Tracing the Mathematical Modeling Phases of Pre-Service Teachers: A MAD Analysis

Mathematical modeling has been receiving increased focus with researchers identifying its benefits for students, such as using mathematics in real world applications and affecting change in attitudes towards mathematics. Mathematical modeling also provides the opportunity to support equitable learning, promoting cooperation among students from various mathematical backgrounds with the use of low-floor and high-ceiling tasks. With numerous benefits, it is important to also examine how groups of pre-service teachers negotiate the modeling process in order to better support those who look to include modeling activities in their future classrooms. While there have been several theoretical modeling cycles published that describe the various phases, these tend to provide a simplified view of the complex nature of these tasks. To gain insight into this phenomena, we created, taught, and observed two mathematical modeling sessions for pre-service teachers. This work enabled us to explore how pre-service teachers move between phases of the modeling cycle and if these shifts mirror what is being represented in current modeling cycle diagrams. Our analysis focuses on a holistic task that was completed after pre-service teachers had learned about mathematical modeling and had attempted an atomistic task. We used a modified version of the Modeling Activity Diagram (MAD) framework to create a visual representation of group movements through the modeling cycle phases. While our analysis is ongoing, our emerging findings show that pre-service teachers are able to adapt to the complex nature of modeling activities to varying degrees as they work together to build their mathematical models.