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Regular and semi-regular solids in higher dimensions
Pekař, Vojtěch ; Surynková, Petra (advisor) ; Hromadová, Jana (referee)
This thesis deals with multidimensional objects, which are known as Platonic and Archimedean solids in common euclidean space. Although we describe especially four-dimensional figures and their relations with lesser grade, this text is formulated in such a way, that includes even different dimensions, if it is possible in particular instances. There exist a few works about this and similar topics in foreign, but usually they require a little basics of algebra teaching at university. Our approach uses methods similar to these, which are normally teaching in descriptive geometry and therefore includes a large number of pictures. The matter is therefore available to secondary school students, who want to increase their space imagination.
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Secondary school conics with internet
Effenberger, Věra ; Hromadová, Jana (advisor) ; Karger, Adolf (referee)
Title: Utilization of the internet by teaching conics at high school Author: Bc. Věra Effenberger Department: Department of Mathematics Education Supervisor: RNDr. Jana Hromadová, Ph.D. Supervisor's e-mail address: Jana.Hromadova@mff.cuni.cz Abstract This diploma thesis is dealing with conics' problems. It is mainly destined for high school (or university) teachers of descriptive geometry and for students too. It can by used in aid of education of conics or by self-study, because it includes many of illustrative pictures and dynamic applets made in the program GeoGebra, which support the written theoretical text. In the work are enumerated definitions, properties and various constructions of individual conics. Further there is their origin as an intersection of a right circular cone (as the case may be of a right circular cylinder) with a plane, their osculating circle and conjugate diameters. Compilation of examples constitutes an addition of this work. The examples have various difficulty and also can serve as a control over got knowledge. Keywords: ellipse, hyperbola, parabola, foci, tangents, normals, construction of conics
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Paper folding geometry
Hatschbachová, Jana ; Hromadová, Jana (advisor) ; Surynková, Petra (referee)
Paper folding is an underappreciated method with a number of interesting applications in real life. From Japanese traditional origami we moved to today's use in space research or medicine, all thanks to the application of mathematical principles on it. The work explains the basic rules of paper geometry and its difference from Euclidean geometry. The problems of doubling the cube or trisection of the angle, which cannot be solved in Euclidean geometry, can be solved quite easily by translating the paper. The thesis contains ideas for mathematics teachers from elementary school to high school on how to use paper folding directly in mathematics teaching. Among the ideas we can find a simple verification of the Pythagorean theorem and the construction of conic sections. Physical handling of paper helps to consolidate the topic, develops spatial imagination and dexterity.
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Descriptive geometry applications in cartography
Vlčková, Jana ; Moravcová, Vlasta (advisor) ; Hromadová, Jana (referee)
Title: Descriptive geometry applications in cartography Author: Jana Vlčková Department: Department of Mathematics Education Supervisor: RNDr. Vlasta Moravcová, Ph.D., Department of Mathematics Education Abstract: This thesis is focused on constructions of geographic nets in maps and serves as a base for studies and teaching for teachers and students of secondary schools or universities, which are focused on the cartography field. The thesis contains seven chapters, the first of which describes basic terms used in the thesis. Other chapters deal with the analysis of chosen cartography projections, whereas first three chapters concerns with the projection of the globe into a plane, another two chapters concerns with a cylindrical surface and the last one concerns with a conical surface. Constructive tasks, which serve for practising the subject matter, are enclosed for each chapter. Key words: cartographic projection, azimuthal projection, ortographic projection, gno- monic projection, stereographic projection, cylindrical projection, conical projection 1
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Financial literacy in primary school
Helus, Jiří ; Hromadová, Jana (advisor) ; Odvárko, Oldřich (referee)
There were about 6.7 % of inhabitants in foreclosure in the Czech Republic in 2020. The most likely cause is population's low financial literacy whose bases we get at primary school. So we asked whether pupils really learn financial literacy at primary school. We found data for teaching plan in the framework educational programme. We realised, using a questionnaire for teachers, among other things that the number of lessons dedicated to financial literacy is really low. We verified fulfilment of framework educational programme by a test for primary school pupils which was completed by 113 pupils. It showed that they have very low knowledge of financial literacy. Then, we evaluated the situation after primary school through the same test which was filled in by 157 people who completed primary school. The results were better than in case of pupils. Finally, we suggested steps for increasing financial literacy, for instance raising the number of lessons. 1
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Application problems in geometry
Dočekalová, Zuzana ; Hromadová, Jana (advisor) ; Surynková, Petra (referee)
This work deals with application problems regarding to geometry issues. A deep search has been performed throughout existing excercise books from various periods and of various difficulties. Then, 10 new application problems have been devised and solved, concerning miscellaneous mathematics education stages and geometry branches.
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Teaching geometric series through CLIL method with using of German language
Korcová, Aneta ; Moravcová, Vlasta (advisor) ; Hromadová, Jana (referee)
The core of the thesis is the realization of three lessons of mathematics conducted in accordance with the CLIL method, which integrates the teaching a non-linguistic subject with foreign language teaching. The topic of the lessons was non-finite geometric series and the chosen foreign language was German. The first part of the thesis introduces key definitions and theorems concerning sequences and geometric series. Comparisons are drawn between approaches of the Czech Republic and two German-speaking countries, Austria and Germany, in relationship to the teaching non-finite geometric series. Furthermore, available teaching materials of the selected countries are compared and applied visualized problems which appear in them are analysed. In the second part, the CLIL teaching method is presented together with the methodology according to which the lessons were prepared, realized and subsequently assessed. To conclude, the thesis presents a detailed analysis of the preparation and progress of the lessons, including the reflection. The appendix comprises of the utilized teaching materials as well as a range of the solved problems.
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A Collection of Solved Problems in Analytical Geometry
Kvapilová, Babeta ; Hromadová, Jana (advisor) ; Surynková, Petra (referee)
This thesis is intended for teachers and students of high schools and universities. It consists collection of solved problems from plane analytical geometry including various solutions and their comparison. The thesis aims to increase the student knowledge of the topic and to provide different approaches to problems and working materials for lessons for teachers. Pictures for better understanding are added for more difficult problems. The practical part focusing on common mistakes and their elimination is included.
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Mirroring in a linear perspective.
Marková, Kateřina ; Hromadová, Jana (advisor) ; Šarounová, Alena (referee)
Title: Mirroring in a linear perspective Author: Kateřina Marková Department: Department of Mathematics Education Supervisor: RNDr. Jana Hromadová, Ph.D., Department of Mathematics Edu- cation Abstract: This text is intended especially for teachers and students of high schools and colleges who are interested in descriptive geometry. The thesis on the topic of mirroring in linear perspective presupposes basic knowledge of linear perspective. It includes short introduction into the topic of linear perspective and its basic terms, explanation of the principle of mirroring and clarification of constructions that are needed to solve tasks. Main part of the thesis is a problem book with solution. It contains examples on the topic of mirroring in linear perspective for all the basic mirror positions. Every task is supplied with step-by-step solution in the GeoGebra software and a PDF file. Another part of the thesis are photographs of different mirror positions in real life situations. Keywords: Linear perspective, mirroring, vertical, horizontal, sloping mirror
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