Building a theoretical model of metacognitive processes in complex modeling activities: a window into the development of students' metacognitive abilities

Abstract

A theoretical model of metacognition in complex modeling activities has been developed based on existing frameworks, by synthesizing the re-conceptualization of metacognition at multiple levels by looking at the three sources that trigger metacognition. Using the theoretical model as a framework, this study was designed to explore how students' thinking becomes metacognitive while collaboratively solving a complex mathematical modeling task. This study used a series of Model-Eliciting Activities (MEAs), which are a type of problem-solving activity in which participants are required to verbalize their thoughts while working within a group, as an authentic method for analyzing verbal metacognitive actions, addressing several criticisms of self-report methods. Multiple cycles of data analysis, including a finer-grained analysis of conversational statements and a cross-case analysis, were conducted. Results from the data analysis provided empirical evidence supporting the soundness and appropriateness of the theoretical model of metacognition on multiple levels in identifying and interpreting students' metacognitive activities in complex mathematical modeling tasks. This study identified several patterns and tendencies of students' spontaneous metacognitive activities. This study provided empirical evidence supporting the potential similarity of students' developing metacognitive abilities to their developing cognitive abilities with respect to the dimensions of development. In addition, this study identified the circumstances facilitating or interfering with students' spontaneous metacognitive activities. This study furthers our understanding about how one develops metacognitive abilities within problem-solving processes, and ultimately informs how to effectively encourage students' metacognition and improve their problem-solving achievement.