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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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Educational environment additive polygons and polyhedrons
Sukniak, Anna ; Jirotková, Darina (advisor) ; Vondrová, Naďa (referee)
Title: Educational environment additive polygons and polyhedrons Summary: The main intention of the work is to introduce a new mathematical educational environment that would be especially attractive for pupils in the grades 6. -9., but also in the secondary schools, universities or primary schools The work consists of six parts. In the introduction are mentioned the reasons that led me to choose this topic. The second chapter describes the theoretical basis of the work. The third section describes in detail the environment of additive polygons, both its aspects - mathematical and educational one. Analogously, as it is in the third chapter, is processed the fourth chapter that is dedicated to the environment of additive polyhedrons. The fifth chapter is devoted to the linking of the environment of additive polygons and polyhedrons into the linear algebra. In conclusion are provided further opportunities of work with this environment.
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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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