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Flatland and student's perception of the fourth dimension
Bouchalová, Kateřina ; Zamboj, Michal (advisor) ; Kvasz, Ladislav (referee)
This diploma thesis deals with the connection between mathematics and literature, two disciplines that may seem distant from each other. The aim of this work is to analyze whether selected students are able to improve their perception of the fourth dimension with the help of the analogy introduced in an excerpt from Edwin Abbott Abbott's book called Flatland. This thesis begins by introducing firstly, the history of the fourth dimension and the way it is conceptualized, and secondly, the author and the book Flatland. The theoretical part continues by providing a description of the occurrence of analogy, literature, and the fourth dimension in the Framework Education Programme for Secondary General Education as well as other sources focused on teaching mathematics. Next, the theory of the general models introduced by Hejný is summarized, followed by the van Hiele model of geometric thinking. The theoretical part of the thesis ends with a description of our limitations regarding the representations of the fourth dimension. This first part of the work stands as the basis for the practical part of the thesis that introduces a quantitative case study which was realized in the following way. Two tests were given a week apart to the fifth-year students of a sixth-year grammar school. The aim was to...
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Relations and their applications
Čulíková, Markéta ; Novotná, Jarmila (advisor) ; Zamboj, Michal (referee)
The thesis deals with relations and their applications. The first chapter summarizes the introductory theoretical knowledge that is necessary for understanding the topic relations: an element, set, ordered pairs, Cartesian Product. The important definitions are introduced for all of these concepts and the related information is summarized within this chapter. The second chapter defines the concept of relations and operations on them. It includes various types of graphical representations of relations and their advantages and disadvantages. The concept of relation on a set and the properties of this relation alongside with some special types of relations derived from them are introduced in this chapter. The concepts of function are also defined in this part of the thesis. The third chapter indicates the relations that appear in real life - in relationships and games, in curriculum and puzzles. The properties of those relations are determined and the knowledge of relations and their properties is used to facilitate the solution of logical problems. It also supports gaining deeper understanding of those problems. The thesis includes two groups of tasks. The first one covers elementary tasks related to the topic of sets, ordered pairs, Cartesian Product and relations. The second part is concerned with...
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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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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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Understanding the concepts of measure in 5th grade students
Kupková, Tereza ; Jirotková, Darina (advisor) ; Zamboj, Michal (referee)
The diploma thesis is devoted to the investigation of the understanding of the concepts of measure among pupils of two fifth grades of a primary school in a small town. In the first part of the thesis, the concept of measure in the didactics of mathematics is presented, its anchoring in the RVP ZV, and then several views of different authors on the concept-forming process in the field of measure in geometry are presented. At the end of the first part of the thesis, the introduction of these concepts in selected textbooks for the 4th year of elementary school is examined. The second part of the work contains research that aims to find out what phase of the concept- forming process of measure in geometry the students of the research sample are in November, to propose further steps in the development of understanding of the concepts of content and perimeter, to implement the design scenario as possible and, finally, to find out the level of understanding of these concepts in March. The means for determining the level of student understanding in November is a research test, which is evaluated in the work and based on the results of which further steps are proposed. Since it turned out that the students have deficiencies in the first stages of the concept formation process and it is necessary to return...
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Angles, areas, volumes: dot product and determinant
Ondič, Milan ; Beran, Filip (advisor) ; Zamboj, Michal (referee)
This bachelor thesis deals with the introduction of scalar product and determinant, which are important tools of analytic geometry. The purpose of the thesis is to provide a parallel interpretation of these two key concepts of advanced algebra - the dot product and the determinant - primarily from a geometric, not an algebraic, point of view. The aim of the thesis is to show how both representations can be derived just by solving geometric problems in two-dimensional space and then how to transfer them to three-dimensional space. The first part of the work is devoted to finding the angle between two vectors in the plane and to calculating the area of a triangle. Both of problems are solved in several ways and then the scalar product and determinant are derived. The second part of the work is devoted to three-dimensional space, in particular the angle between two vectors, lines and planes and the volume of a tetrahedron and parallelogram. This is then supplemented by the introduction of some notions of linear algebra, an investigation of the algebraic properties of the dot product and determinant, and a generalization of the notions to the n-dimensional space. The last part of the thesis is devoted to the analysis of selected czech high school mathematics textbooks in terms of the occurrence and...
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