SUPPORTING LEARNING FOR NAVAJO STUDENTS THROUGH ETHNOMATHEMATICS

The purpose of this research was to address how culturally informed ethnomathematical methods of teaching can be utilized to support the learning of Navajo students in mathematics. The study was conducted over the course of four years on the Navajo Reservations at Tohatchi Middle School in Tohatchi New Mexico. The students involved in the study were all in 8th grade and were enrolled either in Algebra 1 or a Response to Intervention, RTI, class. The data collected came in the form of a student survey, student observation and student assessment. The teacher written survey, a math textbook word problem, and two original math textbook problems along with their rewritten version were the sources of these three studies. The first year of the study consisted of a math attitude survey and how Navajo students perceived math as a subject of interest. The students answered four questions pertaining to their thoughts about mathematics. The students’ responses were positive according to their written answers. The second year of the study involved the observation of how students worked through a math word problem as a group. This method tested how the students culturally interacted in order to solve a math problem. Their questions and reasoning to solve the problem were shared with peers and the teacher. The teacher supported the students in understanding and solving the problem by asking questions that kept the students focused on the goal of solving the problem. The students worked collaboratively and openly in order to complete the activity. During the iv study, the teacher was more able to notice the students’ deficiencies individually or as a group, therefore was able to support them in a more specific manner. The last study was conducted over a period of two different years. This study was used to determine how textbook bias in the form of its sentence structure or word choice affects the performance of students who are not culturally familiar with one or both. It was found that the students performed better and took less time on the rewritten problem than on the original problem. The data suggests that focusing on the culture, language and education of Navajo students can affect how the students learn and understand math.

A PHENOMENOLOGY OF MIMETIC LEARNING AND MULTIMODAL COGNITION: INTEGRATING EXPERIENTIAL KNOWLEDGE INTO PROGRAMS IN RHETORIC, COMPOSITION, AND TECHNICAL COMMUNICATION

My dissertation emphasizes a cognitive account of multimodality that explicitly integrates experiential knowledge work into the rhetorical pedagogy that informs so many composition and technical communication programs. In these disciplines, multimodality is widely conceived in terms of what Gunther Kress calls “socialsemiotic” modes of communication shaped primarily by culture. In the cognitive and neurolinguistic theories of Vittorio Gallese and George Lakoff, however, multimodality is described as a key characteristic of our bodies’ sensory-motor systems which link perception to action and action to meaning, grounding all communicative acts in knowledge shaped through body-engaged experience. I argue that this “situated” account of cognition – which closely approximates Maurice Merleau-Ponty’s phenomenology of perception, a major framework for my study – has pedagogical precedence in the mimetic pedagogy that informed ancient Sophistic rhetorical training, and I reveal that training’s multimodal dimensions through a phenomenological exegesis of the concept mimesis. Plato’s denigration of the mimetic tradition and his elevation of conceptual contemplation through reason, out of which developed the classic Cartesian separation of mind from body, resulted in a general degradation of experiential knowledge in Western education. But with the recent introduction into college classrooms of digital technologies and multimedia communication tools, renewed emphasis is being placed on the “hands-on” nature of inventive and productive praxis, necessitating a revision of methods of instruction and assessment that have traditionally privileged the acquisition of conceptual over experiential knowledge. The model of multimodality I construct from Merleau-Ponty’s phenomenology, ancient Sophistic rhetorical pedagogy, and current neuroscientific accounts of situated cognition insists on recognizing the significant role knowledges we acquire experientially play in our reading and writing, speaking and listening, discerning and designing practices.