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Algebraisation in problems with a geometric context - pupils' difficulties and mistakes
Benešová, Štěpánka ; Vondrová, Naďa (advisor) ; Jančařík, Antonín (referee)
The aim of this thesis are problems in which pupils demonstrate the ability to switch between geometric and algebraic representation. The task of the thesis is to correctly identify the difficulties and mistakes of pupils in the algebraisation of problems with geometric context before the teaching of algebra and after the teaching of algebra. The thesis consists of theoretical and experimental parts. The theoretical part defines the necessary concepts, summarizes selected results of research and studies related to the algebraisation of problems with geometric context and contains an analysis of five selected textbooks for the eighth year of elementary school, which are used by pupils participating in the research. The analysis of textbooks is focused on chapters dealing with the topics of Algebraic expressions with variables and Powers. The experimental part focuses on research identifying difficulties and mistakes of pupils in solving problems in which pupils try to algebraically model geometric relations. The basis of the research was two sets of test problems followed by an individual conversation with the pupils. The first set of problems was made for sixth-graders, seventh-graders and eight- graders. The second set of problems was made for ninth-graders. The tests were used in two primary...
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Solving of problems dealing with volume and surface in the three-dimensional space by 15-16-year old pupils (9th grade)
Dlouhá, Michaela ; Novotná, Jarmila (advisor) ; Vondrová, Naďa (referee)
The topic of my diploma thesis is the solution to exercises of volume and surface of 3D solids. The aim of the thesis is to make own didactic test and to analyse the methods of solution to math exercises in the 9th grade students of ZŠ Amálská. Also to compare the results of the tests in math and science orientated class to "normal1 " class and to find out the success rate of solutions in both classes. I focused only on pyramid and cone, because they are part of curriculum in 9th grade of basic schools after students are admitted to high schools, and after examination of educational programme of chosen school I realised that both classes had the same outputs of given schoolwork. I divided my thesis into two parts - theoretical and practical part. Theoretical part contains five chapters. In the first chapter I focus on didactic tests and their making. In the next chapter I deal with evaluation in general and school evaluation. In the third part there is the term of word exercise defined. In the fourth chapter there are solutions to the word exercises. And in the last chapter I define the term geometrical solid. In the practical part there are the aims and methods of survey, characteristic of research sample, making of didactic test, content of didactic test and analysis of students' solutions...
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Financial literacy in mathematics
Lundáková, Naďa ; Novotná, Jarmila (advisor) ; Tůmová, Veronika (referee)
Title: Financial Literacy in Mathematics Abstract Bachelor thesis Financial Literacy in Mathematics deals with the computational aspects of the financial literacy of grammar school pupils. The first part focuses on the general concepts of financial literacy and financial mathematics and their mutual relationship. The second part is devoted to compiling the examples and exercises that can be used to enhance the level of financial literacy of junior secondary school pupils. Examples and exercises listed here respect the current mathematical knowledge of students of the elementary grades. Most of them are devoted to work with the money. Key words Financial Literacy, Financial Math, Examples, Exercises, Grammar School, Money.
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Problem posing for limits of functions
Prskavcová, Pavla ; Pilous, Derek (advisor) ; Kvasz, Ladislav (referee)
Title: Problem posing for limits of functions Author: Pavla Prskavcová Department: Department of Mathematics and Mathematical Education Supervisor: Mgr. Derek Pilous, Ph.D. The aim of the thesis is to describe methods of limit problems solving and of posing new problems that are solvable by those methods. The first part of the thesis contains the necessary theory (definitions and theorems). In the second part of the thesis there are described the standard methods used for evaluating containing limits. The third part suggest ways of posing problems solvable by using elementary methods, based on the analysis of methods describes in the se- cond part of the thesis (without usage of the differential calculus). Keywords: limit, problem solving, problem posing, elementary function.
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Interpretation of physics graphs by experts and novices followed by the eye-tracker
Vondráčková, Terézia ; Kekule, Martina (advisor) ; Mandíková, Dana (referee)
This thesis is focused on identifying key aspects of mechanics graphs regarded by students and experts. It also contains observations of student's attention focused on each graph. This data was collected using eye tracking camera. 23 high school students and 14 experts participated in this research. Our group of experts contained graduate and post-graduate students as well as researchers from faculty of Mathematics and Physics at Charles University. Our results suggest that experts were able to memorize more information from each graph than high school students. Difference in focus on relevant parts of graphs was obvious from analyzing correct and incorrect answers of high school students and they consider axes and their labeling as the key parts of graphs in contrast to the students. Incorrectly answering students were more focused on parts with no relevance to the task in question. On the contrary, students with correct answers spent less time looking on non-relevant parts of graphs. Ideas of incorrectly answering students were mostly focused on wrong idea about graph as a sketch of real situation, or picture resembling physical situation.
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Nonverbal physical problems
BAČÁKOVÁ, Martina
This diploma thesis explains nonverbal physical tasks in the teaching of physics. The first chapter focuses on the teaching of physics at primary school, marginally educational programs, teaching methods and physical tasks. One chapter also explains creativity and its use in teaching the subject. This thesis includes a set of processed nonverbal physical tasks together with their didactic analysis and solution of some exercised. Some of the mentioned tasks were processed into worksheets, verified by practice and evaluated. The results of verified nonverbal physical tasks are also attached in the diploma thesis.
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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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High school students' interpretation of a graph from mechanics observed by the eye-tracking method
Vondráčková, Terézia ; Kekule, Martina (advisor) ; Snětinová, Marie (referee)
This bachelor thesis deals with the solution of tasks monitored by the eye-tracker. We were examining high school students who solved 6 tasks focused on the interpretation of a graph in mechanics. They were monitored by the eye-tracker during their solving of the tasks. Based on their recorder eyes' position we can figure out their strategies of solution. We identified several typical misconceptions when working with graphs and typical students' approaches to the graph interpretation. Information about this topic can be useful, for example, to teachers for their future teaching.
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