Dynamic Performance Models for Transportation Infrastructure Management

Andrew Morgan Brantliger

doi:https://doi.org/10.21985/N2SH7G

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Dynamic Performance Models for Transportation Infrastructure Management

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The purpose of this dissertation study was to build on scholarly work in the area of critical mathematics by such scholars as Gutstein (2003) and Gutierrez (2002). Critical pedagogy is designed to foster political agency and critical consciousness in students (Freire, 1971). That is the aim of critical mathematics in addition to the general goal of enhancing mathematical power that is outlined in the National Council of Teachers of Mathematics Principles and Standards documents (NCTM, 1989, 1991, 2000). Proponents of critical mathematics argue that it has the potential to be more empowering and equitable than traditional and standards-based reform versions of mathematics instruction because it allows subordinated students to use mathematics to understand, and potentially change, sociopolitical matters that affect themselves and their communities. This dissertation relied on practitioner research; I used qualitative methods to examine my own critical mathematics instruction and curriculum design. It was conducted in a remedial geometry course in a low-income urban high school. Analyses were done on: (1) my approaches to critical curriculum design and my own teacher beliefs, (2) the critical component of my mathematics curriculum, and (3) videotapes of classroom discourse and student participation in standards-based and critical activities. My dissertation findings raise important issues for those interested in issues of equity and social justice in mathematics education to consider. In particular, I found my critical mathematics program provided my low-income students of color with potential political use-values while not providing them the fullest exchange-value possible (e.g., skills valued by universities). Because, as a teacher and curriculum designer, I had not set out to trade in exchange-value for use-value, I dissatisfied with some of my dissertation findings about critical secondary mathematics. At the same time, my findings were not entirely negative for critical mathematics education; some of my students appeared to find critical activities to be more engaging and meaningful than standards-based activities. In addition, my discourse analyses, showed that, over time, there were higher rates of student subjectivization and increased classroom participation - especially regarding student willingness to verbalize their reasoning behind finding mathematical solutions in standards-based activities.

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