Thinking in three dimensions: Exploring students' geometric thinking and spatial ability with the Geometer's Sketchpad

Current reform initiatives recommend that geometry instruction include the study of three-dimensional geometric objects and provide students with opportunities to use spatial skills in problem-solving tasks. Geometer's Sketchpad (GSP) is a dynamic and interactive computer program that enables the user to investigate and explore geometric concepts and manipulate geometric structures. Research using GSP as an instructional tool has focused primarily on teaching and learning two-dimensional geometry. This study explored the effect of a GSP based instructional environment on students' geometric thinking and three-dimensional spatial ability as they used GSP to learn three-dimensional geometry. For 10 weeks, 18 tenth-grade students from an urban school district used GSP to construct and analyze dynamic, two-dimensional representations of three-dimensional objects in a classroom environment that encouraged exploration, discussion, conjecture, and verification. The data were collected primarily from participant observations and clinical interviews and analyzed using qualitative methods of analysis. In addition, pretest and posttest measures of three-dimensional spatial ability and van Hiele level of geometric thinking were obtained. Spatial ability measures were analyzed using standard t-test analysis. ^ The data from this study indicate that GSP is a viable tool to teach students about three-dimensional geometric objects. A comparison of students' pretest and posttest van Hiele levels showed an improvement in geometric thinking, especially for students on lower levels of the van Hiele theory. Evidence at the p < .05 level indicated that students' spatial ability improved significantly. Specifically, the GSP dynamic, visual environment supported students' visualization and reasoning processes as students attempted to solve challenging tasks about three-dimensional geometric objects. The GSP instructional activities also provided students with an experiential base and an intuitive understanding about three-dimensional objects from which more formal work in geometry could be pursued. This study demonstrates that by designing appropriate GSP based instructional environments, it is possible to help students improve their spatial skills, develop more coherent and accurate intuitions about three-dimensional geometric objects, and progress through the levels of geometric thinking proposed by van Hiele. ^

A youth vision of the city: The socio-spatial lives and exclusion of street girls in Bogota, Colombia

This dissertation documents the everyday lives and spaces of a population of youth typically constructed as out of place, and the broader urban context in which they are rendered as such. Thirty-three female and transgender street youth participated in the development of this youth-based participatory action research (YPAR) project utilizing geo-ethnographic methods, auto-photography, and archival research throughout a six-phase, eighteen-month research process in Bogotá, Colombia. ^ This dissertation details the participatory writing process that enabled the YPAR research team to destabilize dominant representations of both street girls and urban space and the participatory mapping process that enabled the development of a youth vision of the city through cartographic images. The maps display individual and aggregate spatial data indicating trends within and making comparisons between three subgroups of the research population according to nine spatial variables. These spatial data, coupled with photographic and ethnographic data, substantiate that street girls’ mobilities and activity spaces intersect with and are altered by state-sponsored urban renewal projects and paramilitary-led social cleansing killings, both efforts to clean up Bogotá by purging the city center of deviant populations and places. ^ Advancing an ethical approach to conducting research with excluded populations, this dissertation argues for the enactment of critical field praxis and care ethics within a YPAR framework to incorporate young people as principal research actors rather than merely voices represented in adultist academic discourse. Interjection of considerations of space, gender, and participation into the study of street youth produce new ways of envisioning the city and the role of young people in research. Instead of seeing the city from a panoptic view, Bogotá is revealed through the eyes of street youth who participated in the construction and feminist visualization of a new cartography and counter-map of the city grounded in embodied, situated praxis. This dissertation presents a socially responsible approach to conducting action-research with high-risk youth by documenting how street girls reclaim their right to the city on paper and in practice; through maps of their everyday exclusion in Bogotá followed by activism to fight against it.^

Regional processes in mangrove ecosystems: spatial scaling relationships, biomass, and turnover rates following catastrophic disturbance

Physiological processes and local-scale structural dynamics of mangroves are relatively well studied. Regional-scale processes, however, are not as well understood. Here we provide long-term data on trends in structure and forest turnover at a large scale, following hurricane damage in mangrove ecosystems of South Florida, U.S.A. Twelve mangrove vegetation plots were monitored at periodic intervals, between October 1992 and March 2005. Mangrove forests of this region are defined by a −1.5 scaling relationship between mean stem diameter and stem density, mirroring self-thinning theory for mono-specific stands. This relationship is reflected in tree size frequency scaling exponents which, through time, have exhibited trends toward a community average that is indicative of full spatial resource utilization. These trends, together with an asymptotic standing biomass accumulation, indicate that coastal mangrove ecosystems do adhere to size-structured organizing principles as described for upland tree communities. Regenerative dynamics are different between areas inside and outside of the primary wind-path of Hurricane Andrew which occurred in 1992. Forest dynamic turnover rates, however, are steady through time. This suggests that ecological, more-so than structural factors, control forest productivity. In agreement, the relative mean rate of biomass growth exhibits an inverse relationship with the seasonal range of porewater salinities. The ecosystem average in forest scaling relationships may provide a useful investigative tool of mangrove community biomass relationships, as well as offer a robust indicator of general ecosystem health for use in mangrove forest ecosystem management and restoration.