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Interesting prime numbers and their properties
KRATOCHVÍL, Daniel
The aim of this bachelor thesis is to introduce special kinds of prime numbers to the reader. The thesis is divided into four parts. The first, introductory, one deals with the definition of prime numbers, provides some basic information about them, and offers one of the methods for finding the prime numbers. The following two parts focus on special kinds of prime numbers, the former of them contains those kinds of prime numbers which are named after famous mathematicians. The latter part is concern with prime numbers which are special for their unique attribute. In the closing part there are some exercises either with or without their solution.
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Divisibility for talented students of secondary schools
Živčáková, Andrea ; Robová, Jarmila (advisor) ; Bečvář, Jindřich (referee)
This thesis is an educational text for high school students. It aims to teach them how to solve typical problems concerning divisibility found in mathematical correspondence seminars and mathematical olympiad. Basic notions from the theory of divisibility are recalled (e.g. prime numbers, divisors, multiples). Criteria of divisibility by 2 to 20 are introduced, as well as diophantine equations and practical applications of prime numbers in real life. One whole chapter is dedicated to problems and exercises. Powered by TCPDF (www.tcpdf.org)
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Divisibility in 6th and 7th grade - textbooks and knowledge of pupils
Mašatová, Zora ; Pilous, Derek (advisor) ; Vondrová, Naďa (referee)
My theses called Divisibility at second grade - textbooks and knowledge of the pupils is devoted to different aspects of schooling of this topic at elementary schools. This work is divided into three chapters. Whilst the first chapter is dedicated to the theory, the subject of two other chapters are two different researches conducted under the divisibility theme. Theoretical resources common to both parts of the research can be found in the first chapter. Among the topics mentioned in this chapter are for example the differences between formal and informal knowledge, constructivist and transmissive way of teaching or the process of solving word problems. The essence of my first research are the textbooks for elementary school concerned with the divisibility theme. Except the part devoted to a textbooks search (all the textbooks approved by the Ministry of Education, Youth and Sports which deal with divisibility), this chapter also contains the propaedeutics of divisibility and interviews with teachers, in which I have tried to cover the most important moments in the schooling of divisibility. Second part of my research is focused on checking of the pupils' knowledge of divisibility with a special emphasis on formal and informal knowledge. I have used the test to this purpose, which was...
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Combinatorial sequences and divisibility
Michalik, Jindřich ; Slavík, Antonín (advisor)
This work contains an overview of the results concerning number-theoretic pro- perties of some significant combinatorial sequences such as factorials, binomial coef- ficients, Fibonacci and Catalan numbers. These properties include parity, primality, prime power divisibility, coprimality etc. A substantial part of the text should be accessible to gifted high school students, the results are illustrated with examples. 1
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Divisibility in mathematics textbooks
Šmídová, Lucie ; Vondrová, Naďa (advisor) ; Pilous, Derek (referee)
The bachelor thesis is focused on the concepts of divisibility in Czech mathematics textbooks for lower secondary schools. Namely, it describes which divisibility rules they include, if pupils are led to participating on their derivation, how are the rules mathematically justified, which models are used in their explanation and if there are real word problems included in the textbook. The thesis is divided into two parts. The first part is theoretical and it introduces main concepts that are essential for the chosen topic. Its big part is dedicated to the divisibility, its characteristics and divisibility rules. The second part consists of the analysis of the selected textbooks focused on the divisibility rules. It was found that the selected textbooks differs not only in which rules they contain but also in the approach to studying the rules of divisibility. Diversity of approaches shows significantly in the number of models used to reasoning the divisibility rules. KEY WORDS Divisibility, divisibility rules, mathematics textbook, primary school
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Combinatorial sequences and divisibility
Michalik, Jindřich ; Slavík, Antonín (advisor)
This work contains an overview of the results concerning number-theoretic pro- perties of some significant combinatorial sequences such as factorials, binomial coef- ficients, Fibonacci and Catalan numbers. These properties include parity, primality, prime power divisibility, coprimality etc. A substantial part of the text should be accessible to gifted high school students, the results are illustrated with examples. 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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Combinatorial sequences and divisibility
Michalik, Jindřich ; Slavík, Antonín (advisor) ; Staněk, Jakub (referee)
This work contains an overview of the results concerning number-theoretic pro- perties of some significant combinatorial sequences such as factorials, binomial coef- ficients, Fibonacci and Catalan numbers. These properties include parity, primality, prime power divisibility, coprimality etc. A substantial part of the text should be accessible to gifted high school students, the results are illustrated with examples. 1
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Didactic approaches to the teaching of some mathematical topics at the primary school in teachers ́ diskurse
Vencovská, Jaroslava ; Vondrová, Naďa (advisor) ; Kvasz, Ladislav (referee)
The aim of the thesis was through a new analysis of interviews with teachers of mathematics, to describe didactic practices used by teachers while teaching selected topics (namely, proportions, linear equations, divisibility, percent, symmetry, Pythagorean theorem ) and compare them with the practices reported in textbooks and other literature. First, teaching methods, teaching forms and the mechanism of concept development by M. Hejný are given. Based on the analysis of more than thirty interview, it was found that teachers use the usual didactic practices but also create their own methods and procedures. These methods and techniques are provided for each critical issue separately in the fourth chapter of the thesis. Furthermore, the content analysis of selected textbooks is given for each topic. Identified practices of teachers which they use in their teaching practice, form the result of my work.
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