Matemática e música

Esta dissertação propõe atividades a fim de estabelecer uma aproximação entre a matemática e a música, aproveitando a estreita relação existente entre esses dois assuntos. Aplica-se a história da matemática como ferramenta para o entendimento de conceitos matemáticos e musicais, bem como a evolução da música. Além disso, utiliza-se a resolução de problemas para estabelecer a relação entre a matemática e a música através das funções exponencial e logarítmica e a sequência numérica chamada progressão geométrica (P.G.) Ações efetivas, como questionários relativos ao assunto a ser estudado, debates com o intuito de perceber o nível de conhecimento dos alunos sobre a música e uma atividade prática, a construção de um xilofone de garrafas, envolvendo os conhecimentos adquiridos, auxiliaram para a obtenção do resultado final deste trabalho. Apresenta-se também a análise das atividades que embasaram a proposta desse trabalho quando aplicadas em uma turma de segundo ano do Colégio Sinodal Alfredo Simon, localizada na cidade de Pelotas no estado do Rio Grande do Sul.

Humor in mathematics teaching

HUMOR: OUR VIEW FOR MATHEMATICS TEACHING Our assumptions and context. Process humor and be able to produce is clearly a sign of intelligence, revealing, when done well, complex reasoning. Humor has an important social role, assuming as a cognitive experience that as well as creating a sense of well-being, predisposes people to work and can improve the productivity of that work. Mathematics is a discipline in which the reasoning occupies a very prominent place, both as a science as a school area. At the same time, students' interest for mathematics is not always the same and some have initially not very favorable feelings (Toh, 2009; Wanzer, Frymier & Irwin, 2010). Recent curriculum changes to the teaching of mathematics have been, in most countries of the world, showing the need for students to develop skills of critical nature, such as communication, thinking and problem solving along with the acquisition of mathematical knowledge. Also in Portugal, it is claimed the importance of promoting learning that combine the construction of mathematical knowledge with its use, when performing mathematical tasks and communicating mathematical ideas and mathematical reasoning. In the early years of schooling, corresponding to primary education in many countries, the use of texts such as short stories or comics, from which we can develop challenging mathematical tasks, is reported in the literature as having potential to promote learning specified in curricular documents (Wanzer, Frymier., & Irwin, 2010). In particular, some texts focus on mathematical topics in a humorous way and to be understood, students must develop their mathematical competence. The development of mathematical tasks from stories and other humorous presents big challenges to teachers (Flores & Moreno, 2011). Our questions. In this context, we put some questions: Primary teachers use in their classes tasks or situations that present, in a humorous way, mathematical ideas? What resources do they use? Also: How to select, adapt or build texts and tasks which have, in a humorous way, mathematical ideas with didactic potential for education in the early years of schooling? If the resources for this purpose have been produced and if teachers have been sensitized for their use, are they able to integrate them in their classes? Our intentions. This research project seeks to address these questions, focused on: (i ) assessment of teachers’ practices and underlying knowledge, resources available for the use of texts with mathematical ideas presented in a humorous way; (ii) selection, adaptation and construction of mathematical tasks from texts that present, in a humorous way, mathematical ideas with didactic potential in education for the early years of schooling; and ( iii ) integration and use, by primary school teachers, of texts that present , in a humorous way, contexts for the teaching of mathematics. So, the project is organized into three tasks and as a methodological design that combines qualitative elements with quantitative elements, the first one prevailing.

Problem-Based SRS: método para especificação de requisitos de software baseado em problemas

Requirements specification has long been recognized as critical activity in software development processes because of its impact on project risks when poorly performed. A large amount of studies addresses theoretical aspects, propositions of techniques, and recommended practices for Requirements Engineering (RE). To be successful, RE have to ensure that the specified requirements are complete and correct what means that all intents of the stakeholders in a given business context are covered by the requirements and that no unnecessary requirement was introduced. However, the accurate capture the business intents of the stakeholders remains a challenge and it is a major factor of software project failures. This master’s dissertation presents a novel method referred to as “Problem-Based SRS” aiming at improving the quality of the Software Requirements Specification (SRS) in the sense that the stated requirements provide suitable answers to real customer ́s businesses issues. In this approach, the knowledge about the software requirements is constructed from the knowledge about the customer ́s problems. Problem-Based SRS consists in an organization of activities and outcome objects through a process that contains five main steps. It aims at supporting the software requirements engineering team to systematically analyze the business context and specify the software requirements, taking also into account a first glance and vision of the software. The quality aspects of the specifications are evaluated using traceability techniques and axiomatic design principles. The cases studies conducted and presented in this document point out that the proposed method can contribute significantly to improve the software requirements specification.

Prática de ensino supervisionada em educação pré-escolar e ensino do 1º ciclo do ensino básico: desenvolver a capacidade de resolver problemas em matemática

O presente relatório insere-se no âmbito das unidades curriculares de Prática de Ensino Supervisionada em Pré-Escolar e em 1º Ciclo do Ensino Básico, inseridas no Mestrado em Educação Pré-Escolar e Ensino do 1º Ciclo do Ensino Básico da Universidade de Évora. A investigação traduzida neste relatório decorreu nos dois contextos acima referidos, sendo primeiramente realizada no contexto de Educação Pré-Escolar e seguidamente no contexto de 1º Ciclo do Ensino Básico. O principal objetivo da investigação centra-se no desenvolvimento das capacidades de resolver problemas em matemática, tanto em crianças mais pequenas, como mais tarde no início da escolaridade obrigatória. Surgiu assim a questão orientadora da investigação: Que práticas devo realizar para contribuir para que as/os crianças/alunos consigam tornar-se bons resolvedores de problemas? Seguiram-se a esta outras três questões no sentido auxiliar a investigação: Como lidam as/os crianças/alunos com a resolução de problemas? Que estratégias utilizam as/os crianças/alunos para resolver problemas? Que representações usam as/os crianças/alunos na resolução de problemas? No desenvolvimento da investigação foi realizada uma sequência didática de tarefas matemáticas de exploração de resolução de problemas onde foram recolhidos os dados para uma posterior análise, tendo em conta não só os objetivos da investigação como os referenciais teóricos. Concluiu-se que a metodologia utilizada desenvolveu a capacidade de resolver problemas dos estudantes, ou seja, a exploração de problemas utilizando diferentes estratégias e representações, tal como a partilha de conhecimentos e a comunicação matemática, são ferramentas essenciais para uma intervenção eficaz no que concerne à resolução de problemas; Supervised Teaching Practice in Preschool Education and Teaching of the Primary School: Developing the capacities to solve problems in mathematics Abstract: The present report is inserted in the context of the curricular unit Supervised Teaching Practice in Preschool Education and in Primary School, integrated in Master in Preschool Education and Teaching Primary School at University of Évora. This research was held in two different contexts, the first one was performed in a pre-school classroom, and later the second one in classroom of first year of Primary School. The main objective of the research was focused on the development of the capacities to solve mathematical problems either in small children, or later in the beginning of compulsory schooling. As so, the question guiding this investigation emerged: Which practices should I perform to help children/students become better problem solvers? After this, other three questions came up in order to help the research: How do children/students deal with solving problems? What strategies do children/students use to solve problems? What representations do children/students use to solve problems? Throughout this research a didactic intervention consisting in a sequence of mathematical tasks to explore the resolution of problems was performed, allowing data collection for a latter analysis, based not only on the objectives and initial research questions, but also on theoretical approaches consulted. We came to the conclusion that the ability of students to solve problems was improved with the methodology used in this research, meaning that, challenging students with problems using different strategies and representations, such as knowledge sharing and mathematical communication, are essential tools for effective intervention concerning problem solving.

Conexões matemáticas na educação pré-escolar

Dissertação de Mestrado, Educação Pré-Escolar, Escola Superior de Educação e Comunicação, Universidade do Algarve, 2016

Processamento de Dados GNSS em Modo Cinemático

O princípio do posicionamento por GNSS baseia-se, resumidamente, na resolução de um problema matemático que envolve a observação das distâncias do utilizador a um conjunto de satélites com coordenadas conhecidas. A posição resultante pode ser calculada em modo absoluto ou relativo. O posicionamento absoluto necessita apenas de um recetor para a determinação da posição. Por sua vez, o posicionamento relativo implica a utilização de estações de referência e envolve a utilização de mais recetores para além do pertencente ao próprio utilizador. Assim, os métodos mais utilizados na determinação da posição de uma plataforma móvel, com exatidão na ordem dos centímetros, baseiam-se neste último tipo de posicionamento. Contudo, têm a desvantagem de estarem dependentes de estações de referência, com um alcance limitado, e requerem observações simultâneas dos mesmos satélites por parte da estação e do recetor. Neste sentido foi desenvolvida uma nova metodologia de posicionamento GNSS em modo absoluto, através da modelação ou remoção dos erros associados a cada componente das equações de observação, da utilização de efemérides precisas e correções aos relógios dos satélites. Este método de posicionamento tem a designação Precise Point Positioning (PPP) e permite manter uma elevada exatidão, equivalente à dos sistemas de posicionamento relativo. Neste trabalho, após um estudo aprofundado do tema, foi desenvolvida uma aplicação PPP, de índole académica, com recurso à biblioteca de classes C++ do GPS Toolkit, que permite determinar a posição e velocidade do recetor em modo cinemático e em tempo real. Esta aplicação foi ensaiada utilizando dados de observação de uma estação estática (processados em modo cinemático) e de uma estação em movimento instalada no NRP Auriga. Os resultados obtidos permitiram uma exatidão para a posição na ordem decimétrica e para a velocidade na ordem do cm/s.

Cognitive Competence and Life Course Change in Multi-Problem Adolescents

The dissertation reports on two studies. The purpose of Study I was to develop and evaluate a measure of cognitive competence (the Critical Problem Solving Skills Scale – Qualitative Extension) using Relational Data Analysis (RDA) with a multi-ethnic, adolescent sample. My study builds on previous work that has been conducted to provide evidence for the reliability and validity of the RDA framework in evaluating youth development programs (Kurtines et al., 2008). Inter-coder percent agreement among the TOC and TCC coders for each of the category levels was moderate to high, with a range of .76 to .94. The Fleiss’ kappa across all category levels was from substantial agreement to almost perfect agreement, with a range of .72 to .91. The correlation between the TOC and the TCC demonstrated medium to high correlation, with a range of r(40)=.68, p Study II reports an investigation of a positive youth development program using an Outcome Mediation Cascade (OMC) evaluation model, an integrated model for evaluating the empirical intersection between intervention and developmental processes. The Changing Lives Program (CLP) is a community supported positive youth development intervention implemented in a practice setting as a selective/indicated program for multi-ethnic, multi-problem at risk youth in urban alternative high schools in the Miami Dade County Public Schools (M-DCPS). The 259 participants for this study were drawn from the CLP’s archival data file. The study used a structural equation modeling approach to construct and evaluate the hypothesized model. Findings indicated that the hypothesized model fit the data (χ2 (7) = 5.651, p = .83; RMSEA = .00; CFI = 1.00; WRMR = .319). My study built on previous research using the OMC evaluation model (Eichas, 2010), and the findings are consistent with the hypothesis that in addition to having effects on targeted positive outcomes, PYD interventions are likely to have progressive cascading effects on untargeted problem outcomes that operate through effects on positive outcomes.

An Artificial Intelligence Approach to Dyscalculia

Dyscalculia stands for a brain-based condition that makes it hard to make sense of numbers and mathematical concepts. Some adolescents with dyscalculia cannot grasp basic number concepts. They work hard to learn and memorize basic number facts. They may know what to do in mathematical classes but do not understand why they are doing it. In other words, they miss the logic behind it. However, it may be worked out in order to decrease its degree of severity. For example, disMAT, an app developed for android may help children to apply mathematical concepts, without much effort, that is turning in itself, a promising tool to dyscalculia treatment. Thus, this work focuses on the development of an Intelligent System to estimate children evidences of dyscalculia, based on data obtained on-the-fly with disMAT. The computational framework is built on top of a Logic Programming framework to Knowledge Representation and Reasoning, complemented with a Case-Based problem solving approach to computing, that allows for the handling of incomplete, unknown, or even contradictory information.

Problems in physics and mathematics contexts with middle and high school classes: vertical and horizontal comparison

My thesis falls within the framework of physics education and teaching of mathematics. The objective of this report was made possible by using geometrical (in mathematics) and qualitative (in physics) problems. We have prepared four (resp. three) open answer exercises for mathematics (resp. physics). The test batch has been selected across two different school phases: end of the middle school (third year, 8\textsuperscript{th} grade) and beginning of high school (second and third year, 10\textsuperscript{th} and 11\textsuperscript{th} grades respectively). High school students achieved the best results in almost every problem, but 10\textsuperscript{th} grade students got the best overall results. Moreover, a clear tendency to not even try qualitative problems resolution has emerged from the first collection of graphs, regardless of subject and grade. In order to improve students' problem-solving skills, it is worth to invest on vertical learning and spiral curricula. It would make sense to establish a stronger and clearer connection between physics and mathematical knowledge through an interdisciplinary approach.

A formação continuada do professor de educação fisica : possibilitando praticas reflexivas

Universidade Estadual de Campinas . Faculdade de Educação Física

Inteligência artificial aplicada à Zootecnia

Os sistemas biológicos são surpreendentemente flexíveis pra processar informação proveniente do mundo real. Alguns organismos biológicos possuem uma unidade central de processamento denominada de cérebro. O cérebro humano consiste de 10(11) neurônios e realiza processamento inteligente de forma exata e subjetiva. A Inteligência Artificial (IA) tenta trazer para o mundo da computação digital a heurística dos sistemas biológicos de várias maneiras, mas, ainda resta muito para que isso seja concretizado. No entanto, algumas técnicas como Redes neurais artificiais e lógica fuzzy tem mostrado efetivas para resolver problemas complexos usando a heurística dos sistemas biológicos. Recentemente o numero de aplicação dos métodos da IA em sistemas zootécnicos tem aumentado significativamente. O objetivo deste artigo é explicar os princípios básicos da resolução de problemas usando heurística e demonstrar como a IA pode ser aplicada para construir um sistema especialista para resolver problemas na área de zootecnia.

Adolescência através dos séculos

A sociedade contemporânea ocidental estendeu o período da adolescência, que não é mais encarada apenas como uma preparação para a vida adulta, mas passou a adquirir sentido em si mesma, como um estágio do ciclo vital. O presente artigo procura descrever como os adolescentes eram vistos e tratados, desde a antiguidade até os dias de hoje, a partir de textos literários ou filosóficos e estudos científicos. O material bibliográfico a respeito da adolescência caracteriza-se por três etapas distintas: a descrição dos padrões de comportamento, ajustamento pessoal e relacionamento; a resolução de problemas reais por meio do conhecimento científico; e o desenvolvimento positivo do indivíduo, considerando os adolescentes como o futuro da humanidade.

Os faróis da sociedade de informação: uma análise crítica sobre a situação da competência em informação no Brasil

This paper presents and reviews the recommendations done by experts during the specialists meeting held in the city of Alexandria, Egypt, in the end of 2005 and, according to this information, the Brazilian situation is analyzed. Internationalization and institutionalization of information literacy and lifelong learning as essential factors to the development of the nations are also explored. Beacons of the Information Society translate the vision and concepts involved. In Brazil, the actions around information literacy are not a consensus. The challenges to be faced include: to discover forms to foster and to appropriately disseminate national and local knowledge, to advance discussions and deepen the subject, to discover adequate alternatives for disseminating information practices that encompass distinct professional groups and populations, to overcome structural development gaps. As a matter that permeates each and every process of learning, research, development, problem-solving and decision-making, information literacy went beyond the boundaries of librarianship and transformed itself into a world transdiciplinary movement, even under the aegis of different denominations and emphasis.

Stress and coping in older people with Alzheimer`s disease

To investigate stress intensity and coping style in older people with mild Alzheimer`s disease. The potential risk assessment of a stress event and the devising of coping strategies are dependent on cognitive function. Although older individuals with Alzheimer`s disease present significant cognitive impairment, little is known about how these individuals experience stress events and select coping strategies in stress situations. Survey. A convenient sample of 30 cognitively healthy older people and 30 individuals with mild Alzheimer`s disease were given an assessment battery of stress indicators (Symptom Stress List, Cornell Scale for Depression in Dementia, State-Trait Anxiety Inventory), coping style (Jalowiec Coping Scale) and cognitive performance (mini-mental state exam) were applied in both groups. Statistical analysis of the data employed the Mann-Whitney test to compare medians of stress indicators and coping style, Fischer`s exact test to compare proportions when expected frequencies were lower than five, and Spearman`s correlation coefficient to verify correlation between coping style and cognitive performance. Both groups suffered from the same stress intensity (p = 0.254). Regarding coping styles, although differences were not statistically significant (p = 0.124), emotion-oriented coping was predominant in the patients with Alzheimer`s disease. However, those individuals displaying better cognitive performance in the Alzheimer`s disease group had selected coping strategies focused on problem solving (p = 0.0074). Despite a tendency for older people with Alzheimer`s disease to select escape strategies and emotional control, rather than attempting to resolve or lesser the consequences arising from a problem, coping ultimately depends on cognitive performance of the individual. The findings of this study provide information and data to assist planning of appropriate support care for individuals with Alzheimer`s disease who experience stress situations, based on their cognitive performance.

Identification of nurses` competencies in primary health care through a Delphi study in southern Brazil

Objective: This investigation aimed to identify and analyze the general and specific competencies of nurses in the primary health care practice of Brazil. Design: The Delphi Technique was used as the method of study. Sample: 2 groups of participants were selected: One contained primary health care nurses (n=52) and the other specialists (n=57), including public health nurses and public or community health faculty. Measurements: 3 questionnaires were developed for the study. The first asked participants to indicate general and specific competencies, which were compiled into a list for each group. A Likert scale of 1-5 was added to these 2 lists in the second and third questionnaires. A consensus criterion of 75% for score 4 or 5 was adopted. Results: In the nurses` group, 17 general and 8 specific competencies reached the consensus criterion; 19 general and 9 specific competencies reached the criterion in the specialists` group. These competencies were classified into 10 domains: professional values, communication, teamwork, management, community-oriented, health promotion, problem solving, health care, and education and basic public health sciences. Conclusions: These competencies reflect Brazilian health policy and constitute a reference for health professional practice and education.