A Dynamic AI Scaffolding System Based on ZPD Theory: Reducing Cognitive Load and Enhancing Transfer in Mathematical Proof Learning

DOI: https://doi.org/10.62517/jnse.202617104

Author(s)

Ning Yao1, Pengtao Huang2,*

Affiliation(s)

1School of Mathematics and Physics, Hechi University, Yizhou, Guangxi, China 2Department of Science and Technology, Hechi University, Yizhou, Guangxi, China *Corresponding Author

Abstract

Although large language models (LLMs) offer new possibilities for personalized instruction, most educational implementations rely on static prompting that ignores learners’ moment-to-moment cognitive and metacognitive needs. Grounded in Vygotsky’s Zone of Proximal Development, this study introduces a four-layer dynamic AI scaffolding system that adaptively regulates LLM support during complex problem solving. In a randomized controlled experiment, 60 non-mathematics majors solved series convergence proof problems under either dynamic scaffolding or static prompting conditions. Learners receiving dynamic scaffolding reported lower extraneous cognitive load, demonstrated superior far-transfer performance, and engaged in more metacognitive questioning. Within the dynamic condition, metacognitive questioning was positively associated with transfer outcomes. These results indicate that dynamically operationalizing ZPD in generative AI tutors is more effective than static prompting for fostering deep learning and knowledge transfer.

Keywords

AI in Education; Zone of Proximal Development (ZPD); Cognitive Load Theory (CLT); Intelligent Tutoring System (ITS); Mathematical Problem Solving; Prompt Engineering

References

[1] Kasneci E, Seßler K, Küchemann S, et al. ChatGPT for good? On opportunities and challenges of large language models for education. Learning and Individual Differences, 2023, 103: 102274. [2] Kojima T, Gu S S, Reid M, Matsuo Y, Iwasawa Y. Large language models are zero-shot reasoners. Advances in Neural Information Processing Systems, 2022, 35: 22199–22213. [3] Savel’ska O, Savel’skyy O. Prompt engineering in education: Towards a systematic framework for teaching and learning with large language models. arXiv preprint, arXiv:2310.16746, 2023. [4] Sweller J. Cognitive load during problem solving: Effects on learning. Cognitive Science, 1988, 12(2): 257–285. [5] Vygotsky L S. Mind in Society: The Development of Higher Psychological Processes. Cambridge, MA: Harvard University Press, 1978. [6] VanLehn K. The relative effectiveness of human tutoring, intelligent tutoring systems, and other tutoring systems. Educational Psychologist, 2011, 46(4): 197–221. [7] Alvarez I, Ruiz M A. Scaffolding metacognitive strategies in LLM-based tutoring: Effects on self-regulated learning and problem-solving transfer. Computers & Education, 2023, 205: 104888. [8] Van de Pol J, Volman M, Beishuizen J. Scaffolding in teacher–student interaction: A decade of research. Educational Psychology Review, 2010, 22(3): 271–296. [9] Sweller J, van Merriënboer J J G, Paas F. Cognitive architecture and instructional design: 20 years later. Educational Psychology Review, 2019, 31(2): 261–292. [10] Flavell J H. Metacognition and cognitive monitoring: A new area of cognitive–developmental inquiry. American Psychologist, 1979, 34(10): 906–911. [11] Azevedo R, Aleven V, eds. International Handbook of Metacognition and Learning Technologies. New York: Springer, 2013. [12] Kasneci E, Seßler K, Küchemann S, et al. ChatGPT for good? On opportunities and challenges of large language models for education. Learning and Individual Differences, 2023, 103: 102274. [13] Wiggins J B, Grafsgaard J F. Do adaptive scaffolds improve help-seeking in an intelligent tutoring system?. Proceedings of the 12th International Learning Analytics and Knowledge Conference (LAK ’22). New York: ACM, 2022: 220–230 [14] Hoyle E, Carpenter A. The cognitive structure of mathematical proof. Journal for Research in Mathematics Education, 2019, 50(3): 315–340. [15] Sweller J. Element interactivity and intrinsic, extraneous, and germane cognitive load. Educational Psychology Review, 2010, 22(2): 123–138. [16] Schoenfeld A H. Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In: Grouws D A, ed. Handbook of Research on Mathematics Teaching and Learning. New York: Macmillan, 1992: 334–370. [17] Sweller J, van Merriënboer J J G, Paas F. Cognitive architecture and instructional design: 20 years later. Educational Psychology Review, 2019, 31(2): 261–292