O GeoGebra e a geometria sintética: uma investigação com estudantes brasileiros

Apresenta-se resultados parciais de uma pesquisa, na qual a segunda autora investigou com alunos do ensino médio brasileiro demonstrações visuais utilizando o software GeoGebra. Teve-se como objetivo investigar como um grupo de estudantes do ensino médio brasileiro utilizou os princípios de geometria sintética com a ferramenta computacional GeoGebra para realizar argumentações na demonstração da proposição 5 do livro I de Euclides, a qual afirma que os ângulos da base de um triângulo isósceles são congruentes. A metodologia, de cunho investigativo, comparou a forma original, segundo Euclides, e a adaptada para a linguagem atual. A análise dos registros dos investigados mostrou que o software foi um facilitador para as argumentações dos estudantes enunciarem a proposição de forma pertinente

GEOMETRIA SINTÉTICA: INVESTIGAÇÃO SOBRE O USO DE UM SOFTWARE DE GEOMETRIA DINÂMICA COMO MEIO PARA DEMONSTRAÇÕES VISUAIS

Submitted by MARCIA ROVADOSCHI ([email protected]) on 2018-08-20T17:09:11Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertacao_NadiaRobertaQuainiBresolin.pdf: 2962274 bytes, checksum: 08e27819aea17dfb2d8c955d8761f265 (MD5)Made available in DSpace on 2018-08-20T17:09:11Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertacao_NadiaRobertaQuainiBresolin.pdf: 2962274 bytes, checksum: 08e27819aea17dfb2d8c955d8761f265 (MD5) Previous issue date: 2016-11-30This research aimed to investigate how the GeoGebra software can provide the development of creative, intuitive and visual abilities in the statement of theorems of synthetic geometry. The research was carried out with five students of the first year of high school in a state school of Rio Grande do Sul. This is a qualitative research carried out in the computer lab; data collection was obtained through the records of the constructions carried out by students and analyzed existing protocols in the software itself. The investigative activities, developed in workshop mode, consisted of four specific theorems of plane geometry, chosen at random and feasible to be offered to students of elementary school. The research results showed that the activities provided through the GeoGebra software, the development of creativity, the use of intuitive thinking and visualization as a way of analyzing the operation of ideas in the formulation of conjectures, which contributed to the construction of theorems, providing meaningful learning. Also, it indicates synthetic geometry as a way to perform logical statements of theorems, developing reasoning skills and justifications. In turn, the results showed that the use of GeoGebra software, used in construction, was key to achieving the goals in the research.Este trabalho de pesquisa teve como objetivo investigar de que forma o software GeoGebra pode proporcionar o desenvolvimento de habilidades criativas, intuitivas e visuais na demonstração de teoremas de Geometria Sintética. A investigação foi realizada com cinco alunas do primeiro ano do Ensino Médio de uma Escola Estadual do Rio Grande do Sul. Trata-se de uma pesquisa de cunho qualitativo realizada em laboratório de informática; a coleta de dados foi obtida pelos registros das construções realizadas pelas estudantes e analisados os protocolos existentes no próprio software. As atividades investigativas, desenvolvidas na modalidade de oficina, consistiram de quatro teoremas específicos de Geometria Plana, escolhidos aleatoriamente e viáveis de serem propostos aos estudantes da escola básica. Os resultados da investigação demonstraram que as atividades propostas oportunizaram, por meio do software GeoGebra, o desenvolvimento da criatividade, o uso do pensamento intuitivo e a visualização como forma de analisar a exploração de ideias na formulação de conjecturas, o que contribuiu para a construção dos teoremas, propiciando uma aprendizagem significativa. Além disso, indica Geometria Sintética como uma forma de realizar demonstrações lógicas de teoremas, desenvolvendo habilidades de argumentação e justificativas. Por sua vez, os resultados mostraram que o uso do software GeoGebra, utilizado nas construções, foi fundamental para atingir os objetivos propostos na pesquisa

Geometria Sintética: investigação por meio de demonstrações visuais

In this article, we present a research, qualitative nature, conducted with twelve students of the first year of High School to a public school in Rio Grande do Sul, Brazil, which aimed to investigate the use of GeoGebra software in visual demonstrations in Synthetic Geometry. It was held in the computer lab and the collect of data was obtained through the records of the constructions made by the students, analyzing the existing protocols in the software itself. The activity consisted of a specific theorem of plane geometry and served as a pilot project for the first author prepare research instruments that served to constant further research in a professional master dissertation concluded. The results of this project proved to be possible to explore visual abilities in GeoGebra for synthetic statements of theorems and properties in Geometry.Neste artigo, apresenta-se uma investigação, de cunho qualitativo, realizada com doze estudantes do primeiro ano do Ensino Médio de uma escola estadual no Rio Grande do Sul, a qual teve por objetivo investigar o uso do software GeoGebra nas demonstrações visuais em Geometria Sintética. Foi realizada em laboratório de informática e a coleta de dados foi obtida pelos registros das construções feitas pelos estudantes, analisando-se os protocolos existentes no próprio software. A atividade consistiu de um teorema específico de geometria plana e serviu de projeto piloto para a primeira autora elaborar os instrumentos de investigação que serviram para pesquisa posterior constante de uma dissertação de mestrado profissional concluída. Os resultados deste projeto mostraram ser possível explorar habilidades visuais no GeoGebra para obter demonstrações sintéticas de teoremas e propriedades em Geometria

Signs of cardiac autonomic imbalance and proarrhythmic remodeling in FTO deficient mice

In humans, variants of the fat mass and obesity associated (FTO) gene have recently been associated with obesity. However, the physiological function of FTO is not well defined. Previous investigations in mice have linked FTO deficiency to growth retardation, loss of white adipose tissue, increased energy metabolism and enhanced systemic sympathetic activation. In this study we investigated for the first time the effects of global knockout of the mouse FTO gene on cardiac function and its autonomic neural regulation. ECG recordings were acquired via radiotelemetry in homozygous knockout (n = 12) and wild-type (n = 8) mice during resting and stress conditions, and analyzed by means of time- and frequency-domain indexes of heart rate variability. In the same animals, cardiac electrophysiological properties (assessed by epicardial mapping) and structural characteristics were investigated. Our data indicate that FTO knockout mice were characterized by (i) higher heart rate values during resting and stress conditions, (ii) heart rate variability changes (increased LF to HF ratio), (iii) larger vulnerability to stress-induced tachyarrhythmias, (iv) altered ventricular repolarization, and (v) cardiac hypertrophy compared to wild-type counterparts. We conclude that FTO deficiency in mice leads to an imbalance of the autonomic neural modulation of cardiac function in the sympathetic direction and to a potentially proarrhythmic remodeling of electrical and structural properties of the heart

Cardiac autonomic response to the injection of saline.

<p>Time course of changes in heart rate (panel A), RMSSD values (panel B), high frequency (HF) spectral power (panel C) and LF to HF ratio (panel D) following the injection of saline, in Fto^+/+ (n = 8) and Fto^−/− (n = 12) mice. Baseline reference value (bas) is the mean value of the ten 3-min time points in resting conditions. Values are expressed means ± SEM. * and ^# indicate a significant difference between Fto^+/+ and Fto^−/− mice (p&lt;0.05 and p&lt;0.01, respectively).</p

Radiotelemetric and HRV parameters in response to the saline injection test.

<p>Values are reported as means ± SEM of data obtained by averaging multiple 3-min segments acquired in baseline conditions (30 min) and following the injection of saline (60 min) in Fto^+/+ (n = 8) and Fto^−/− mice (n = 12). Abbreviations: HRV = heart rate variability; HR = heart rate; RMSSD = square root of the mean squared differences of successive RR intervals; HF = high-frequency; LF = low-frequency; T = body temperature; LOC = locomotor activity. * and ^# indicate a significant difference between Fto^+/+ and Fto^−/− mice (p&lt;0.05 and p&lt;0.01, respectively).</p

Radiotelemetric and HRV parameters in response to the restraint test.

<p>Values are reported as means ± SEM of data obtained by averaging multiple 3-min segments acquired in baseline conditions (30 min), during the restraint (15 min) and the recovery phase (45 min) in Fto^+/+ (n = 8) and Fto^−/− mice (n = 12). Abbreviations: HRV = heart rate variability; HR = heart rate; RMSSD = square root of the mean squared differences of successive RR intervals; HF = high-frequency; LF = low-frequency; T = body temperature; LOC = locomotor activity. * and ^# indicate a significant difference between Fto^+/+ and Fto^−/− mice (p&lt;0.05 and p&lt;0.01, respectively).</p

Gross cardiac characteristics.

<p>Values are reported as means ± SEM. Abbreviations: HW = heart weight; BW = body weight; LVW = left ventricular weight; RVW = right ventricular weight. * and ^# indicate a significant difference between Fto^+/+ and Fto^−/− mice (p&lt;0.05 and p&lt;0.01, respectively).</p

Cardiac interval duration.

<p>Values are expressed as means ± SEM. * and ^# indicate a significant difference between Fto^+/+ (n = 8) and Fto^−/− (n = 12) mice (p&lt;0.05 and p&lt;0.01, respectively).</p