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Abstract

This small-scale design study describes disciplinary learning in mathematical modeling and science from an authentic engineeringthemed module. Current research in tissue engineering served as source material for the module, including science content for readings and a mathematical modeling activity in which students work in small teams to design a model in response to a problem from a client. The design of the module was guided by well-established principles of model-eliciting activities (a special class of problem-solving activities deeply studied in mathematics education) and recently published implementation design principles, which emphasize the portability of model-eliciting activities to many classroom settings.

Two mathematical modeling research questions were addressed: 1. What mathematical approaches did student-teams take when they designed mathematical models to evaluate the quality of blood vessel networks? and 2. What attributes of mature mathematical models were captured in the mathematical models that the student-teams designed? One science content research question was addressed: 1. Before and after the module, what aspects of angiogenesis did students describe when they were asked what they knew about the process of blood vessel growth from existing vessels?

Participants who field-tested the module included high school students in a summer enrichment program and early college students enrolled in four general-studies mathematics courses. Data collected from participants included mathematical models produced by small teams of students, as well as students’ individual responses before and after the module to a prompt asking them what they knew about the process of new blood vessel growth from existing vessels. The data were analyzed for mathematical model type and science content by adopting methods of grounded theory, in which researchers suspend expectations about what should be in the data and, instead, allow for the emergence of patterns and trends. The mathematical models were further analyzed for mathematical maturity using an a priori coding scheme of attributes of a mathematical model. Analyses showed that student-teams created mathematical models of varying maturity using four different mathematical approaches, and comparisons of students’ responses to the science prompt showed students knew essentially nothing about angiogenesis before the module but described important aspects of angiogenesis after the module. These findings were used to set up an agenda for future research about the design of the module and the relationship between disciplinary learning and authentic engineering problems.

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