The sub-dimensions of metacognition and their influence on modeling competency

Mathematical modeling is indeed a versatile skill that goes beyond solving real-world problems. Numerous studies show that many students struggle with the intricacies of mathematical modeling and find it a challenging and complex task. One important factor related to mathematical modeling is metacognition which can significantly impact expert and student success in a modeling task. However, a notable gap of research has been identified specifically in relation to the influence of metacognition in mathematical modeling. The study's main goal was to assess whether the different sub-dimensions of metacognition can predict the sub-constructs of a student's modeling competence: horizontal and vertical mathematization. The study used a correlational research design and involved 538 participants who were university students studying mathematics education in Riau Province, Indonesia. We employed structural equation modeling (SEM) using AMOS version 18.0 to evaluate the proposed model. The measurement model used to assess metacognition and modeling ability showed a satisfactory fit to the data. The study found that the direct influence of awareness on horizontal mathematization was insignificant. However, the use of cognitive strategies, planning, and self-checking had a significant positive effect on horizontal mathematization. Concerning vertical mathematization, the direct effect of cognitive strategy, planning, and awareness was insignificant, but self-checking was positively related to this type of mathematization. The results suggest that metacognition, i.e., awareness and control over a person's thinking processes, plays an important role in modeling proficiency. The research implies valuable insights into metacognitive processes in mathematical modeling, which could inform teaching approaches and strategies for improving mathematical modeling. Further studies can build on these findings to deepen our understanding of how cognitive strategies, planning, self-assessment, and awareness influence mathematical modeling in both horizontal and vertical contexts.