Secondary Teachers\u27 Perspectives of Mathematical Modeling

The inception of Common Core State Standards for Mathematics (CCSSM) has increased the focus on mathematical modeling in high school mathematics curriculum in the United States. While the expectation that students engage in mathematical modeling is established by the standards, the standards do not include a clear and consistent definition of a mathematical model (Cirillo et al., 2016). The absence of a common description of a mathematical model or the mathematical modeling process, a single goal for mathematical modeling, and a standard process for designing modeling tasks has resulted in Kaiser and Sriraman’s (2008) conception of “perspectives of mathematical modeling.” Using this conception as a frame, this study employed a qualitative case study design (Yin, 2018) to explore the research question, “In what ways are teachers’ perspectives of mathematical modeling connected to the ways in which they plan learning experiences for students?” The participants in this study were five experienced Algebra II teachers from a southeastern state in the United States which include the CCSSM demand for mathematical modeling in the course curricula. Data were collected through a survey, two interviews, a teacher selected task, and a task exemplar. The results of this study are framed by participants reporting limited learning experiences involving mathematical modeling. The learning described included: (a) an emphasis on using identified manipulatives to develop an understanding of content standards; (b) the use of representations to solve problems; and (c) the importance and impact of mathematical modeling as teacher practice, absent of a clear description, examples of classroom implementation, or opportunities for practice. The cross-case analysis uncovered two themes: (1) content mastery and connections to students which grounded participants’ perspectives of mathematical modeling, and (2) the ways they planned to engage students. Three categories of descriptions of mathematical models and modeling were present: (a) mathematical models as concrete tools for the progression from concrete to abstract understanding, (b) mathematical models as representations transformed to solve mathematical and real-world problems, and (c) mathematical models as teacher models with the purpose of exposing students to replicable thinking useful in solving mathematical and real-world problems