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Propedeutics of differential and integral calculi
Malachov, Martin ; Halas, Zdeněk (advisor) ; Slavík, Antonín (referee)
Propaedeutics of Differential and Integral Calculi Author: Ing. Martin Malachov Department: Department of Mathematics Education Supervisor: Zdeněk Halas, DiS., Ph.D. Department of Mathematics Education Keywords: propaedeutics, derivative, Riemann integral, applications Differential and integral calculi both are interesting and beautiful branches of mathematics with many interdisciplinary overlaps and significant and practi- cal applications. Learning as well as teaching of these topics is very difficult and demanding. In this thesis we show that the derivatives and integrals have much to offer in the high school education while the schooling can be eased and made attractive with intentional propaedeutics and knowledge of rich background of applications. First part of the thesis presents short contem- plation on the current state of teaching and literature, we focus on the urge for the propaedeutics of the differential and integral calculi revealed by us. We identify key terms that can be used to build useful preconcepts during the whole high school education, even in the elementary education. In the latter part of the thesis we offer teacher innovative texts and a rich set of origi- nal exercises that can be used for motivation, application and propaedeutics of the differential and integral calculi. We also present...
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Introduction to variables in the teaching of teachers using the method of building schemes in mathematics
Smutná, Anežka ; Vondrová, Naďa (advisor) ; Kvasz, Ladislav (referee)
This thesis deals with an introduction to variables. The aim of the thesis was to compare different approaches to teaching the introduction to variables in teachers who teach a method based on building schemes (known as Hejny method). The theoretical part of the thesis is a search of literature on the topic of introduction to variables and the theoretical background of teaching methods based on building schemes. Further, the thesis analyses textbooks designed for this method with a focus on tasks important for the propaedeutics of the variables. The research itself consisted of interviews with four teachers and observations of the lessons they taught in the 7th and 8th grades of secondary school, the topic of which was an introduction to the "language of letters". In total, there were fifteen lessons taught by these teachers in six classes (2-3 lessons in each class). Data were analyzed by qualitative methods. Although the observed teachers taught using the same method, I identified differences in the approach to the introduction of the variables and in the style of their teaching. There were differences in the organization of the lesson, in the selection of tasks and their style of assignments to pupils, teaching methods and ways in which teachers communicate with pupils. At the moment of entering the...
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Programming tools for development of algorithms and programs at elementary school
Dümont, Jan ; Novák, Jaroslav (advisor) ; Vaňková, Petra (referee)
This thesis monitors the past and current status of the educational area of algorithms and computer programming in elementary school, on the basis of research carried out at the Department of Information Technology and Technical Education of the Pedagogical Faculty of Charles University in Prague. It provides an overview of the different teaching methods and programs that contribute to the development of the skills of pupils, due to their age and skills achieved in this area. In the theoretical part of the thesis are explained the basic concepts of the topic of algorithms and programming, which follows the practical part with the use of these procedures in the ICT lessons and in other school subjects.
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