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Algebraic Curves in History and School
Fabián, Tomáš ; Kvasz, Ladislav (advisor) ; Jančařík, Antonín (referee)
TITLE: Agebraic Curves in History and School AUTHOR: Bc. Tomáš Fabián DEPARTMENT: The Department of mathematics and teaching of mathematics SUPERVISOR: prof. RNDr. Ladislav Kvasz, Dr. ABSTRACT: The thesis includes a series of exercises for senior high school students and the first year of university students. In these exercises, students will increase their knowledge about conics, especially how to draw them. Furthermore, students can learn about two unfamiliar curves: Conchoid and Quadratrix. All these curves are afterwards used for solving other problems - some Apollonius's problems, Three impossible constructions etc. Most of the construction is done in GeoGebra software. All the tasks are designed for students to learn how to work with this software. The subject discussed is put into historical context, and therefore the exercises are provided with historical commentary. The thesis also includes didactic notes, important or interesting solutions of exercises, possible issues, mistakes and another relevant notes. KEYWORDS: conic, circle, ellipse, parabola, hyperbole, conchoid, quadratrix, trisecting an angle, squaring the circle, rectification of the circle, doubling a cube, Apollonius's problem, GeoGebra
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Beneficial utilisation of GeoGebra software in geometric constructions at the lower secondary level of basic school
Krejčíčková, Klára ; Holíková, Marie (advisor) ; Jančařík, Antonín (referee)
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
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GeoGebra in mathematics education
Havelková, Veronika ; Zhouf, Jaroslav (advisor) ; Jančařík, Antonín (referee)
The aim of this work is to introduce and assess the potential of using GeoGebra software on multiple levels of mathematical education process and to analyze the expectation of pupils and students using this program. A reader is introduced to GeoGebra program itself and to various researches and articles sharing this common topic - usage of dynamic geometry educational programs and GeoGebra in mathematical education. This work is supported by two field researches that were carried out at the second stage of an elementary school and by another reseach made with students of mathematical education at the Charles University, the Faculty of Education. Next part of this work presents and covers more possibilities of using this program in the educational process of the second stage of elementary schools, and it also shows various options the program offers not just for teaching of mathematics, but also for other fields.
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Algebraic curves in history and school
Fabián, Tomáš ; Kvasz, Ladislav (advisor) ; Vondrová, Naďa (referee)
TITLE: Agebraic Curves in History and School AUTHOR: Bc. Tomáš Fabián DEPARTMENT: The Department of mathematics and teaching of mathematics SUPERVISOR: prof. RNDr. Ladislav Kvasz, Dr. ABSTRACT: The thesis includes a series of exercises for senior high school students and the first year of university students. In these exercises, students will increase their knowledge about conics, especially how to draw them. Furthermore, students can learn about two unfamiliar curves: Conchoid and Quadratrix. All these curves are afterwards used for solving other problems - some Apollonius's problems, Three impossible constructions etc. Most of the construction is done in GeoGebra software. All the tasks are designed for students to learn how to work with this software. The subject discussed is put into historical context, and therefore the exercises are provided with historical commentary. The thesis also includes didactic notes, important or interesting solutions of exercises, possible issues, mistakes and another relevant notes. KEYWORDS: conic, circle, ellipse, parabola, hyperbole, conchoid, quadratrix, trisecting an angle, squaring the circle, rectification of the circle, doubling a cube, Apollonius's problem, GeoGebra
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Experiments in DGS
Sláma, Michal ; Jančařík, Antonín (advisor) ; Zamboj, Michal (referee)
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...
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Spatial Geometry in Secondary School Education
Smetana, Adam ; Surynková, Petra (advisor) ; Šarounová, Alena (referee)
1 Title: Curriculum of solid geometry at czech high schools Author: Adam Smetana Department: Department of Mathematics Education Supervisor: RNDr. Petra Surynková, Ph.D Abstract: The topic of the bachelor thesis is Curriculum of solid geometry at Czech high schools. All of the basic and advanced terms are explained and shown in simple illustrations. The thesis contains a number of solved examples and exercises that are being taught at Czech high schools. All the examples are supported by 2D and 3D applets in GeoGebra software. Keywords: curriculum, solid geometry, cross sections, GeoGebra
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Mathematics with touch-screen devices
KŘÍHOVÁ, Tereza
The aim of my bachelor thesis on the topic of "Math on touch devices" is to provide information about the possibilities of teaching mathematics with the help of electronic touch devices, namely tablets and smart mobile phones. Chart availability learning online resoucre and learning aplications.
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Exploring qualities of functions with GeoGebra software
KODADOVÁ, Veronika
My thesis is about functions, like linear functions, quadratic functions, goniometric functions etc. Goal of my work ist to design appropriate tasks with focus on function links. Students can with help of matematic program GeoGebra discover and adopt needed properties of functions. In this work you can find Cartesian coordinates and overview of basic properties of functions too.
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Visual proofs using dynamic geometry software
ŠTRAUSOVÁ, Irena
The dissertation is divided into two main parts. The first part defines the concept of dynamic visual proof and is placed in the context of proving in mathematics as a subject of science and in mathematics as a subject taught at school. The digital component of the dissertation is a collection of 19 applets with dynamic visual proofs created in the GeoGebra program and arranged in thematic chapters in the so-called GeoGebra-Book, available on-line on geogebra.org. In the second part of the work the research focused on the use of dynamic visual proofs in secondary school mathematics lessons and their influence on fulfilment of educational objectives is described. This a qualitative research where a case study focused on the detailed study of a mathematics teacher who uses dynamic visual proofs in her class. To identify educational objectives, a revised Bloom's taxonomy was chosen.
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Creation and use of teaching materials for lower secondary school mathematics in GeoGebra
KOŠAŘOVÁ, Monika
Although the GeoGebra programme is known at basic schools, its online form on the web site geogebra.org is almost completely unused. This bachelor thesis, named The Creation and Use of Teaching materials for Lower Secondary School Mathematics in GeoGebra, introduces possibilities the programme offers in the online world. It mainly focuses on the creation of materials, dynamic applets, individual working sheets and their following grouping into the so called GeoGebra books. Furthermore, the thesis deals with the sharing of materials through the so called Groups and samples of options, which they offer. My own book, The Creation and Use of Material in the GeoGebra Programme for Basic School, available on the geogebra.org site, is also a part of the thesis. The chosen topics aim at lower secondary school. The resulting work gives readers instructions to the creation of materials and use of GeoGebra's online service for tuition of mathematics.
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