This study explores the dynamic interplay between undergraduate students' task-related knowledge and self-regulation strategies during problem-solving activities, leading to the development of a conceptual framework that describes how these two constructs—metacognitive knowledge about tasks (MKT) and self-regulation (SR)—are simultaneously applied in problem-solving contexts. Conducted in two second-year engineering mathematics courses (Engineering Statics and Ordinary Differential Equations), the study involved 20 undergraduate students (7 females and 13 males; 11 from mathematics and 9 from engineering).

The methodology included one-on-one interviews before and after problem-solving sessions and think-aloud protocols during the sessions to capture real-time verbalizations. Each participant engaged in two problem-solving activities of varying difficulty, culminating in 40 problem-solving events. Through qualitative analyses, the research provides insights into the nature of these interactions and their impact on problem-solving performance, guided by the central question: How do the interactions between students' metacognitive knowledge and self-regulation influence their task performance?

The qualitative analysis of the pre-problem-solving interview data aimed to capture participants' understanding of the tasks and their confidence levels. Think-aloud data collected during problem-solving were analyzed to understand students' self-regulation strategies. Post-problem-solving exit interviews assessed participants' perceptions of their problem-solving experiences. Course instructors and two graduate students with expertise in the relevant topics evaluated the participants’ solutions.

During data analysis, seven distinct problem-solving episodes were identified, each potentially influencing students' task performance. These episodes underscore the interactions between students' metacognitive understanding of the problems and their monitoring and evaluation strategies during problem solving. The paper concludes by discussing these findings, their implications for instructional practices, and conclusions.

Keywords: Knowledge about tasks, problem-solving, self-regulation, mathematics education, engineering education, learning episodes.