The purpose of this meta-analysis was to better understand the relationship between the substantive-content focus of professional development for inservice teachers of mathematics and their students' achievement. That professional development for teachers enhances student achievement has been well established by recent studies; however, those meta-analyses have studied structural characteristics such as the duration and the format/delivery method of the professional development. It is important to understand how the focus of professional development relates to student achievement because different foci must still compete not only among themselves but also with other instructional-improvement strategies (such as high-stakes testing, accountability, and curriculum reform) for limited resources, such as time and money. Hence, having evidence that professional development works and, more importantly, a better understanding of what focus comprises more effective professional development is not just of theoretical importance, it is also a policy-relevant imperative. The study's results indicated that the focus of professional development is, in fact, a significant and educationally important predictor of variation in student-achievement effect sizes.

The performance of 223 Grade 4 children, with Average overall IQ and no disability (ND), or reading disability (RD), or math disability (MD), or reading/math disability (RD+MD), was compared on theoretically-derived factors measuring specific cognitive processes underlying reading and math achievement. The processes included automatic visual/orthographic and visual/math fact retrieval, working memory span, phonological and algorithmic processing, and IQ (e.g., verbal/nonverbal reasoning). Good readers and good mathematicians (ND group) showed solid performance across all tasks. Compared to the ND group, achievement and cognitive profiles of single disability (RD and MD), and RD+MD were elucidated. Structural equation models (SEM) for the entire sample confirmed a theoretically-derived four factor READ model and a four factor MATH model, both with identical Working Memory Span and IQ factors. Two other READ model factors were Automatic (RAN/Words) and Phonological Processing. Two additional MATH model factors were Automatic (RAN/Facts) and Algorithmic Processing. Based on the cognitive and functional neurobiological literatures, these models supported a systems view of the unique and collaborative relations among the automatic, processing, working memory, and IQ cognitive processes underlying reading and math achievement. Through regression analyses, the specific factors from both the READ and MATH models predicted each group’s reading and math achievement. Regression results enhanced our understanding of what factors/cognitive processes (strong or weak) contribute to good or poor reading and math achievement. Findings that automatic RAN/Words and RAN/Facts both predict fluent math fact retrieval for all groups suggest potential overlap in basic automatic visual/orthographic and visual/fact routes. Possible overlap in these automatic processes was also seen in the weakest RD+MD group for word reading.

Recent research has begun focusing on the connections between reading and mathematics. Little research, however, has examined connections between mathematics and other reading related skills, such as spelling. Moreover, working memory may a play a significant role in both systems. Results indicated a significant predictive relationship between spelling and mathematics. Furthermore, this relationship was found to be partially mediated by measures of phonological working memory.

The performance of 223 Grade 4 children, with Average overall IQ and no disability (ND), or reading disability (RD), or math disability (MD), or reading/math disability (RD+MD), was compared on theoretically-derived factors measuring specific cognitive processes underlying reading and math achievement. The processes included automatic visual/orthographic and visual/math fact retrieval, working memory span, phonological and algorithmic processing, and IQ (e.g., verbal/nonverbal reasoning). Good readers and good mathematicians (ND group) showed solid performance across all tasks. Compared to the ND group, achievement and cognitive profiles of single disability (RD and MD), and RD+MD were elucidated. Structural equation models (SEM) for the entire sample confirmed a theoretically-derived four factor READ model and a four factor MATH model, both with identical Working Memory Span and IQ factors. Two other READ model factors were Automatic (RAN/Words) and Phonological Processing. Two additional MATH model factors were Automatic (RAN/Facts) and Algorithmic Processing. Based on the cognitive and functional neurobiological literatures, these models supported a systems view of the unique and collaborative relations among the automatic, processing, working memory, and IQ cognitive processes underlying reading and math achievement. Through regression analyses, the specific factors from both the READ and MATH models predicted each group’s reading and math achievement. Regression results enhanced our understanding of what factors/cognitive processes (strong or weak) contribute to good or poor reading and math achievement. Findings that automatic RAN/Words and RAN/Facts both predict fluent math fact retrieval for all groups suggest potential overlap in basic automatic visual/orthographic and visual/fact routes. Possible overlap in these automatic processes was also seen in the weakest RD+MD group for word reading.

Dewey provides a rich context in which to develop an understanding of education as growth. By developing an understanding of education as growth, educational research can be incorporated into that context so that a more comprehensive model of education may be considered. Education as growth suggests that education is about progress rather than end states. The knowledge and skills of inquiry must be understood as part of an interconnected whole that includes the physical, social, and intellectual growth of the individual and the community. The role of inquiry in the development of concepts and habits that foster the intellectual and cultural growth of the individual and community are discussed. The work of researchers on math learning disabilities is presented and examined in light of Dewey’s concepts of growth and inquiry so that the educational needs of students with math learning disabilities might be included in a model of education. The quality of the educational experiences of students with math learning disabilities has significant implications for the growth and development of all students, parents, teachers, researchers, and the community. / Thesis (Master, Education) -- Queen's University, 2009-04-16 19:58:52.504

Det finns ett problem angående vilka undervisningsmetoder som ska användas för att lyckas höja elevers kunskapsnivå i matematik. Denna studie görs för att undersöka math trails plats i matematikundervisning och då utifrån tre aspekter: de fem förmågorna, verklighetsanknytning och motivation. Math trail är en promenad där olika uppgifter genomförs längs vägen i syfte att upptäcka matematiken som finns runt omkring oss. Math trail kan ses vara en del av utomhuspedagogiken. På grund av att ingen forskning presenterats inom math trail väljer vi därför att lyfta fram forskning kring utomhuspedagogik. Många av dessa tidigare studier är gjorda utifrån lärares eller forskares perspektiv och därför väljer vi ett elevperspektiv. Syftet med studien är att beskriva elevers uppfattningar av att använda math trail i matematikundervisningen. Undersökningen görs kvalitativt där det empiriska materialet samlas in genom fokusgruppsamtal med elever från två högstadieklasser som genomfört ett math trail vi konstruerat. Materialet analyseras utifrån den fenomenografiska metoden och ger sex beskrivningskategorier: yttre omständigheter inverkar, lärares närvaro påverkar, gynnar samarbete, utmanande uppgifter, har nytta av samt variation från det ”vanliga”. Slutsatser som dras är kopplade till de tre aspekterna av matematikundervisning. Eleverna har uppfattningen att de får öva på alla fem förmågorna i ett math trail. Eleverna har uppfattningen att math trail grundas i verkligheten, visar på en nytta av matematiken och leder till en insikt att matematik kan finnas överallt. Math trail, uppfattar eleverna, påverkar deras motivation genom att det är en variation från deras ”vanliga” lektioner, eleverna vill bidra till att gruppen klarar uppgifterna och de ser en användning av matematiken. Eleverna uppfattar även math trail som ett praktiskt inslag.

Fay's identity on Riemann surfaces is a powerful tool in the context of algebro-geometric solutions to integrable equations. This relation generalizes a well-known identity for the cross-ratio function in the complex plane. It allows to establish relations between theta functions and their derivatives. This offers a complementary approach to algebro-geometric solutions of integrable equations with certain advantages with respect to the use of Baker-Akhiezer functions. It has been successfully applied by Mumford et al. to the Korteweg-de Vries, Kadomtsev-Petviashvili and sine-Gordon equations. Following this approach, we construct algebro-geometric solutions to the Camassa-Holm and Dym type equations, as well as solutions to the multi-component nonlinear Schrödinger equation and the Davey-Stewartson equations. Solitonic limits of these solutions are investigated when the genus of the associated Riemann surface drops to zero. Moreover, we present a numerical evaluation of algebro-geometric solutions of integrable equations when the associated Riemann surface is real.

Thesis (Ph. D.)--Drexel University, 2005. / Includes abstract and vita. Includes bibliographical references (leaves 119-128).

Thesis (Ph. D.)--West Virginia University, 2000. / Title from document title page. Document formatted into pages; contains v, 160 p. : ill. Vita. Includes abstract. Includes bibliographical references (p. 64-80).

Thesis, PlanB (M.S.)--University of Wisconsin--Stout, 2006. / Includes bibliographical references.