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.

Nitrogen Oxides in the North Atlantic Troposphere: Impacts of Boreal Wildfire and Anthropogenic Emissions

Nitrogen oxides play a crucial role in the budget of tropospheric ozone (O sub(3)) and the formation of the hydroxyl radical. Anthropogenic activities and boreal wildfires are large sources of emissions in the atmosphere. However, the influence of the transport of these emissions on nitrogen oxides and O sub(3) levels at hemispheric scales is not well understood, in particular due to a lack of nitrogen oxides measurements in remote regions. In order to address these deficiencies, measurements of NO, NO sub(2) and NO sub(y) (total reactive nitrogen oxides) were made in the lower free troposphere (FT) over the central North Atlantic region (Pico Mountain station, 38 degree N 28 degree W, 2.3 km asl) from July 2002 to August 2005. These measurements reveal a well-defined seasonal cycle of nitrogen oxides (NO sub(x) = NO+NO sub(2) and NO sub(y)) in the background central North Atlantic lower FT, with higher mixing ratios during the summertime. Observed NO sub(x) and NO sub(y) levels are consistent with long-range transport of emissions, but with significant removal en-route to the measurement site. Reactive nitrogen largely exists in the form of PAN and HNO sub(3) ( similar to 80-90% of NO sub(y)) all year round. A shift in the composition of NO sub(y) from dominance of PAN to dominance of HNO sub(3) occurs from winter-spring to summer-fall, as a result of changes in temperature and photochemistry over the region. Analysis of the long-range transport of boreal wildfire emissions on nitrogen oxides provides evidence of the very large-scale impacts of boreal wildfires on the tropospheric NO sub(x) and O sub(3) budgets. Boreal wildfire emissions are responsible for significant shifts in the nitrogen oxides distributions toward higher levels during the summer, with medians of NO sub(y) (117-175 pptv) and NO sub(x) (9-30 pptv) greater in the presence of boreal wildfire emissions. Extreme levels of NO sub(x) (up to 150 pptv) and NO sub(y) (up to 1100 pptv) observed in boreal wildfire plumes suggest that decomposition of PAN to NO sub(x) is a significant source of NO sub(x), and imply that O sub(3) formation occurs during transport. Ozone levels are also significantly enhanced in boreal wildfire plumes. However, a complex behavior of O sub(3) is observed in the plumes, which varies from significant to lower O sub(3) production to O sub(3) destruction. Long-range transport of anthropogenic emissions from North America also has a significant influence on the regional NO sub(x) and O sub(3) budgets. Transport of pollution from North America causes significant enhancements on nitrogen oxides year-round. Enhancements of CO, NO sub(y) and NO sub(x) indicate that, consistent with previous studies, more than 95% of the NO sub(x) emitted over the U.S. is removed before and during export out of the U.S. boundary layer. However, about 30% of the NO sub(x) emissions exported out of the U.S. boundary layer remain in the airmasses. Since the lifetime of NO sub(x) is shorter than the transport timescale, PAN decomposition and potentially photolysis of HNO sub(3) provide a supply of NO sub(x) over the central North Atlantic lower FT. Observed Delta O sub(3)/ Delta NO sub(y) and large NO sub(y) levels remaining in the North American plumes suggest potential O sub(3) formation well downwind from North America. Finally, a comparison of the nitrogen oxides measurements with results from the global chemical transport (GCT) model GEOS-Chem identifies differences between the observations and the model. GEOS-Chem reproduces the seasonal variation of nitrogen oxides over the central North Atlantic lower FT, but does not capture the magnitude of the cycles. Improvements in our understanding of nitrogen oxides chemistry in the remote FT and emission sources are necessary for the current GCT models to adequately estimate the impacts of emissions on tropospheric NO sub(x) and the resulting impacts on the O sub(3) budget.

THE HOLOGRAPHIC DETECTOR FOR CLOUDS FROM TRL 5 TO TRL 8

Clouds are one of the most influential elements of weather on the earth system, yet they are also one of the least understood. Understanding their composition and behavior at small scales is critical to understanding and predicting larger scale feedbacks. Currently, the best method to study clouds on the microscale is through airborne in situ measurements using optical instruments capable of resolving clouds on the individual particle level. However, current instruments are unable to sufficiently resolve the scales important to cloud evolution and behavior. The Holodec is a new generation of optical cloud instrument which uses digital inline holography to overcome many of the limitations of conventional instruments. However, its performance and reliability was limited due to several deficiencies in its original design. These deficiencies were addressed and corrected to advance the instrument from the prototype stage to an operational instrument. In addition, the processing software used to reconstruct and analyze digitally recorded holograms was improved upon to increase robustness and ease of use.