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The aim of this thesis is to create a web portal dedicated to teaching of a topic of high school mathematics - Functions. The work contains sections focusing on creating didactic teaching materials, inclusion of ICT in teaching mathematics and sections dedicated to the creation of new www learning portal. It also discusses the dynamic mathematics software, GeoGebra, which is extensively used in this portal. The work is boosted by two studies which measure the suitability of the project for the purposes of teaching mathematics on secondary schools. Research was focused on teachers and high school pupils. The results and conclusions of the research part of the thesis point out how to modify the material, adapt it and thus make it more suitable for educational purposes. Keywords www project, teaching of mathematics, functions, GeoGebra

A utilização do computador nas aulas de Matemática contribui para que o educando perceba esta disciplina de forma mais abrangente, permitindo novas estratégias de abordagem a variados problemas. Pensando nisso, o objetivo foi analisar o impacto que trabalhar geometria com software de geometria dinâmica tem nas aulas regulares do ensino fundamental. Para tal, esta pesquisa iniciou-se com uma análise de quais são os programas de geometria dinâmica utilizados nas pesquisas científicas com aplicação parafins educacionais nas aulas de geometria de alunos do ensino fundamental. Foram considerados apenas trabalhos voltados para alunos do ensino fundamental, que abrangem algum tópico de geometria usando programa de geometria dinâmica. Em virtude da predominância da utilização do software GeoGebra, o mesmo adotado neste trabalho. Caracterizaram-se então, o campo e os sujeitos da pesquisa e escreveram-se as etapas da aplicação de dez atividades, usando o software GeoGebra, nas quais foram aplicadas ao longo do ano de 2014 e ilustradas com as respostas corretas e incorretas dos próprios educandos. Aplicou-se uma mesma atividade para dois grupos: um grupo de tratamento, o qual trabalhou com o software e um grupo de controle, o qual não trabalhou com o software, para se testar a hipótese. A atividade selecionada para esta aplicação foi a construção de um triângulo equilátero, no qual o grupo de controle utilizou-se de régua e compasso. Concluiu-se que os educandos do grupo de tratamento tiveram um melhor aproveitamento do que o grupo de controle. A escolha destas atividades foi baseada na importância do ensino da matemática e, em particular, da geometria para o ensino fundamental e em como despertar o interesse dos alunos pela geometria. / The use of computer on Math classes helps the student\'s perception of the subject in a widely way allowing development of new approach strategies in different kinds of issues. With that in mind the purpose of this dissertation was to analyze the impact of learning geometry in regular classes of elementar school with dynamic geometry software. To do so this research began with na analysis of which dynamic geometry softwares are being utilized in scientific studies driven by students in elementar school classes. Only geometry studies with elementar school students using dynamic geometry software were considered be cause of it predominancy the GeoGebra software was adopted in this dissertation. It was chosen thenfield and subjects to be analyzed and the conceptualization often stages using the GeoGebra software which were described during 2014 classes illustrated by correct and wrong answers given by the students themelves. To test the hypothesis the students were divided in two diferente groups: the treatment group which used the dynamic geometry software and the control group which have not used the dynamic geometry software. The selected test was to draw a equilateral triangle, with the treatment group using GeoGebra software and the control group using a compass and ruler. This application confirmed that students from the treatment group had better results than students from the control group by presenting both groups images of diferente kinds of triangles and asking them to identify the equilateral ones. The choice of this activities was based on the importance of teaching Math, in particular Geometry to ELEMENTARY SCHOOL students and how to develop their interest on the subject.

This thesis broadens the contents of the schoolbooks "Matematika pro gymnázia." It is written primarily as a source material for teachers, however, as it is close to the aforementioned schoolbooks, can be used by students as well.

This thesis deals with the mathematical knowledge of the geometry, which were used in the Gothic period. This is mainly the knowledge that was reflected in the architecture. It is also concerned with the geometrical modeling of the Gothic architectural elements using computer systems of dynamic geometry and potential use of these figures in the mathematics, because the visible connection between theory and practice is very good motivation. The thesis briefly introduces characteristic features of the Gothic style and also describes the historical background that enabled the rise of this new style. This work shows closer also how Gothic building was technically built up. Part of this work is dynamic geometric computer models, which were made with using the gathered information. The interactivity of these models helps students to get better insight into the principles of Gothic architecture elements and also into geometric relationships used in these elements.

A AplicaÃÃo do Software GeoGebra no ensino da Geometria Plana consiste em uma alternativa para o professor de MatemÃtica ou Ãreas afins, que deseja implementar em suas aulas, uma metodologia dinÃmica de ensino. O objetivo à levar aos alunos do ensino bÃsico, uma ferramenta tecnolÃgica contemporÃnea e educativa, que auxilia no ensino de Geometria Plana, fomentando os alunos na retiradas de possÃveis dÃvidas quanto visualizar desenhos geomÃtricos, acompanhado de sua Ãlgebra relacionada. Todo o trabalho, foi desenvolvido principalmente com o auxilio do software GeoGebra (versÃo 4.2.30) e do livro MatemÃtica Elementar (vol. 9 - 1999, de Osvaldo Dolce e Josà Nicolau Pompeo), e em geral, tem caracterÃsticas de aÃÃo, ou seja, busca novos mÃtodos de ensino e aprendizagem a serem implementados no ensino bÃsico, com o propÃsito de melhorar o nÃvel de aprendizagem dos alunos. / The Application Software GeoGebra in teaching plane geometry consists of an alternative to the teacher of Mathematics or related fields who wish to implement in their classes, dynamic methodology of teaching. The goal is to bring basic education students a contemporary technological and educational tool that assists in teaching plane geometry, encouraging students withdrawn in view of possible doubt as geometric designs, accompanied by his algebra related. All work was mainly developed with the help of GeoGebra software (version 4.2.30) and the book Elementary Mathematics (vol. 9-1999, Osvaldo Dolce and Joseph Nicholas Pompeo), and generally have characteristics of action, or is, seeking new methods of teaching and learning to be implemented in basic education, in order to improve the level of student learning.

A utilização do computador nas aulas de Matemática contribui para que o educando perceba esta disciplina de forma mais abrangente, permitindo novas estratégias de abordagem a variados problemas. Pensando nisso, o objetivo foi analisar o impacto que trabalhar geometria com software de geometria dinâmica tem nas aulas regulares do ensino fundamental. Para tal, esta pesquisa iniciou-se com uma análise de quais são os programas de geometria dinâmica utilizados nas pesquisas científicas com aplicação parafins educacionais nas aulas de geometria de alunos do ensino fundamental. Foram considerados apenas trabalhos voltados para alunos do ensino fundamental, que abrangem algum tópico de geometria usando programa de geometria dinâmica. Em virtude da predominância da utilização do software GeoGebra, o mesmo adotado neste trabalho. Caracterizaram-se então, o campo e os sujeitos da pesquisa e escreveram-se as etapas da aplicação de dez atividades, usando o software GeoGebra, nas quais foram aplicadas ao longo do ano de 2014 e ilustradas com as respostas corretas e incorretas dos próprios educandos. Aplicou-se uma mesma atividade para dois grupos: um grupo de tratamento, o qual trabalhou com o software e um grupo de controle, o qual não trabalhou com o software, para se testar a hipótese. A atividade selecionada para esta aplicação foi a construção de um triângulo equilátero, no qual o grupo de controle utilizou-se de régua e compasso. Concluiu-se que os educandos do grupo de tratamento tiveram um melhor aproveitamento do que o grupo de controle. A escolha destas atividades foi baseada na importância do ensino da matemática e, em particular, da geometria para o ensino fundamental e em como despertar o interesse dos alunos pela geometria. / The use of computer on Math classes helps the student\'s perception of the subject in a widely way allowing development of new approach strategies in different kinds of issues. With that in mind the purpose of this dissertation was to analyze the impact of learning geometry in regular classes of elementar school with dynamic geometry software. To do so this research began with na analysis of which dynamic geometry softwares are being utilized in scientific studies driven by students in elementar school classes. Only geometry studies with elementar school students using dynamic geometry software were considered be cause of it predominancy the GeoGebra software was adopted in this dissertation. It was chosen thenfield and subjects to be analyzed and the conceptualization often stages using the GeoGebra software which were described during 2014 classes illustrated by correct and wrong answers given by the students themelves. To test the hypothesis the students were divided in two diferente groups: the treatment group which used the dynamic geometry software and the control group which have not used the dynamic geometry software. The selected test was to draw a equilateral triangle, with the treatment group using GeoGebra software and the control group using a compass and ruler. This application confirmed that students from the treatment group had better results than students from the control group by presenting both groups images of diferente kinds of triangles and asking them to identify the equilateral ones. The choice of this activities was based on the importance of teaching Math, in particular Geometry to ELEMENTARY SCHOOL students and how to develop their interest on the subject.

TITLE: Experiments in DGS AUTHOR: Michal Sláma DEPARTMENT: Department of Mathematics and Mathematical Education SUPERVISOR: doc. RNDr. Antonín Jančařík, Ph. D. ABSTRACT The aim of this diploma thesis is to find out whether the pupils of the second stage of primary school, specifically the pupils of the 6th grade, are able to experiment independently in the environment of dynamic geometry with a suitably prepared material. The theoretical basis of the work includes the study of the valid intended curriculum of geometry at the second stage of primary school, the relationship of so-called inquiry-oriented teaching to the possibility of student experimentation in learning geometry, the study of pedagogical theories in connection with inquiry education and also in relation to mathematisation, which is in the teaching of mathematics and geometry necessarily required. The student experiment is conceived here as an independent didactic method. From the point of view of the feasibility of the experiment and subsequent research, the environment of dynamic geometry was chosen - the GeoGebra system. The theoretical part of the work ends with a description of parameters important for the feasibility of experimentation in the environment of dynamic geometry in the teaching of geometry. The research part deals with the...

Diplomová práce se zabývá využitím programu GeoGebra ve výuce ma- tematiky, konkrétně v tématu konstrukce trojúhelník·. Cílem práce bylo na- vrhnout přípravu na hodiny výuky konstrukce trojúhelník· s využitím pro- gramu GeoGebra a následně ověřit, zda využití softwaru dynamické geometrie mělo vliv na zvládnutí nového učiva. Teoretická část obsahuje použité pojmy z planimetrie. V dalších dvou kapitolách se čtenář seznámí s programem GeoGebra a GeoTest a některými výzkumy, které jsou zaměřené na použití program· dynamické geometrie ve výuce matematiky. Následuje kapitola se- znamující s úlohami, které jsou v experimentu využity, a popisuje přípravu jednotlivých hodin. Poslední část je věnovaná pr·běhu experimentu, srovnání výsledk· žák· pomocí test· s kontrolní třídou. Získaná data jsou zpracována na základě pozorování a test·. Výsledky pozorování a analýzy potvrzují, že GeoGebra je vhodným doplňkem výuky konstrukce trojúhelník·. 1

Neste trabalho, apresentamos o desenvolvimento de ferramentas no programa iGeom - Geometria Interativa na Internet, para ensino-aprendizagem de Geometria, dando destaque aos recursos que facilitam a integração e uso deste programa, principalmente em ambientes de educação a distância via Internet. Atualmente, este tipo de programa é bastante conhecido e a Geometria que ele possibilita é usualmente denominada Geometria Dinâmica. Em poucas palavras, um programa de Geometria Dinâmica é a implementação computacional da régua e do compasso, permitindo que os objetos construídos sejam movidos mantendo-se às propriedades da construção. Dentre os principais recursos desenvolvidos, destacamos a autoria e a validação automática de exercícios e a comunicação com servidores, que podem ser utilizados para integrarem o iGeom em sistemas gerenciadores de cursos pela Web. Deste modo, se integrado a um sistema gerenciador, estes recursos podem ser utilizados para facilitar a tarefa do professor, que poderá criar exercícios diretamente pela Web e não precisará avaliar pessoalmente as respostas de cada aluno, e também para que o aluno saiba de imediato se sua solução está dentro do esperado pelo professor.¶ / In this work, we present the development of tools on the software iGeom - Interactive Geometry on Internet, which can be used for teaching and learning Geometry. We highlight the features that simplify the integration and the use of the iGeom in distance education through Internet mainly. Presently, this kind of program is well known and the Geometry it allows is usually named Dynamic Geometry. Concisely, a Dynamic Geometry software is the computational implementation of the ruler and compass. It allows the user to drag objects and to automatically redraw the whole construction while preserving their mathematical properties. We focus three features among the main developed ones: the communication, the authoring and the automatic checking of exercises. These resources simplify the teacher’s task, when integrated into a learning management system. With them, the teacher can create exercises directly on the Web leaving to the software the task of checking each student’s answer. Moreover, the student can have, in real time, an evaluation of his own performance.