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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)
The bachelor thesis is centred on an educational area algorithm development and programming at basic schools. The main aim is an overview and a description of teaching methods and programmes which promote the development of student's computional thinking. The thesis contains an analysis of researches which describes the situation of teaching algorithm development and programming at basic schools in 2006-2007 and in 2013. The analysis was realized by Department of Information Technology and Education at Faculty of Education at Charles University. Next part is a definition of basic concepts relating to this topic and at the end there are two examples of worksheets prepared for concrete methods.
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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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Attitudes towards teaching mathematics focusing on fractions
Moulisová, Martina ; Jirotková, Darina (advisor) ; Slezáková, Jana (referee)
This diploma thesis is concerned with the attitude towards teaching mathematics focusing on teaching fractions. The first part pays attention to the attitudes towrsd teaching and specifies two different styles, classical and constructivism. In case of constructivism, I also pay attention to the term genetic constructivism in connection to Hejný's methodology. After that I present teaching methodology and roles of teacher. The other part of this piece of work engages in fractions especially in children pre- concepts and developing activities which lead to understanding fractions. This piece of work answers the question on how to cope with pre-concept knowledge and in which way it should be developed. I present different kinds of models of fractions and how to work with them in practical part of this thesis. The aim of the practical part is to map the attitudes towards teaching fractions and work with pre-concepts of beginning teachers which is made by interviewing 4 teachers and observing their lessons. Those interviews are analyzed in practical part and the answers of respondents are compared to each other as well as to my expected answers. The reflection of observing the lesson is full of activities which may lead to understanding fractions. At the end I summarize the results of the analysis of...
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Division with remainders as a diagnostic tool for studying cognitive skills of Czech pupils
Kotrbatá, Jana ; Kloboučková, Jaroslava (advisor) ; Kaslová, Michaela (referee)
This thesis deals with the algorithm of division with a remainder in connection with the development of cognitive abilities of Czech pupils. Due to the usual inclusion of this thematic unit (division with a remainder) in the third year of primary school, theoretically focused chapters dedicated to human ontogenesis, with regard to the child's cognitive development and educational system in the Czech Republic, are incorporated. From the thematic perspective, the work analyzes selected comprehensive series of textbooks for first grade of primary school, differentiating the exercises from propaedeutic through an introduction and application to non-standard tasks. Thesis examines the commonalities and differences in the concept of the analyzed textbooks by various authors. One of the criteria is the evaluation of approach to teaching based on identifying elements of constructivism or transmission. Another objective of the work is a research of selected problem-solving strategies of students dealing with tasks comprising division with a remainder. Solution methods were obtained by assigning of diagnostic test to pupils of a first grade of primary school. KEYWORDS division with a remainder, a primary school aged child, cognitive development of a child, teaching styles - transmission, constructivism,...
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Creating images of fraction at the elementary school
Siblíková, Marta ; Tichá, Marie (advisor) ; Macháčková, Jana (referee)
This thesis "Creating images of fraction at the elementary school" is divided into theoretical and practical part. The theoretical part defines the subject matter of fractions in curriculum, deals with a mathematical literacy concept and introduces basic conceptions related to fractions and propaedeutic of fractions at the Primary School. The practical part consists of a preparatory research and a consequential research. The goal of the preparatory research is fractions knowledge mapping on Primary School pupils comparing to an expert knowledge acquired in the theoretical part. The consequential research focuses on confirming results of the preparatory research, respectively preferring the circle model off other models. It also checks if pupils get acquainted with other models (line segment, rectangle, and set of discrete objects). Key words Fraction, propaedeutic, models, representation, primary education, curricula.
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