The mathematics in mathematical modeling
Fulton, Elizabeth Anne White
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The purpose of this research was to investigate how teachers interact with mathematics while teaching mathematical modeling to elementary students. To conduct this study, I used a case study approach with four elementary teachers. Each teacher participated in professional development on mathematical modeling prior to the study and incorporated mathematical modeling into their classroom. Modeling task lessons were observed and teachers participated in interviews before and after each lesson. I qualitatively explored what mathematical decisions teachers made while teaching mathematical modeling and how students' mathematical contributions influenced the modeling cycle. This analysis took place through three analytical lenses: the mathematics used, the teacher's interactions with their student's mathematical ideas, and as compared to components of the mathematical modeling cycle. Findings indicate that students engaged in meaningful mathematics to explore real-world problems. Across all cases, teachers prepared students to use mathematics by creating tasks with mathematical opportunities and by orienting the students towards using mathematics to investigate the problems. Each teacher allowed their students to introduce most of the mathematical ideas used to investigate the modeling questions. Each task became a mathematical modeling task by the way it was implemented, through teachers' and students' contributions to the activity.