Occasional white boarding : examining the effects of physics students' understanding of motion graphs

The Modeling method of teaching has demonstrated well--‐documented success in the improvement of student learning. The teacher/researcher in this study was introduced to Modeling through the use of a technique called White Boarding. Without formal training, the researcher began using the White Boarding technique for a limited number of laboratory experiences with his high school physics classes. The question that arose and was investigated in this study is “What specific aspects of the White Boarding process support student understanding?” For the purposes of this study, the White Boarding process was broken down into three aspects – the Analysis of data through the use of Logger Pro software, the Preparation of White Boards, and the Presentations each group gave about their specific lab data. The lab used in this study, an Acceleration of Gravity Lab, was chosen because of the documented difficulties students experience in the graphing of motion. In the lab, students filmed a given motion, utilized Logger Pro software to analyze the motion, prepared a White Board that described the motion with position--‐time and velocity--‐time graphs, and then presented their findings to the rest of the class. The Presentation included a class discussion with minimal contribution from the teacher. The three different aspects of the White Boarding experience – Analysis, Preparation, and Presentation – were compared through the use of student learning logs, video analysis of the Presentations, and follow--‐up interviews with participants. The information and observations gathered were used to determine the level of understanding of each participant during each phase of the lab. The researcher then looked for improvement in the level of student understanding, the number of “aha” moments students had, and the students’ perceptions about which phase was most important to their learning. The results suggest that while all three phases of the White Boarding experience play a part in the learning process for students, the Presentations provided the most significant changes. The implications for instruction are discussed.

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.

The Planned and the Emergent: An Alternative Model of Learning and Literacy

Within academic institutions, writing centers are uniquely situated, socially rich sites for exploring learning and literacy. I examine the work of the Michigan Tech Writing Center's UN 1002 World Cultures study teams primarily because student participants and Writing Center coaches are actively engaged in structuring their own learning and meaning-making processes. My research reveals that learning is closely linked to identity formation and leading the teams is an important component of the coaches' educational experiences. I argue that supporting this type of learning requires an expanded understanding of literacy and significant changes to how learning environments are conceptualized and developed. This ethnographic study draws on data collected from recordings and observations of one semester of team sessions, my own experiences as a team coach and UN 1002 teaching assistant, and interviews with Center coaches prior to their graduation. I argue that traditional forms of assessment and analysis emerging from individualized instruction models of learning cannot fully account for the dense configurations of social interactions identified in the Center's program. Instead, I view the Center as an open system and employ social theories of learning and literacy to uncover how the negotiation of meaning in one context influences and is influenced by structures and interactions within as well as beyond its boundaries. I focus on the program design, its enaction in practice, and how engagement in this type of writing center work influences coaches' learning trajectories. I conclude that, viewed as participation in a community of practice, the learning theory informing the program design supports identity formation —a key aspect of learning as argued by Etienne Wenger (1998). The findings of this study challenge misconceptions of peer learning both in writing centers and higher education that relegate peer tutoring to the role of support for individualized models of learning. Instead, this dissertation calls for consideration of new designs that incorporate peer learning as an integral component. Designing learning contexts that cultivate and support the formation of new identities is complex, involves a flexible and opportunistic design structure, and requires the availability of multiple forms of participation and connections across contexts.