The Models and Modeling Perspectives (MMP) has evolved out of research that began 26 years ago. MMP researchers use Model Eliciting Activities (MEAs) to elicit students' mental models. In this study MMP was used as the conceptual framework to investigate the nature of students' models of curve fitting in a problem-solving environment consisting of an MEA, the Time-on-Drill, and the Test-Scores (TDTS) problem. The study had two research goals: (1) to investigate the nature of students' models of curve fitting and (2) to lay the groundwork for pedagogical activities, also known as Model eXploration Activities (MXAs), that can be used by teachers and/or researchers after investigating the nature of students' models. Participants of this study were elementary teacher education students enrolled in a mathematics problem-solving course. Videotapes of the MEA session, class observation notes, and anecdotes from class discussions served as the sources of data for this study. Iterative videotape analyses as described in Lesh and Lehrer (2000) were used to analyze the videotapes of the participants working on the MEA. Results of this study center on the nature of students' models of curve fitting and eventually MXAs are suggested that can be used following the investigation of the nature of students' models. Thus, this research adds to existing MMP research by introducing new set of activities following MEAs and also adds to the statistics education research by investigating the learning of the topic curve fitting. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]