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.

Structural Health Monitoring using Index Based Reasoning for Unmanned Aerial Vehicles

Unmanned Aerial Vehicles (UAVs) may develop cracks, erosion, delamination or other damages due to aging, fatigue or extreme loads. Identifying these damages is critical for the safe and reliable operation of the systems. ^ Structural Health Monitoring (SHM) is capable of determining the conditions of systems automatically and continually through processing and interpreting the data collected from a network of sensors embedded into the systems. With the desired awareness of the systems’ health conditions, SHM can greatly reduce operational cost and speed up maintenance processes. ^ The purpose of this study is to develop an effective, low-cost, flexible and fault tolerant structural health monitoring system. The proposed Index Based Reasoning (IBR) system started as a simple look-up-table based diagnostic system. Later, Fast Fourier Transformation analysis and neural network diagnosis with self-learning capabilities were added. The current version is capable of classifying different health conditions with the learned characteristic patterns, after training with the sensory data acquired from the operating system under different status. ^ The proposed IBR systems are hierarchy and distributed networks deployed into systems to monitor their health conditions. Each IBR node processes the sensory data to extract the features of the signal. Classifying tools are then used to evaluate the local conditions with health index (HI) values. The HI values will be carried to other IBR nodes in the next level of the structured network. The overall health condition of the system can be obtained by evaluating all the local health conditions. ^ The performance of IBR systems has been evaluated by both simulation and experimental studies. The IBR system has been proven successful on simulated cases of a turbojet engine, a high displacement actuator, and a quad rotor helicopter. For its application on experimental data of a four rotor helicopter, IBR also performed acceptably accurate. The proposed IBR system is a perfect fit for the low-cost UAVs to be the onboard structural health management system. It can also be a backup system for aircraft and advanced Space Utility Vehicles. ^

Differential effects of single -sex versus coed education on the mathematical reasoning ability, verbal reasoning ability, and self-concept of high school girls

This study explored the differential effects of single-sex versus coed education on the cognitive and affective development of young women in senior year of high school. The basic research question was: What are the differential effects of single-sex versus coed education on the development of mathematical reasoning ability, verbal reasoning ability, or self-concept of high school girls?^ This study was composed of two parts. In the first part, the SAT verbal and mathematical ability scores were recorded for those subjects in the two schools from which the sample populations were drawn. The second part of the study required the application of the Piers-Harris Children's Self-Concept Scale to subjects in each of the two sample populations. The sample schools were deliberately selected to minimize between group differences in the populations. One was an all girls school, the other coeducational.^ The research design employed in this study was the causal-comparative method, used to explore causal relationships between variables that already exist. Based on a comprehensive analysis of the data produced by this research, no significant difference was found to exist between the mean scores of the senior girls in the single-sex school and the coed school on the SAT 1 verbal reasoning section. Nor was any significant difference found to exist between the mean scores of the senior girls in the single-sex school and the coed school on the SAT 1 mathematical reasoning section. Finally, no significant difference between the mean total scores of the senior girls in the single-sex school and the coed school on the Piers-Harris Children's Self-Concept Scale was found to exist.^ Contrary to what many other studies have found in the past about single-sex schools and their advantages for girls, this study found no support for such advantages in the cognitive areas of verbal and mathematical reasoning as measured by the SAT or in the affective area of self-concept as measured by the Piers-Harris Children's Self-Concept Scale. ^