Um problema de dispersão de poluentes em rios e canais por meio do método de separação de variáveis

Neste trabalho obtém-se uma solução analítica para a equação de advecção-difusão aplicada a problemas de dispersão de poluentes em rios e canais. Para tanto, consideram-se os casos unidimensionais e bidimensionais em regime transiente com coeficientes de difusividade e velocidades constantes. A abordagem utilizada para a resolução deste problema é o método de Separação de Variáveis. Os modelos resolvidos foram simulados utilizando o MatLab. Apresentam-se os resultados das simulações numéricas em formato gráfico. Os resultados de algumas simulações numéricas existem na literatura e puderam ser comparados. O modelo proposto mostrou-se coerente em relação aos dados considerados. Para outras simulações não foram encontrados comparativos na literatura, todavia esses problemas governados por equações diferenciais parciais, mesmo lineares, não são de fácil solução analítica. Sendo que, muitas delas representam importantes problemas de matemática e física, com diversas aplicações na engenharia. Dessa forma, é de grande importância a disponibilidade de um maior número de problemas-teste para avaliação de desempenho de formulações numéricas, cada vez mais eficazes, já que soluções analíticas oferecem uma base mais segura para comparação de resultados.

Royal Artillery Centre for Personal Development case study

Case study on online delivery and support for functional skills in Mathematics, English and ICT

Teaching Sight-Reading to Undergraduate Choral Ensemble Singers: Lessons from Successful Learners

This study was designed to investigate professional choral singers’ training, perceptions on the importance of sight-reading skill in their work, and thoughts on effective pedagogy for teaching sight-reading to undergraduate choral ensemble singers. Participants in this study (N=48) included self-selected professional singers and choral conductors from the Summer 2015 Oregon Bach Festival’s Berwick Chorus and conducting Master Class. Data were gathered from questionnaire responses and audio recorded focus group sessions. Focus group data showed that the majority of participants developed proficiency in their sight-reading skills from instrumental study, aural skills classes, and through on-the-job training at a church job or other professional choral singing employment. While participants brought up a number of important job skills, sightreading was listed as perhaps the single most important skill that a professional choral singer could develop. When reading music during the rehearsal process, the data revealed two main strategies that professional singers used to interpret the pitches in their musical line: an intervallic approach and a harmonic approach. Participants marked their scores systematically to identify problem spots and leave reminders to aid with future readings, such as marking intervals, solfege syllables, or rhythmic counts. Participants reported using a variety of skills other than score marking to try to accurately find their pitches, such as looking at other vocal or instrumental lines, looking ahead, and using knowledge about a musical style or time period to make more intuitive “guesses” when sight-reading. Participants described using additional approaches when sight-reading in an audition situation, including scanning for anchors or anomalies and positive self-talk. Singers learned these sight-reading techniques from a variety of sources. Participants had many different ideas about how best to teach sight-reading in the undergraduate choral ensemble rehearsal. The top response was that sight-reading needed to be practiced consistently in order for students to improve. Other responses included developing personal accountability, empowering students, combining different teaching methods, and discussing real-life applications of becoming strong sight-readers. There was discussion about the ultimate purpose of choir at the university level and whether it is to teach musicianship skills or produce excellent performances.

On L2 grammar and processing: the case of oblique relative clauses and the Null-Prep phenomenon

This dissertation investigates the acquisition of oblique relative clauses in L2 Spanish by English and Moroccan Arabic speakers in order to understand the role of previous linguistic knowledge and its interaction with Universal Grammar on the one hand, and the relationship between grammatical knowledge and its use in real-time, on the other hand. Three types of tasks were employed: an oral production task, an on-line self-paced grammaticality judgment task, and an on-line self-paced reading comprehension task. Results indicated that the acquisition of oblique relative clauses in Spanish is a problematic area for second language learners of intermediate proficiency in the language, regardless of their native language. In particular, this study has showed that, even when the learners’ native language shares the main properties of the L2, i.e., fronting of the obligatory preposition (Pied-Piping), there is still room for divergence, especially in production and timed grammatical intuitions. On the other hand, reaction time data have shown that L2 learners can and do converge at the level of sentence processing, showing exactly the same real-time effects for oblique relative clauses that native speakers had. Processing results demonstrated that native and non-native speakers alike are able to apply universal processing principles such as the Minimal Chain Principle (De Vincenzi, 1991) even when the L2 learners still have incomplete grammatical representations, a result that contradicts some of the predictions of the Shallow Structure Hypothesis (Clahsen & Felser, 2006). Results further suggest that the L2 processing and comprehension domains may be able to access some type of information that it is not yet available to other grammatical modules, probably because transfer of certain L1 properties occurs asymmetrically across linguistic domains. In addition, this study also explored the Null-Prep phenomenon in L2 Spanish, and proposed that Null-Prep is an interlanguage stage, fully available and accounted within UG, which intermediate L2 as well as first language learners go through in the development of pied-piping oblique relative clauses. It is hypothesized that this intermediate stage is the result of optionality of the obligatory preposition in the derivation, when it is not crucial for the meaning of the sentence, and when the DP is going to be in an A-bar position, so it can get default case. This optionality can be predicted by the Bottleneck Hypothesis (Slabakova, 2009c) if we consider that these prepositions are some sort of functional morphology. This study contributes to the field of SLA and L2 processing in various ways. First, it demonstrates that the grammatical representations may be dissociated from grammatical processing in the sense that L2 learners, unlike native speakers, can present unexpected asymmetries such as a convergent processing but divergent grammatical intuitions or production. This conclusion is only possible under the assumption of a modular language system. Finally, it contributes to the general debate of generative SLA since in argues for a fully UG-constrained interlanguage grammar.

The Role of College Students' Perceptions of Effort Source on Self-Evaluations of Academic Ability

In the present studies I investigated whether college students’ perceptions of effort source influenced their perceptions of the relation between levels of their own effort and ability in mathematics. In Study 1 (N = 210), I found using hypothetical vignettes that perceptions of task-elicited effort (i.e., effort that arises due to the subjective difficulty or ease of the task) led to perceptions of an inverse relation between one’s effort and ability, and perceptions of self-initiated effort (i.e., effort that arises due to one’s own motivation or lack of motivation) led to perceptions of a positive relation between one’s effort and ability, consistent with my hypotheses and prior research. In Study 2 (N = 160), participants completed an academic task and I used open-ended questions to manipulate their perceptions of effort source. I found that participants in the task-elicited condition endorsed no overall relation between effort and ability, and participants in the self-initiated condition endorsed an overall inverse relation, which is inconsistent with my hypotheses and prior research. Possible explanations for the findings, as well as broader theoretical and educational implications are discussed.

Construções geométricas como recurso pedagógico no ensino médio

This work aims to provide high school students an development in his mathematical and geometrical knowledge, through the use of Geometric Constructions as a teaching resource in Mathematics classes. First a literature search to understand how it emerged and evolved the field of geometry was carried out and the Geometric Constructions. The ways in which the teaching of geometry happened in our country, also were studied some theories related to learning and in particular the Van Hiele theory which deals with the geometric learning also through the literature search were diagnosed. Two forms of the Geometric Constructions approach are analyzed in class: through the design of hand tools - ruler and compass - and through the computational tool - geometric software - being that we chose to approach using the ruler and compass instruments. It is proposed a workshop with nine Geometric Construction activities which was applied with a group of 3rd year of high school, the Escola de Educac¸ ˜ao B´asica Professor Anacleto Damiani in the city of Abelardo Luz, Santa Catarina. Each workshop activity includes the following topics: Activity Goals, Activity Sheet, Steps of Construction Activity Background and activity of the solution. After application of the workshop, the data were analyzed through content analysis according to three categories: Drawing Instruments, angles and their implications and Parallel and its Implications. Was observed that most of the students managed to achieve the research objectives, and had an development in their mathematical and geometrical knowledge, which can be perceived through the analysis of questionnaires administered to students, audio recordings, observations made during the workshop and especially through the improvement of the students in the development of the proposed activities.

A operacionalização do programa de matemática em vigor no 1.º Ciclo do Ensino Básico pelos professores do concelho de Machico

Trabalho de projeto apresentado à Escola Superior de Educação de Paula Frassinetti para obtenção do grau de Mestre em Ciências da Educação Especialização em Supervisão Pedagógica

Viel bringt viel? Effekte lernzeitverlängernder Maßnahmen auf die Lese- und Mathematikleistungen von Grundschülerinnen und Grundschülern mit ungünstiger Lernausgangslage

Der vorliegende Beitrag untersucht die Effekte von lernzeitverlängernden Maßnahmen für Grundschülerinnen und Grundschüler in Mecklenburg-Vorpommern mit einer ungünstigen Lernausgangslage zum Zeitpunkt der Einschulung. Dazu wurde über die gesamte Grundschulzeit hinweg die Leistungsentwicklung von 67 Kindern in den Bereichen Lesen und Rechnen erfasst. Bei 19 Kindern wurde eine Lernzeitverlängerung durch Diagnoseförderklassen (DFK) realisiert, bei 18 durch eine Klassenwiederholung (KW) und 30 Kinder lernten in regulären Grundschulklassen (GSK) ohne eine Lernzeitverlängerung. Die Auswertungen der Daten mittels Hierarchisch-linearer Modelle (HLM) weisen auf gleiche Entwicklungsverläufe der drei Untersuchungsgruppen in den Bereichen Lesen und Mathematik hin. Zum Ende der Klasse 4 erreichten die drei Gruppen ähnliche Leistungsniveaus. In allen drei Settings fiel auf, dass die Entwicklung mathematischer Kompetenzen über die Schulzeit hinweg verzögert erfolgte. Ungünstige Lernausgangslagen im Bereich Mathematik konnten den Analysen zufolge durch keine der untersuchten Beschulungsformen ausreichend kompensiert werden. (DIPF/Orig.)

EXAMINING THE IMPLEMENTATION CHALLENGES OF PROJECT-BASED LEARNING: A CASE STUDY

Title of Thesis: Thesis directed by: ABSTRACT EXAMINING THE IMPLEMENTATION CHALLENGES OF PROJECT-BASED LEARNING: A CASE STUDY Stefan Frederick Brooks, Master of Education, 2016 Professor and Chair Francine Hultgren Teaching and Learning, Policy and Leadership Department Project-based learning (PjBL) is a common instructional strategy to consider for educators, scholars, and advocates who focus on education reform. Previous research on PjBL has focused on its effectiveness, but a limited amount of research exists on the implementation challenges. This exploratory case study examines an attempted project- based learning implementation in one chemistry classroom at a private school that fully supports PjBL for most subjects with limited use in mathematics. During the course of the study, the teacher used a modified version of PjBL. Specifically, he implemented some of the elements of PjBL, such as a driving theme and a public presentation of projects, with the support of traditional instructional methods due to the context of the classroom. The findings of this study emphasize the teacher’s experience with implementing some of the PjBL components and how the inherent implementation challenges affected his practice.

Atividades de matemática e de ciências no horto de Amato Lusitano

Relatório de Estágio apresentado à Escola Superior de Educação do Instituto Politécnico de Castelo Branco para cumprimento dos requisitos necessários à obtenção do grau de Mestre em Educação Pré- Escolar e Ensino do 1.º Ciclo do Ensino Básico.

Resolução de problemas de dedução lógica na promoção da comunicação matemática na oralidade

Relatório de Estágio apresentado à Escola Superior de Educação do Instituto Politécnico de Castelo Branco para cumprimento dos requisitos necessários à obtenção do grau de Mestre em Educação Pré-Escolar e Ensino do 1º Ciclo do Ensino Básico.

Prática de ensino supervisionada em ensino do 1.º e do 2.º Ciclo do Ensino Básico

O Relatório Final de estágio, que apresentamos, foi elaborado como parte integrante da unidade curricular da Prática de Ensino Supervisionada (de agora em diante mencionada por PES), no âmbito do Mestrado em Ensino do 1.º e do 2.º Ciclo do Ensino Básico da Escola Superior de Educação, do Instituto Politécnico de Bragança, referente ao ano letivo de 2011/2012. Referimos que a PES foi realizada em dois níveis de ensino, 1.º e 2.º Ciclos do Ensino Básico, e em diferentes áreas curriculares destes dois ciclos de estudos. No 1.º Ciclo do Ensino Básico (de agora em diante, referido como 1.ºCEB), realizou-se Língua Portuguesa, Estudo do Meio, Matemática, e Expressão Plástica, numa turma de 4.º ano de escolaridade do Centro Escolar da Sé, agrupamento da Escola Paulo Quintela. No 2.º Ciclo de Ensino Básico (de agora em diante, referido como 2.ºCEB), o estágio nas áreas de Matemática, Língua Portuguesa e História e Geografia de Portugal foi realizado na mesma escola, Paulo Quintela, com a mesma turma de 5.º ano de escolaridade. Na área de Ciências da Natureza, a PES foi realizada na escola Augusto Moreno, numa turma de 6.º ano. Consideramos ter obtido bastante sucesso educativo com os alunos do 1.º ciclo e com os alunos de 2.º ciclo, na área de Ciências da Natureza. Relativamente aos alunos do 2.º ciclo, nas áreas de Matemática, Língua Portuguesa e História e Geografia de Portugal, o sucesso educativo foi mais limitado mas, mesmo assim, pensamos que foi relevante, como explicaremos na reflexão sobre as experiências de ensino-aprendizagem.

O papel das representações na resolução de problemas de Matemática: um estudo no 1º ano de escolaridade

Este estudo tem como objectivo investigar o papel que as representações, construídas por alunos do 1.o ano de escolaridade, desempenham na resolução de problemas de Matemática. Mais concretamente, a presente investigação procura responder às seguintes questões: Que representações preferenciais utilizam os alunos para resolver problemas? De que forma é que as diferentes representações são influenciadas pelas estratégias de resolução de problemas utilizadas pelos alunos? Que papéis têm os diferentes tipos de representação na resolução dos problemas? Nesta investigação assume-se que a resolução de problemas constitui uma actividade muito importante na aprendizagem da Matemática no 1.o Ciclo do Ensino Básico. Os problemas devem ser variados, apelar a estratégias diversificadas de resolução e permitir diferentes representações por parte dos alunos. As representações cativas, icónicas e simbólicas constituem importantes ferramentas para os alunos organizarem, registarem e comunicarem as suas ideias matemáticas, nomeadamente no âmbito da resolução de problemas, servindo igualmente de apoio à compreensão de conceitos e relações matemáticas. A metodologia de investigação segue uma abordagem interpretativa tomando por design o estudo de caso. Trata-se simultaneamente de uma investigação sobre a própria prática, correspondendo os quatro estudos de caso a quatro alunos da turma de 1.0 ano de escolaridade da investigadora. A recolha de dados teve lugar durante o ano lectivo 2007/2008 e recorreu à observação, à análise de documentos, a diários, a registos áudio/vídeo e ainda a conversas com os alunos. A análise de dados que, numa primeira fase, acompanhou a recolha de dados, teve como base o problema e as questões da investigação bem como o referencial teórico que serviu de suporte à investigação. Com base no referencial teórico e durante o início do processo de análise, foram definidas as categorias de análise principais, sujeitas posteriormente a um processo de adequação e refinamento no decorrer da análise e tratamento dos dados recolhidos -com vista à construção dos casos em estudo. Os resultados desta investigação apontam as representações do tipo icónico e as do tipo simbólico como as representações preferenciais dos alunos, embora sejam utilizadas de formas diferentes, com funções distintas e em contextos diversos. Os elementos simbólicos apoiam-se frequentemente em elementos icónicos, sendo estes últimos que ajudam os alunos a descompactar o problema e a interpretá-lo. Nas representações icónicas enfatiza-se o papel do diagrama, o qual constitui uma preciosa ferramenta de apoio ao raciocínio matemático. Conclui-se ainda que enquanto as representações activas dão mais apoio a estratégias de resolução que envolvem simulação, as representações icónicas e simbólicas são utilizadas com estratégias diversificadas. As representações construídas, com papéis e funções diferentes entre si, e que desempenham um papel crucial na correcta interpretação e resolução dos problemas, parecem estar directamente relacionadas com as caraterísticas da tarefa proposta no que diz respeito às estruturas matemáticas envolvidas. ABSTRACT; The objective of the present study is to investigate the role of the representations constructed by 1st grade students in mathematical problem solving. More specifically, this research is oriented by the following questions: Which representations are preferably used by students to solve problems? ln which way the strategies adopted by the students in problem solving influence those distinct representations? What is the role of the distinct types of representation in the problems solving process? ln this research it is assumed that the resolution of problems is a very important activity in the Mathematics learning at the first cycle of basic education. The problems must be varied, appealing to diverse strategies of resolution and allow students to construct distinct representations. The active, iconic and symbolic representations are important tools for students to organize, to record and to communicate their mathematical ideas, particularly in problem solving context, as well as supporting the understanding of mathematical concepts and relationships. The adopted research methodology follows an interpretative approach, and was developed in the context of the researcher classroom, originating four case studies corresponding to four 1 st grade students of the researcher's class. Data collection was carried out during the academic year of 2007/2008 and was based on observation, analysis of documents, diaries, audio and video records and informal conversations with students. The initial data analysis was based on the problems and issues of research, as well in the theoretical framework that supports it. The main categories of analysis were defined based on the theoretical framework, and were subjected to a process of adaptation and refining during data processing and analysis aiming the -case studies construction. The results show that student's preferential representations are the iconic and the symbolic, although these types of representations are used in different ways, with different functions and in different contexts. The symbolic elements are often supported by iconic elements, the latter helping students to unpack the problem and interpret it. ln the iconic representations the role of the diagrams is emphasized, consisting in a valuable tool to support the mathematical reasoning. One can also conclude that while the active representations give more support to the resolution strategies involving simulation, the iconic and symbolic representations are preferably used with different strategies. The representations constructed with distinct roles and functions, are crucial in the proper interpretation and resolution of problems, and seem to be directly related to the characteristics of the proposed task with regard to the mathematical structures involved.

Estrategias metodológicas para contribuir el aprendizaje del álgebra y geometría en el primero de bachillerato del Colegio Nacional Mixto San Joaquín, durante el año lectivo 2012– 2013

Las estrategias metodológicas utilizadas en este trabajo tratan de mejorar el rendimiento y conocimiento del bloque curricular Álgebra y Geometría en los estudiantes del primero de bachillerato del Colegio Nacional Mixto “San Joaquín”. Las estrategias metodológicas planificadas para el bloque curricular Álgebra y Geometría fueron aplicadas en su totalidad, pero hubieron inconvenientes que se fueron solucionando en el proceso de la enseñanza – aprendizaje del bloque como: la utilización del laboratorio de computación, las diferentes actividades extra curriculares y las políticas de la institución. Las actividades lúdicas elaboradas en este bloque curricular,son las que más disfrutaron los estudiantes, por ser diferentes a las actividades tradicionales que se realiza en la enseñanza de la Matemática, otra actividad que causo novedad, es la aplicación de las TIC, como es el caso de la utilización del software GeoGebra y Modellus que permiten resolver ejercicios y problemas mediante gráficas y animaciones, otra herramienta de aprendizaje didáctico es la aplicación del internet como medio de consulta para reforzar significativamente los conocimientos. Los resultados de las evaluaciones aplicadas a los estudiantes de los primeros de bachillerato de esta institución, demuestran que las estrategias metodológicas utilizadas, lograron mejorar el rendimiento y conocimientos del bloque Álgebra y Geometría.

As concepções e práticas avaliativas em matemática de um grupo de professores do 5º ano do ensino fundamental e suas relações com a prova Brasil

Dissertação (mestrado)—Universidade de Brasília, Faculdade de Educação, Programa de Pós-Graduação em Educação, 2015.