Teorema de Pitágoras: algumas extensões/generalizações e atividades com o Software GeoGebra

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Experimentação-com-Geogebra: revisitando alguns conceitos da análise real

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Situações didáticas no ensino de geometria com o aplicativo GeoGebra

Pós-graduação em Matemática - IBILCE

Um estudo de retas do plano e uma abordagem para o ensino médio com o software GeoGebra

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

GeoGebra e o método de Briot & Bouquet para a resolução gráfica de equações cúbicas

In the mid-nineteenth century, french mathematicians Briot and Bouquet have proposed an intriguing graphical method for solving cubic equations "depressed" - the third degree equations that do not have the quadratic term. The proposal is simple geometric construction, though based on an ingenious algebra. We propose here the verification and testing graphical method through an instructional sequence using the software GeoGebra also present the ingenious algebraic development that resulted in this graphic method for determination of real roots of a cubic equation of the type x³ + px + q = 0 where p and q are real numbers. The method states that these solutions are summarized in the abscissas of the points of intersection of the circumference containing the origin and the center C (-q/2, 1-p/2) with the parable y = x².

O auxílio do software Geogebra na aquisição do conhecimento da função seno

This article aims to reflect on the qualitative analysis regarding the modification and the acquisition of new knowledge, as well as to identify the contribution of computer use in an intervention activity. It was used content analysis and it was created categories and units of analysis and from the frames containing the analysis of the categories it was randomly chosen four groups which led to their evaluation. Concerning to such frames of analysis and evaluation of the frequency of the records it was structured a metatext. The result of the analysis has shown the students' difficulty to realize their records, to express their interpretations and understandings in their mathematical activities by using the English language. It was noticed that the activity performed using the software Geogebra, based on the constructionist view, make possible the students to identify the modification and acquisition of new concepts.

A visualização no ensino de geometria com o Geogebra 3D

This research presents an investigation about the relevance of visualization in teaching geometry. Our interest turns to analyzing the use of technology in teaching geometry, seeking to highlight their contribution to learning. The students of today - second decade of the 21st century - require that, each time more, the school move towards the integration of technologies for teaching since tablets, smartphone, netbook, notebook are items present on daily life of most students. Thereby, we investigate, taking the phenomenological orientation, the potential of educational software, especially the Geogebra 3D, directed at teaching math and favoring the work with the geometry viewing. At work we bring some theoretical considerations about the importance of viewing for the geometric learning and the use of technologies. We build an intervention proposal for the classroom of the 7th year of elementary school with tasks aimed at visual exploration and allow the teacher to work the concept of volume of geometric solids

A visualização no ensino de geometria com o Geogebra 3D

This research presents an investigation about the relevance of visualization in teaching geometry. Our interest turns to analyzing the use of technology in teaching geometry, seeking to highlight their contribution to learning. The students of today - second decade of the 21st century - require that, each time more, the school move towards the integration of technologies for teaching since tablets, smartphone, netbook, notebook are items present on daily life of most students. Thereby, we investigate, taking the phenomenological orientation, the potential of educational software, especially the Geogebra 3D, directed at teaching math and favoring the work with the geometry viewing. At work we bring some theoretical considerations about the importance of viewing for the geometric learning and the use of technologies. We build an intervention proposal for the classroom of the 7th year of elementary school with tasks aimed at visual exploration and allow the teacher to work the concept of volume of geometric solids

Calcolo numerico ed esplorazioni con geogebra

Il lavoro di tesi svolto propone diversi argomenti di geometria la cui costruzione è stata fatta con il software GeoGebra. Propone anche alcuni metodi di integrazione numerica realizzati con esso e anche un modo di approssimare la superficie di rotazione di una funzione sfruttando tali metodi. Gli argomenti trattati spaziano da quelli classici della geometria euclidea a temi affrontati più recentemente esaminando sia oggetti rappresentabili sul piano sia nello spazio tridimensionale.

Análisis y métodos numéricos con Geogebra

Cuaderno de prácticas de Matemáticas II, Grado en Ingeniería Informática, Universidad de Alicante.

O PTE, as Tic, a Matemática e o GeoGebra

O Plano Tecnológico da Educação veio facilitar o acesso aos recursos tecnológicos (equipamentos e programas) e a utilização, desenvolvimento e partilha de conteúdos. Entre os diversos recursos disponibilizados, encontra-se o quadro interativo, que apresenta várias vantagens em relação ao quadro tradicional: permite a interação entre o aluno/professor e o recurso. Nas aulas de Matemática, a utilização dos quadros interativos com múltiplos recursos aumenta a motivação no processo ensinoaprendizagem. Permite a análise coletiva e a construção colaborativa do saber por parte dos alunos da turma. Possibilita a utilização em conjunto de vários programas relacionados com a Matemática, nomeadamente o Geogebra, que foi utilizado por uma turma na unidade das Isometrias.

A matemática e as tic no processo de ensino e aprendizagem : o geogebra no ensino de funções e gráficos de uma função

Dissertação de mestrado, Educação (Área de especialidade em Educação e Tecnologias Digitais), Universidade de Lisboa, Instituto de Educação, 2016

A geometria do compasso (1797) de Mascheroni (1750 – 1800) em atividades com o GeoGebra

The present work aims to show a possible relationship between the use of the History of Mathematics and Information and Communication Technologies (TIC) in teaching Mathematics through activities that use geometric constructions of the “Geometry of the Compass” (1797) by Lorenzo Mascheroni (1750-1800). For this, it was performed a qualitative research characterized by an historical exploration of bibliographical character followed by an empirical intervention based on use of the History of Mathematics combined with TIC through Mathematical Investigation. Thus, studies were performed in papers dealing with the topic, as well as a survey to highlight problems and /or episodes of the history of mathematics that can be solved with the help of TIC, allowing the production of a notebook of activities addressing the resolution of historical problems in a computer environment. In this search, we came across the problems of geometry that are presented by Mascheroni stated previously in the work that we propose solutions and investigations using GeoGebra software. The research resulted in the elaboration of an educational product, a notebook of activities, which was structure to allow during its implementation, students can conduct historical and/or Mathematics research, therefore, we present the procedures for realization of each construction, followed at some moments by original solution of the work. At the same time, we encourage students to investigate/reflect its construction (GeoGebra), in addition to making comparisons with the solution Mascheroni. This notebook was applied to two classes of the course of Didactics of Mathematics I (MAT0367) Course in Mathematics UFRN in 2014. Knowing the existence of some unfavorable arguments regarding the use of history of mathematics, such as loss of time, it was found that this factor can be mitigated with the aid of computational resource, because we can make checks using only the dynamism of and software without repeating the construction. It is noteworthy that the minimized time does not mean loss of reflection or maturation of ideas, when we adopted the process of historical and/or Mathematics Investigation

GeoGebra sähköisessä ylioppilaskokeessa

Tutkielman aiheena on sähköistyvä ylioppilaskoe matematiikan ja GeoGebra-ohjelman näkökulmasta. Tarkasteltavia aihealueita ovat lukion pitkän matematiikan geometriaa sekä numeerisia menetelmiä käsittelevät kurssit. Tarkoituksena on ensin tutustua pääpiirteissään sähköiseen matematiikan ylioppilaskokeeseen sekä GeoGebra-ohjelmaa ja perehtyä sitten edellä mainittujen kurssien aiheisiin ja lopuksi ratkaista niihin liittyviä eri tasoisia tehtäviä GeoGebralla. Ylioppilaskokeella on edessään uudistus sähköiseen muotoon syksystä 2016 alkaen. Matematiikan osalta sähköinen ylioppilaskoe on ensi kertaa käytössä keväällä 2019. Sähköisessä ylioppilaskokeessa opiskelijalla on käytössään päätelaitteella erilaisia ohjelmistoja, joista yksi on dynaaminen matematiikkaohjelma GeoGebra. Sähköinen koe tarjoaa uusia mahdollisuuksia tehtävätyyppien ja mahdollisesti käytettävän aineiston ja taustamateriaalin suhteen. Matematiikan tehtävien ratkaiseminen sähköisessä muodossa muuttaa tehtävien luonnetta ja siksi uudistuksen myötä on tarpeellista pohtia myös uudenlaisia matematiikan tehtäviä. GeoGebra sisältää esimerkiksi paljon valmiita työkaluja geometristen ongelmien ratkaisuun ja siksi perinteiset tehtävät eivät ole aina mielekkäitä sähköisin välinein ratkaistaviksi. Lukion pitkän matematiikan geometrian kurssin keskeisiä sisältöjä ovat yhdenmuotoisuus, sini- ja kosinilause, ympyrän geometria sekä kuvioihin ja kappaleisiin liittyvät pinta-alat, tilavuudet, kulmat sekä pituudet. Työssä käsiteltäviä numeerisia menetelmiä ovat Newtonin menetelmä funktion nollakohtien ratkaisemiseksi sekä erilaiset pinta-alan approksimointiin käytetävät menetelmät, joista yksi on Simpsonin sääntö.