| Model-Eliciting Activities (MEAs) have been characterized in the Models and Modeling (M&M) literature as being "thought-revealing" activities. But what does the characterization of "thought-revealing" mean? And what justification is there for such a characterization? This dissertation explores this characterization by conceptually analyzing one of its key theoretical premises, namely, that the mathematical models students create while working on MEAs are a rich source of information about their mathematical thinking.; I argue that the M&M literature associates three distinct aspects of students' mathematical thinking with their mathematical models: (1) Their mathematical interpretations of real situations; (2) Their mental frameworks that are used to interpret real situations; (3) Their conceptual understandings of abstract mathematical ideas.; However, I argue that the M&M literature fails to theoretically demonstrate how these three aspects of mathematical thinking are revealed in students' mathematical models. As evidence, I point to inconsistent usages of three key terms in the M&M literature---"conceptual system," "construct," and "model"---and I show how these usages lead to considerable confusion. I then present my own attempt to create a clear conceptual framework, which I use to demonstrate that mathematical models are a rich source of information about students' mathematical interpretations of real situations. I also discuss the theoretical issues involved with extending this conceptual framework to include the other two aspects of students' mathematical thinking. |
