Mathematical voices: The experiences, perceptions and self-images of three women as learners of developmental mathematics and statistics.

摘要

Through qualitative case study methods and situated in the context of learning developmental mathematics and statistics, this dissertation portrays the mathematical experiences, perceptions, and self-images of three nontraditional women students. Based on tutoring sessions that were conducted during an academic quarter, detailed narratives along with their analyses provide insights into how the women view themselves as learners of mathematics or statistics as well as how they express themselves mathematically or statistically. Taking into account how intricately the affective and cognitive aspects of a learner weave together, the psychological theory of "ways of knowing" is used as a conceptual framework and interpretive tool. The "ways of knowing" theory was developed in 1986 by Mary Field Belenky, Blythe McVicker Clinchy, Nancy Rule Goldberger, and Jill Mattuck Tarule and has since been incorporated into many fields of study including mathematics education.;This dissertation demonstrates how the "ways of knowing" theory can be used as a conceptual framework through which teachers and researchers may gather insights to better understand students' mathematical voices. Prominent research findings indicate that it may be very difficult for students to transform their mathematical voices by making connections among the perspectives of knowing and thus broadening their approaches to learning, doing, and understanding mathematics. A crucial step in the development of mathematical voice may be a "subjective" perspective of knowing involving intuitive ideas and personal connections with mathematics and mathematical ideas. Implications for further research include identifying aspects of a subjective way of knowing more thoroughly as well as investigating teaching strategies that may facilitate and integrate subjective ways of knowing and voices of reasoning.