Thesis (Ph. D.)--Washington State University, May 2007. / Includes bibliographical references (p. 71-86). Also available via the World Wide Web.

Various studies have found differences in males’ and females’ mathematical achievement, with boys’ achievement scores higher than girls’. However, the difference in mathematical achievement does not appear to exist yet when children are younger (e.g., in preschool or kindergarten), but rather we begin to observe this gender achievement gap in middle school and high school. These findings raise the question about what is happening in pre- and elementary school that may cause this achievement gap to appear. Research suggests that there is a relationship between the amount of teachers’ math talk and preschool children’s conventional mathematical knowledge. Studies suggest that teachers’ math talk is significantly related to the growth of mathematical knowledge. The amount of input boys and girls receive from preschool teachers’ can be one of the causes of the gap in their math achievement in later years. Various studies measured the amount of teachers’ math talk in the classroom however there are very few research that investigated the influence of gender on the amount of preschool teachers’ math talk. The current study investigated the effects of children’s gender on preschool teachers’ math talk. The purpose of the study was to investigate the amount of preschool teachers’ math talk with children as well as the effect of children’s gender on the amount and type of preschool teachers’ math talk. The data was collected as part of another study which aimed to create a database of quality early childhood practices. The participants of the current study were 2 teachers (1 teacher and 1 assistant teacher) in a preschool classroom and the 16 (7 girls. 9 boys) children in their classroom. Permissions were obtained from teachers and children’s families. The teachers were videotaped during the free play time and the videos were coded for the amount and type of math talk using Observational Coding Matrix which is a checklist of 8 different math categories. The results showed a statistically significant difference for the amount of total math talk that boys received comparing to girls, in favor of the boys. Although, boys received more math talk in most of the math categories, the operation was the type in which the gender difference was statistically significant. Although the sample size was small the gender difference was statistically significant, which shows the importance of studies that investigate the gender differences in teachers’ math talk.

I conducted a study among the middle school students to examinetheir attitudes to school mathematics both inside and outside of the classroom. Also, I have examined teachers’ perceptions of how everyday math examples can be integrated into the classroom experience. The purpose of the study is to investigate the effect of using everyday mathematics in teaching and how this will contribute to a further development of students' ability to think mathematically in different contexts. Parallels between prior research efforts and my study “The art of thinking mathematically - School mathematics in everyday life”are drawn by using qualitative analysis techniques such as the organized empirical data based on student survey questionnaire and teacher interviews. The theoretical perspectives utilized in the study are about the pragmatic perspective and its centralized concepts emphasizing continuity, experience, and interaction. The socio-cultural perspective sheds light on interaction between people and perceptions of themselves and others. Within a broader context I will address the proximal developmental zone (ZPD) by Vygotsky, scaffolding and mediating as those concepts apply to the aforementioned issues. In conclusion I will provide what advantages and disadvantages do teachers and students experience in linking everyday mathematics to the school mathematics.  I will give also approaches for teachers and suggestions for further research and investigation.

In addition to the memorization, algorithmic skills and vocabulary which is the default focus in many mathematics classrooms, professional mathematicians are expected to creatively apply known techniques, construct new mathematical approaches and communicate with and about mathematics. We propose that students can learn these professional, higher level skills through Laboratory Experiences in Mathematical Biology (LEMBs) which put students in the role of mathematics researcher creating mathematics to describe and understand biological data. LEMBs are constructed so they require no specialized equipment and can easily be run in the context of a college math class. Students collect data and develop mathematical models to explain the data. In this work examine how LEMBs are designed with the student as the primary focus. We explain how well-designed LEMBs lead students to interact with mathematics at higher levels of cognition while building mathematical skills sought after in both academia and industry. Additionally, we describe the online repository created to assist in the teaching and further development of LEMBs. Since student-centered teaching is foreign to many post-secondary instructors, we provide research-based, pedagogical strategies to ensure student success while maintaining high levels of cognition.

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This study investigated the effects of motivational email messages on learner self-efficacy and achievement in an asynchronous college algebra and trigonometry course. A pretest-posttest control group design was used. Of the 196 initial participants randomly assigned to treatment groups, 125 participants with an average age of 18.21 years completed the study. The final control and experimental groups consisted of 57 (n=17 male, n=40 female) and 68 (n=14 male, n=54 female) participants respectively. Self-efficacy to learn mathematics asynchronously (SELMA) was measured before the treatment was administered. Email messages designed to be efficacy enhancing were sent to the experimental group weekly for 4 weeks. The control group was sent email messages designed to be neutral with respect to self-efficacy weekly for 4 weeks. SELMA and math achievement were measured after the email messages were sent in week 4. Analysis of covariance was performed using the pretest SELMA measure as a covariate to detect post-treatment differences in SELMA between the control and experimental groups. No significant differences were detected at the 0.05 alpha level. Paired-sample t-Tests revealed significant increases in SELMA for both the control and experimental groups over the treatment period. Linear regression analysis revealed a weak positive relationship between SELMA and math achievement. The findings are discussed in the context of the related literature and directions for future research are suggested. / Ph. D.

In this thesis I will describe the methods used and problems I have faced and attempted to solve during my time developing a math game for younger kids, a game that makes an attempt to teach kids something called number sense. Teaching pre school kids about number sense is something relatively new and the group I have been working with are of the understanding that it’s something that is very likely to be important to prevent children from falling behind in math during the earlier years of school. Number sense basically means the ability to connect symbolic numbers to their meaning interms of sets, amounts and dimensions such as larger-smaller, higher-shorter, more-less, etc. If this proves to be useful then the quality of education will improve as a result of more children being able to keep up with their math from an early stage.

Ce mémoire comprend 7 chapitres où sont présentées les différentes contributions de l'auteur : 1. Introduction. 2. Sur la stabilité des filtres récursifs bidimensionnels (deux algorithmes et une étude comparative de la robustesse de différents algorithmes face aux erreurs d'arrondi) 3. Bancs de filtres adaptés, application au codage sans perte des images (généralisation de la structure en lifting scheme des bancs de filtres avec application à la compression sans perte des images). 4. Bancs de filtres hybrides et conversion analogique/numérique. 5. Analyse en composantes indépendantes (ACI) et compression de données (un nouveau point de vue, permettant de faire le lien entre l'ACI et la compression de données par transformées pour de faibles distorsions, est introduit ; il est basé sur le critère que doit minimiser une transformation optimale en codage par transformée – sans l'hypothèse de données gaussiennes – ; présentation de deux algorithmes de recherche de transformation optimale en codage à faibles distorsions. 6. ACI appliquée au codage des images multicomposantes (extension de l'étude précédente à des images multi- et hyper-spectrales, critère minimisé par une transformation spectrale optimale pour un schéma de compression compatible avec JPEG2000 Partie 2, présentation de deux algorithmes de recherche de transformation spectrale optimale – OST et OrthOST –) 7. Conclusion et perspectives. Il est complété par deux annexes, l'une rappelant des éléments de la théorie de l'information et de la quantification, l'autre présentant quelques publications de l'auteur.

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