Thesis (M.S.) -- Central Connecticut State University, 2007. / Thesis advisor: Phillip Halloran. "... in partial fulfillment of the requirements for the degree of Master of Science in Middle School Mathematics." Includes bibliographical references (leaf 21). Also available via the World Wide Web.

Thesis (Ph. D.)--Florida State University, 2006. / Advisors: Kenneth Shaw, Leslie Aspinwall, Florida State University, College of Education, Dept. of Middle and Secondary Education. Title and description from dissertation home page (viewed Sept. 14, 2006). Document formatted into pages; contains xii, 129 pages. Includes bibliographical references.

In this thesis we construct rogue waves occurring in the sine-Gordon equation. An algebraic method is used to find explicit solutions to a Lax pair of equations. The Lax pair being studied is compatible with solutions to the sine-Gordon equation. Rotational and librational traveling wave solutions to the sine-Gordon equation are considered in the Lax pair. The Darboux transformation is applied with the Lax pair solutions computed at the rotational and librational waves to generate algebraic solitons and rogue waves, respectively. The rogue waves occur on the end points of the Floquet-Lax spectrum bands and can achieve a magnification factor of at most 3. / Thesis / Master of Science (MSc)

L'objet de la thèse est d'exposer une démarche méthodologique qui vise à prendre en compte, dans les modèles de séries temporelles, des effets exogènes mesurés à l'aide de variables additionnelles, et de l'illustrer par un certain nombre d'applications au secteur des transports. Dans ces applications, le pas de temps est le jour, le mois, le trimestre voire le semestre : il s'est agi de prendre en compte des effets exogènes, de nature transitoire ou de nature durable, qui se manifestent dans le court terme. La première partie de la thèse traite de la modélisation des séries temporelles. Nous situons le cadre formel des modèles auxquels nous nous intéressons, nous exposons la démarche suivie dans le cadre des modèles ARMA avec variables explicatives, puis dans le cadre des modèles markoviens avec variables explicatives en y détaillant le cas particulier des modèles structurels. Les deuxième et troisième parties de la thèse regroupent deux ensembles d'applications. Le premier porte sur des données de trafics, de voyageurs et de marchandises, agrégées par mode de transport ou par grande catégorie de réseau, et le second sur des données d'accidents corporels et de victimes de la circulation routière, agrégées par grande catégorie de réseau routier. La période couverte la plus large est 1970-2000. La plupart des applications intègre la prise en compte des effets transitoires, de nature climatique et calendaire, sur la demande de transport et sur le risque routier, et nous donnons dans la thèse les premiers résultats détaillés démontrant pour la France la significativité du facteur climatique sur le bilan routier national, mesuré en nombres d'accidents corporels et de tués

The math achievement of students is low in a small rural district in Colorado. The purpose of this study was to explore the efficacy of a summer third through fifth grade math program in improving math scores. Piaget's theory of cognitive development was used as the theoretical foundation for the math instructional resource delivered to the struggling students in the program. A quasi-experimental design was used to address whether the math scores improved for the participating students (n = 145) and whether the participating students experienced a smaller summer loss in academic achievement than the students who did not participate (n = 457). Ex post facto data included pre- and post- math assessments. The math instruction and assessments were administered to third through fifth grade students as part of the school district's academic program during the 2012, 2013, and 2014 summer schools. A dependent samples t test was used to analyze the data to determine if the students' achievement scores improved for those attending summer school. The results did not indicate any significant improvement. An ANOVA was then used to determine if the summer math program decreased summer loss of learning in participating students. Participating students experienced significantly less summer loss than did non-participating students. Therefore, recommendations for the summer math program include more instructional time and moving the program closer to the beginning of the school year to avoid any summer loss. This study will have a positive social impact as it influences decisions made by the school district to improve the summer math program and produce students who are better prepared for postsecondary school options.

The present study was designed to investigate the effects of divergent production activities with math inquiry and think aloud strategy of students with math difficulty. Multiple baseline across behaviors design was replicated across four participants. This research also investigated relationships between the interventions and creativity scores by employing pretest and posttest design as measured by the Torrance Tests of Creative Thinking (TTCT). The results varied with the participants and the interventions. The overall mean in all three treatments increased a mild degree based on descriptive statistics. All four participants showed a drastic variability in math problem solving. T-test results from the TTCT showed that there were significant differences in both fluency and flexibility scores. Elaboration and originality scores appeared unaffected since the instructions were mean in all three treatments increased to a mild degree based on descriptive statistics. All four primarily involved in fluency and flexibility creativity constructs. Originality was excluded as a measure and elaboration was not instructed intensely enough in the program. Conclusively, 5th grade students with math difficulty improved both think aloud and math inquiry scores based on visual/statistical inspection of Mean+Trend difference analysis. It was found that only math inquiry intervention was effective to a mild degree for three out of four participants. Fluency and flexibility scores increased as a result of divergent production activities, however not enough to say that overall creativity is fostered directly by the program. Issues emerged out of the math problem solving in terms of controlling variability and developing content materials for the instruction. Further research is needed to ascertain the effects of multiple interventions on students with math difficulty. Replications are needed to expand the findings to the development of viable instructions. Future study is also needed to use varied math inquiry skills and think aloud strategy in order to improve both problem solving ability and creativity associated with mathematics.

Test anxiety can act as a major inhibitor for students to perform to their ability. Students can find that what life decisions they are going to be afforded is going to be determined by a series of multiple choice mathematics questions. There must be a way to deal with their test anxiety so that the true nature of their knowledge is displayed, and in the process promote learning. Meditative breathing, stretching, and physical activity have been shown to reduce stress. Furthermore, physical activity has also shown an effect on behavioral and cognitive states. This study investigates if these activities can be used in the classroom to promote learning and achievement within a mathematics course. In order to find students who share a minimum level of physical fitness and operate under some of the most stressful conditions possible, the participants were chosen from mathematics courses taught to sailors while on deployment. Two same class ships were chosen to be a part of the study. Each ship had courses split into exercise groups and a control group. Students were given a pre-test followed by eight weeks of instruction and then a post-test, interview data was collected after the course. During the instruction, weekly reviews were set so control groups were rewarded with points for correct answers and exercise groups were tasked with physical activity for incorrect answers. Study A found that post test scores were not significantly different between the exercise and control group. However, the exercise group did attend more tutoring events than their counterparts. Interview data did indicate students in the exercise group felt a greater sense of engagement, fun, and camaraderie. Based upon variations in mathematic exposure between the two groups another study was planned to find participant groups that were closer reflections of each other. Study B was conducted with a more reflective representation of student math background. The results found that the exercise group scored higher in post-test and tutoring events than the control group. Interview data also showed consistent results with Study A, where the exercise group reported a greater sense of engagement, fun and camaraderie.

The aim of this research is to study changes resulting from parents attending a study group designed by class teacher that include reading a chosen book and engaging in teacher¡¦s designated activities relating to grade 1 elementary school mathematics contents; and trying ideas at home with school children. By referring to literature she decided on a study group format and adopted equal interaction and co-operative discussion setting. The math contents are: Number (1-10); Knowing about Geometric Shapes, Classifications (Color, Shapes). Data collection included questionnaire about study group meetings, children¡¦s interviews, parents¡¦ interviews, teacher¡¦s diaries, video tapes of in-class activities. Analyzes of interviews is by Goldin (2000). The findings are four: through the above mentioned study group (1) parents upgraded themselves in math ability and in confidence and set goals relating to different age of children; (2) children were given the opportunities to learn in a variety of ways; (3) promoted parent-child interaction, especially at home; and, (4) enhanced parent-teacher relationships and stimulated creativity in teacher¡¦s instruction.

The present study was designed to investigate the effects of divergent production activities with math inquiry and think aloud strategy of students with math difficulty. Multiple baseline across behaviors design was replicated across four participants. This research also investigated relationships between the interventions and creativity scores by employing pretest and posttest design as measured by the Torrance Tests of Creative Thinking (TTCT). The results varied with the participants and the interventions. The overall mean in all three treatments increased a mild degree based on descriptive statistics. All four participants showed a drastic variability in math problem solving. T-test results from the TTCT showed that there were significant differences in both fluency and flexibility scores. Elaboration and originality scores appeared unaffected since the instructions were mean in all three treatments increased to a mild degree based on descriptive statistics. All four primarily involved in fluency and flexibility creativity constructs. Originality was excluded as a measure and elaboration was not instructed intensely enough in the program. Conclusively, 5th grade students with math difficulty improved both think aloud and math inquiry scores based on visual/statistical inspection of Mean+Trend difference analysis. It was found that only math inquiry intervention was effective to a mild degree for three out of four participants. Fluency and flexibility scores increased as a result of divergent production activities, however not enough to say that overall creativity is fostered directly by the program. Issues emerged out of the math problem solving in terms of controlling variability and developing content materials for the instruction. Further research is needed to ascertain the effects of multiple interventions on students with math difficulty. Replications are needed to expand the findings to the development of viable instructions. Future study is also needed to use varied math inquiry skills and think aloud strategy in order to improve both problem solving ability and creativity associated with mathematics.

Despite the fact that boys and girls in the US perform at equal rates on most standardized math exams, girls report lower self-confidence in, positive affect toward, and valuation of this subject. Internationally, the gap between girls’ and boys’ math scores is mostly accounted for by gender socialization and the rights of women in society. The present research uses Eccles’ (Parsons [Eccles] et al., 1983) Expectancy Value framework in considering the importance of math self-confidence, math valuation, and sex role egalitarianism on math achievement. Multiple regression will be used to determine the predictive ability of the independent variables. It is proposed that sex role egalitarianism and attitudes toward math will each significantly predict math achievement scores. Additionally, sex role egalitarianism will add to the prediction of math scores above what attitudes towards math contribute. Implications and future directions are discussed. / text