Students Becoming Mathematicians through Mathematical Modeling Learning Environments: A Design-Based Study
Algebra has functioned as a gatekeeper for urban school students. Interventions have involved everything from doubling math time to new technologies. However, it is clear that change will not occur unless we address the content of mathematics, the pedagogical approach, attention to students and context together. In this Design-Based Research (Design Experiment) Study, I designed a learning environment that re-envisions the urban school algebra classroom using the "science of patterns" (Devlin, 1996; Kneebone, 2001; Steen, 1988; Resnik, 1997; Mason, Burton, Stacey, 1982). Undergirding this learning environment is the engagement of students in mathematical modeling - iterative cycles of expressing, testing, and revising of their interpretations (Doerr & Lesh, 2011). The design experiment provided insights about students' learning trajectories as they used functions to construct their models as well as the pedagogy and tools that supported participation. It was found that when students engaged in the classroom tasks, that specific mediating process (interactions and activity) emerged that led to student learning. In this case, learning included: 1) students using their derived mathematical models to answer/pose contextual questions about the quantities, and in the process of deriving models, 2) students developing an understanding of the underlying structure of functions as it relates to its symbolic and graphical representations.