Examining secondary teachers' practical rationality of mathematical modeling

Abstract

Research on mathematical modeling is growing rapidly in the field of mathematics education, and there are numerous benefits of engaging students in modeling activities. However, mathematical modeling is still marginalized in mathematics instruction. In order to understand the challenges and obstacles secondary teachers face to incorporate modeling into their classrooms, this study drew upon the theoretical perspective of practical rationality. It used a breaching experiment survey of 176 secondary teachers in Missouri and follow-up interviews with six purposefully selected survey respondents to examine secondary teachers' norms and professional obligations related to mathematical modeling. After data collection, I used descriptive statistical analyses to examine the norms and applied the professional obligation framework to analyze teacher obligations. My findings confirmed four of the six hypothesized norms: Teachers tend to precisely identify which factors should be included in students' solutions, expect students to find a symbolic representation as their model, expect students to primarily work on politically neutral tasks, and are open to students doing model revisions. However, this study did not have robust enough evidence to confirm or disconfirm whether teachers tend to give students unambiguous directions about mathematical operations or components. Nor could it uncover whether students are expected to primarily engage in mathematical thinking rather than nonmathematical thinking during the modeling process. The findings also revealed that teachers' preferred actions among the scenarios presented were influenced by their perceived professional obligations, including commitments to individual students, the classroom's interpersonal dynamics, the practice of the mathematics discipline, and the institutions they work for. More specifically, disciplinary obligations featured most often in the survey responses of those teachers who complied with canonical actions. In contrast, those who selected noncanonical options (such as opening up the beginning phases of the modeling process) most often cited their obligations to individual student thinking to justify their survey responses. The findings suggested that the mathematics education community needs to increase awareness about complex and often conflicting teacher obligations related to mathematical modeling. To support teachers in enacting modeling, the field might consider qualified professional development, viable modeling tasks and tools, and a flexible schedule as well as opportunities to build shared understandings of disciplinary practices and obligations to students' individual needs.