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Mapping of the trial and error method in solving problems in structural environments Spider web and Exhibition grounds
Kučerová, Lucie ; Havlíčková, Radka (advisor) ; Jirotková, Darina (referee)
The aim of this diploma thesis is to observe and describe the use of the trial-and-error strategy in two didactic environments from the Hejné method among pupils in the second and third year of primary school, who are educated using the usual method of teaching mathematics. The theoretical part deals with the definition of heuristic strategies, their classification and a closer description of some selected heuristic strategies. The key chapter is devoted to the description of the trial-and-error strategy and its inclusion among the solving strategies. It also deals with the problematic attitude of teachers and the wider public towards this strategy. At the end of the chapter, the advantages of its use in solving mathematical problems are included. The next chapters deal with work with mistakes, the child's experiment not only in teaching, and thus follow on from chapter 1.3. Chapter 1.7 describes Hejné's method of teaching mathematics and the didactic environments with which this method works and which are important for the practical part. At the end of the theoretical part, I define the distribution of the curriculum in the second and third years, which influence the students' approaches to solving. In the practical part, the research methods of unstructured observation and the method of verbal...
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Teacher's approach to language and situational context of mathematical word problem
Viktorová, Martina ; Havlíčková, Radka (advisor) ; Macháčková, Jana (referee)
The focus of this thesis is to investigate how the elementary school teachers work with mathematical word problem from the perspective of language and situational-contextual level of word problem. Furthermore it is focused on the teachers' work approach to the word problem and identification of phenomena oriented to one of cognitive modes - paradigmatic and narrative described by J. S. Bruner (1986) and O. Chapman (2006). The main research method of this thesis is based on observing how the teachers work with the word problem in class and interviewing them as well as pupils. In the theoretical part of the thesis the mathematical word problem is determined, and it is focused on the word problem on the level of language and context. The cognitive functioning of pupil is described as well as the two problem solving approaches - narrative and paradigmatic by J. S. Bruner, and their application during solving the word problem according to O. Chapman's elaboration. Furthermore the definition of word problem and specification of non-standard word problem in curriculum document FEP BE is described. The practical part is based on qualitative research. The research is designed to provide objective information about the teachers' approach to the word problem and teachers' way of working with language and...
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Analysis of critical situations at solving verbal tasks for pupils in first grade of elementary school
Chudík, Jan ; Havlíčková, Radka (advisor) ; Kloboučková, Jaroslava (referee)
The aim of this document is to familiarize first grade elementary school readers with the critical points in solving word problems in mathematics and to analyze various problem- solving strategies in concrete tasks. Primarily, the document is focused on determining pupils' difficulties and acquiring information about the problem-solving process through a written record of the solution and subsequent in-depth interviews. The theoretical part is divided into six sections dealing with terminology (e.g. word problem) and the areas influencing success in the solution of word problems and partial processes. The practical part contains an analysis of each pupil's solutions and a description of phenomena found in them, together with the grading teacher's help. KEYWORDS Word problem, pupil's solutions, analysis of interviews, questions, solution process
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Methods for overcoming differences in pace of students in mathematics lessons
Plívová, Anežka ; Havlíčková, Radka (advisor) ; Macháčková, Jana (referee)
- 4 - ABSTRACT This diploma thesis is focused on teacher's strategies in mathematics lessons with different work paces of pupils, specifically pupils with above-average pace. The theoretical part of the thesis summarizes and explains the basic concepts related to the identification of smart and gifted pupils. The next part is focused on models of talent, teaching pupils with above- average pace, as well as a transmissive and a constructivist approach to teaching. The used research method was observation and discussion in focus groups. The basis of the practical part of the diploma thesis is a set of collected information and its arrangement into the so- called typology of teacher strategies when working with a pupil who works at an above- average pace in mathematics lessons with the described advantages or risks of individual strategies. The main goal of this diploma thesis was to collect ways in which the teacher copes with the different paces of students in mathematics lessons, mainly focusing on pupils with above-average work rates. Thesis describes benefits as well as risks that could arise in the application of strategies for the described individual methods. KEYWORDS above-average pace, mathematics teaching, gifted pupil, bright pupil, teacher's strategy
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Logical problems zebra with pupils in primary school
Laštovková, Tereza ; Slezáková, Jana (advisor) ; Havlíčková, Radka (referee)
This diploma thesis is focusing on analysis of logical zebra problems and finding strategies of pupils solutions and development of these strategies in primary school. For this diploma thesis was created two gradation of those logical problems for pupils from the 1st - 5th class in primary school. Theoretical part is focused on characteristics of logical problems zebra, its definition, history of logical problems zebra and its todays use. In more detail it is based on examples and ways of strategies, how to solve these problems, like with tablets or full charts and so on. It's also focused on parameters of gradation, which serve the possibilities of making gradation for pupils in primary school in the next part, the research part. Research part is based on description and comments of pupils strategies in solving logical problems zebra in two gradation, wich contains ten tasks.. Research part shows how pupils can develop their solving strategies based on their experience with solving logical problems zebra, with described phenomena for pupils solution and for tasks. KEY WORDS graded parameters of problems, context of problems, logic, negation, problems with conditions, relations, solving strategy of pupils in primary school, table as tool for problem solving
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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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Use of music education in mathematics lessons at the 1st stage of elementary school or Let's sing, Mr. teacheronnection between mathematics and music in primary school
Jánošková, Zuzana ; Jirotková, Darina (advisor) ; Havlíčková, Radka (referee)
The work deals with the possibility of interconnecting the teaching of mathematics with music. The theoretical part focuses on the relationship between mathematics and music, student motivation, the theory of multiple intelligence and also on whether music can contribute to the development of mathematical thinking. The practical part delivers five lesson preparations, where the main topic is music education and several other ways to use music education in another mathematical topic. KEYWORDS Music in mathematics, rhythm in mathematics, musical instruments in mathematics, motivation, word problems, equations, intersubject relations, Gardner's theory of multiple intelligence.
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Word problems with different results at primary school
Švihnosová, Kristýna ; Havlíčková, Radka (advisor) ; Kvaszová, Milena (referee)
The diploma thesis is focused on the issue of word problems with different results, to which is not given systematic attention in the specialized literature. The focus of the work is to observe how pupils and teachers of elementary school work with a word problem with different results. The theoretical part focuses on the typology of word problems, the phases of their solution and solving strategies. Furthermore, the classification of word problems according to the number of results and the typology of word problems with different results is proposed. A significant part consists of the goals with which this type of task can be assigned in the teaching of mathematics and which change depending on the teacher and his approach to teaching. The work also deals with the basic characteristics of teaching styles. The selected qualitative research using the method of observation and questionnaire allows to describe the work of teachers with a word problem with different results and to identify elements of teaching styles, namely transmissive and constructivist approaches, which are reflected in the actions of teachers. An additional method is the analysis of selected textbooks in terms of the presence of word problems with different results, which reveals whether such tasks occur in textbooks and what...
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