Articles
Reconceptualizing Mathematical Problem-Solving Skills in The Digital Age: Teachers’ Perspectives Through the Lens of Theory of Didactical Situations
- Received
- April 25, 2026
- Revised
- May 10, 2026
- Accepted
- June 8, 2026
- Published
- July 6, 2026
Abstract
Mathematical problem-solving skills are a critical 21st-century competency, yet their development still faces various challenges in the digital age. This study aims to explore teachers’ perspectives on students’ mathematical problem-solving skills, analyze teaching practices through the Theory of Didactical Situations framework, and formulate a reconceptualization of mathematical problem-solving skills relevant to the era of artificial intelligence. The study employed a qualitative approach with an exploratory design involving 11 junior high school mathematics teachers selected through purposive sampling. Data were collected via semi-structured interviews and analyzed using the Bogdan and Biklen model. Findings indicate that mathematics instruction remains dominated by a procedural approach that reinforces students’ reliance on examples and teacher authority. Students struggle to understand non-routine problems, design independent strategies, engage in reflection, and verify solutions. Furthermore, the use of digital technology remains instrumental and does not yet support exploration or critical thinking. From a TDS perspective, the digital milieu has not yet functioned as an exploratory environment, while the didactic contract still positions the teacher as the primary authority. Based on a synthesis of empirical findings and studies on AI hallucination and Retrieval-Augmented Generation, this research proposes an expansion of the problem-solving framework by adding a dimension of digital information verification and formulating a conceptual model of the Didactic RAG-System to support mathematics learning in the era of artificial intelligence.
Keywords
mathematical problem solving skills; theory of didactical situations; retrieval-augmented generation; AI hallucination; digital mathematics learning
Downloads
Download data is not yet available.
References
- Amalina, I. K., & Vidákovich, T. (2023). Development and differences in mathematical problem-solving skills: A cross-sectional study of differences in demographic backgrounds. Heliyon, 9(5), e16366. https://doi.org/10.1016/j.heliyon.2023.e16366
- Artigue, M., & Trouche, L. (2021). Revisiting the French Didactic Tradition through Technological Lenses. Mathematics, 9(6), 629. https://doi.org/10.3390/math9060629
- Bogdan, R. C., & Biklen, S. K. (2007). Qualitative research for education: An introduction to theory and methods (5th ed.). Pearson.
- Bolstad, O. H. (2023). Lower secondary students’ encounters with mathematical literacy. Mathematics Education Research Journal, 35(1), 237–253. https://doi.org/10.1007/s13394-021-00386-7
- Borba, M. C., Engelbrecht, J., & Llinares, S. (2021). Using Digital Technology and Blending to Change the Mathematics Classroom and Mathematics Teacher Education (pp. 21–42). https://doi.org/10.1007/978-3-030-80230-1_2
- Bouck, E. C., Cox, S. K., Long, H., Bullock, E., & Whorley, A. (2024). Exploring Modified Schema Based Instruction to Support Data Analysis Problem Solving: A Systematic Replication. Journal of Behavioral Education. https://doi.org/10.1007/s10864-024-09572-6
- Bransford, J., Zech, L., Schwartz, D., Barren, B., & Vye, N. (2000). Designs for Environments That Invite and Sustain Mathematical Thinking (1st Edition). Routledge.
- Brousseau, G. (1997). Theory of didactical situations in mathematics: Didactique des mathématiques, 1970–1990 (N. C. M. S. R. W. V. Balacheff, Ed.). Kluwer Academic Publishers.
- Cai, J., & Lester, F. K. (2010). Why is teaching with problem solving important? . National Council of Teachers of Mathematics. .
- Cevikbas, M., Greefrath, G., & Siller, H.-S. (2023). Advantages and challenges of using digital technologies in mathematical modelling education – a descriptive systematic literature review. Frontiers in Education, 8. https://doi.org/10.3389/feduc.2023.1142556
- Clark-Wilson, A., Robutti, O., & Thomas, M. (2020). Teaching with digital technology. ZDM, 52(7), 1223–1242. https://doi.org/10.1007/s11858-020-01196-0
- Creswell, J. W., & Creswell, J. D. (2018). Research Design: Qualitative, Quantitative, and Mixed Methods Approaches (5th ed.). SAGE Publications.
- Creswell, J. W., & Poth, C. N. (2018). Qualitative Inquiry and Research Design: Choosing among Five Approaches (4th ed.). SAGE Publications.
- 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
- Engelbrecht, J., & Borba, M. C. (2024). Recent developments in using digital technology in mathematics education. ZDM – Mathematics Education, 56(2), 281–292. https://doi.org/10.1007/s11858-023-01530-2
- Ferretti, F., & Gambini, A. (2025). The didactic contract in high schools: insights from macro-phenomena revealed in large-scale assessment. Teaching Mathematics and Its Applications: An International Journal of the IMA. https://doi.org/10.1093/teamat/hraf012
- Gao, Y. , Xiong, Y. , Gao, X. , Jia, K. , Pan, J. , Bi, Y. , Dai, Y. , Sun, J. , Wang, H., & Wang, H. (2023). Retrieval-augmented generation for large language models: A survey. ArXiv Preprint ArXiv:2312.10997, 2(1), 32.
- Gradini, E., Firmansyah B, F. B., Noviani, J., & Ulya, K. (2025). Fostering Higher-Order Thinking Skills in Mathematics Education: Strategies, Challenges, and Classroom Practices. Prisma Sains : Jurnal Pengkajian Ilmu Dan Pembelajaran Matematika Dan IPA IKIP Mataram, 13(2), 135. https://doi.org/10.33394/j-ps.v13i2.15099
- Hannula, M., Evans, J., Philippou, G., & Zan, R. (2004). Affect in Mathematics Education--Exploring Theoretical Frameworks. Research Forum. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education , 107–109.
- Hiebert, J., & Grouws, D. A. (2007). The Effects of Classroom Mathematics Teaching on Students’ Learning. In Second Handbook of Research on Mathematics Teaching and Learning (pp. 371–404). Emerald Publishing Limited. https://doi.org/10.1108/978-1-28141-200-320251013
- 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, 103897. https://doi.org/10.1016/j.compedu.2020.103897
- Hwang, S., Flavin, E., & Lee, J.-E. (2023). Exploring research trends of technology use in mathematics education: A scoping review using topic modeling. Education and Information Technologies, 28(8), 10753–10780. https://doi.org/10.1007/s10639-023-11603-0
- Ikenga, G. U., & van der Sijde, P. (2024). Twenty-First Century Competencies; about Competencies for Industry 5.0 and the Opportunities for Emerging Economies. Sustainability, 16(16), 7166. https://doi.org/10.3390/su16167166
- Jacinto, H., & Carreira, S. (2023). Knowledge for teaching mathematical problem-solving with technology: An exploratory study of a mathematics teacher’s proficiency. European Journal of Science and Mathematics Education, 11(1), 105–122. https://doi.org/10.30935/scimath/12464
- Jessen, B., Bos, R., Doorman, M., & Winsløw, C. (2023). Lesson study in mathematics with TDS and RME as theoretical support: two cases from the European TIME project. International Journal for Lesson & Learning Studies, 12(1), 52–64. https://doi.org/10.1108/IJLLS-01-2022-0009
- Ji, Z., Lee, N., Frieske, R., Yu, T., Su, D., Xu, Y., Ishii, E., Bang, Y. J., Madotto, A., & Fung, P. (2023). Survey of Hallucination in Natural Language Generation. ACM Computing Surveys, 55(12), 1–38. https://doi.org/10.1145/3571730
- Jiang, P., Zhang, Y., Jiang, Y., & Xiong, B. (2022). Preservice mathematics teachers’ perceptions of mathematical problem solving and its teaching: A case from China. Frontiers in Psychology, 13. https://doi.org/10.3389/fpsyg.2022.998586
- Kasneci, E., Sessler, K., Küchemann, S., Bannert, M., Dementieva, D., Fischer, F., Gasser, U., Groh, G., Günnemann, S., Hüllermeier, E., Krusche, S., Kutyniok, 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, 102274. https://doi.org/10.1016/j.lindif.2023.102274
- Lester, F. K. (2013). Thoughts About Research On Mathematical Problem- Solving Instruction. The Mathematics Enthusiast, 10(1–2), 245–278. https://doi.org/10.54870/1551-3440.1267
- Lewis, P. , Perez, E. , Piktus, A. , Petroni, F. , Karpukhin, V. , Goyal, N. , Küttler, H. , Lewis, M. , Yih, W. T. , Rocktäschel, T., & Riedel, S. ,. (2020). Retrieval-augmented generation for knowledge-intensive nlp tasks. Advances in Neural Information Processing Systems, 33, 9459–9474.
- Li, M., Vale, C., Tan, H., & Blannin, J. (2025). Factors influencing the use of digital technologies in primary mathematics teaching: Voices from Chinese educators. Education and Information Technologies, 30(9), 12573–12608. https://doi.org/10.1007/s10639-024-13309-3
- Liljedahl, P., Santos-Trigo, M., Malaspina, U., & Bruder, R. (2016). Problem Solving in Mathematics Education (pp. 1–39). https://doi.org/10.1007/978-3-319-40730-2_1
- Ling, A. N. B., & Mahmud, M. S. (2023). Challenges of teachers when teaching sentence-based mathematics problem-solving skills. Frontiers in Psychology, 13. https://doi.org/10.3389/fpsyg.2022.1074202
- Lithner, J. (2017). Principles for designing mathematical tasks that enhance imitative and creative reasoning. ZDM, 49(6), 937–949. https://doi.org/10.1007/s11858-017-0867-3
- Mangiante-Orsola, C., Perrin-Glorian, M.-J., & Strømskag, H. (2018). Theory of didactical situations as a tool to understand and develop mathematics teaching practices. Annales de Didactique et de Sciences Cognitives, Special issue, 145–174. https://doi.org/10.4000/adsc.334
- Mayer, R. (2020). Principles of Multimedia Design. In Multimedia Learning (pp. 397–416). Cambridge University Press. https://doi.org/10.1017/9781316941355.026
- Niss, M., & Højgaard, T. (2019). Mathematical competencies revisited. Educational Studies in Mathematics, 102(1), 9–28. https://doi.org/10.1007/s10649-019-09903-9
- Novotná, J., & Hošpesová, A. (2022). Theory of Didactical Situations in Mathematics as one of the theoretical approaches to the LPS analysis of classroom data: the case of institutionalization. ZDM – Mathematics Education, 54(2), 303–316. https://doi.org/10.1007/s11858-022-01331-z
- OECD. (2019). PISA 2018 Results (Volume I): What students know and can do. OECD Publishing. https://doi.org/10.1787/5f07c754-en
- OECD. (2023). PISA 2022 Results (Volume I): The state of learning and equity in education. OECD Publishing. https://doi.org/10.1787/53f23881-en
- Pardos, Z. A., & Bhandari, S. (2024). ChatGPT-generated help produces learning gains equivalent to human tutor-authored help on mathematics skills. PLOS ONE, 19(5), e0304013. https://doi.org/10.1371/journal.pone.0304013
- Patton, M. Q. (2014). Qualitative research & evaluation methods: Integrating theory and practice. SAGE Publications.
- Pepin, B., Gueudet, G., & Trouche, L. (2017). Refining teacher design capacity: Mathematics teachers’ interactions with digital curriculum resources. ZDM, 49(5), 799–812. https://doi.org/10.1007/s11858-017-0870-8
- Pittalis, M., & Drijvers, P. (2023). Embodied instrumentation in a dynamic geometry environment: eleven-year-old students’ dragging schemes. Educational Studies in Mathematics, 113(2), 181–205. https://doi.org/10.1007/s10649-023-10222-3
- Polya, G. (2004). How to solve it: A new aspect of mathematical method. Princeton University Press.
- Rawte, V. , Sheth, A. , & Das, A. (2023). A survey of hallucination in large foundation models. ArXiv Preprint ArXiv:2309.05922.
- Rizaldi, D. R., & Fatimah, Z. (2023). Merdeka curriculum: Characteristics and potential in education recovery after the COVID-19 pandemic. International Journal of Curriculum and Instruction, 15(1), 260–271.
- Ruslin, Mashuri, S., Rasak, M. S. A., Alhabsyi, F., & Syam, H. (2022). Semi-structured Interview: A Methodological Reflection on the Development of a Qualitative Research Instrument in Educational Studies. IOSR Journal of Research & Method in Education (IOSR-JRME), 12(1), 22–29.
- Schindler, L. A., Burkholder, G. J., Morad, O. A., & Marsh, C. (2017). Computer-based technology and student engagement: a critical review of the literature. International Journal of Educational Technology in Higher Education, 14(1), 25. https://doi.org/10.1186/s41239-017-0063-0
- Schoenfeld, A. H. (2016). Learning to Think Mathematically: Problem Solving, Metacognition, and Sense Making in Mathematics (Reprint). Journal of Education, 196(2), 1–38. https://doi.org/10.1177/002205741619600202
- Stipek, D. J., Givvin, K. B., Salmon, J. M., & MacGyvers, V. L. (2001). Teachers’ beliefs and practices related to mathematics instruction. Teaching and Teacher Education, 17(2), 213–226. https://doi.org/10.1016/S0742-051X(00)00052-4
- Tamborg, A. L. (2021). Improving mathematics teaching via digital platforms? Implementation processes seen through the lens of instrumental genesis. ZDM – Mathematics Education, 53(5), 1059–1071. https://doi.org/10.1007/s11858-021-01282-x
- Thurm, D., & Barzel, B. (2022). Teaching mathematics with technology: a multidimensional analysis of teacher beliefs. Educational Studies in Mathematics, 109(1), 41–63. https://doi.org/10.1007/s10649-021-10072-x
- Tondeur, J., Scherer, R., Baran, E., Siddiq, F., Valtonen, T., & Sointu, E. (2019). Teacher educators as gatekeepers: Preparing the next generation of teachers for technology integration in education. British Journal of Educational Technology, 50(3), 1189–1209. https://doi.org/10.1111/bjet.12748
- Trouche, L., Rocha, K., Gueudet, G., & Pepin, B. (2020). Transition to digital resources as a critical process in teachers’ trajectories: the case of Anna’s documentation work. ZDM, 52(7), 1243–1257. https://doi.org/10.1007/s11858-020-01164-8
- Voogt, J., & Roblin, N. P. (2012). A comparative analysis of international frameworks for 21st century competences: Implications for national curriculum policies. Journal of Curriculum Studies, 44(3), 299–321. https://doi.org/10.1080/00220272.2012.668938
- Weigand, H.-G., Trgalova, J., & Tabach, M. (2024). Mathematics teaching, learning, and assessment in the digital age. ZDM – Mathematics Education, 56(4), 525–541. https://doi.org/10.1007/s11858-024-01612-9
- Zawacki-Richter, O., Marín, V. I., Bond, M., & Gouverneur, F. (2019). Systematic review of research on artificial intelligence applications in higher education – where are the educators? International Journal of Educational Technology in Higher Education, 16(1), 39. https://doi.org/10.1186/s41239-019-0171-0
- Zhao, P. , Zhang, H. , Yu, Q. , Wang, Z. , Geng, Y. , Fu, F. , Yang, L. , Zhang, W. , Jiang, J., & Cui, B. ,. (2026). Retrieval-augmented generation for ai-generated content: A survey. Data Science and Engineering, 1–29.
