This poster presents findings from design and early implementation work of the NSF DRK-12 project which positions 6th and 7th grade students as decision makers in their own learning, integrating culturally responsive mathematical modeling problems into their regular curriculum. We take a sociocritical perspective on modeling, supporting students in using mathematics to understand their life experiences and, when appropriate, to challenge the existing social order (e.g., Aguirre et al., 2019; Author, 2021; Cirillo et al., 2016; Felton-Koestler, 2020). By learning to recognize mathematical dimensions of their emerging identities in classroom settings, we hope to inspire excitement about mathematics and boost students’ experiences of mathematical agency (Boaler & Greeno, 2000).
Our approach to task design within mathematical modeling is also grounded in the Models and Modeling Perspective (Lesh & Doerr, 2003), which aims to engage students with problem-settings typical of mathematical work beyond school (Lesh, Hamilton, & Kaput, 2007). Such problems often involve trade-offs or feedback; where goals (e.g., “fair distribution of resources” or “comfortable living space”) must be quantified before they can be tackled mathematically; and where one is often interested in optimizing, maximizing, or minimizing these quantities. This approach to modeling connects modeling with engineering (Diefes-Dux et al, 2008; Hamilton et al, 2008) in ways that we explore in the activity we present in this poster.
The Homeless Shelter task (Author, 2021) invites students to create a design for an individual mini-shelter for the homeless. Students are introduced to the problem through videos showing how communities across the US have been implementing such shelters; the problem is also situated locally in the particular needs of the homeless population in the communities served by our partner schools. Given the goal to produce many of these mini-shelters using a fixed budget, students are faced with the challenge of creating a design that optimizes the qualities they believe most important within realistic budgetary constraints (Authors, in preparation). Students work in groups of 3-4 to develop a shared design. Each group is given a price sheet with various items they can incorporate—including plywood of different thicknesses, different potential materials for windows, etc. These options provoke or reinforce students’ recognition that while the size (i.e., enclosed volume) of a mini-shelter is an important consideration, they value additional factors (such as sturdiness, light and ventilation, etc) as well. In addition, we provide material support for student groups to envision and communicate their mini-shelter designs.
In this poster, we analyze video data and student-created artifacts from our initial implementations of this activity, describing the distinctive design rationales and the strategies for mathematizing and optimizing that emerged in different groups’ work. We use discourse analysis (Gee, 2014), defining discourse broadly, to include multimodal communication (Radford, 2014). We present three illustrative cases, describing groups’ distinctive approaches and the mathematical insights that they produced.
Brady, C., Jung, H., de Alejandro, J., Coleman-King, C., de Araujo, Z., & Sutcliffe, K. (2023). Engineering connections in culturally-responsive mathematical modeling problems. American Society for Engineering Education. Baltimore Convention Center, MD.