Addressing symbolic obstacles in undergraduate calculus through artificial intelligence scaffolding
Isbadar Nursit 1 2 , Toto Nusantara 3 * , Erry Hidayanto 3
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1 Doctoral Student of Mathematics Education Department, State University of Malang, INDONESIA2 Mathematics Education Study Program, Universitas Islam Malang, East Java, INDONESIA3 Department of Mathematics Education, State University of Malang, East Java, INDONESIA* Corresponding Author

Abstract

Symbolic obstacles in calculus prevent students from moving away from intuition and towards formal thinking, but are rarely studied in the context of artificial intelligence (AI) interaction logs. We investigated symbolic obstacles and AI-supported representational transitions among 12 Indonesian undergraduate mathematics education students in a non-intrusive intrinsic case study. Semi-structured interviews, eight classroom observations, diagnostic tests, academic artifacts, and AI logs were analyzed through inductive-deductive thematic analysis, based on Tall’s Three Worlds of Mathematics. Four obstacles are highlighted: graph-to-symbol translation, integral and sigma notation, limit notation, and symbolic algebraic manipulation. Participant-level comparisons showed 27.4%–53.8% fewer coded symbolic errors in post-activity assessments than at baseline. AI scaffolding through dynamic visualization, adaptive feedback, step-by-step guidance, and solution validation was associated with representational cycling, metacognitive reflection, reported self-efficacy gains, and lower mathematics anxiety. The study integrates AI-log evidence with the Three Worlds framework to explain how scaffolding can support students in addressing symbolic obstacles.

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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: Research Article

PEDAGOGICAL RES, Volume 11, Issue 4, October 2026, Article No: em0295

https://doi.org/10.29333/pr/19631

Publication date: 16 Oct 2026

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Article Downloads: 4

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