| 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 generally 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 standards of the National Council of Teachers of Mathematics (NCTM, 2000). Proponents of critical mathematics argue that a Freirean approach to mathematics instruction has the potential to be more empowering and equitable than dominant versions of mathematics instruction because it allows subordinated students to use mathematics to develop their understandings of 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. The first analysis was conducted primarily on an instructional diary that I kept as I engaged in curriculum design and instruction; it documented evolutions in my approach to critical curriculum development and in my beliefs about secondary mathematics and the potential it offers for political and academic student empowerment. The curriculum analysis was based on a sociological framework developed by Dowling (1998) for the analysis of school mathematics texts. Using his approach, I found that the attention my critical mathematics placed on critical themes and contexts tended to displace the development of mathematical power. In the discourse analysis I examined the ways students engaged in, or resisted, standards-based and critical mathematics activities and also raised issues of power, status, and equity. There were a number of interrelated findings regarding student participation, including: marked differences in student participation in critical and standards-based activities and a positive shift in student stances towards the expression of personal agency, student-centered (subjectified) control of the classroom activities, and their ability to verbally reason about mathematical functions and take risks in classroom participation.; 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. 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. The balance between teacher and student responsibility for learning tipped toward the students in a constructive way in some critical mathematics 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. Further research is recommended to: (1) enhance the mathematics power of critical mathematics and standards-based texts and activities; (2) explore the ways that the personal and politica... |
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