry, particularly in understanding shapes, their properties, and the calculations of three-dimensional figures. A Design-Based Research (DBR) approach was applied through five stages: problem identification, solution design, development and validation, limited implementation, and evaluation. The participants were 80 eighth-grade students divided into an experimental group and a control group, each consisting of 40 students. Expert validation showed that the learning materials and AR media were highly valid, with an average score of 87.3%. The model was implemented over 10 learning sessions using a combination of face-to-face and online instruction supported by AR media and a learning management system. The results showed that the experimental group achieved significantly higher conceptual understanding than the control group, with an average N-Gain score of 0.78 (high category) compared to 0.41 (medium category). Statistical analysis using a t-test confirmed a significant difference between the two groups. Student questionnaire results also indicated high satisfaction and learning engagement. These findings demonstrate that AR-based hybrid learning effectively enhances students’ spatial visualization and understanding of geometry concepts and supports the integration of digital technology in 21st-century education.

 © 2026 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords

 Hybrid learning, Augmented reality, Geometry learning, TPACK framework, Conceptual understanding

 Article history

 Received 31 July 2025, Received in revised form 13 December 2025, Accepted 12 January 2026

 Acknowledgment

This work was funded by the Directorate of Research and Community Service (Direktorat Penelitian dan Pengabdian kepada Masyarakat), Ministry of Higher Education, Science, and Technology (Kementerian Pendidikan Tinggi, Sains, dan Teknologi), Republic of Indonesia, under the Applied Research - Model Output (Penelitian Terapan – Luaran Model) scheme. 

 Compliance with ethical standards

 Ethical considerations

Informed consent was a mandatory ethical procedure for all participants involved in the human questionnaire. This process ensured that every respondent was fully briefed on the purpose, nature, risks, and benefits of the study before agreeing to participate.

 Conflict of interest: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

 Citation:

 Pujiastuti H, Haryadi R, Utomo DW, and Rohman R (2026). Integration of the TPACK approach and augmented reality technology in a hybrid learning model to improve the understanding of geometry concepts. International Journal of Advanced and Applied Sciences, 13(1): 190-200

  Permanent Link to this page

 Figures

 No Figure

 Tables

  Table 1 Table 2 Table 3  Table 4  Table 5  Table 6  Table 7  Table 8   Table 9   Table 10

----------------------------------------------   

 References (34)

  1. Akremi H, Ayadi MG, and Zghal S (2024). Hyperbolic geometry embedding for complex ontology matching. Procedia Computer Science, 246: 3512-3521.  https://doi.org/10.1016/j.procs.2024.09.205    [Google Scholar]
  2. Alharbi AA (2025). Cognitive learning approach to enhance university students' visualization of molecular geometry in chemical compounds: A case study in Saudi Arabia. Journal of Radiation Research and Applied Sciences, 18(1): 101283.  https://doi.org/10.1016/j.jrras.2024.101283    [Google Scholar]
  3. Baabdullah AM, Alsulaimani AA, Allamnakhrah A, Alalwan AA, Dwivedi YK, and Rana NP (2022). Usage of augmented reality (AR) and development of e-learning outcomes: An empirical evaluation of students’ e-learning experience. Computers & Education, 177: 104383.  https://doi.org/10.1016/j.compedu.2021.104383    [Google Scholar]
  4. Batool H, Al-Otaibi S, and Khan M (2025). Decision making model for evaluation of TPACK knowledge constructs as critical success factors for language learning classes. Heliyon, 11(2): e42061.  https://doi.org/10.1016/j.heliyon.2025.e42061    [Google Scholar] PMid:39911429 PMCid:PMC11795055
  5. Bujak KR, Radu I, Catrambone R, MacIntyre B, Zheng R, and Golubski G (2013). A psychological perspective on augmented reality in the mathematics classroom. Computers & Education, 68: 536-544.  https://doi.org/10.1016/j.compedu.2013.02.017    [Google Scholar]
  6. Cabero-Almenara J, Fernández-Batanero JM, and Barroso-Osuna J (2019). Adoption of augmented reality technology by university students. Heliyon, 5(5): e01597.  https://doi.org/10.1016/j.heliyon.2019.e01597    [Google Scholar] PMid:31193247 PMCid:PMC6522688
  7. Caswell H, Alidoust S, and Corcoran J (2025). Planning for livable compact vertical cities: A quantitative systematic review of the impact of urban geometry on thermal and visual comfort in high-rise precincts. Sustainable Cities and Society, 119: 106007.  https://doi.org/10.1016/j.scs.2024.106007    [Google Scholar]
  8. Chung S and Abbott LF (2021). Neural population geometry: An approach for understanding biological and artificial neural networks. Current Opinion in Neurobiology, 70: 137-144.  https://doi.org/10.1016/j.conb.2021.10.010    [Google Scholar] PMid:34801787 PMCid:PMC10695674
  9. De La Rosa Á and Ruiz G (2025). A new approach to the study of the size and the geometry effect on compressive strength in concrete. Results in Engineering, 25: 104261.  https://doi.org/10.1016/j.rineng.2025.104261    [Google Scholar]
  10. del Cerro Velázquez F and Morales Méndez G (2021). Application in augmented reality for learning mathematical functions: A study for the development of spatial intelligence in secondary education students. Mathematics, 9(4): 369.  https://doi.org/10.3390/math9040369    [Google Scholar]
  11. Elzohbi M and Zhao R (2024). Poems, pulses and polygons: How classical Arabic poetry resonates with music and geometry. Procedia Computer Science, 244: 432-442.  https://doi.org/10.1016/j.procs.2024.10.218    [Google Scholar]
  12. Heath MK and Moore S (2024). Locating TPACK XK between theory and practice: Reflective practice, applied ethics, and technoskeptical dispositions. Computers and Education Open, 7: 100204.  https://doi.org/10.1016/j.caeo.2024.100204    [Google Scholar]
  13. Heinrich L, Fillingim KB, Nandwana P, Kannan R, Burl A, Saldaña C, and Feldhausen T (2025). Impact of lead on an axisymmetric, single bead blown powder DED overhung geometry. Journal of Manufacturing Processes, 142: 44-57.  https://doi.org/10.1016/j.jmapro.2025.03.046    [Google Scholar]
  14. Huang L, Yu X, Niu L, and Feng Z (2023). Solving algebraic problems with geometry diagrams using syntax-semantics diagram understanding. Computers, Materials & Continua, 77(1): 516-539.  https://doi.org/10.32604/cmc.2023.041206    [Google Scholar]
  15. Iftene A and Trandabăț D (2018). Enhancing the attractiveness of learning through augmented reality. Procedia Computer Science, 126: 166-175.  https://doi.org/10.1016/j.procs.2018.07.220    [Google Scholar]
  16. Kim H, Yoo H, Paik K, and Kim DH (2025). Qualitative assessment model for longitudinal riverbed erosion and deposition based on suspended sediment impacts and hydraulic geometry relationship. Journal of Hydrology, 657: 133049.  https://doi.org/10.1016/j.jhydrol.2025.133049    [Google Scholar]
  17. Libertus M, Miller P, Zippert EL, Bachman HJ, and Votruba-Drzal E (2024). Predicting individual differences in preschoolers’ numeracy and geometry knowledge: The role of understanding abstract relations between objects and quantities. Journal of Experimental Child Psychology, 247: 106035.  https://doi.org/10.1016/j.jecp.2024.106035    [Google Scholar] PMid:39128443 PMCid:PMC12422785
  18. Mohammadpour E and Maroofi Y (2025). The disparity between performance-based and self-reported measures of TPACK: Implications for teacher education and professional development. Computers in Human Behavior Reports, 17: 100554.  https://doi.org/10.1016/j.chbr.2024.100554    [Google Scholar]
  19. Narasimhamurthy SK and Praveen J (2024). Cosmological constant roll of inflation within Finsler-Barthel-Kropina geometry: A geometric approach to early universe dynamics. New Astronomy, 108: 102187.  https://doi.org/10.1016/j.newast.2024.102187    [Google Scholar]
  20. Peschl R, Peschl H, Bortolin L, and Reid V (2023). A case of design based research methodology to create curriculum for an entrepreneurial thinking course. The International Journal of Management Education, 21(3): 100838.  https://doi.org/10.1016/j.ijme.2023.100838    [Google Scholar]
  21. Praveen J and Narasimhamurthy SK (2025). The role of Finsler-Randers geometry in shaping anisotropic metrics and thermodynamic properties in black holes theory. New Astronomy, 119: 102404.  https://doi.org/10.1016/j.newast.2025.102404    [Google Scholar]
  22. Pujiastuti H and Haryadi R (2023a). Enhancing mathematical literacy ability through guided inquiry learning with augmented reality. Journal of Education and E-Learning Research, 10(1): 43-50.  https://doi.org/10.20448/jeelr.v10i1.4338    [Google Scholar]
  23. Pujiastuti H and Haryadi R (2023b). Hybrid learning impact with augmented reality to improve higher order thinking skills of students. International Journal of Advanced and Applied Sciences, 10(12): 7-18.  https://doi.org/10.21833/ijaas.2023.12.002    [Google Scholar]
  24. Pujiastuti H and Haryadi R (2024). The effectiveness of using augmented reality on the geometry thinking ability of junior high school students. Procedia Computer Science, 234: 1738-1745.  https://doi.org/10.1016/j.procs.2024.03.180    [Google Scholar]
  25. Sarfaraz W, Yigit G, Barreira R, Remaki L, Alhazmi M, and Madzvamuse A (2024). Understanding the dual effects of linear cross-diffusion and geometry on reaction–diffusion systems for pattern formation. Chaos, Solitons & Fractals, 186: 115295.  https://doi.org/10.1016/j.chaos.2024.115295    [Google Scholar]
  26. Schubatzky T, Burde JP, Große-Heilmann R, Lachner A, Riese J, and Weiler D (2025). From knowledge to intention: The role of TPACK and self-efficacy in technology integration. Computers and Education Open, 8: 100246.  https://doi.org/10.1016/j.caeo.2025.100246    [Google Scholar]
  27. Shambare B and Simuja C (2024). Unveiling the TPACK pathways: Technology integration and pedagogical evolution in rural South African schools. Computers and Education Open, 7: 100206.  https://doi.org/10.1016/j.caeo.2024.100206    [Google Scholar]
  28. Teo T, Khazaie S, and Derakhshan A (2022). Exploring teacher immediacy-(non)dependency in the tutored augmented reality game-assisted flipped classrooms of English for medical purposes comprehension among the Asian students. Computers & Education, 179: 104406.  https://doi.org/10.1016/j.compedu.2021.104406    [Google Scholar]
  29. Tripathi P and Lee SJ (2025). Particle geometry space: An integrated characterization of particle shape, surface area, volume, specific surface, and size distribution. Transportation Geotechnics, 52: 101579.  https://doi.org/10.1016/j.trgeo.2025.101579    [Google Scholar]
  30. Wampler CW and Plecnik M (2025). Finding mechanisms of exceptional mobility using numerical algebraic geometry. Mechanism and Machine Theory, 211: 106033.  https://doi.org/10.1016/j.mechmachtheory.2025.106033    [Google Scholar]
  31. Xu G, García A, Jia M, and Monsalve-Serrano J (2021). Computational optimization of the piston bowl geometry for the different combustion regimes of the dual-mode dual-fuel (DMDF) concept through an improved genetic algorithm. Energy Conversion and Management, 246: 114658.  https://doi.org/10.1016/j.enconman.2021.114658    [Google Scholar]
  32. Yang Z and Lee YY (2025). Challenges and opportunities of design-based research in applied linguistics: Insights from a scoping review. Research Methods in Applied Linguistics, 4(1): 100178.  https://doi.org/10.1016/j.rmal.2024.100178    [Google Scholar]
  33. Yao X (2020). Unpacking learner’s growth in geometric understanding when solving problems in a dynamic geometry environment: Coordinating two frames. The Journal of Mathematical Behavior, 60: 100803.  https://doi.org/10.1016/j.jmathb.2020.100803    [Google Scholar]
  34. Zhu W, Jiang Z, and He Y (2025). Geometry-sensitive semantic modeling in visual and visual-language domains for image captioning. Engineering Applications of Artificial Intelligence, 147: 110330.  https://doi.org/10.1016/j.engappai.2025.110330    [Google Scholar]