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Teaching mathematics online at the first year of grammar school
Flejberková, Dorota ; Kaslová, Michaela (advisor) ; Vondrová, Naďa (referee)
The diploma thesis deals with equations introducing at 8-year gymnasium in the framework of teaching online. This thesis is focused on an action survey in a context of teaching online in prima of 8-year gymnasium. This is a series of lessons focused on equations which were taught at Gymnázium OPEN GATE. The aim of the thesis is to follow the shift in a didactic area in a non-standard form of teaching. The diploma thesis is based on the theoretical background, the practical part is focused on a teaching experiment. For reaching the aim, the following tasks were established: -To discuss possible forms of teaching online. -To summarise the theory of linear equations. -To analyse textbooks for both primary school and lower-secondary school first from the viewpoint of a preparatory stage of equations and then the propaedeutics of equations in the framework of lower-secondary school. - To record the surveyed events connected by reflection. The thesis is divided into two main parts, theoretical and practical. The theoretical part is divided into four chapters. The practical part follows the theoretical one; it is based on analyses a priori of continued reflection. The description of scripts implementation is accompanied by a continued reflection and a posterior reflection. The conclusion provides the key...
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The use of GeoGebra by solving problems in geometry
BUZEK, Štěpán
This diploma thesis is focused on new funkcionalities of dynamic geometry systems and computer algebra systems. In first part of the diploma thesis I research new functions of dynamic geometry systems. Second part is focused on examples which are possible to solve by usage of said methods. Especially it is focused on automatic discovery of locus. Main focus is on finding of equations of locuses. In last example is compared principle of automatic discovery with automatic proving.
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Non-standard application tasks and problems
PRŮDKOVÁ, Kamila
The bachelor thesis deals with non-standard application tasks and problems in mathematics. The aim was to create a collection of tasks with their sample solution using the computer program GeoGebra for interactive geometry, algebra, and analysis. In addition to the content of tasks and their sample solution in text form, the result of this work is an online output in the form of a GeoGebra book. The above-mentioned multiplatform dynamic software GeoGebra can be recommended for teaching, visualization, solution, and analysis of tasks in mathematics.
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Worksheets for teaching mathematics at secondary school from selected topics
ONDRÁČKOVÁ, Kamila
The main aim of the thesis is to verify the pupils knowledge in arithmetic on the basis of worksheets at lower-secondary schools and selected grammar schools. The theoretical part of the thesis is focused on the knowledge that each pupil should already know. The practical part contains 4 working sheets intended for pupils of the sixth, seventh, eighth and ninth grades of lower-secondary school and for the pupils of equal corresponding grade of grammar schools. The results with detailed solution of the work sheets is listed in the appendix of the thesis. The practical part includes is the results of the research which show the pupils´ differences of knowledge of the selected schools.
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Elementary mathematics from an advanced standpoint
Kučera, Jiří ; Bečvář, Jindřich (advisor) ; Staněk, Jakub (referee)
Mine thesis is written for self-study of secondary school graduates students which prepare for the mathematically oriented high schools. It clarifies theoretical approach to mathematics. It was chosen topics exponents, square roots, logarithms and equations that contain these objects for this purpose. For this reason students are given the opportunity to gain stance to university mathematics knowledge that should be known from high school. In addition, his work allows him to enlarge knowledge of those topics and learn heavier and unusual examples.
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Real-life problems solved by quadratic equations
Hanzal, Petr ; Zhouf, Jaroslav (advisor) ; Pilous, Derek (referee)
This thesis contains a set of real-life problems solved using quadratic equations. The aim is to gather avaiable practical problems, with which students of all ages can meet at school or in everyday life and create additional model problems that could be used in teaching or mathematical competitions. Part of this work are pictures for a better understanding of some tasks. Images were created in Geogebra.
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Use of music education in mathematics lessons at the 1st stage of elementary school or Let's sing, Mr. teacheronnection between mathematics and music in primary school
Jánošková, Zuzana ; Jirotková, Darina (advisor) ; Havlíčková, Radka (referee)
The work deals with the possibility of interconnecting the teaching of mathematics with music. The theoretical part focuses on the relationship between mathematics and music, student motivation, the theory of multiple intelligence and also on whether music can contribute to the development of mathematical thinking. The practical part delivers five lesson preparations, where the main topic is music education and several other ways to use music education in another mathematical topic. KEYWORDS Music in mathematics, rhythm in mathematics, musical instruments in mathematics, motivation, word problems, equations, intersubject relations, Gardner's theory of multiple intelligence.
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Web application for teaching algebraic equations in complex numbers
Kneblík, Radovan ; Robová, Jarmila (advisor) ; Staněk, Jakub (referee)
This thesis deals with algebraic equations in the field of complex numbers and teaching of them in high school mathematics. The thesis is a web page, it includes the definition of complex numbers in various forms (form of ordered pair, algebraic, polar and exponential form) and operations with them, as well as conversions between forms. The main part of the thesis includes solving of linear, quadratic, binomial, trinomial, reciprocal and cubic equations in the field of complex numbers. The lecture is enhanced with interactive applets demonstrating given topic. The thesis also includes solved exercises, as well as exercises leading to sets of points satisfying a condition and two overall tests. Web page created within the thesis can be used by high school pupils and teachers. 1
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The Gibbs phenomenon in the discontinuous Galerkin method
Stará, Lenka ; Kučera, Václav (advisor) ; Sváček, Petr (referee)
The solution of the Burgers' equation computed by the standard finite element method is degraded by oscillations, which are the manifestation of the Gibbs phenomenon. In this work we study the following numerical me- thods: Discontinuous Galerkin method, stable low order schemes and the flux corrected technique method in order to prevent the undesired Gibbs phenomenon. The focus is on the reduction of severe overshoots and under- shoots and the preservation of the smoothness of the solution. We consider a simple 1D problem on the interval (0, 1) with different initial conditions to demonstrate the properties of the presented methods. The numerical results of individual methods are provided. 1
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Equation editor for Android
Marek, Jiří ; Kučera, Petr (advisor) ; Jančík, Pavel (referee)
Title: Equation editor for Android Author: Jiří Marek Department: Department of Theoretical Computer Science and Mathematical Logic Supervisor: RNDr. Petr Kučera, Ph.D. Abstract: The goal of this project is to implement an application for the mobile operating system Android, which allows user to interactively create mathematical expressions and typeset them in LATEX. The application is also capable of saving and sharing its output in various file formats. The application contains a general editor and compiler of LaTeX documents. It is possible to use the equation editor to create a formula, place it into a full LaTeX document and to edit it later in the equation editor again. The application is designed in such a way that even a user, who doesn't know LATEX, is capable of creating complex mathematical expressions. It is also possible to seamlessly switch between an interactive type of input and direct editing of a LATEX code. Keywords: Equation, Editor, LaTeX, Android
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