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Creation of worksheets for teaching financial mathematics at lower and upper secondary levels
Dolák, Tomáš ; Novotná, Jarmila (advisor) ; Janda, David (referee)
In this thesis, I focus on the creation and application of worksheets for teaching financial mathematics in primary and secondary schools. Not only do these worksheets enhance students' knowledge of financial mathematics, but they also bolster their financial literacy. Furthermore, these tools can be employed to practice a range of skills such as programming, algorithm design, information retrieval, group discussions, and independent problem-solving. A key feature of these worksheets is their structure, which follows the Cornell Notes system. This system emphasizes formulating questions, taking notes, and creating indi- vidual summaries. Additionally, I have incorporated a student-centered self-assessment system into the worksheets, enabling students to track their achievement of the goals set by the worksheets. The main objective of this work is to create worksheets for teaching, and then test these worksheets in the classroom. Another aim is to analyze the students' solutions and propose potential approaches to individual tasks that teachers can implement in their lessons. After the students completed the worksheets, I analyzed their solutions and sub- sequently conducted a questionnaire survey among the pupils to gather further infor- mation. This survey either supported or contradicted my...
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The use of 3D printers in mathematics education
Rohelová, Jitka ; Jančařík, Antonín (advisor) ; Janda, David (referee)
The aim of this thesis is to design, implement, and evaluate an educational model that integrates 3D printing into the teaching process, linking computer science and mathematics education with the goal of increasing student engagement and understanding. Furthermore, it explores the challenges associated with the use of 3D printing and 3D printers in mathematics teaching and subsequently proposes recommendations and creates materials that would allow the effective use of this technology in mathematics education. The collected data was analyzed using both quantitative and qualitative methods. The educational model was designed around the topic of stereometry and was implemented through an educational experiment involving 5 classes of a vocational high school. The conclusions drawn from the data analysis are consistent with theoretical assumptions about increased motivation and success of students when using 3D printers in education. A meeting was organized for teachers to share best practices on the topic of using 3D printing and 3D printers in mathematics teaching. Following group discussions with teachers, challenges faced by teachers (or schools) when integrating 3D printing into their curriculum were identified and described in two separate chapters. Additionally, a set of 3D models of...
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Hejný's method in comparison with the Realistic mathematics education of Hans Freudenthal
Jandová, Sára ; Kvasz, Ladislav (advisor) ; Janda, David (referee)
The aim of the content of the thesis is mainly to find and compare the common principles of Hejny's method of teaching mathematics with Realistic mathematics education, the foundations of which were discussed by Hans Freudenthal in his work. Both approaches to teaching are always briefly described theoretically and then presented by examples from exercisebook, from manuals and from practice. Theese are supplemented by a didactic commentary. In order to write the thesis, materials summarizing individual methods were first studied, and then appropriate teaching topics and links were searched for, on which a mutual comparison was made, and which represent different components of mathematics education (arithmetic, geometry and algebra). In the section of examples, the work is oriented to links derived from the 2nd grade of elementary school. For each teaching topic, the specifics that attribute it to the given teaching styles, their similarities and differences are summarized. The basic similarities and differences regarding the organization of teaching and the textbooks used are summarized. At the end of the thesis, the results and evaluation are briefly mentioned. KEYWORDS Mathematics teaching, Realistic mathematics education, Freudenthal, Hejny's method, Hejny
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Critical parts in solving constructive tasks by pupils-refugees from Ukraine
Kukhtenko, Anna ; Zamboj, Michal (advisor) ; Janda, David (referee)
Title: Critical parts in solving constructive tasks by pupils-refugees from Ukraine Author: Bc. Anna Kukhtenko Supervisor: Mgr. Michal Zamboj, Ph.D. Abstract: Construction problems are considered to be one of the most difficult problems in mathematics education, as they are the connection of the space of geometric objects and relations (theoretical) with the space of pro-spatial graphical entities (representational). For pupil refugees from Ukraine, who have gone through the traumatic experience of emigration and adjusting to a new environment, these tasks may present additional specific challenges. The thesis analyses Czech and Ukrainian textbooks, examines differences in procedures and solution methods, individual experience and readiness of pupil-applicants going to Czech schools. The methodology is based on qualitative research, which includes working with a group of pupils from Ukraine with a worksheet and interviews with the pupils themselves to better evaluate the results. Based on these findings, appropriate pedagogical strategies and approaches can be further designed and refined to better support the success and adaptation of these pupils in the school environment. Keywords: Construction tasks, pupils-refugees, pupils with different mother language, critical places in mathematics.
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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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Changes in pupils' understanding of models of fractions
Hillebrandová, Eliška ; Janda, David (advisor) ; Kvasz, Ladislav (referee)
Fractions are a dreaded topic not only for students but also for teachers. The reason is that it is a breakthrough subject in primary schools, without which one cannot successfully continue in further studies. Therefore, in the first chapter of this thesis we will focus on understanding fractions through visual models (discrete and continuous - chocolate, circle, line segment, rectangle) that can be commonly found in textbooks aimed at teaching fractions. In the second chapter, using action research tools, we investigated how students' understanding changed over time following the interventions. The research consisted of two pilot tests and three iterations of the test over a two-month period in three seventh grade classes in a Prague elementary school. Specifically, the test focused on part-from- whole and whole-from-part search for the following three models: the discrete ordered model, the fraction-as-part-of-an-area model in a lattice network, and the number axis model. All results were graphically processed using tables, boxplots and we relied on statistical tests. In the third chapter, we summarized these results in detail and also pointed out the shortcomings of the research and how they can be addressed. It showed that there was a positive change in students' understanding of fraction...
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How secondary school pupils solve metric problems in 3D geometry
Jankovcová, Anna ; Vondrová, Naďa (advisor) ; Janda, David (referee)
The aim of this thesis is to gain a deeper understanding of how high school students solve tasks in three-dimensional metric space. All of the selected tasks are solvable using similarity. Since this is not the only way to solve these problems, I also observe the procedures and strategies that students employ whilst solving them. The thesis is divided into a theoretical and a practical part. In the theoretical part I define the basic terms and deal with difficulties which might occur while solving the selected problems. I also describe the expected outcomes of stereometry teaching in curricular documents. In the practical part, I firstly analyse the way certain metric problems are solved in high school textbooks. Then I describe how I did my research, in which 12 students participated. As my method for conducting the research I chose to interview the students about their solutions to the selected tasks in order to obtain enough information about the challenges that the students have in solving these problems and to observe the strategies they use. In the closing section of this thesis, I summarize the procedures which high school students use to solve metric problems, as well as the difficulties that some students had. My research has shown that students use various techniques to solve metric...
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Functions in examples and counterexamples
Janda, David ; Pilous, Derek (advisor) ; Zhouf, Jaroslav (referee)
The aim of my Bachelors thesis is to explicate students coming to the uni- versity the key problems in fundamentals of mathematical analysis. I focus on the most notable terms of continuity and limit, which these secondary students were acquainted with. However, majority of them just intuitively and informaly. I am trying to point out the fact, that the knowledge of many students is distortid and uncomplete. As a result it is necessary to practise and clarify this knowledge so that the intuitive imagination of these terms corresponds to the formal definition. I am trying to get this point by brea- king of intuitive imaginations of students by counterexamples. Important is a chapter named The Construction of Functions, which contains instructi- ons leading to the finding functions with specific features. Not only these features, described in this thesis, but also more complex such as derivation, primitive function or uniform convergence. It is a consequence of the fact, that the principle of examples to practise these terms is in many sights similar and repetitious. In chapters named Continuity and Limit, I am interpreting these terms using the special examples, which are in my opinion optimal for rehearsing. My intention is to help illustrate selected problematical sections of mathematical analysis.
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Understanding of the notion of a coordinate system by secondary school students
Klápa, Petr ; Janda, David (advisor) ; Zamboj, Michal (referee)
The aim of a thesis High school students' understanding of the coordinate system concept is to research the level of student's understanding of the topic by using analysis and a description of student's problems with given topic. A written non-standard test with exercises from non- Cartesian coordinate system is used as a tool to analyse the level of students' understanding. The first part of the thesis describes the historical development of the topic with emphasize on the renaissance era, in which were the basics of the modern concept of coordinate system set. The first part also includes the description of educational requirements from course books, curricular documents and the theory of concept image and concept definition, which focuses on understanding of mathematical terms. Second part of the study concentrates on the experiment with a non-standard test given to students at mathematical lessons at high school. The results are presented and analysed by previously specified phenomena and interpreted in the concept image and concept definition theory. Results of the practical part show a great variety of students' level of understanding the examined concept in theoretical and also in practical level. Results of students with good theoretical knowledge but low success in practical part are...
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Simple categorization of mathematical objects: Examining students' decisions
Janda, David ; Vondrová, Naďa (advisor) ; Simpson, Adrian (referee) ; Klusák, Miroslav (referee)
The aim of the thesis is to describe the decision making process of students in the so-called simple categorization, i.e., decision whether a particular object is or is not an element of a category. This process is examined in the context of categories of mathematical objects. The theoretical part of the thesis presents arguments why the study of simple categorization of mathematical objects is important for mathematics education. These arguments are not only based on the available literature in mathematics education, but also partly draw on historical, mathematical and psychological literature. The practical chapters of the thesis describe the design and piloting of a research tool suitable for this research. The dominant elements of this tool are the measurement of the binary answers (yes / no) of the respondent and of his/her reaction time. This tool is then used in the Main study based on mixed, qualitative-quantitative methodology. It was found that with the help of the proposed tool, while adhering to appropriate methodological rules, it is possible to distinguish different approaches of respondents to categorization. In addition, the basic patterns in the decision-making process of the respondents were described. These are, for instance, differences in the categorization of examples and non-...
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