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Students' problem posing as an indicator of mathematical culture of lower secondary students
Bureš, Jiří ; Novotná, Jarmila (advisor) ; Hošpesová, Alena (referee) ; Zhouf, Jaroslav (referee)
TITLE: Studentsʼ problem posing as an indicator of mathematical culture of lower secondary students AUTHOR: Mgr. Jiří Bureš DEPARTMENT: Department of Mathematics and Mathematical Education SUPERVISOR: Prof. RNDr. Jarmila Novotná, CSc. ABSTRACT: This thesis is focused on studentsʼ problem posing as an indicator of mathematical culture of lower secondary students. The theoretical background consists of research on problem posing, word problems in mathematics, mathematical culture and the Theory of didactical situations in mathematics. The goal of the thesis is to analyse links between problem posing and studentsʼ mathematical culture through the analysis and description of the posed problems. The thesis consists of two parts, theoretical and research part. In the theoretical part, there are the main findings about studentsʼ problem posing and some approaches to the concepts of word problems and mathematical culture, and the main concepts of the Theory of didactical situations used in the thesis. The research part starts with the analysis of the pre-experiment, which constitutes the basis for creation and characteristics of the conception of mathematical culture of problem posing. These parts are followed by the analysis of the main experiment, which provides the complete description of the posed problems...
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The Influence of the Attractiveness of Context of a Mathematical Word Problem on Performance and Solving Processes
Havlíčková, Radka ; Jirotková, Darina (advisor) ; Novotná, Jarmila (referee) ; Hošpesová, Alena (referee)
This thesis focuses on to word problems and elementary school pupils. Research on mathematical word problems suggests that differences in success are not only due to different levels of pupils' cognitive abilities but that their motivation plays a role, too. Therefore, in this study, I focused on the context of word problem as a potential source of situational interest, which may affect the quality of pupils' cognitive function in the short term or permanently. I used my participation in a broader quantitatively oriented research on variables influencing the difficulty of word problems and using its methodology, I investigated the influence of different types of contexts on pupils' success in solving the problems. The examined aspect of context was attractiveness - the question was whether pupils would be more successful in solving word problems with elements of fairy tale, science fiction or humour than in similar problems with the same structure but with a neutral context. Pupils of the 3rd to 6th grades of primary school (n = 2 092) were divided into two groups of a comparable ability and each was presented with one of the variants - attractive or neutral. To evaluate the results quantitatively, the Item Response Theory was used allowed us to determine the difficulty of the problem depending on...
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Non-mathematical world of mathematics textbook for 6th grade of lower secondary schools and in the area of financial literacy
Moraová, Hana ; Bendl, Stanislav (advisor) ; Hošpesová, Alena (referee) ; Voňková, Hana (referee)
The aim of the dissertation thesis is to study the non-mathematical content of textbooks of mathematics. Textbooks of mathematics are not only a pedagogical document but also a cultural artefact that is produces in a particular society with its own cultural norms. While working with a textbook of mathematics, pupils come across many images of everyday life. Yet, since the main goal of a mathematics textbook is to help pupils gain knowledge and skills in mathematics, not much attention is paid to textual (non-mathematical, cultural) content. This means that pupils almost on everyday basis visit a world that tries to awaken the illusion of being "real", of being model of reality but in fact is a model for what is perceived as normal. The question asked in the presented research is what images of everyday life pupils come across while working with Czech textbooks of mathematics and whether there are differences among textbooks by different authors in this respect. Within the frame of this research, five sets of textbooks for 6th grade of lower secondary schools and four textbooks for 9th grade (only the chapter on financial mathematics, an area closely connected to everyday life) were analysed with respect to their non-mathematical, cultural content. The method used in the research comes out of the...
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Students' problem posing as an indicator of mathematical culture of lower secondary students
Bureš, Jiří ; Novotná, Jarmila (advisor) ; Hošpesová, Alena (referee) ; Zhouf, Jaroslav (referee)
TITLE: Studentsʼ problem posing as an indicator of mathematical culture of lower secondary students AUTHOR: Mgr. Jiří Bureš DEPARTMENT: Department of Mathematics and Mathematical Education SUPERVISOR: Prof. RNDr. Jarmila Novotná, CSc. ABSTRACT: This thesis is focused on studentsʼ problem posing as an indicator of mathematical culture of lower secondary students. The theoretical background consists of research on problem posing, word problems in mathematics, mathematical culture and the Theory of didactical situations in mathematics. The goal of the thesis is to analyse links between problem posing and studentsʼ mathematical culture through the analysis and description of the posed problems. The thesis consists of two parts, theoretical and research part. In the theoretical part, there are the main findings about studentsʼ problem posing and some approaches to the concepts of word problems and mathematical culture, and the main concepts of the Theory of didactical situations used in the thesis. The research part starts with the analysis of the pre-experiment, which constitutes the basis for creation and characteristics of the conception of mathematical culture of problem posing. These parts are followed by the analysis of the main experiment, which provides the complete description of the posed problems...
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Joint reflection in pre-servise primary school mathematics teacher training
Macháčková, Jana ; Tichá, Marie (advisor) ; Vondrová, Naďa (referee) ; Hošpesová, Alena (referee)
TITLE: Joint reflection in pre-servise primary school mathematics teacher training AUTHOR: Jana Macháčková DEPARTMENT: Department of mathematics and didactics of mathematics SUPERVISOR: Mgr. Marie Tichá, CSc. Abstract: The thesis focuses on the potential of development of pre-service and in- service teachers' self-reflection as one of the ways leading to development of pedagogical content knowledge. The thesis starts with definitions of the background concepts (teacher competences, pedagogical content knowledge, reflection, self- reflection, joint reflection). Also, as the experiments were carried out in the environment of fraction, the introductory part discusses issues related to interpretation and representation of fractions and sources of problems with fractions, their interpretation and representation. The first aim of the research was to monitor the quality of teachers' reflections. The subsequent goal was, on the basis of findings of this monitoring, to look for ways leading to refinement of this reflection. When monitoring and developing reflections, the main method used was the method of joint reflection of a video recording of a lesson. However, other methods were employed simultaneously (observation, group interview). Materials collected in the experiments (students' production, students'...
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Operator thinking
Ruppeldtová, Janka ; Hejný, Milan (advisor) ; Hošpesová, Alena (referee) ; Harminc, Matúš (referee)
Resumé The initial goal of the thesis was to nd out the ability of pupils to understand the text of additive word problems, grasp their objects and relations, distinguish numerical data in the function of states and operators, solve such word problems, correctly interpret acquired results, but also to detect possible obstacles to solving or reasons for a pupil's failure in order to draw methods how to eliminate them. After realizing some pre-experiments the goal was shifted to a qualitatively higher level { to investigate the level of an individual's operator thinking via specic word problems, additive word problems with operators, and to design possible ways how to develop a scheme of an individual's operator thinking. For illustrating our research tool we present an example of word problems of a conceptual character and a situation of a procedural character both containing only operators. Bob is 13cm taller than Adam. Chris is 4cm shorter than Bob. Compare the height of Chris and Adam and say how many cm Chris is taller or shorter than Adam. In January the price of a coat was reduced by 500 Sk. Then in February the price rose by 800 Sk, but in March it went down again by 600 Sk. For our purpose we used the assigned word problem for pupils in dierent research methods, such as interview, tests, transfer...
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Inductive reasoning of 10-12 year old children in mathematical environment
Herman, Jan ; Novotná, Jarmila (advisor) ; Hošpesová, Alena (referee) ; Rendl, Miroslav (referee)
Inductive reasoning of 10-12 year old children in mathematical environment Formation of inductive inference is a complex process influenced by a number of diverse phenomena, whose study is at present moving to the spotlight of the community of psychologists. So far, conclusions of researches in this domain have been used in mathematical environment only very rarely, this despite the fact that inductive reasoning is crucial in many operations which are perceived as essential in development of mathematical reasoning. In my thesis I summarized conclusions of the relevant research, mostly in the domain of psychology, and put them in context of other research in this field. I dissected phenomena described by other authors, then applied their consequences in mathematical environment and finally designed and carried out two experiments. The aim of the first was to explore the genesis of inductive inference in natural environment, with the focus on the conditions of its genesis. The aim of the other experiment was exploration of genesis of inductive inference in a stimulating environment, with the focus on the quantity of experience prerequisite for formation of inductive inference and on the relation between the quantity of the experience and confidence in the consequent inference. The conclusions of the...
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Perception of Computer Mediated Representations of Space
Dvořák, Petr ; Koman, Milan (advisor) ; Hošpesová, Alena (referee) ; Titzl, Boris (referee)
There was and is written a big amount of literatuře with the topič of three-dimensional imagery, this literatuře afflicts almost all areas connected with this problematic. But just a few places are given to the possibility ofusing information technology for development of three-dimensional imagery. Simultaneously the children grow into the world of computers and we can not neglect this fact. Children approach to computers with a quite commonplace and without fear (in contrast to adults). They are moving in virtual environments, which simulate a real world more and more punctually and also with its physical rules. Every of these experiences can influence their three-dimensional imagery. Also the ability of transformation of the surrounding three-dimensional world into the picture-two- dimensional form (and of course contrariwise) - it closely bears on the three-dimensional imagination. Mainly the ability to read the planar pictures and to use the gained information in the creation of three- dimensional conceptions. This ability is at school knowingly evolved, for example through channelling the body in free parallel projection. Emphasis insists on the work with real models and their pictures. In my work I try to refer to the advantages and crags of using computer programmes, which simulate to us real models...
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