AI artifacts in the mathematics didactical tetrahedron: A developed model

Joseph Mani; Chia Zargeh

doi:10.29333/ejmste/16307

Full Text (PDF)

Joseph Mani ¹ , Chia Zargeh ¹ ^*

More Detail

¹ Modern College of Business and Science, Muscat, OMAN^* Corresponding Author

Abstract

This paper studies the well-known model for didactic situations called socio-didactical tetrahedron in mathematics education. This study presents a developed model and considers a new vertex for artificial intelligence artifacts. Additionally, it emphasizes the mediator role of teachers in creating a favourable environment in student-centered mathematics education in the era of large language models. The idea of our proposed model comes from the differences between information technology artifacts and artificial intelligence artifacts.

Keywords

mathematics education
artificial intelligence
IT artifacts
AI artifacts
socio-didactical tetrahedron

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Review Article

EURASIA J Math Sci Tech Ed, Volume 21, Issue 5, May 2025, Article No: em2630

https://doi.org/10.29333/ejmste/16307

Publication date: 01 May 2025

Article Views: 199

Article Downloads: 136

Open Access References How to cite this article

References

Albano, G., Antonini, S., Coppola, C., Dello Iacono, U., & Pierri, A. (2021). “Tell me about”: A logbook of teachers’ changes from face-to-face to distance mathematics education. Educational Studies in Mathematics, 108(1-2), 15-34. https://doi.org/10.1007/s10649-021-10108-2
Amirali, M., & Halai, A. (2021). Teachers’ perceptions about mathematics in a socio-religious context: A case from Pakistan. Eurasia Journal of Mathematics Science and Technology Education, 17(12), Article em2059. https://doi.org/10.29333/ejmste/11434
Ansari, A. N., Ahmad, S., & Bhutta, S. M. (2023). Mapping the global evidence around the use of ChatGPT in higher education: A systematic scoping review. Education and Information Technologies, 29(9), 11281-11321. https://doi.org/10.1007/s10639-023-12223-4
Appiah, J. B., Korkor, S., Arthur, Y. D., & Obeng, B. A. (2022). Mathematics achievement in high schools, the role of the teacher-student relationship, students’ self-efficacy, and students’ perception of mathematics. International Electronic Journal of Mathematics Education, 17(3), Article em0688. https://doi.org/10.29333/iejme/12056
Baccaglini-Frank, A., Carotenuto, G., Funghi, S., Lisarelli, G., & Miragliotta, E. (2024). Digital artifacts in mathematics education: How can we study the learning processes they promote? Bollettino dell’Unione Matematica Italiana, 1-32. https://doi.org/10.1007/s40574-024-00439-2
Bagno, E., Dana-Picard, T., & Reches, S. (2024). ChatGPT in teaching linear algebra: Strides forward, steps to go. Open Education Studies, 6(1), 20240031. https://doi.org/10.1515/edu-2024-0031
Bawack, R., Fosso Wamba, S., & Carillo, K. D. (2019). From IT to AI artifact: Implications for IS research on AI adoption and use. DIGIT 2019 Proceedings, 6. https://aisel.aisnet.org/digit2019/6
Bonne, L. (2016). New Zealand students’ mathematics-related beliefs and attitudes: Recent evidence. New Zealand Journal of Educational Studies, 51(1), 69-82. https://doi.org/10.1007/s40841-016-0035-2
Botana, F., & Recio, T. (2024). Geometric loci and ChatGPT: Caveat emptor! Computation, 12(2), Article 30. https://doi.org/10.3390/computation12020030
Cao, Y., Zhang, S., Chan, M. C. E., & Kang, Y. (2021). Post-pandemic reflections: Lessons from Chinese mathematics teachers about online mathematics instruction. Asia Pacific Education Review, 22, 157-168. https://doi.org/10.1007/s12564-021-09694-w
Churchhouse, R. F., Cornu, B., Howson, A. G., Kahane, J.-P., van Lint, J. H., Pluvinage, F., Ralston, A., & Yamaguti, M. (1984). The influence of computers and informatics on mathematics and its teaching. Cambridge University Press. https://doi.org/10.1017/CBO9781139013482
Coppola, C., Di Martino, P., Pacelli, T., & Sabena, C. (2012). Primary teachers’ effect: A crucial variable in the teaching of mathematics. Nordic Studies in Mathematics Education, 17(3-4), 101-118. https://doi.org/10.7146/nomad.v17i3-4.148477
Dasari, D., Hendriyanto, A., Sahara, S., Suryadi, D., Muhaimin, L. H., Chao, T., & Fitriana, L. (2024). ChatGPT in didactical tetrahedron, does it make an exception? A case study in mathematics teaching and learning. Frontiers in Education 8, Article 1295413. https://doi.org/10.3389/feduc.2023.1295413
DeCoito, I., & Richardson, T. (2018). Teachers and technology: Present practice and future directions. Contemporary Issues in Technology and Teacher Education, 18(2), 362-378.
Drijvers, P., & Sinclair, N. (2024). The role of digital technologies in mathematics education: Purposes and perspectives. ZDM-Mathematics Education, 56(2), 239-248. https://doi.org/10.1007/s11858-023-01535-x
Drijvers, P., & Trouche, L. (2008). From artifacts to instruments. Research on technology and the teaching and learning of mathematics, 2, 363-391.
Dwivedi, Y. K., Kshetri, N., Hughes, L., Slade, E. L., Jeyaraj, A., Kar, A. K., Baabdullah, A. M., Koohang, A., Raghavan, V., Ahuja, M.,Albanna, H., Albashrawi, M. A., Al-Busaidi, A. S., Balakrishnan, J., Barlette, Y., Basu, S., Bose, I., Brooks, L., Buhalis, D., ... Wright, R. (2023). “So, what if ChatGPT wrote it?” Multidisciplinary perspectives on opportunities, challenges, and implications of generative conversational AI for research, practice, and policy. International Journal of Information Management, 71, Article 102642. https://doi.org/10.1016/j.ijinfomgt.2023.102642
Einarsson, H., Lund, S. H., & Jónsdóttir, A. H. (2024). Application of ChatGPT for automated problem reframing across academic domains. Computers and Education: Artificial Intelligence, 6, Article 100194. https://doi.org/10.1016/j.caeai.2023.100194
Farooq, U., & Grudin, J. (2016). Human-computer integration. Interactions, 23(6), 26-32. https://doi.org/10.1145/3001896
Flint, A., Rubie-Davies, C. M., & Peterson, E. (2024). Teacher views of relationships between their teaching practices and beliefs, the school context, and student achievement. New Zealand Journal of Educational Studies, 59(1), 157-173. https://doi.org/10.1007/s40841-024-00321-x
Funes, J. O., Parada, B. D., Julian, P. M. D., & Burgos, A. (2024). Geogebra applets and Gemini artificial intelligence in separable variable differential equations in engineering students of Antofagasta, Chile. Mathematics and Computer Science: Contemporary Developments, 5, 116-124. https://doi.org/10.9734/bpi/mcscd/v5/2337
Ghavifekr, S., & Rosdy, W. A. W. (2015). Teaching and learning with technology: Effectiveness of ICT integration in schools. International journal of research in education and science, 1(2), 175-191. https://doi.org/10.21890/ijres.23596
Ginting, D., Sabudu, D., Barella, Y., Madkur, A., Woods, R., & Kemala Sari, M. (2024). Student-centered learning in the digital age: In-class adaptive instruction and best practices. International Journal of Evaluation and Research in Education, 13(3), 2006-2019. https://doi.org/10.11591/ijere.v13i3.27497
Gonzalez Thompson, A. (1984). The relationship of teachers’ conceptions of mathematics and mathematics teaching to instructional practice. Educational studies in mathematics, 15(2), 105-127. https://doi.org/10.1007/BF00305892
Green, B. N., Johnson, C. D., & Adams, A. (2006). Writing narrative literature reviews for peer-reviewed journals: Secrets of the trade. Journal of chiropractic medicine, 5(3), 101-117. https://doi.org/10.1016/S0899-3467(07)60142-6
Haddaway, N. R., Page, M. J., Pritchard, C. C., & McGuinness, L. A. (2022). PRISMA2020: An R package and shiny app for producing PRISMA 2020‐compliant flow diagrams, with interactivity for optimised digital transparency and open synthesis. Campbell systematic reviews, 18(2), Article e1230. https://doi.org/10.1002/cl2.1230
Hillmayr, D., Ziernwald, L., Reinhold, F., Hofer, S. I., & Reiss, K. M. (2020). The potential of digital tools to enhance mathematics and science learning in secondary schools: A context-specific meta-analysis. Computers & Education, 153, Article 103897. https://doi.org/10.1016/j.compedu.2020.103897
Hjelmborg, M. D., Larsen, D. M., Jensen, M. E., Gents, S. D., Christensen, M. S., Junge, L., & Hansen, R. (2020). From teachers’ predispositions to different socio-didactical situations. IARTEM e-Journal, 12(1). https://doi.org/10.21344/iartem.v12i1.728
Hossein-Mohand, H., Gómez-García, M., Trujillo-Torres, J. M., Hossein-Mohand, H., & Boumadan-Hamed, M. (2021). Uses and resources of technologies by mathematics students prior to COVID-19. Sustainability, 13(4), Article 1630. https://doi.org/10.3390/su13041630
Huang, W., & Sutherland, S. M. (2022). The impact of technology artifacts on mathematics classroom discourse. Digital Experiences in Mathematics Education, 8(3), 317-351. https://doi.org/10.1007/s40751-022-00114-1
Hwang, S., & Son, T. (2021). Students’ attitude toward mathematics and its relationship with mathematics achievement. Journal of Education and e-Learning Research, 8(3), 272–280. https://doi.org/10.20448/journal.509.2021.83.272.280.
Iqbal, N., Ahmed, H., & Azhar, K. A. (2022). Exploring teachers’ attitudes towards using ChatGPT. Global Journal for Management and Administrative Sciences, 3(4), 97-111. https://doi.org/10.46568/gjmas.v3i4.163
Kasneci, E., Sessler, K., Küchemann, S., Bannert, M., Dementieva, D., Fischer, F., Gasser, U., Groh, G., Günnemann, S., Hüllermeier, E., Krusche, S., Kutynniok, G., Michaeli, T., Nerdel, C., Pfeffer, J., Poquet, O., Sailer, M., Schmidt, A., Seidel, T., … Kasneci, G. (2023). ChatGPT for good? On opportunities and challenges of large language models for education. Learning and Individual Differences, 103, Article 102274 https://doi.org/10.1016/j.lindif.2023.102274
Kim, J., Ham, Y., & Lee, S.-S. (2024). Differences in student-AI interaction process on a drawing task: Focusing on students’ attitude towards AI and the level of drawing skills. Australasian Journal of Educational Technology, 40(1), 19-41. https://doi.org/10.14742/ajet.8859
Kim, J., Lee, H., & Cho, Y. H. (2022). Learning design to support student-AI collaboration: Perspectives of leading teachers for AI in education. Education and Information Technologies, 27, 6069-6104. https://doi.org/10.1007/s10639-021-10831-6
Lagrange, J.-B., Artigue, M., Laborde, C., & Trouche, L. (2003). Technology and mathematics education: A multidimensional study of the evolution of research and innovation. In A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Second international handbook of mathematics education (pp. 237-269). Springer. https://doi.org/10.1007/978-94-010-0273-8_9
Li, X., Gould, T., & Zaki, R. (2024). The impact of artificial intelligence on learners and teachers: A mathematics education perspective. In S. Papadakis, & M. Kalogiannakis (Eds.), Education, development and intervention (Vol. 23). Springer. https://doi.org/10.1007/978-3-031-60713-4_9
Lo, C. K. (2023). What is the impact of ChatGPT on education? A rapid review of the literature. Education Sciences, 13(4), Article 410. https://doi.org/10.3390/educsci13040410
Matić, L. J., & Gracin, D. G. (2015). Teacher and textbook: Reflection on the SDT-model. In CERME 9 - Ninth Congress of the European Society for Research in Mathematics Education (pp. 3072-3076). Charles University in Prague, Faculty of Education.
Matić, L. J., & Gracin, D. G. (2016). The use of the textbook as an artefact in the classroom. Journal für Mathematik-Didaktik, 37(Suppl 1), 349-374. https://doi.org/10.1007/s13138-016-0091-7
Mohamed, M. Z. B., Hidayat, R., Suhaizi, N. N. B., Sabri, N. B. M., Mahmud, M. K. H. B., & Baharuddin, S. N. B. (2022). Artificial intelligence in mathematics education: A systematic literature review. International Electronic Journal of Mathematics Education, 17(3), Article em0694. https://doi.org/10.29333/iejme/12132
Mota Lopes, A. M., & De Magalhães Netto, J. F. (2021). Designing pedagogical agents toward the recommendation and intervention based on students’ actions in an ITS. IEEE Frontiers in Education Conference. https://doi.org/10.1109/FIE49875.2021.9637406
Ní Shé, C., Ní Fhloinn, E., & Mac an Bhaird, C. (2023). Student engagement with technology-enhanced resources in mathematics in higher education: A review. Mathematics, 11(3), Article 787. https://doi.org/10.3390/math11030787
Olive, J., Makar, K., Hoyos, V., Kor, L. K., Kosheleva, O., & Sträßer, R. (2010). Mathematical knowledge and practices resulting from access to digital technologies. In New ICMI study series (Vol. 13, pp. 133-177). International Commission on Mathematical Instruction. https://doi.org/10.1007/978-1-4419-0146-0_8
Paliwal, V., & Patel, S. (2025). Can artificial intelligence facilitate mathematics instruction? In A. Walters (Ed.), Transforming special education through artificial intelligence (pp. 223-244). IGI Global Scientific Publishing. https://doi.org/10.4018/979-8-3693-5538-1.ch008
Pepin, B., Kock, Z., & Rezat, S. (2024). Toward student agency in the selection and use of digital resources for learning and studying mathematics. In B. Pepin, G. Gueudet, & J. Choppin (Eds.), Handbook of digital resources in mathematics education (pp. 1-29). Springer International Handbooks of Education. Springer. https://doi.org/10.1007/978-3-030-95060-6_26-2
Pournara, C. (2013). Teachers’ knowledge of teaching compound interest. Pythagoras, 34(2), 1-10. https://doi.org/10.4102/pythagoras.v34i2.238
Prediger, S., Arzarello, F., Bosch, M., & Lenfant, A. (2008). Comparing, combining, coordinating– Networking strategies for connecting theoretical approaches. Thematic issue of ZDM-Mathematics Education, 40(2), 163-327. https://doi.org/10.1007/s11858-008-0093-0
Rai, A., Constantinides, P., & Sarker, S. (2019). Next-generation digital platforms: Toward human-AI hybrids. MIS Quarterly, 43(1), 3-9.
Raman, R., Mandal, S., Das, P., Kaur, T., Sanjanasri, J. P., & Nedungadi, P. (2024). Exploring university students’ adoption of ChatGPT using the diffusion of innovation theory and sentiment analysis with gender dimension. Human Behavior and Emerging Technologies, 2024(1), 3085910. https://doi.org/10.1155/2024/3085910Remillard, J. T., & Heck, D. J. (2014). Conceptualizing the curriculum enactment process in mathematics education. ZDM, 46, 705-718. https://doi.org/10.1007/s11858-014-0600-4
Rezat, S., & Geiger, V. (2023). The role of digital technologies in transforming student learning landscapes. In Handbook of digital resources in mathematics education (pp. 1-22). Cham: Springer International Publishing. https://doi.org/10.1007/978-3-030-95060-6_21-1
Rezat, S., & Sträßer, R. (2012). From the didactical triangle to the socio-didactical tetrahedron: Artifacts as fundamental constituents of the didactical situation. ZDM, 44, 641-651. https://doi.org/10.1007/s11858-012-0448-4
Sträßer, R. (2009). Instruments for learning and teaching mathematics. An attempt to theorize about the role of textbooks, computers and other artefacts to teach and learn mathematics. In Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 67-81). Thessaloniki, Greece: International Group for the Psychology of Mathematics Education.
Tall, D. (1986). Using the computer as an environment for building and testing mathematical concepts: A tribute to Richard Skemp. Papers in honour of Richard Skemp, 21-36.
Van Vaerenbergh, S., & Pérez-Suay, A. (2022). A classification of artificial intelligence systems for mathematics education. In Mathematics education in the age of artificial intelligence: How artificial intelligence can serve mathematical human learning (pp. 89-106). Cham: Springer International Publishing. https://doi.org/10.1007/978-3-030-86909-0_5
Vygotsky, L. (1997). The instrumental method in psychology. In R. W. Rieber, & J. Wollock (Eds.), The collected works of L. S. Vygotsky (Vol. 3, pp. 134-143). Springer.
Wardat, Y., AlBadarin, M., & Saqr, M. (2024). Adopting AI in education: Optimizing human resource management and addressing challenges. Frontiers in Education, 5, Article 1488147. https://doi.org/10.3389/feduc.2025.1488147
Xu, W., Dainoff, M. J., Ge, L., & Gao, Z. (2023). Transitioning to human interaction with AI systems: New challenges and opportunities for HCI professionals to enable human-centered AI. International Journal of Human-Computer Interaction, 39(3), 494-518. https://doi.org/10.1080/10447318.2022.2041900
Yilmaz, H., Maxutov, S., Baitekov, A., & Balta, N. (2023). Student attitudes towards Chat GPT: A technology acceptance model survey. International Educational Review, 1(1), 57-83. https://doi.org/10.58693/ier.114

How to cite this article

APA

Mani, J., & Zargeh, C. (2025). AI artifacts in the mathematics didactical tetrahedron: A developed model. Eurasia Journal of Mathematics, Science and Technology Education, 21(5), em2630. https://doi.org/10.29333/ejmste/16307

Vancouver

Mani J, Zargeh C. AI artifacts in the mathematics didactical tetrahedron: A developed model. EURASIA J Math Sci Tech Ed. 2025;21(5):em2630. https://doi.org/10.29333/ejmste/16307

AMA

Mani J, Zargeh C. AI artifacts in the mathematics didactical tetrahedron: A developed model. EURASIA J Math Sci Tech Ed. 2025;21(5), em2630. https://doi.org/10.29333/ejmste/16307

Chicago

Mani, Joseph, and Chia Zargeh. "AI artifacts in the mathematics didactical tetrahedron: A developed model". Eurasia Journal of Mathematics, Science and Technology Education 2025 21 no. 5 (2025): em2630. https://doi.org/10.29333/ejmste/16307

Harvard

Mani, J., and Zargeh, C. (2025). AI artifacts in the mathematics didactical tetrahedron: A developed model. Eurasia Journal of Mathematics, Science and Technology Education, 21(5), em2630. https://doi.org/10.29333/ejmste/16307

MLA

Mani, Joseph et al. "AI artifacts in the mathematics didactical tetrahedron: A developed model". Eurasia Journal of Mathematics, Science and Technology Education, vol. 21, no. 5, 2025, em2630. https://doi.org/10.29333/ejmste/16307