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. ^

Dynamic image precompensation for improving visual performance of computer users with ocular aberrations

With the progress of computer technology, computers are expected to be more intelligent in the interaction with humans, presenting information according to the user's psychological and physiological characteristics. However, computer users with visual problems may encounter difficulties on the perception of icons, menus, and other graphical information displayed on the screen, limiting the efficiency of their interaction with computers. In this dissertation, a personalized and dynamic image precompensation method was developed to improve the visual performance of the computer users with ocular aberrations. The precompensation was applied on the graphical targets before presenting them on the screen, aiming to counteract the visual blurring caused by the ocular aberration of the user's eye. A complete and systematic modeling approach to describe the retinal image formation of the computer user was presented, taking advantage of modeling tools, such as Zernike polynomials, wavefront aberration, Point Spread Function and Modulation Transfer Function. The ocular aberration of the computer user was originally measured by a wavefront aberrometer, as a reference for the precompensation model. The dynamic precompensation was generated based on the resized aberration, with the real-time pupil diameter monitored. The potential visual benefit of the dynamic precompensation method was explored through software simulation, with the aberration data from a real human subject. An "artificial eye'' experiment was conducted by simulating the human eye with a high-definition camera, providing objective evaluation to the image quality after precompensation. In addition, an empirical evaluation with 20 human participants was also designed and implemented, involving image recognition tests performed under a more realistic viewing environment of computer use. The statistical analysis results of the empirical experiment confirmed the effectiveness of the dynamic precompensation method, by showing significant improvement on the recognition accuracy. The merit and necessity of the dynamic precompensation were also substantiated by comparing it with the static precompensation. The visual benefit of the dynamic precompensation was further confirmed by the subjective assessments collected from the evaluation participants.

Dynamic Image Precompensation for Improving Visual Performance of Computer Users with Ocular Aberrations

With the progress of computer technology, computers are expected to be more intelligent in the interaction with humans, presenting information according to the user's psychological and physiological characteristics. However, computer users with visual problems may encounter difficulties on the perception of icons, menus, and other graphical information displayed on the screen, limiting the efficiency of their interaction with computers. In this dissertation, a personalized and dynamic image precompensation method was developed to improve the visual performance of the computer users with ocular aberrations. The precompensation was applied on the graphical targets before presenting them on the screen, aiming to counteract the visual blurring caused by the ocular aberration of the user's eye. A complete and systematic modeling approach to describe the retinal image formation of the computer user was presented, taking advantage of modeling tools, such as Zernike polynomials, wavefront aberration, Point Spread Function and Modulation Transfer Function. The ocular aberration of the computer user was originally measured by a wavefront aberrometer, as a reference for the precompensation model. The dynamic precompensation was generated based on the resized aberration, with the real-time pupil diameter monitored. The potential visual benefit of the dynamic precompensation method was explored through software simulation, with the aberration data from a real human subject. An "artificial eye'' experiment was conducted by simulating the human eye with a high-definition camera, providing objective evaluation to the image quality after precompensation. In addition, an empirical evaluation with 20 human participants was also designed and implemented, involving image recognition tests performed under a more realistic viewing environment of computer use. The statistical analysis results of the empirical experiment confirmed the effectiveness of the dynamic precompensation method, by showing significant improvement on the recognition accuracy. The merit and necessity of the dynamic precompensation were also substantiated by comparing it with the static precompensation. The visual benefit of the dynamic precompensation was further confirmed by the subjective assessments collected from the evaluation participants.

Connecting visual and analytic reasoning to improve students' spatial visualization abilities: A constructivist approach

Current reform initiatives recommend that school geometry teaching and learning include the study of three-dimensional geometric objects and provide students with opportunities to use spatial abilities in mathematical tasks. Two ways of using Geometer's Sketchpad (GSP), a dynamic and interactive computer program, in conjunction with manipulatives enable students to investigate and explore geometric concepts, especially when used in a constructivist setting. Research on spatial abilities has focused on visual reasoning to improve visualization skills. This dissertation investigated the hypothesis that connecting visual and analytic reasoning may better improve students' spatial visualization abilities as compared to instruction that makes little or no use of the connection of the two. Data were collected using the Purdue Spatial Visualization Tests (PSVT) administered as a pretest and posttest to a control and two experimental groups. Sixty-four 10th grade students in three geometry classrooms participated in the study during 6 weeks. Research questions were answered using statistical procedures. An analysis of covariance was used for a quantitative analysis, whereas a description of students' visual-analytic processing strategies was presented using qualitative methods. The quantitative results indicated that there were significant differences in gender, but not in the group factor. However, when analyzing a sub sample of 33 participants with pretest scores below the 50th percentile, males in one of the experimental groups significantly benefited from the treatment. A review of previous research also indicated that students with low visualization skills benefited more than those with higher visualization skills. The qualitative results showed that girls were more sophisticated in their visual-analytic processing strategies to solve three-dimensional tasks. It is recommended that the teaching and learning of spatial visualization start in the middle school, prior to students' more rigorous mathematics exposure in high school. A duration longer than 6 weeks for treatments in similar future research studies is also recommended.

A large-scale dynamic vector and raster data visualization geographic information system based on parallel map tiling

With the exponential increasing demands and uses of GIS data visualization system, such as urban planning, environment and climate change monitoring, weather simulation, hydrographic gauge and so forth, the geospatial vector and raster data visualization research, application and technology has become prevalent. However, we observe that current web GIS techniques are merely suitable for static vector and raster data where no dynamic overlaying layers. While it is desirable to enable visual explorations of large-scale dynamic vector and raster geospatial data in a web environment, improving the performance between backend datasets and the vector and raster applications remains a challenging technical issue. This dissertation is to implement these challenging and unimplemented areas: how to provide a large-scale dynamic vector and raster data visualization service with dynamic overlaying layers accessible from various client devices through a standard web browser, and how to make the large-scale dynamic vector and raster data visualization service as rapid as the static one. To accomplish these, a large-scale dynamic vector and raster data visualization geographic information system based on parallel map tiling and a comprehensive performance improvement solution are proposed, designed and implemented. They include: the quadtree-based indexing and parallel map tiling, the Legend String, the vector data visualization with dynamic layers overlaying, the vector data time series visualization, the algorithm of vector data rendering, the algorithm of raster data re-projection, the algorithm for elimination of superfluous level of detail, the algorithm for vector data gridding and re-grouping and the cluster servers side vector and raster data caching.