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Solving optimization problems in lower and upper secondary school
Michal, Jakub
The goal of this diploma thesis is to gather and describe ways the optimisation problems had been solved before the calculus was invented. Some of the methods identified through history are generalised and these which could be utilised at secondary or primary school education are described more in depth. Thesis descri- bes the method, where educator follows historical development of the problem in classroom and what benefits it might bring, as well. There is a section dedicated to evaluation of experiment which goal was to investigate understanding of pupils to certain concepts in the field of optimisation, mainly concerning isoperimetric problem. It was also focused on the pupils fe- edback to different approaches of optimisation problem solving. 1
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Analysis of multiplication methods and their application to teaching aids
BOUDOVÁ, Anna
The aim of the dissertation is to analyse various methods of multiplication. Present and historical methods of multiplication will be included in analysis. Each method will be described and then they will be compared together. Based on some selected methods didactic aids will be created to support the teaching of mathematics. There will be following process of elaboration: - Research of literature related to the issue - Analysis of methods of multiplication - Study of Framework Education Programme for Basic Education - Analysis of the development of multiplication in selected sets of textbooks - Comparison of multiplication methods - Creation of didactic aids
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History of Kurzweil integral
Berková, Andrea ; Halas, Zdeněk (advisor) ; Slavík, Antonín (referee)
The presented work deals with history of Kurzweil integral. It focuses primarily on its comparison with other important integrals, namely Newton, Rie- mann, Lebesgue, Perron and McShane integral. Each of them is discussed in a separate chapter which acquaints with their authors and theories. Attention is also oriented to Jaroslav Kurzweil and Ralph Henstock. There are also mentioned the circumstances of the discovery of the Kurzweil integral. The aim is to high- light the theory of integration, which has its origins in Bohemia and despite its elementary definition, which is very general and usable in many applications.
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Origins of Matrix Theory in Czech Lands (and the responses to them)
Štěpánová, Martina ; Bečvář, Jindřich (advisor) ; Slavík, Antonín (referee) ; Hora, Jaroslav (referee)
In the 1880s and early 1890s, the Prague mathematician Eduard Weyr published his important results in matrix theory. His works represented the only significant contribution to matrix theory by Czech mathematicians in many decades that followed. Although Eduard Weyr was one of the few European mathematicians acquainted with matrix theory and working in it at that time, his results did not gain recognition for about a century. Eduard Weyr discovered the Weyr characteristic, which is a dual sequence to the better known Segre characteristic, and also the so-called typical form. This canonical form of a matrix is nowadays called the Weyr canonical form. It is permutationally similar to the commonly used Jordan canonical form of the same matrix and it outperforms the Jordan canonical form in some mathematical situations. The Weyr canonical form has become much better known in the last few years and even a monograph dedicated to this topic was published in 2011.
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Bernard Bolzano and Czech Intellectual Culture, 1945-1989
Konůpka, Petr ; Putna, Martin (advisor) ; Havelka, Miloš (referee)
The thesis focuses on the reception history of Bernard Bolzano (1781- 1848) in the Czech intellectual culture of the 1945-1989 period. The aim of the thesis is not only to summarize existing studies of Bolzano's life and work or to study some of the partial themes related to Bolzano - but to discover basic features of Bolzano reception that can be found accross the different fields of Bolzano research and that are also connected to intellectual and political history background. The expected merit of the thesis can be considered from two different perspectives: In the context of intellectual history the reception of Bolzano is just a very partial theme, however it can expose some of more general features concerning Czech intellectual history of investigated period. From this point of view Bolzano is just a criterion of historical sources selection that enables to study very complex issue of the Czech intellectual history. In the context of Bolzano research this thesis is also a contribution to the better understanding of Bolzano's life and work. The thesis is pointing out themes which should be researched more thoroughly and, it is more important, it discovers the basic contexts of the potential further studies. Keywords: Bernard Bolzano (1781-1848), Czech history 1945-1989, Czech culture 1945-1989,...
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Solving algebraic problems in history and in the classroom
Vojáček, Josef ; Kvasz, Ladislav (advisor) ; Zamboj, Michal (referee)
This diploma thesis deals with the comparison of historical solutions of word problems with student solutions. Its aim was to describe how students solve historical word problems, while looking for analogies between student and historical solutions. This intention led me to a better understanding of student solutions. The theoretical part of the thesis describes important concepts for algebraic word problems, such as a variable, algebraic expression or algebraic word problem. In the historical part I describe chronologically the development of algebra from antiquity through the Middle Ages and the Renaissance to the Baroque. In each period, I mention important mathematicians of the time and present several solved word problems. In most cases, I analyze these solutions from the perspective of today's mathematics. The theoretical part describes the research that took place at the eight-year grammar school. As part of the research, I gave students 6 historical tasks across historical periods and then analyzed the ways in which students solved problems. I found that for most of the tasks, there were solutions similar to the historical solutions among the student's solutions. Some historical methods appeared very often. An example is the use of addition instead of multiplication, or division, as used by the...
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Solving optimization problems in lower and upper secondary school
Michal, Jakub ; Novotná, Jarmila (advisor) ; Pilous, Derek (referee)
The goal of this diploma thesis is to gather and describe ways the optimisation problems had been solved before the calculus was invented. Some of the methods identified through history are generalised and these which could be utilised at secondary or primary school education are described more in depth. Thesis descri- bes the method, where educator follows historical development of the problem in classroom and what benefits it might bring, as well. There is a section dedicated to evaluation of experiment which goal was to investigate understanding of pupils to certain concepts in the field of optimisation, mainly concerning isoperimetric problem. It was also focused on the pupils fe- edback to different approaches of optimisation problem solving. 1
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Historical development of numerical methods and computational techniques, from the perspective of mathematics education in elementary school.
DIVÍŠKOVÁ, Michaela
In my diploma thesis I deal with historical numerical procedures and their application in teaching. In a total of eight chapters, I describe counting techniques from history, such as magic squares, interesting counting algorithms, unconventional divisibility criteria, ancient numeration techniques, golden ratio, figurate numbers, and graphic papers. I deal with the use of historical numerical methods in teaching in the final chapter. This chapter contains eight worksheets and activity suggestions with methodical commentary.
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