Mathematics

This ethnographic study investigated teacher leadership and professional learning in a secondary mathematics department. Qualitative data were collected through in-depth face-to-face interviews, observations, and document analysis. It is the social aspect of the school environment and specifically, the subject department, which presents an opportunity for teachers to learn and share their expertise with one another in an informal setting and for teacher leaders to emerge using their expertise and close proximity to affect the learning of colleagues. Teachers were asked to share their thoughts on leadership and learning within their department. A narrative was written to give the reader a better understanding of the day-to-day practices, behaviors, and habits of the teachers in the department, creating a holistic picture of the culture studied. ... teacher leadership is experienced informally through teachers sharing and talking about their practice. Teacher leadership is also experienced outside the department when teachers have opportunities to lead school professional development seminars and to practice leadership through role modeling. Professional learning is experienced one-on-one, as well as formally and informally through colleagues and organized workshops. Implications for administrators, department and team leaders, and policy implementation are discussed. This study may contribute to the development of teacher leadership and professional learning, which ultimately may lead to improving student achievement.

This study described, analyzed, and compared the internal and external factors that prevented or fostered the implementation of a cognitive tool, GeoGebra, in the mathematics practices of 12 middle school teachers who had completed a master's degree program in mathematics successfully. Through the application of a case study approach as a systematic method for the analysis of qualitative data, and under a social constructivist framework, the study examined different factors such as concerns of teachers; their beliefs about technology, mathematics as a subject, math teaching, and learning; external factors such as resources and school support; their TPACK development; and their instrumental orchestration approach through classroom observations. Among the major findings, the study revealed that the personal concerns of the teacher users of GeoGebra included the desire to continue learning the new features of the software, as well as the desire to connect themselves with others in common endeavors for the benefit of other teachers and, ultimately, the students... There was a consensus among the teacher users that they had to strike a balance between their professional goals and the available resources.

Mathematics can be a difficult topic both to teach and to learn. Word problems specifically can be difficult for students with disabilities because they have to conceptualize what the problem is asking for, and they must perform the correct operation accurately. Current trends in mathematics instruction stem from the National Council of Teachers of Mathematics (NCTM) Principles and Standards for School Mathematics that call for an inquiry learning model (NCTM, 2000). Unfortunately, this model may not be sufficient to meet the needs of students with disabilities. Researchers are currently looking at what elements will assist students with disabilities to learn mathematics both conceptually and procedurally. Explicit direct instruction, modeling, guided and independent practice, and providing advanced organizers have been found to help students with disabilities to be successful. Results indicated that students with mild disabilities were able to use the strategy independently to accurately solve the training word problems using division or multiplication. Also, students were able to generalize both the strategy use as well as the word problem accuracy to the measurement of area problems. Additionally, two of the three students continued to use the strategy appropriately to accurately solve word problems in the 6-week follow-up phase. Suggestions for future studies are provided as well as educational implications.

With more and more focus on accountability, algebra achievement has become a major focus of math curriculum developers. In many states, students are expected to pass standardized Algebra achievement tests in order to satisfy graduation requirements. The purpose of this study was to identify teacher qualities and teaching qualities linked to teacher effectiveness in 7th-grade Algebra I Honors. This study examined two aspects of teachers, teacher quality and teaching quality. Teacher quality refers to the characteristics that teachers possess and teaching quality refers to what teachers do in the classroom to foster student learning. For this study, teacher quality included teacher professional preparation characteristics and teacher knowledge. Also, aspects of teaching quality that promote conceptual understanding in Algebra were examined. The difference between more and less effective teachers in this study lies in teaching quality, what teachers do in the classroom, as opposed to teacher quality, what those teachers bring with them to the classroom. The findings of this study indicate that elements of teaching quality are more indicative of teacher effectiveness than elements of teacher quality among teachers in the study. Although there was some evidence of a relationship between elements of teacher quality and teacher effectiveness, there were clear differences in teaching quality among more effective and less effective teachers in this study.

The family of algebraic surfaces X dened by the single equation zn = (y a1x) (y anx)(x 1) over an algebraically closed eld k of characteristic zero, where a1; : : : ; an 2 k are distinct, is studied. It is shown that this is a rational surface with a non-rational singularity at the origin. The ideal class group of the surface is computed. The terms of the Chase-Harrison-Rosenberg seven term exact sequence on the open complement of the ramication locus of X ! A2 are computed; the Brauer group is also studied in this unramied setting. The analysis is extended to the surface eX obtained by blowing up X at the origin. The interplay between properties of eX , determined in part by the exceptional curve E lying over the origin, and the properties of X is explored. In particular, the implications that these properties have on the Picard group of the surface X are studied.

Fine-scale urban land cover information is important for a number of applications, including urban tree canopy mapping, green space analysis, and urban hydrologic modeling. Land cover information has traditionally been extracted from satellite or aerial images using automated image classification techniques, which classify pixels into different categories of land cover based on their spectral characteristics. However, in fine spatial resolution images (4 meters or better), the high degree of within-class spectral variability and between-class spectral similarity of many types of land cover leads to low classification accuracy when pixel-based, purely spectral classification techniques are used. Object-based classification methods, which involve segmenting an image into relatively homogeneous regions (i.e. image segments) prior to classification, have been shown to increase classification accuracy by incorporating the spectral (e.g. mean, standard deviation) and non-spectral (e.g. te xture, size, shape) information of image segments for classification. One difficulty with the object-based method, however, is that a segmentation parameter (or set of parameters), which determines the average size of segments (i.e. the segmentation scale), is difficult to choose. Some studies use one segmentation scale to segment and classify all types of land cover, while others use multiple scales due to the fact that different types of land cover typically vary in size. In this dissertation, two multi-scale object-based classification methods were developed and tested for classifying high resolution images of Deerfield Beach, FL and Houston, TX. These multi-scale methods achieved higher overall classification accuracies and Kappa coefficients than single-scale object-based classification methods.

Implementing Shamir's secret sharing scheme using floating point arithmetic would provide a faster and more efficient secret sharing scheme due to the speed in which GPUs perform floating point arithmetic. However, with the loss of a finite field, properties of a perfect secret sharing scheme are not immediately attainable. The goal is to analyze the plausibility of Shamir's secret sharing scheme using floating point arithmetic achieving the properties of a perfect secret sharing scheme and propose improvements to attain these properties. Experiments indicate that property 2 of a perfect secret sharing scheme, "Any k-1 or fewer participants obtain no information regarding the shared secret", is compromised when Shamir's secret sharing scheme is implemented with floating point arithmetic. These experimental results also provide information regarding possible solutions and adjustments. One of which being, selecting randomly generated points from a smaller interval in one of the proposed schemes of this thesis. Further experimental results indicate improvement using the scheme outlined. Possible attacks are run to test the desirable properties of the different schemes and reinforce the improvements observed in prior experiments.

This thesis develops methodologies for continuous estimation of hydrological variables which infill missing daily rainfall data and the forecast of weekly streamflows from a watershed. Several mathematical programming formulations were developed and used to estimate missing historical rainfall data. Functional relationships were created between radar precipitation and known rain gauge data then are used to estimate the missing data. Streamflow predictions models require highly non-linear mathematical models to capture the complex physical characteristics of a watershed. An artificial neural network model was developed for streamflow prediction. There are no set methods of creating a neural network and the selection of architecture and inputs to a neural network affects the performance. This thesis addresses this issue with automated input and network architecture selection through optimization. MATLABª scripts are developed and used to test many combinations and select a model through optimization.

The purpose of this study was to identify factors that are associated with encourage the persistence of undergraduate women majoring in Engineering and Math (EM) at Florida Atlantic University, University of Central Florida, and University of South Florida. The persistence factors were examined through an analysis of university data and the use of a survey for enrolled senior standing students who declared their first major in engineering or math. Both quantitative and qualitative methods were utilized to collect and analyze data from the three sites. Factor analysis and logistic regression were used to analyze the quantitative data. The quantitative data retrieved from the survey instrument revealed that participants who were self motivated, felt they had a safe learning environment, and were engaged by the university were more likely to persist in engineering and math. Additionally, the survey revealed that race and ethnicity does not predict persistence of undergraduate women maj oring in engineering and math. Qualitative analysis of open-ended survey questions revealed that the most important factor that helps female students persist in engineering and math major was self-confidence and determination. They also indicated that discrimination and stereotyping were the most difficult factors for female students to overcome. To enable more women to be successful in the pursuit of a engineering or math degree, participants made an overwhelming reference to intervention as student engagement.

Phylogenies constructed from skeletal data often contradict those built from genetic data. This study evaluates the phylogenetic utility of adult male, female, and juvenile hominoid cranial bones. First, I used geometric morphometric methods to compare the cranial bone shapes of seven primate genera (Gorilla, Homo, Hylobates, Macaca, Nomascus, Pan, and Pongo). I then coded these shapes as continuous characters and constructed cladograms via parsimony analysis for the adult male, female, and juvenile character matrices. Finally, I evaluated the similarity of these cladograms to one another and to the genetic phylogeny using topological distance software. Cladograms did not differ from one another or the genetic phylogeny less than comparisons of randomly generated trees. These results suggest that cranial shapes are unlikely to provide accurate phylogenetic information, and agree with other analyses of skeletal data that fail to recover the molecular phylogeny (Collard & Wood, 2000, 2001; Springer et al., 2007).