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Students' procedures for mathematical word problems solvable by systems of equations during the school leaving examination
Doubrava, Jiří ; Chvál, Martin (advisor) ; Vondrová, Naďa (referee)
This diploma thesis investigates different approaches to solving word problems with systems of equations. The thesis aims to discover which strategies are used by senior students when solving these word problems and documents the processes involved. The research presented in the thesis is based on an in-depth analysis of the database of student cut-outs from five word problems of the common part of the Maturita exam, specifically from the spring terms between the years 2016 and 2020. The theoretical part involves an analysis of three textbooks for high school students in the Czech Republic which incorporate the named phenomena. Furthermore, this part includes a list of student strategies for solving word problems, moreover, the reader is provided with a description of the state Maturita exam in Mathematics. The empirical part contains an overview of several possible procedures prepared during an a priori analysis. It also presents psychometric features of the chosen word problems by incorporating statistical outcomes. In addition, cut-outs of students' answers are divided into various groups based on the chosen solving strategies, thus demonstrating the possible techniques used by the students when solving this type of tasks. The principal conclusions demonstrate immense omissions, supporting the...
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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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The influence of a used unit on the difficulty of a word problem
Blatská, Dagmar ; Vondrová, Naďa (advisor) ; Kvasz, Ladislav (referee)
The difficulty of word problems in mathematics is influenced by a number of parameters, both mathematical and non-mathematical. The influence of the esed unit, as one of the linguistic charakteristice, has already been partially tested within the framework of research GAČR 16-6134S. The subject of this testing were pairs of word problems with the same assigment, wich differed only in the unit esed. In one task, there was a commonly used currency unit, the koruna, in the other task, a fictious currency unit, zed. The conclusion of this research were ambiguous. While some tasks showed statistically significant differences in succes, other did not. The aim of this work was to find out what effect the used unit has on the succes of the solution and on the perception of the difficulty of word problems. The subject of testing was a trio of tasks with the same structure, but with different contexts. These tasks varied in the unit used. In one task there is a common currency unit, the koruna, in the second there are unusual units of currency and volume, the US dollar and barrel, in the third task are unusual units of currency unit, zed. The target group was pupils of the 6th and 8th grade of elementary school. The assumption was that the task with a common unit would be more succesful for the solver and that it...
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Individualization, differentiation, and personalization in mathematics in the Czech Republic through three different approaches: Scheme-oriented, Child-centred, and Undesignated
Brožová, Miroslava ; Coufalová, Jana (advisor) ; Vondrová, Naďa (referee) ; Rowland, Tim (referee)
The goal of the presented work was to determine whether and how individualization, differentiation, and personalization are utilized in the principles of the selected programs and in the teachers' beliefs and practices in the teaching of mathematics at elementary school. In order to collect data, six teachers in the Czech Republic were selected with three different approaches to teaching- Scheme oriented approach, child-centred educational approach, and an undesignated mainstream approach. The basic concepts and all three selected approaches to teaching were defined in the theoretical part of the work. In the experimental part, episodes from interviews about beliefs and practices identified in teaching were interpreted within the context of characteristics of individualization, differentiation, and personalization. Practices such as the use of textbooks and homework assignments were specifically described. The study shows that teachers of a scheme-oriented approach and a child-centred educational approach use elements of individualization, differentiation, and personalization in their practices. Individualization appears in the teaching of the undesignated mainstream approach, but this approach does not contain aspects of differentiation and personalization. The analysis in all monitored areas of...
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Teaching word problems using teaching materials "Comparison"
Hrúzová, Eva ; Vondrová, Naďa (advisor) ; Novotná, Jarmila (referee)
This paper focuses on the implementation of methodological materials based on concept cartoons for teaching word problems at the lower level of secondary school. The theoretical part of the work deals with the description of word problems and their teaching in schools, including the role of the teacher and the constructivist approach. It also addresses the concept of concept cartoons, which is used as the basis for implementing methodological materials. In the practical part, these materials are implemented over five teaching hours in the seventh and eight grades. The results indicate that the implementation of methodological materials using concept cartoons in teaching word problems at the lower secondary school level was succesful, and students evaluated this new teaching approach positively. One of the main benefits of using concept cartoons, based on the experience from teaching experiment, is that they createa non-threatening learning environment where students do not experience the fear of failureThis is because mistakes and difficulties in solving problems are attributed to fictional cartoon character. Additionally, the use of concept cartoons encourages discussion and interaction among students, as there is often more than one correct solution to a given problem. This approach helps to...
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Selected parameters influencing the difficulty of word problems
Vokounová, Lenka ; Novotná, Jarmila (advisor) ; Vondrová, Naďa (referee)
This thesis deals with selected parameters influencing the difficulty of word problems and also the student's ability to solve them. The aim of the thesis is to theoretically look into it and practically test some of these parameters from the project of the Grant Agency of the Czech Republic number 16-06134S - Word Problems as a Key to Application and Understanding of Mathematical Concepts and point out the difficulties that mathematics teachers may not perceive at first sight and consider as a problem. The first part of the thesis is devoted to word problems in general. It deals with the importance of word problems in mathematics lessons, classification of word problems. Finally, it deals with the solution of word problems. In the second part there are some parameters influencing the difficulty of word problems. These parameters are selected mainly on the basis of the project of the Grant Agency of the Czech Republic number 16-06134S - Word Problems as a Key to Application and Understanding of Mathematical Concepts and based on own experience in teaching. Some of these parameters I analyzed in mini case studies and my own teaching experience. In the last part of the thesis is my own recommendation for working with word problems. KEYWORDS word problems, parameters influencing the solution of word...
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Teaching mathematics online at the first year of grammar school
Flejberková, Dorota ; Kaslová, Michaela (advisor) ; Vondrová, Naďa (referee)
The diploma thesis deals with equations introducing at 8-year gymnasium in the framework of teaching online. This thesis is focused on an action survey in a context of teaching online in prima of 8-year gymnasium. This is a series of lessons focused on equations which were taught at Gymnázium OPEN GATE. The aim of the thesis is to follow the shift in a didactic area in a non-standard form of teaching. The diploma thesis is based on the theoretical background, the practical part is focused on a teaching experiment. For reaching the aim, the following tasks were established: -To discuss possible forms of teaching online. -To summarise the theory of linear equations. -To analyse textbooks for both primary school and lower-secondary school first from the viewpoint of a preparatory stage of equations and then the propaedeutics of equations in the framework of lower-secondary school. - To record the surveyed events connected by reflection. The thesis is divided into two main parts, theoretical and practical. The theoretical part is divided into four chapters. The practical part follows the theoretical one; it is based on analyses a priori of continued reflection. The description of scripts implementation is accompanied by a continued reflection and a posterior reflection. The conclusion provides the key...
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Introducing the volume of solids using Cavalieri's principle
Fialová, Eliška ; Vondrová, Naďa (advisor) ; Janda, David (referee)
The aim of the thesis is to use a series of pedagogical experiments to introduce the volume of a pyramid, a cone and a sphere using Cavalieri's principle for pupils of the ninth year of primary school. First, the thesis characterizes the theories and approaches on the basis of which the experiment was built, such as the generic model theory and constructivism. The next part deals with the analysis of schoolbooks for the upper primary school and gymnasium, which are devoted to the introduction of the volumes of solids of pyramids, cones and spheres, and especially those schoolbooks which introduce the given volumes using the Cavalieri principle. The pedagogical experiment was preceded by a series of lessons focused on familiarizing pupils with given geometric solids and deriving calculations of their surfaces. This was followed by the introduction of the Cavalieri principle in the plane and also in space. In the practical part of the thesis, the tasks that were used in the pedagogical experiment are presented. The description of the course of the pedagogical experiment is supplemented by copies of the pupils' solutions. The conclusions are illustrated by the pupils' observations and summaries, which they arrived at in the form of a discussion on the tasks. At the end of the thesis, an evaluation of...
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Development of understanding the area of rectangle and triangle
Hájková, Adéla ; Vondrová, Naďa (advisor) ; Zamboj, Michal (referee)
This thesis focuses on developing an understanding of the concept of the area of a rectangle and a triangle in the form of a pedagogical experiment for sixth-grade primary school pupils. Before the experiment, a diagnostic test was conducted to reveal the mechanical knowledge of the students. The tasks in the test were based on the same typology of exercises that can be found in regular student's books and exercise books used for Mathematics teaching and one of the exercises worked with the notion of a square grid. The exercises used within the actual teaching were transformed in order to match the current situation in the classroom. The experiment was subdivided into two parts that followed each other - understanding the notion of a rectangle and understanding the notion of a triangle. The pedagogical experiment was conceived according to the conceptual process of measure in geometry and a hypothetical learning trajectory. The experiment aimed to reeducate the pupils' possible mechanical knowledge, to lead the pupils to a conceptual understanding of the area of rectangles and triangles. At the end of the experiment, a test was again administered to check whether understanding had occurred and whether mechanical knowledge had been removed. The final test shared the same typology of exercises as the...
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