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Students' problem posing as an indicator of mathematical culture of lower secondary students
Bureš, Jiří
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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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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Word problems about money in the 2nd year of primary school
Vodrážková, Lucie ; Slezáková, Jana (advisor) ; Kaslová, Michaela (referee)
The principal objective of this thesis is the comprehension of students' mental processes while solving verbal math problems about money. There searchis focused on pupils in the first stage of primary school and in particular verbal math problems, in which nominal value of coins, quantity of coins and their total particular verbal math problems, in which nominal value of coins, quantity of coins and their total sum play a key role. There fore, the objective of this diploma thesis is to lay out classify mony-related exprecises in thee currently used lies of elementary school mathematics text books for grade. The theoretical part consist of demarcation of early school age, a certain number of fanticipate dacts by RVP ZV for the first and second educational period, numeracy, literacy, verbal math problems, various strategies on how to solve such problems, basic is sues pipils encounter whilw solving those problems, coments on the topic of verbal math problems which appear in theree volume soft text books in tended for primary schools (Prodos, Taktic, H-mat). Their division into three types (a total sum of coins, nominal value of coins and number of coins) and their mutual comparision. The goal of the practial part is to analyse thought processes of and grade pupils when solving word problems about...
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Influence of cultural contexts on word problems solutions
Spurová, Markéta ; Kaslová, Michaela (advisor) ; Kvasz, Ladislav (referee)
The aim of this work is to determine the extent to which the cultural context of a word problem influences its solution by pupils of the 9th grade of secondary schools. Two research questions were set. The first: Will the different cultural context affect the solution of the word problem? How? The second: What do pupils think about word problems with different cultural contexts? The thesis consists of two parts: the theoretical and the practical. In the theoretical part, the general concepts such as culture and the word problem are addressed, followed by a discussion of the cultural context of word problems and their analysis in chosen textbooks. Furthermore, a significant part is devoted to ethnomathematics and multiculturalism in Czech schools. Finally, the difference between the word problem with a typical Czech context and the word problem with a different cultural context is established based on the results of textbooks analysis and the pre-research. The research, which is described in the practical part was conducted qualitatively, and the data were obtained from written tests and semi-structured interviews. The results have shown that the different cultural context of a word problem affects the time needed to solve the problem. In addition, the choice of the type of solution and the type of...
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Word problems about money in the 2nd year of primary school
Vodrážková, Lucie ; Slezáková, Jana (advisor) ; Kaslová, Michaela (referee)
The principal objective of this thesis is the comprehension of students' mental processes while solving verbal math problems about money. The research is focused on pupils in the first stage of primary school and in particular verbal math problems, in which nominal value of coins, quantity of coins and their total sum play a key role. The theoretical part consists of demarcation of early school age, a certain number of anticipated acts by RVP ZV for the first and second educational period, numeracy, literacy, verbal math problems, various strategies on how to solve such problems, basic issues pupils encounter while solving those problems, teaching aids used in dealing with verbal math problems about money, comments on the topic of verbal math problems which appear in three volumes of textbooks intended for primary schools (Prodos, Tak-tic, H-mat), and their mutual comparison. The practical part is launched by methodology of a quantitative research (in the form of three experiments). The first pre-experiment is carried out by seven pupils, the first and second by ten pupils. This part thoroughly describes the preparation of each experiment, along with their subsequent realisation, as well as analysed verbal math problems for individual experiments, expectations, example of one of the interview...
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Pupils' problem solving strategies at lower and upper secondary level
Hoffmann, Jan ; Novotná, Jarmila (advisor) ; Mošna, František (referee)
This thesis Pupils' problem solving strategies at lower and upper secondary level brings a focus on the issue outlined by the name. At the same time, it focuses on pupils' strategies to solve problems that are closely related to information literacy. At first I define basic terms for the area of word problems. Consecutively I focus on the theoretical knowledge from the area of problem solving strategies themselves. The content of the experimental part of the thesis is the survey of pupils' solutions of eight selected tasks, by which I was looking for an answer of the three basic questions of this thesis. My experiment is divided into two branches. The first branch of the experiment took place at the lower level of the multi-year grammar schools. The second branch of the experiment took place at the higher grade of the multi-year grammar schools and, to a small extent, at the secondary school. The theoretical part contains views of various authors on issue of problems and word problems. I present and compare these individual approaches. The result is the demarcation of the terms needed for the experimental part of the work. The main aim of the experimental part of the thesis is to find the answers of three basic questions of this thesis, where I was using data from lower and higher grades of...
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Collection of word problems for lower secondary school
GUBÁNI, Barbora
In my thesis deals with the solution of word problems in secondary schools. The goal of my work is to describe various ways of solving word problems. I dividend my work into two parts. The first part deals with the theory and explain what they are word problems, how to count and what we types of word problems. The second part is practical where I show how jobs are counted and the appropriate way to compare what the solution is for the type of job easier.
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Symmetric and asymmetric context of word problems and its influence on the success of pupils' and on the types of their mistakes
Matějková, Klára ; Vondrová, Naďa (advisor) ; Novotná, Jarmila (referee)
The thesis deals with the connection between the way the mathematical word problems are formulated and their being understood correctly by the pupils. The main focus is on the semantic cues present in the assignment of the word problem. The thesis can be divided into two parts. The first part, which provides the theoretical framework for the whole thesis, contains the definition of a word problem. The phases of word problems solving and the possible classification of word problems are mentioned. More attention is paid to the problems with translation cues; new concepts of asymmetric context and symmetric context, called semantic cues, are introduced. An overview of several related research studies from abroad follows. The core of the thesis lies in its second part, containing a study that examines whether the pupils would be more successful in solving problems with asymmetric contexts than in solving problems with symmetric contexts. The influence had been examined on two types of problems and four age categories of pupils and students. The research was carried out through the short tests and it was attended by the total of 503 pupils of selected elementary schools and grammar schools in Prague and students of the Faculty of Education of Charles University. A higher success rate for the asymmetric...
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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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