Exploring students’ metacognitive processes in scaffolded integration problem solving

Source abstract

Background: Integration techniques are fundamental to advanced mathematics, yet students frequently encounter difficulties in recognizing problem structures, selecting appropriate integration methods, and regulating their problem-solving processes. Scaffolding may facilitate these processes by supporting students’ metacognitive awareness, monitoring, and evaluation. Aim: This study aimed to explore students’ metacognitive processes during scaffolded integration problem solving. Method: A qualitative case study was conducted with three Mathematics Education students enrolled in an Integral Calculus course at UIN Walisongo. Participants represented different performance levels and were examined through open-ended integration problems and follow-up interviews. Their problem-solving processes were analyzed according to three metacognitive dimensions: awareness, monitoring, and evaluation. Results: The findings revealed varying levels of metacognitive engagement across participants. Awareness and monitoring were more evident among higher-performing students, particularly in recognizing problem characteristics, selecting appropriate integration strategies, and controlling procedural steps. In contrast, evaluation remained consistently underdeveloped, as students rarely verified their answers or reflected on the effectiveness of their strategies. Conclusion: Scaffolded integration problem solving can facilitate the emergence of metacognitive awareness and monitoring; however, explicit evaluative prompts are needed to strengthen verification and reflection during mathematical problem solving.