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Grade 7 and 8 Pupils' Problems with Negative Numbers
Bejčková, Lucie ; Vondrová, Naďa (advisor) ; Kvasz, Ladislav (referee)
This diploma thesis deals with the topic negative numbers, especially with strategies and difficulties of 7th and 8th grade primary school pupils when solving selected tasks with negative numbers. This thesis is divided into theoretical and experimental parts. The theoretical part deals with negative numbers, their development, didactic difficulty and work with them. The thesis deals with selected international comparative and foreign researches with the focus on negative numbers. The most extensive part of the thesis contains an analysis of mathematics textbooks used in schools in the Czech Republic with the focus on negative numbers. The experimental part, which aim is the identification of pupils' difficulties and the analysis of mistakes they make when working with negative numbers, is the key part of the thesis. 185 pupils of 7th and 8th grade from three different schools took part in the research. The methodology consisted of the preparation of a didactic test on negative numbers and assigning it to the pupils. After completing the test, selected pupils were asked to explain their written solutions. The didactic test was prepared on the basis of mentioned research results and the analysis of mathematics textbooks. The data were analysed in terms of pupils' strategies and mistakes. The thesis...
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Pupils' problems when solving problems requiring substitution
Schánělec, Jan ; Vondrová, Naďa (advisor) ; Novotná, Jarmila (referee)
Title: Pupils' problems when solving problems requiring substitution Abstract: The work focuses on 8th and 9th graders' difficulties and mistakes when solving problems using substitution. The theoretical part defines the used concepts and discusses selected results from international comparative studies and studies focusing on substitution. The main goal of the work is to identify pupils' difficulties and mistakes they make when solving problems using substitution and to discover their origin or cause. To achieve this goal the empirical part begins with an analysis of three sets of textbooks used by pupils involved in this research study. This is followed by a description of conducting and subsequent analysis of fifteen clinical interviews on problems with substitution with 14 to 15 year old pupils (9th graders from elementary schools and 3rd graders from lower secondary grammar schools). In the final part the most common mistakes are summarised and relations to their possible origin in the set of textbooks used looked for. The conclusion is that pupils do not have problems with substitution as such when substituting natural numbers into first power variables. However, this does not hold for substitution of variable in the second power. Pupils have problems when substituting for a variable with a negative...
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Pupils' Problems and Mistakes when Manipulating Algebraic Expressions
Bílek, Vladimír ; Vondrová, Naďa (advisor) ; Žalská, Jana (referee)
The thesis focuses on mistakes and problems in manipulations with the algebraic expressions occurring to pupils at the second level of Elementary school. The thesis is divided into a theoretical and experimental part. The theoretical part contains description of manipulations with algebraic expressions, selected results of international comparative surveys, and an analysis of related foreign research. Analysis of three series of textbooks, according to which pupils involved in the experimental project are taught, is essential for understanding of possible origins of their mistakes. The classification of mistakes in manipulations with algebraic expressions is included. At the core of the work is the experimental part aiming to identify problems and mistakes of pupils when manipulating and working with algebraic expressions. The participants of the research consisted of six third-grade pupils of an eight-year Grammar school (13-14 years old) and eight ninth-grade pupils of an Elementary school (14-15 years old). Test used for my experiment came from the GA ČR project Critical parts of mathematics in primary school. The investigation was carried out individually with each pupil by the method of monitoring clinical interviews over the solution of the test tasks. The obtained data was qualitatively...
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Transfer between verbal and algebraic descriptions. Pupils' strategies and problems
Novotná, Anežka ; Vondrová, Naďa (advisor) ; Roubíček, Filip (referee)
The aim of this thesis is to gain insight into the problems that pupils have when switching between verbal and algebraic expressions, through the analysis of their problem-solving processes. The work is divided into theoretical and experimental parts. The theoretical part of the paper contains three sections. The first describes the analysis of three selected Czech textbooks series for primary schools in terms of teaching the concept of variables and algebraic expressions. The next section deals with international comparative research TIMSS and the success of Czech pupils of year 8 in algebra. In the third section, results of international research concerning the issue of transition between verbal and algebraic expressions are described. The main part of the work is the experimental part, it aims to describe the difficulties encountered by pupils in algebra and to identify their likely sources. The basis for the own research was a set of 9 problems based on released TIMSS problems. The target group of pupils was year 9 of primary school, with whom the investigation was carried out via think-aloud interviews. First, a pilot study was conducted on a sample of 3 pupils, during which a set of test problems was checked. The main study involved 8 pupils. The think-aloud interviews were recorded and later...
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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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Hodnocení vzdělávacích systémů v EU prostřednictvím studií o mzdách a úrovni vzdělávání.
Kukačková, Kamila
This bachelor thesis deals with the quality of education and teachers salaries in countries of the European Union. The aim of the thesis is to identify the relationship between teachers salaries and level of education. The literature review summarizes the main finding of the international comparative studies of education, teachers salaries and selected economic factors affecting the quality of education. At the conclusion of this work are proposed recommendations for economy policy makers in the Czech Republic.
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Mathematics tasks in PISA and TIMSS tests.
MÍKOVÁ, Lucie
The aim of this bachelor thesis is to summarize the basic characteristic of the projects PISA and TIMSS, their history, realization, their purpose and results of Czech students in the mathematical field during the existence of these projects. The work describes both projects and then points out their differences. The practical part is formed by a collection of solved problems which is intended to be used as a teaching tool in the 4th and 8th grades of primary school. Some tasks are supplemented with visual illustration for better understanding.
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