Metacognitive Patterns in Technology-Assisted Calculus Problem-Solving with GeoGebra

Dynamic mathematics environments are increasingly serving as spaces where learners can visualize, test, and refine their thinking. Correspondingly, this study investigates how students regulate and reflect on their reasoning while solving calculus problems using GeoGebra. This widely used digital tool promotes reflective problem-solving. Using a qualitative multiple-case approach, six secondary students completed non-routine calculus tasks involving derivatives and optimization while verbalizing their reasoning. In addition, analysis of think-aloud, screen recording, interview, and reflection journal data revealed four metacognitive pathways: Procedural-Verification, Exploratory-Tinkering, Strategic-Integration, and Reflective-Control. These represent different ways students coordinated awareness, regulation, and evaluation using GeoGebra. Accordingly, findings reveal that technology can both scaffold and constrain metacognitive activity: it supports regulation through feedback but often limits deeper evaluation. Therefore, by mapping how students think with and through digital tools, the study offers insights for designing technology-integrated mathematics instruction that promotes reflective and adaptive engagement with calculus concepts.