Teachers' Perspectives on How They Learn Mathematical Modelin

Mathematical modeling is a teaching approach that incorporates many reform-based, ambitious teaching practices, and it is the focus of the Common Core State Standards for Mathematics Standards for Mathematical Practices 4, (SMP4): Model with Mathematics. Although SMP4 applies to Grades K--12, most teachers have not been exposed to mathematical modeling either in their teacher preparation programs or in their teaching practice. Teaching mathematical modeling is demanding, and teachers need a specialized pedagogical content knowledge to do it effectively. This study used a qualitative case-study approach to explore teachers' perspectives on how they learned mathematical modeling and the changes that resulted from their learning. Teachers learned about mathematical modeling by participating in a professional development initiative and by using mathematical modeling in their classrooms. The study was part of a grant-funded professional development initiative consisting of a four-day summer institute followed by a fall lesson study. Data collection included interviews, observations, field notes and memos, and participant reflections. Themes emerging from a thematic analysis indicated that (a) teachers felt mathematical modeling was a new way to see, teach, and experience mathematics; (b) teachers learned mathematical modeling by seeing and doing; (c) expectations (external and personal) and characteristics of mathematical modeling constrained teacher learning; and (e) learning mathematical modeling was a process that affected teachers' instructional practices and mind-sets. Key findings were that (a) the teachers' freedom of choice and the opportunity they had to experience mathematical modeling the same way a student would helped them learn this approach; (b) as they learned mathematical modeling, teachers realized they needed to modify some of their instructional practices; and (c) learning, using, and teaching mathematical modeling positively affected teachers' feelings about mathematics and mathematical modeling.