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Individualization, differentiation, and personalization in mathematics in the Czech Republic through three different approaches: Scheme-oriented, Child-centred, and Undesignated
Brožová, Miroslava ; Coufalová, Jana (advisor) ; Vondrová, Naďa (referee) ; Rowland, Tim (referee)
The goal of the presented work was to determine whether and how individualization, differentiation, and personalization are utilized in the principles of the selected programs and in the teachers' beliefs and practices in the teaching of mathematics at elementary school. In order to collect data, six teachers in the Czech Republic were selected with three different approaches to teaching- Scheme oriented approach, child-centred educational approach, and an undesignated mainstream approach. The basic concepts and all three selected approaches to teaching were defined in the theoretical part of the work. In the experimental part, episodes from interviews about beliefs and practices identified in teaching were interpreted within the context of characteristics of individualization, differentiation, and personalization. Practices such as the use of textbooks and homework assignments were specifically described. The study shows that teachers of a scheme-oriented approach and a child-centred educational approach use elements of individualization, differentiation, and personalization in their practices. Individualization appears in the teaching of the undesignated mainstream approach, but this approach does not contain aspects of differentiation and personalization. The analysis in all monitored areas of...
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Personality-situational constellation of boredom
Boháčová, Aneta ; Pavelková, Isabella (advisor) ; Coufalová, Jana (referee) ; Chvál, Martin (referee)
The dissertation tries to capture the development of the concept of boredom from ancient times to the present. Historical concepts of boredom are grasped of the philosophical and literary concepts. We analyze modern scientific approaches to boredom, their definitions and understanding of the concept, differences between them and methods of measurement. The research is focused on the verification of psychometric properties of two foreign questionnaire sclales for measuring boredom and on the analysis of the concept of boredom in the Czech environment. The main goal of the research is to expose the levels of boredom in the Czech population of high school students, and to identify personality and situational factors affect their the concept and experience of boredom. The results of the research show the problem of using the Boredom Proneness Scale by Farmer & Sundberg (1986) for the Czech population. On the contrary, the outputs of confirmatory and exploratory factor analysis and comparative analysis confirm the suitability of using the Multidimensional State Boredom Scale by Fahlman et al. (2011) for the Czech population of high school students. The analysis of the concept of boredom points to some connections between its perception, its experience and personality characteristics of the individual...
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Expert Evidence
Coufalová, Jana ; Jelínek, Jiří (advisor) ; Vanduchová, Marie (referee)
The thesis called "Expert proofs" deals with one of the types of proper evidence which is applied in cases when an expert report is necessary to clarify facts important for criminal trial proceedings. Thesis is divided into 5 basic chapters. The first chapter is introductory and talks about some of the general problems of expert laws - evaluation of the current legal regulations of expert's function - expert law and expert ordinance, especially from the point of view of the changes that these legal regulations have undergone as well as the forthcoming changes in the form of updating of the current law and preparation of a brand new law. It also talks about definition of an expert, especially the difference between a witness and a consultant, then briefly about their rights and duties in the criminal trial proceedings in general. The second chapter deals with the presence of an expert explicitly in criminal trial proceedings and is divided into three parts. The first one provides basic information about admitting an expert and its form. The second one concerns the definition of an expert's assignment and the third one concerns preparation of an expert report, in which the expert familiarizes themselves with the criminal case. The third chapter deals with the actual output of an expert's investigation, its...
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Conceptions of area and volume of pupils at the elementary school
Tůmová, Veronika ; Vondrová, Naďa (advisor) ; Coufalová, Jana (referee) ; Kubáček, Zbyněk (referee)
Conceptions of area and volume of pupils at the elementary school Veronika Tůmová ABSTRACT: The aim of my thesis is to investigate how the conceptions of area and volume are built, what the major pitfalls and problems are, what skills and strategies are helpful for solving problems and what are the frequent unsuccessful strategies and pupils' misconceptions. I used the concept of the hypothetical learning trajectory as a tool to describe this process. Based on existing research review, I compiled two hypothetical learning trajectories - one for area and one for volume. The crucial building blocks that were identified based on these trajectories are: space abilities, structuration of space into arrays of units and multiplicative thinking. A test was designed to measure these factors and the correlation of these factors with success in volume and area problems ranged from week (multiplicative thinking) to very strong (spatial abilities). These findings confirm that these factors constitute an important part of the hypothetical learning trajectory for both concepts. Several structuration tasks were selected to investigate pupils' structuration skills and mistakes in more detail. Three main categories of problems were identified in the pupils' solutions: incorrect space structuration, disconnection between...
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Comparison of Pupils ́ Strategies of Solving Word Problems
Králová, Michaela ; Hejný, Milan (advisor) ; Coufalová, Jana (referee) ; Jirotková, Darina (referee)
Primary intention of this doctoral thesis is to examine the potential of mathematical word problems and comparison of various solving processes of mathematical word problems among pupils. The theoretical part of this thesis is based on definition of the term "problem" and shows how different basic psychological directions approach this concept. This is followed with narrower definition of mathematical problem with particular regards to solving process itself, its phases and factors affecting its success rate. Afterwards, the mathematical problem is put in concrete terms with mathematical word problem and its diagnostic and didactic potential is examined. Using real examples and modifications, this thesis shows concrete task situation and its practical use in teaching. The actual research processed data obtained as a result of active survey focused on analysis of solutions used by pupils, putting emphasis on occurrence and type of a mistake and the moment of its emergence. The target group was pupils of lower primary schools. This research showed significantly higher success rate of pupils lead by constructive approach. Also, it proved false certain beliefs held by some traditionalists especially about the importance of written mathematical word problems, usage of unknowns or using the routine...
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Construction of elementary pupils' geometric schemas via motivating learning environments
Kloboučková, Jaroslava ; Jirotková, Darina (advisor) ; Coufalová, Jana (referee) ; Novák, Bohumil (referee)
Title: Construction of elementary pupils' geometric schemas via motivating learning environments Author: Jaroslava Kloboučková Department: Department of mathematics and mathematics education Supervisor: doc. RNDr. Darina Jirotková, Ph.D. Abstract: The aim of the dissertation is to discuss teaching geometry as integral part of mathematics education at the primary school level. The thesis also documents a longitudinal teaching study which was initiated in 2010 and which gives us a base for discussion of some fundamental questions regarding the process of learning geometry for pupils in their early school years. The main objective here is to attempt to answer the following four didactic questions: In which way do pupils learn about geometrical objects? How do they share their geometrical knowledge, experience and discoveries with one another? How much (at what level) are they able to understand mathematical concepts that the official curricular documents (the Czech Framework for Education Program) place in later years of schooling? What phenomena are they able to grasp and describe using their mother tongue? The theoretical framework focuses on the learning process and the typology of mathematical problems in geometry. Four specific engaging environments (Cube Buildings, Origami, Wooden Sticks, and Tiles) and...
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Activities of a class when discovering mathematics (A study on the educational style of Scheme-oriented education)
Peclinovská, Sylva ; Hejný, Milan (advisor) ; Coufalová, Jana (referee) ; Jirotková, Darina (referee)
The dissertation describes qualitative research undertaken to study the discovery process in a class at the individual, group and whole class levels. This process is demonstrated on the case of discovering the parity of number zero (odd or even) in two class discussions. These discussions took place in a class of fourth year pupils at primary school, taught by the author in a constructivist way, within a one month period of each other. The research database contains also audio and video recordings, written work of the observed pupils, the author's teaching diary and it is analyzed and compared with literature. The methodology focuses on classifying the broad spectrum of pupils' responses and thinking processes not only in relation to the selected problem but also to related problems. Some of the described events are commented on with recommendations how to handle the didactic situations that occurred or compared with hypothetical situations typical for transmissive teaching. The main results of this work fall in the cognitive, metacognitive and social area are summarized into seventeen points that highlight the importance of discussion for the complexity of pupils' knowledge, for the enriching and refining their ideas, increasing their autonomy and ability to cooperate.
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A priori analysis as a part of teacher's lesson planning
Nováková, Hana ; Novotná, Jarmila (advisor) ; Vondrová, Naďa (referee) ; Coufalová, Jana (referee)
5 TITLE: A priori analysis as a part of teacher's lesson planning AUTHOR: Mgr. Hana Nováková DEPARTMENT: Department of Mathematics and Mathematical Education SUPERVISOR: Prof. RNDr. Jarmila Novotná, CSc. This thesis focuses on a priori analysis as a part of teacher's lesson planning. The theoretical background consists of the Theory of didactical situations in Mathematics (TDSM). In TDSM, the a priori analysis is seen as one of the teacher's tools that he/she has when planning a lesson. The goal of the thesis is to analyse differences between a priori analysis as described in TDSM and the reality in teacher's practice, to compare lesson plans of experienced teachers with those of students and demonstrate the significance and application of a priori analysis in teacher's and researcher's practice. The thesis consists of three parts, theoretical, experimental and applicational. In the theoretical part, the main concepts of TDSM linked with a priori analysis are explained and the issue of teacher's lesson planning is presented. The experimental part starts with a pre-experiment. Its results contributed to precise the structure of a priori analysis for further use. During the main experiment, the lesson plans of experienced teachers were compared with those of pre-service teachers. The differences and the...
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Expert Evidence
Coufalová, Jana ; Jelínek, Jiří (advisor) ; Vanduchová, Marie (referee)
The thesis called "Expert proofs" deals with one of the types of proper evidence which is applied in cases when an expert report is necessary to clarify facts important for criminal trial proceedings. Thesis is divided into 5 basic chapters. The first chapter is introductory and talks about some of the general problems of expert laws - evaluation of the current legal regulations of expert's function - expert law and expert ordinance, especially from the point of view of the changes that these legal regulations have undergone as well as the forthcoming changes in the form of updating of the current law and preparation of a brand new law. It also talks about definition of an expert, especially the difference between a witness and a consultant, then briefly about their rights and duties in the criminal trial proceedings in general. The second chapter deals with the presence of an expert explicitly in criminal trial proceedings and is divided into three parts. The first one provides basic information about admitting an expert and its form. The second one concerns the definition of an expert's assignment and the third one concerns preparation of an expert report, in which the expert familiarizes themselves with the criminal case. The third chapter deals with the actual output of an expert's investigation, its...
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Pupils' Construction of Knowledge in Mathematics (the Example of Pythagoras' Theorem)
Ulrychová, Michaela ; Vondrová, Naďa (advisor) ; Coufalová, Jana (referee) ; Hejný, Milan (referee)
The thesis deals with the process of construction of mathematical knowledge of an individual and a group of pupils. At the outset, some concepts are discussed which belong to the theoretical background of our research (knowledge construction process and its mechanism, typology of mathematical knowledge, character of a mathematical structure, constructivist approaches to the teaching of mathematics, creative teaching, action research). Some results of selected local and foreign research focusing on constructivist approaches and action research in mathematics education are given. The methodology mainly consists of teaching experiments which can, to a certain extent, be seen as cycles of cooperative action research. The target group consists of pupils of lower secondary grammar school. The data gathered through traditional methods of qualitative research (participation observation, audio and videorecordings, pupils' artefacts, notes of an external observer, etc.) were analysed using the techniques of grounded theory. The research has generated results of three types: (1) The categories of individual and group constructions in mathematics have been described in depth including their dimensions (the measures of the teacher's influence on the construction, of the pupils' cooperation, of pupils' formal acceptance...
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