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Teaching basic calculus at the secondary school, case study
Hamšík, Karel ; Vondrová, Naďa (advisor) ; Kvasz, Ladislav (referee)
This thesis deals with teaching the basics of calculus in secondary school. These are specifcally those areas of mathematics (functions, derivatives, integrals) that are subsequently discussed in more depth at universities of science, technology, economics, and also other felds. Most university students will encounter these math problems at least to a small extent. Therefore, I am interested in the extent to which pupils are prepared to solve these problems after leaving high school. The second topic that I am interested in is how much the pupils encountered the topics and terms of calculus during their secondary school studies, how they understand them and whether or not they can use them. The aim of this thesis is to describe the methods used in education of elementary school calculus in a specifc seminar where this material is discussed and subsequently verify the ability of the pupils to independently solve problems from this feld of mathematics by a set of didactic tests and their subsequent analysis. The analysis showed that the subject of calculus is for the most part well understood by the pupils. The seminar therefore fulflls the prerequisites for a successful introduction to this subject, which can be successfully expanded on in further higher education. Key words: teaching calculus,...
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Comparison of the approach to didactical environment by Erich Wittmann and in Genetic constructivism
Tuška, Jan ; Kvasz, Ladislav (advisor) ; Vondrová, Naďa (referee)
The aim of the thesis is primarily the comparison of takes on didactical environment between german didactic Erich Wittmann and movement called genetic constructivism. A little more content is dedicated to work of Erich Wittmann and the reader can make a solid image of what is his approach to teaching mathematics. Both approaches are first described theoretically from different points of view and are then demonstrated on examples from teacher handbooks and textbooks, including didactical commentary. Methodology of the thesis consisted of first studying theoretical content of both approaches and then finding relevant examples that represent applications of mentioned theoretical content in a clear way. The examples are taken from elementary and secondary grades of education. In the following part of the thesis, both approaches are compared next to each other with the help of relevant citations regarding following questions: communication in class, usage of instruments in education, role of the teacher, usage of learning environments for mathematics education and the genetic principle. In this comparison, the thesis demonstrates that both didactical environments have a lot in common - this is specified with commentary and summarized in final conclusions. As a distinct element of Wittmann's didactics...
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Goniometric functions and their inverses
Šimková, Jana ; Kvasz, Ladislav (advisor) ; Nižňanská, Kristýna (referee)
This bachelor thesis shows four basic ways how to introduce trigonometric and cyclometric functions. The work is primarily intended for high school students who have encountered some of these introductions at school. The aim of the bachelor thesis is to show comprehensive definitions of trigonometric functions and cyklometric functions according to various methods and to present their basic properties. The aim of the work is also to show the difference and transition between introductions and their equivalence.
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Labyrinths - in the role of an instrument developping space and plane orientation of pre-school child
Černá, Lenka ; Kaslová, Michaela (advisor) ; Kvasz, Ladislav (referee)
The aim of the thesis is to determine whether the practice of using a graded series of labyrinths affect their final solution, hence the orientation in the plane, check the level of understanding of labyrinths and determine whether the sex of children affect the resulting solution. Thus, the work environment uses of labyrinths to develop a structured orientation in a limited space for pre-school children aged five to six (seven) years. The theoretical part characterizes preschool child and explains the context pre- mathematical literacy and orientation in space/plane with the delegation on labyrinthsurthermore, the labyrinths of focus in terms of historical, semantic and didactic.Furthermore, the labyrinths of focus in terms of historical, semantic and didactic. The practical part describes research which in obtaining information from the set of samples used structured observations and findings to the final results of the comparative analysis. They are discussed in connection with: the needs of the child and their saturation; orientation in space/plane; problem situation; interactions of teachers and children. KEY WORDS Pre-school children, pre-mathematical literacy, space orientation, plane orientation, labyrinths, applied methods and phormes of solution.
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The construction of curves by Descartes
Fabián, Tomáš ; Kvasz, Ladislav (advisor) ; Zhouf, Jaroslav (referee)
This work studies the construction of algebraic curves by means of mechanical plotting tools designed by René Descartes. The work includes a brief biography of Descartes, an outline of his scientific method and a description of Descartes' views on curves, their construction and use. By means of dynamic geometry several curves established by Descartes are constructed. These include curves constructed by means of a drawing instrument composed of several rulers; a drawing instrument designed for the hyperbola and its different variations, in which the guiding line is replaced by one of conics in a special position. In the final part we present the construction of four ovals, which are usable in catoptric and dioptric that Descartes constructed by a point wise construction. All drawings are made in Cabri Geometry II and are accompanied by a derivation of the equations of the resulting curves. In deriving these equations we used only elementary algebraic methods, which could be used by Descartes himself and which are comprehensible by secondary school students. Keywords: Descartes, ruler device, curve, conchoid, trident, oval
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On the Method's Disappearance: Analysis between philosophies of social contract and classical sociologies. A Study in Epistemology
Maršálek, Jan ; Balon, Jan (advisor) ; Kvasz, Ladislav (referee) ; Karsenti, Bruno (referee)
The Method and its Disappearance: Analysis between philosophies of social contract and classical sociologies. A Study in Epistemology Jan Maršálek Université de Franche-Comté/Charles University in Prague Supervisors: prof. Frédéric Brahami, prof. Miloslav Petrusek (†), dr. Jan Balon. Résumé: In a doubly disloyal continuity with regard to the French epistemological tradition, largely preoccupied with the formation of scientific concepts, the present work addresses the phenomenon of disappearance of 'analytical' method. Nevertheless, the present work does not constitute an historical investigation: its very goal is to show (within the works of T. Hobbes, J.-J. Rousseau, H. Spencer and E. Durkheim) the variation of the epistemological status of the analysis, and thus to set up the concept of an 'epistemological event'. Examining the disappearance of the analysis requires its identification in the theoretical work whereby its leverage remains unacknowledged. Thus, having the status of a method in the philosophies of the social contract of Hobbes and Rousseau, the analysis 'continues' to structure, in a tacit way, the work of Spencer and Durkheim, both of them founders of scientific sociology. Is it possible to claim that, in the 19th century, the analysis manifests itself in the sociology's common recourse to...
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