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Surface problem-solving strategies of primary school students in solving word problems and activities leading to their overcoming
Brejchová, Eva ; Havlíčková, Radka (advisor) ; Kvaszová, Milena (referee)
The thesis focuses on the process of solving word problems. The theoretical part defines the typology of word problems, the phases of solving a word problem, and the description of surface solving strategies. The practical part sets goals: 1. to map the difficulties students face when solving word problems and 2. to design, implement, and evaluate activities that could help students reduce these difficulties. The core of the work is action research conducted by a classroom teacher with third-grade students. The research is divided into two phases. The first phase includes tasks: 1. to identify the types of problems that cause difficulties for students, i.e., problems with a low overall success rate of solution, 2. to determine representatives of students with characteristic areas of difficulty. The selected types of problems will be assigned to students in various forms in the second phase of the research with the goal of implementing and subsequently evaluating the interventions mentioned below. The selection of student representatives on whom I focused the intervention activities in the second phase was carried out based on observations of all students solving word problems, analysis of their written solutions, reflections, and short semi-structured interviews. The interventions are designed to...
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Development of understanding of numebr positional notation in primary school pupils
Suchá, Anna ; Jirotková, Darina (advisor) ; Havlíčková, Radka (referee)
The notation of a number in the position system, especially in the decimal system, is the most widely used representation of a number by humans. There are various ways of developing pupils' understanding of this notation in the classroom. According to the literature, the key elements for developing understanding of number notation in the positional system are, in particular, problem solving tasks and their discussion. In Czech schools, a method persists which, according to the literature and the possible interpretation of qualitative research, does not seem to be effective. The observed level of pupils' understanding of the place value varies and does not seem to increase with the grade level. Pupils' demonstrated misunderstandings take different forms and are described in detail. KEYWORDS number notation, place value, type of assignment, didactic test, analysis of pupils' solutions
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Back and forth between science and reality: Mathematical modelling in tasks with a science context (didactic experiment)
Šmíd Ridzoňová, Ráchel ; Havlíčková, Radka (advisor) ; Vondrová, Naďa (referee)
Mathematical modelling is part of the focus of the educational area "Mathematics and its applications" in the Czech national curriculum and is also a widely studied topic abroad. However, it does not receive much attention in Czech research. This thesis aims to introduce the concept to Czech readers and test the connection of mathematical modelling with science topics and the implementation of modelling tasks in the 5th grade of primary school. The thesis presents mathematical modelling as solving process of a complex problem with a real context in steps (0) undertanding the problem, (1) creating the real model, (2) mathematization, (3) mathematical operations, (4) interpretation of the result and (5) validation of the solution. Modelling competence, the modelling probem, and the relationship to word problems are also described. The chosen qualitative research method of didactic experiments explores the application of a holistic and analytical approach to teaching, identifies the difficult steps of modelling for 5th- grade students, and provides insights into cross-curricular relationships and organizational forms in the teaching of modelling. The research findings positively demonstrate that incorporating modelling tasks into regular lessons and linking them to science topics is possible but...
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Number as a length in the environment Trains in 1st and 2nd grade of primary school
Nachtmannová, Iveta ; Slezáková, Jana (advisor) ; Havlíčková, Radka (referee)
This thesis focuses on the tasks from the environment Vláčky, as one of the isolated environments in the first grade mathematics of primary schools taught according to the elaborated methodology of prof. RNDr. Milan Hejný, CSc.. The theoretical part of the thesis explains the principles and concepts of Milan's methodology, the importance of isolated environments in the process of building the ideas of natural number in children in the 1st and 2nd year of primary school, highlights the environment Vláčky as a propaedeutic environment essential for further education according to this method and introduces the manipulative aid necessary for this environment, the Cuisenaire prisms. The theoretical part explains which tasks are used to introduce the environment into the classroom, explains the important concepts of this environment, describes the different types of tasks and their gradations, the relation of this environment to the 3rd to 5th year of primary school, and last but not least, similar tasks from different workbooks that do not deal with the above methodology are collected here. The goal of the practical part was to check the clarity of the formulations in the assignment, to investigate the students' solving strategies and the difficulties that may occur when solving the problems. The...
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Preparing for school mathematics via a serie of activities inspired by creations of artist Zdeněk Sýkora
Tydlitátová, Lucie ; Kaslová, Michaela (advisor) ; Havlíčková, Radka (referee)
The Bachelor's thesis deals with the connection between pre-math literacy and art education in kindergarten. The paper refers to similar activities suitable for primary school, but the scenarios and their implementation in practice fully respect the specifics of preschool age. Both the methods and the material are adapted to this, as is the language. Activities linking pre-math literacy and visual arts are embedded in a specific didactic structure. The thesis has three main parts. The theoretical part deals with the areas on which the practical part is based: motor and cognitive development of the preschool child, a brief biography of the artist Zdeněk Sýkora, and pre-math literacy. The methodology part defines the aims, tasks and methods of the Bachelor's thesis, and is based on action research with elements of qualitative research. The practical part includes scenarios and description of their implementation, records of the observed phenomena and their analysis based on direct observation, video recording and reflection with post-reflection. Children aged 5 years and 7 months to 6 years and 7 months were observed in a kindergarten setting. On the basis of the partial conclusions, minor modifications in the scenario are proposed, which are complemented by didactic recommendations for the possible...
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Mathematics for the first grade through the touch, hearing, smell, taste and sight
Michková, Žaneta ; Havlíčková, Radka (advisor) ; Kvaszová, Milena (referee)
This master's thesis deals with the usage of senses - sight, smell, taste, hearing and touch in mathematics lessons. The aim of the thesis is to offer teachers a collection of non-traditional activities whose objective is to not only strengthen and practise, but also to comprehend the mathematics curriculum in the 1st grade of primary school with overlaps into the subjects of basic science, physical education, music education, Czech language - writing, reading. The theoretical part describes the mental development of younger school age pupils focusing on individual senses and their usage in mathematics lessons. The activities correspond with the valid education legislation of the Czech Republic and its documents. The conclusion of the theoretical part is devoted to one of the ways of learning - game and its meaning. The practical part includes the collection of activities in math lessons, which is focused primarily on the usage of one of the senses - touch, hearing, smell, taste and sight. The activities comprise: their descriptions, preparations, helping materials, processes, assessments and modifications, some activities also include a worksheet. The collection is in accordance with the outputs and objectives of the FEP and the set of key competencies.
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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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