Numerical Simulation of the Dynamic-Control Model of Technological Pedagogical Content Knowledge Based on Artificial Intelligence

Ebadi, M.

doi:10.22061/tej.2026.11312.3179

Document Type : Original Research Paper

Author

M. Ebadi

Department of Mathematics Education, University of Farhangian, Tehran, Iran

10.22061/tej.2026.11312.3179

Abstract

Background and Objectives: Teacher professional development in a world based on artificial intelligence, alongside other modern technologies, is among the most critical and pivotal topics in education. Artificial Intelligence-based Technological Pedagogical Content Knowledge (AI-TPACK) has recently become a focus of research for scholars in the field of teacher education. Examining the interplay between the components of AI-TPACK holds significant importance. This paper presented a dynamic control model for AI-TPACK, where a control function is applied to teachers’ knowledge of technology and artificial intelligence to analyze the mutual effects on other components. This model is expected to play a key role in guiding policymakers in making informed decisions regarding teacher professional development.
Methods: This research was an applied and developmental study focused on the design and simulation of a dynamic-control model (AI-TPACK). In this context, a model based on relevant data was first used from a reputable article to serve as the foundation for the model design. Subsequently, using a numerical simulation method, the designed model was analyzed, and its performance under various conditions was examined. This process involved several stages, including defining key variables, establishing relationships among them, and executing simulations to assess the model’s effectiveness in achieving educational and technological objectives.

Findings: The analysis of the designed dynamic model by using MATLAB indicated that the existence of solutions for the model emphasized the accuracy of the coefficients used in the state equations, which were derived from empirical data. To solve the model, two control functions were employed to manage the variable of teachers’ technological knowledge based on artificial intelligence. Additionally, the mutual influence of AI-based components on technological pedagogical content knowledge was determined through numerical solutions of the model. Detailed graphs related to each variable over time were presented.
Conclusion: Artificial intelligence, through its unique capabilities, can enhance the optimized and controlled development of AI-based technological pedagogical content knowledge (AI-TPACK) for teachers. A precise examination of teachers’ professional competencies in the age of artificial intelligence requires the design of a dynamic control model and the analysis of its behavior using advanced methods with higher accuracy. This research proposes a dynamic control model for analyzing and regulating the components of AI-based technological pedagogical content knowledge, grounded in factors related to technology and artificial intelligence. Employing a logistic control function in two distinct scenarios to examine the model’s dynamic behavior can be utilized to determine the level of investment in the application of artificial intelligence and to evaluate its effectiveness on other components of teachers’ AI-TPACK. This model, in essence, also facilitates the advancement of interdisciplinary studies in teacher.

Keywords

Main Subjects

Educational Technology - Teacher Education

COPYRIGHTS
© 2025 The Author(s). This is an open-access article distributed under the terms and conditions of the Creative Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) (https://creativecommons.org/licenses/by-nc/4.0/)

References

[1] Cleary, Yvonne. Fostering communities of inquiry and connectivism in online technical communication programs and courses. Journal of Technical Writing and Communications. 2021, 51(1): 11-30

https://doi.org/10.1177/0047281620977138

[2] Bakhshi Khilgavani V., Aliabadi K., Nili M.R., Borzoian S., Delavar A. Exploring the elements of the educational model for connectivism teaching-learning environment. Tech. Edu. J. 2023, 17(4): 837-848

http:// doi.org/10.22061/tej.2023.9623.2873

[3] Barnett, John, McPherson, Vance and Sandieson Rachel M., Connected teaching and learning: The uses and implications of connectivism in an online class. Australasian Journal of Educational Technology. 2013, 29(5): 685-698

[4] Seimens G. Connectivism: A learning theory for the digital age. International journal of Industrial Technology and Distance Learning. 2005; 2(1): 3-10

[5] Prensky M. Digital natives, digital immigrants’ Part 2: Do they really think differently? On horizon. 2001, Nov. 1; 9(6): 1-6.

http://doi.org/10.1108/10748120110424843

[6] Garzón Artacho E, Martínez TS, Ortega Martín JL, Marín Marín JA, Gómez García G. Teacher training in lifelong learning—The importance of digital competence in the encouragement of teaching innovation. Sustainability. 2020, 12(7):2852. https://doi.org/10.3390/su12072852

[7] Instituto Nacional de Tecnologías Educativas y Formación del Profesorado (INTEF). Marco de Competencia Digital; Ministerio de Educación: Ciencia y Deportes, Madrid, Spain, 2017. [Google Scholar]

[8] Ferrari, A. Digital Competence in Practice: An Analysis of Frameworks; European Commission Joint Research Centre (JRC): Seville, Spain, 2012. [Google Scholar]

[9] Alizadehjamal M, Shahvarani A, Iranmanesh A, Tehranian A. [The effect of mathematical education based on TPACK model on changing teachers' beliefs]. Tech. Edu. J. 2020; 14(3): 591-602. http://dx.doi.org/10.22061/jte.2019.4990.2148

[10] Koehler, M. J. ‎‎& Mishra, P. Introducing technological pedagogical content knowledge. In AACTE committee on innovation and technology (Eds). Handbook of technological pedagogical content knowledge (TPCK) for ‎educators, 2008,‎ pp. 3-29. New York: Routledge.‎

[11] Koehler, M., & Mishra, P. What is technological pedagogical content knowledge? Contemporary Issues in Technology and Teacher Education, 2009, 9(1), 60-70.

[12] Wijaya, T.T.; Weinhandl, R. Factors Influencing Students’ Continuous Intentions for Using Micro-Lectures in the Post-COVID-19 Period: A Modification of the UTAUT-2 Approach. Electronics 2022, 11, 1924.

[13] Luckin, R., George, K., & Cukurova, M. AI for school teachers. 2022, CRC Press.

[14] Luan, H., Geczy, P., Lai, H., Gobert, J., Yang, S. J., Ogata, H., … Tsai, C. C. Challenges and future directions of big data and artificial intelligence in education. Frontiers in Psychology,2020, 2748. https://doi.org/10.3389/fpsyg.2020.580820

[15] Chen, X., Zou, D., Xie, H., & Cheng, G. Twenty years of personalized language learning: Topic modeling and knowledge mapping. Educational Technology & Society, 2021, 24(1), 205–222.

[16] Jobirovich, Y.M. The Role of digital technologies in reform of the education system. Am. J.Soc. Sci. Educ. Innov. 2021, 3, 461–465.

[17] Yimin Ning , Cheng Zhang, Binyan Xu, Ying Zhou and Tommy Tanu Wijaya.Teachers’ AI-TPACK: Exploring the relationship between knowledge elements sustainability, 2024, 16, 978.

https://doi.org/10.3390/ su16030978

[18] Kong, S.-C.; Lai, M.; Li, Y. Scaling up a teacher development program for sustainable computational thinking education: TPACK surveys, concept tests and primary school visits. Comput. Educ. 2023, 194, 104707.

[19] Elmaadaway MAN, Abouelenein YAM. In-service teachers' TPACK development through an adaptive e-learning environment (ALE). Educ Inf Technol (Dordr). 2022, Dec 20:1-26.

doi: 10.1007/s10639-022-11477-8

[20] Ismail Celik, Towards Intelligent-TPACK: An empirical study on teachers’ professional knowledge to ethically integrate artificial intelligence (AI)-based tools into education, Computers in Human Behavior, 2023, Volume 138, 107468,

https://doi.org/10.1016/j.chb.2022.107468.

[21] Li, M., Li, B. Unravelling the dynamics of technology integration in mathematics education: A structural equation modelling analysis of TPACK components. Educ Inf Technol, 2024, 29, 23687–23715.

https://doi.org/10.1007/s10639-024-12805-w

[22] Voogt, J., Fisser, P., Pareja Roblin, N., Tondeur, J., & van Braak, J. Technological pedagogical content knowledge - a review of the literature. Journal of Computer Assisted Learning, 2013, 29(2), 109–121.

https://doi.org/10.1111/j.1365-2729.2012.00487.x

[23] Mishra, P. Considering contextual knowledge: The TPACK diagram gets an upgrade. Journal of Digital Learning in Teacher Education, 2019, 35(2), 76–78.

https://doi.org/10.1080/21532974.2019.1588 611

[24] Mishra, P., & Koehler, M. J. Technological pedagogical content knowledge: A framework for teacher knowledge. Teachers College Record, 2006, 108(6), 1017–1054.

https://doi.org/10.1111/j.14679620.2006.00684.x.