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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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Mathematical environment Bus in primary school
Pártl, David ; Slezáková, Jana (advisor) ; Jirotková, Darina (referee)
The diploma thesis deals with the topic of the mathematical environment Bus realized through mathematical tasks in textbooks Hejný et al. The issue is aimed at pupils of the fourth grade of primary school. The main point of the theoretical part is study of gradual gradation of tasks in environment Bus from 1st to 5th grade of primary school. It was found that the frequency of the tasks in the textbook for the fourth grade is impaired and on the basis has been prepared experiment that complement the tasks so that the frequency has been unimpaired. The practical part includes the preparation of an experiment in which custom- designed tasks were formulated. They were linked with fourth-year primary school curriculum. By performing two experiments was obtained 262 pupil's solutions of tasks, in which were recorded and analyzed pupil's mistakes. This enabled to formulate phenomenons that could be caused by impaired frequency of tasks in environment Bus in textbooks Hejný et al. KEYWORDS graduaded problems, experiment, Hejný's teaching method, mathematical environment Bus, word problems, work with table
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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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Ways and strategies of 10-12 years old pupils when solving selected type of word problems
Strnádková, Ivana ; Jirotková, Darina (advisor) ; Hejný, Milan (referee)
Title: Ways and strategies of 10-12 years old pupils when solving selected type of word problems Abstract This Diploma thesis is focused on word problems that, to some extent, make pupils troubles with their solution. In the first theoretical part there are word problems that the work deals with. These are word problems with ant signal, dynamic, complementary, graphic and their characteristics. The next section is about the strategy of solving word problems and work with mistakes. The second part is focused on experiment of all types of word problems that are described in the theoretical part. This experiment is analysed according to strategies of pupils' and teachers' solutions. Those strategies are later described and commented in detail. Key words word problem, solving strategy, mistake, source of mistake, grasping of word problem
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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 in the First and Scond Year of Primary School
Weinzettel, Pavla ; Kaslová, Michaela (advisor) ; Bureš, Jiří (referee)
TITLE: Word Problems in the First and Second Year of Primary School AUTHOR: Pavla Weinzettel DEPARTMENT: Departmement of Mathematics and Mathematical Education SUPERVISOR: PhDr. Michaela Kaslová ABSTRACT: This thesis focuses on word problems in maths books for Year One and Two of primary schools, published by Alter and Prodos. The objective is to analyse the word problems set out in these maths books and to classify them according to the following criteria: context, methods of solution, time management, and non- standard types of maths problems. A partial aim of the thesis is a comparison of the textbook word problem analysis and the analysis of those word problems which the students can create themselves. The conclusions of the work point out the importance of the teacher's role in maths teaching and learning. Teachers should use their judgement when using the published maths books and endeavour to expand on them, taking into consideration the above mentioned criteria in order to increase the students' eagerness to not only to solve the maths problems but also to understand as to why they solved them the way they did. The thesis recommends practical tools for teaching material evaluation and for assessing to what extent the students understand what the purpose of word problems is. KEYWORDS: word problem,...
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Pupils' difficulties in solving selected word problems from TIMSS research
Matěka, Petr ; Vondrová, Naďa (advisor) ; Novotná, Jarmila (referee)
Pupils' difficulties in solving selected word problems from TIMSS research. (Diploma Thesis.) Abstract The theoretical part of the diploma thesis describes international comparative surveys, namely PISA and TIMSS, and analyses results of Czech pupils. Some areas are distinguished in which our pupils were unsuccessful and from them, the area of word problems and their mathematisation was selected for further work. Next, a solving strategy is characterised and some relevant research from this area is given. The core of the work lies in the experimental part whose goal was to find out what strategies pupils use when solving selected problems from TIMSS research and why they fail in them, via the analysis of pupils' written solutions complemented by interviews with them. Causes of failure of our pupils in these problems in TIMSS 2007 are looked for in mistakes pupils make, while it is also followed in what phase of the solving process they appear. The participants of research were pupils of Grade 9 of a primary school who solved three selected word problems from TIMSS research. Their written solutions were complemented by interviews with the experimenter focused on their mistakes and lack of clarity of the solutions. Four pupils participated in a pilot study. The atomic analysis of their solutions confirmed...
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Text properties as a factor in solving word problems with the use of Venn diagrams
Návarová, Daniela ; Novotná, Jarmila (advisor) ; Vondrová, Naďa (referee)
Title: Text properties as a factor in solving word problems with the use of Venn diagrams Author: Bc. Daniela Návarová Department: Department of Mathematics and Mathematical Education Supervisor: doc. RNDr. Jarmila Novotná, CSc. Supervisor's e-mail address: Jarmila.Novotna@pedf.cuni.cz This diploma thesis deals with the word problems where Venn diagrams can be used. The word problems are studied as texts and their specific text properties are scrutinised in the first, theoretical, part of the thesis. The second part describes an experiment that focuses on the importance of text properties of word problems for the problem solvers. The main aims of this diploma thesis are to show the possibility of textual examination of the chosen texts and to unfold some connections between the mathematical and linguistic views on the area of word problems. Keywords: text, word problem, Venn diagram
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Solving strategies for word problems that can be solved with equations
Chromá, Stanislava ; Novotná, Jarmila (advisor) ; Pilous, Derek (referee)
The aim of this work is to get acquainted with the issue of solving word problems by means of equations, to state and to analyse various ways of solving them. The thesis also includes the comparison of strategies for solving word problems that are selected by students who have been already taught the given type of the equation, and students who have not yet mastered these procedures. The introductory part of the work deals with word problems in general. There the terms such as the word problems, procedures, methods and strategies used for solving word problems are specified. In the next part of the text, the basic types of equations are characterized. For each type of the equation, one typical word problem was selected and it was experimentally found out which solving strategies were used by students most often. Keywords: word problem, algebraic equation, non-algebraic equation, system of equations
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Word problems on basic arithmetics
ŠIMÁNKOVÁ, Zuzana
This bachelor work deals with curriculum of students in the 3rd and 4th year in the elementary school and it´s topic is Word problems on basic arithmetics. This work concentrate on werbal tasks, it´s correct formulation and monitoring of effects of small ganges in instructions of tasks on course of it´s solution. This work is devided into individual thematic units in which exaples are put according to it´s difficulty. It is designed to be teaching aid. The work is enriched with pictures and illustrations to be attractive and understandable.
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