Abstract:

Mathematical modeling is unique as both a standard for mathematical practice and a conceptual category under the United States’ Common Core State Standards for Mathematics (CCSSM). However, many teachers lack expertise with mathematical modeling for two reasons. First, the CCSSM does not distinguish between the two distinct constructs of mathematical modeling and modeling mathematics: mathematical modeling describes using mathematics to solve real-world problems that may not be inherently mathematical, whereas modeling mathematics describes using visual representations of mathematics to communicate mathematical ideas. Second, the complexity of mathematical modeling suggests unconventional solution processes that may be unfamiliar to teachers. Thus, teachers are often unsure what an authentic mathematical modeling activity looks like and the affordances and challenges associated with implementing it in classrooms.

This study aimed to gain insights about implementation that affect teachers as they learn about incorporating mathematical modeling into secondary classrooms. We studied 12 mathematics teachers enrolled in a virtual mathematical modeling education course. Teachers engaged with mathematical modeling activities as a student would, to learn first-hand about the nature of such activities and how they may be enacted. In this paper, we present teachers’ experience with a geometric mathematical modeling activity involving flooring in which teachers reflected on their successes and challenges associated with implementing the activity in an actual classroom. The activity prompted groups to investigate using tile, carpet, or hardwood to upgrade the floors of a house and provide pricing quotes to a fictional client. A non-rectangular floor plan blueprint was provided and tools were available for use, including Google Jamboard for virtual collaboration and a hardware store’s pricing website.

Our findings showed that the teachers found the flooring activity provided authentic opportunities for mathematical modeling in a secondary classroom. Teachers valued the activity’s structure, specifically that the wide variety of flooring options and prices established wide parameters for genuine solutions, which can support equity and accessibility in the classroom. Additionally, teachers valued the extensions made possible by the activity, which could support more sophisticated mathematical models by considering additional variables. Furthermore, teachers valued the available tools, specifically that the hardware store’s website offered a flooring calculator to help with pricing and planning to inform their real-world decision-making. Teachers also noticed some overarching challenges associated with implementation. For instance, most teachers commented on time constraints associated with the activity and, if possible, they would have preferred more time to allow modelers to refine their recommendations. Also, some teachers worried about oversimplification of the task when enacted in a classroom, such as by conceptualizing rectangular areas instead of a compound polygon, as intended. The primary takeaway for teachers was that activities like these can provide opportunities for students to engage with mathematical modeling as both a practice and concept, as recommended by the CCSSM. Future research will study enactments of similar activities in real secondary classrooms to better ascertain the implementation concerns around mathematical modeling.

Keywords:

Mathematical modeling, mathematics education.