AI-Integrated Student Worksheets: Scaffolding Spatial and Representational Reasoning in Double Integrals

Abstract

This study aims to develop and examine the effectiveness of Artificial Intelligence (AI)-integrated student worksheets as scaffolding for students' spatial and representational reasoning in double integral material. Using an explanatory sequential mixed-methods approach, this exploratory study employed a one-group pretest-posttest design involving the entire cohort of 11 third-semester students from the 2023 batch of the Mathematics Education Study Program at Universitas PGRI Ronggolawe. Data were analyzed using the Wilcoxon Signed-Rank test and N-Gain. The qualitative phase involved in-depth observations and semi-structured interviews to explore the mechanisms of AI scaffolding. Expert validation yielded a score of 87.7% (highly valid), while practicality reached 85.5% (highly practical). The effectiveness test showed a significant improvement ( , large effect size) with a mean N-Gain of 0.556 (moderate category), and all students surpassed the minimum mastery score of 75. Qualitative findings revealed three distinct AI scaffolding mechanisms: (1) externalized thinking through Socratic interaction for high-ability students; (2) progressive fading aligned with Vygotsky's Zone of Proximal Development (ZPD) for moderate-ability students; and (3) graphical-to-symbolic representational transfer facilitated by graduated AI prompts for low-ability students. As a preliminary, theoretically informed contribution, this exploratory study proposes an initial framework for differentiating AI-driven scaffolding in multivariable calculus pedagogy, to be further tested in future research with larger samples and controlled designs.