Orientador: Vinício de Macedo Santos / Banca: Célia Maria Carolino Pires / Banca: José Carlos Miguel / Abstract: The rational numbers are shown as a subject that the students of the Elementary and High School have difficulties to learn. Some of these difficulties are due to the difference established between the daily use of the rational numbers by the student and the way it is taught at the school and, also for the ignorance, on the part of the school, of the multiplicity of their meanings. While the social use is centered in the decimal form, the school use lies more on the fractional form of the rational numbers. It is an undesirable separation that the school practices have accentuated through time. This study tried to characterize the existent dichotomization between it the use and the teaching of the Mathematics, starting from bibliographical research and of documental study that end up being responsible for damages in the students' learning.. This can be verified in the mistakes committed in the official tests (SARESP, SAEB...). It was sought to analyze how that separation has been reinforced in the official documents, by the pedagogic proposals and curricula. It was verified how the different documents and official publications deal with the rational numbers and the articulation among perspectives of the school use and the daily use of the rational numbers. That analysis made possible to understand different types of arguments and justifications for the teaching of the fractions, present in the official curricula, as well as explain the contents and the most appropriate methodologies of the conceptions presented in such documents. All this made possible to know part of the problems that happen with the teaching of fractions and their causes, and so, make suggestions on how these problems can be solved. Although the establishment of relationships between the social use and school use still doesn't happen in an effective way, it is recognized... (Complete abstract, click electronic address below) / Resumo: Os números racionais apresentam-se como conteúdo que os alunos do Ensino Fundamental e Médio têm dificuldades para aprender. Parte dessas dificuldades decorre da diferença instituída entre o uso cotidiano dos números racionais pelo aluno e a maneira como são ensinados na escola e, também pelo desconhecimento, por parte da escola, da multiplicidade dos significados dos racionais. Enquanto o uso social centra-se na forma decimal o uso escolar recai mais sobre a forma fracionária dos números racionais. É uma separação indesejável que as práticas escolares trataram de acentuar ao longo do tempo. A partir de pesquisa bibliográfica e de estudo documental procurou-se caracterizar, nesse trabalho, a dicotomização existente entre o uso e o ensino da Matemática, que acabam sendo responsáveis por prejuízos na aprendizagem dos alunos. Isto pode ser verificado nos erros que os alunos cometeram nas provas oficiais (SARESP, SAEB...). Procurou-se analisar como essa separação vem sendo reforçada nos documentos oficiais, por meio das propostas pedagógicas e curriculares. Verificaram-se como diferentes documentos e publicações oficiais abordam os números racionais e tratam da articulação entre a perspectivas do uso escolar e a do uso cotidiano dos números racionais. Essa análise possibilitou compreender diferentes tipos de argumentações e justificativas para o ensino das frações, presentes nos currículos oficiais, bem como explicitar os conteúdos e metodologias adequadas às concepções apresentadas em tais documentos. Tudo isso possibilitou conhecer parte dos problemas que ocorrem com o ensino de frações e suas causas e por isso sugerir propostas que sinalizam para a sua superação. Embora o estabelecimento de relações entre o uso social e uso escolar ainda não ocorra de maneira efetiva, reconhece-se que aquelas orientações... (Resumo completo, clicar acesso eletrônico abaixo) / Mestre

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This Research and Design (R&D) study models the methodology necessary to replicate an online assessment instrument designed to assess student skills and facets of thought while understanding Multiple Meanings and Models of Fractions (MUL) in college level developmental mathematics. The researcher used cognitive research done in the area of fractions to design this instrument that both documents and assesses facets of thought or reasoning strategies used by students. The final facet cluster is a table that ranks these facets from least to most problematic, documenting the student facets of thought across the content objective MUL. Over 500 student and teacher participants were used in the design and development of Fraction Diagnoser. All participants were affiliated with college developmental mathematics in Texas, representing four colleges and universities. Forty-eight student participants were individually interviewed to ascertain facets of understanding on the topic of MUL. Seven teacher participants were individually interviewed as to the effectiveness of Fraction Diagnoser in the classroom after the final step of the R&D cycle. Content experts were used to design the questions assessing skills and facets. Fraction Diagnoser was built using the Borg and Gall R&D cycle as its blueprint. Nine of the ten steps of the R&D cycle were used in the development of the instrument, excluding just the final product revision due to cost and time restraints. According to Borg and Gall (1996), a dissertation R&D should be limited to a few steps, but all of the steps used for this R&D allowed for the researcher to completely address all of the research questions. During the steps of the R&D cycle, validation and reliability analyses were done to statistically address the effectiveness of Fraction Diagnoser. Final interviews with the teacher participants supported findings in recent research on the effective use of online assessment. Implications for practice and recommendations for further study were also addressed.

Polycyclic aromatic hydrocarbons (PAHs) and polychlorinated biphenyls (PCBs) are persistent, ubiquitous, and toxic organic contaminants in coastal sediments. Being hydrophobic in water column, PAHs and PCBs tend to sorb rapidly on particles and eventually accumulate in sediments. Re-suspension of fine or low-density particles from the surface sediment would lead to release of the pollutants bound in sediment particles into water column. This study was to evaluate the potential of remobilization of sediment-bound pollutants into harbor water column by measuring the concentrations and compositions of PAHs and PCBs in different particle size (size fraction: 1000, 500, 250, 125 and 63 £gm) and the different density fractions (density: > 2.15, < 2.15 g/cm3) in the Kaohsiung Harbor area. The total PAH concentrations obtained from the sediments of Kaohsiung sub-channel (KH1) is higher than those of Shang-Zhu-Li fishing ferry (KH2), but it presents the opposite situation in total PCB concentrations. Total PAH concentrations are 3400 and 1700 (ng/g dw) and total PCB concentrations are 103 and 141 (ng/g dw) at sites of KH1 and KH2. PAH and PCB concentrations in the low-density fraction sediment made up more than 91% and 87% of the total concentration of the bulk sediment, respectively; while low-density fraction sediment made up only 4.3 to 7.7% of the bulk sediment in dry weight. According to the chemical fingerprinting, PAH source of Kaohsiung sub-channel (KH1) is from pyrogenic which might be from the diesel oil burning of shipping activities and containerized traffic. But the PAH sources in Shang-Zhu-Li fishing ferry (KH2) were from the combustion of coal and petroleum, which is possibly from iron and steel plant and the power plant nearby. The Toxic equivalents (TEQ) of dioxin-like PCBs in low and high-density fraction sediments were ranged from 1.1-7.6 pg-TEQ/g and 8.9-1500 pg-TEQ/g, respectively. Based on the Sediment Quality Guidelines (SQGs), only few PAH concentrations in the high-density fraction sediments were higher than the TEL value, while most of PAH concentrations in the low-density fraction sediments ranged between ERL and ERM values. This suggests the low-density sediment particles possessed higher potential of adverse effects to organisms in the aquatic environment.

Thesis (Ph. D.)--University of Washington, 2000. / Vita. Includes bibliographical references (p. 120-123).

Thesis (doctoral)--Universitate Litteraria Friderica Guilelma, 1835. / Vita.

Thesis (Ph.D.)--University of Central Florida, 2009. / Adviser: Juli K. Dixon. Includes bibliographical references (p. 251-259).

Thesis (M.A.)--West Virginia University, 2003. / Title from document title page. Document formatted into pages; contains iii, 60 p. : ill. Includes abstract. Includes bibliographical references (p. 33-36).

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This report examines the theory of continued fractions and how their use enhances the secondary mathematics curriculum. The use of continued fractions to calculate best approximants of real numbers is justified geometrically, and famous irrational numbers are described as continued fractions. Periodic continued fractions and other applications of continued fractions are also discussed. / text