
Comparing strategies when solving some types of word problems
Kohout, Ondřej ; Vondrová, Naďa (advisor) ; Novotná, Jarmila (referee)
The bachelor's thesis deals with the issue of comparing strategies when solving selected types of word problems. The theoretical part deals with the notion of concept cartoons, selected types of word problems, the process and strategies for solving word problems and the results of foreign studies that focus on the influence of the comparison of solving strategies in teaching mathematics. The practical part of the work includes an analysis of selected Czech textbooks of mathematics for the lower secondary school, including teacher books, focusing both on the occurrence of multiple solving strategies for the same word problem and on didactic approach to the selected types of word problems. The core of the work is 15 original worksheets, consisting of concept cartoons, in which two hypothetical students present their solutions to the same type of a word problem. This work also includes a proposal on how to implement such a worksheet in class, along with a proposal for a possible continuation of the use of comparing strategies in mathematics teaching.


Problems of pupils of high school in solving geometric construction exercises
Dyntarová, Miroslava ; Zamboj, Michal (advisor) ; Vondrová, Naďa (referee)
Title: Problems of pupils of high school in solving geometric construction exercises Author: Miroslava Dyntarová Department: Department of Mathematics and Mathematical Education Supervisor: Mgr. Michal Zamboj, Ph.D., Department of Mathematics and Mathema tical Education Abstract: The aim of this thesis is to reveal various errors and issues that high school students face in triangle construction problems. The thesis is divided into two parts for clarity. In the theoretical part we deal with construction problems in general and look into their various solution methods and formal procedures recommended by high school textbooks. Next, we focus on sets of points of a given property (that are part of the high school curriculum), give related denitions, basic properties and use cases. For better understanding of the demonstrated problems the thesis is lled with au xiliary graphs made in the program GeoGebra. In the last chapter of the theoretical part, we introduce various problems that are expected to occur during geometry con struction problem solving by students themselves. Those were the main focus of the following study. The preparation of the study, its implementation and subsequent ana lysis of collected data is described in the practical part of the thesis. The study was conducted with 10 students....


Origami as didacktical environment in matematical education
Boháčová, Jana ; Roubíček, Filip (advisor) ; Vondrová, Naďa (referee)
The thesis deals with origami as a learning environment in mathematics education. The two main aims of the thesis are to show the possibilities of using origami in various areas of mathematics teaching and learning, especially in synthetic geometry and calculations in geometry, and to suggest specific origamibased activities for secondary education. First, origami is introduced in its historical context and its geometrical axioms are described. Further, advantages and difficulties of using origami in mathematics education are discussed, with respect to the type and level of school. The fundamental part of the thesis consists of description and didactical analysis of tasks based on folding of an equilateral triangle and various polyhedra. Some of these tasks are adapted from other resources, some were designed by the author. Based on direct experience with employing origamibased tasks in different classrooms, methodological recommendations are added to the individual analyses, facilitating the practical usage of the thesis.


Tandemat  didactic game for the teaching of mathematics at the secondary school
Šilhánová, Lucie ; Vondrová, Naďa (advisor) ; Jančařík, Antonín (referee)
Tandemat  didactic game for the teaching of mathematics at the secondary school The thesis concerns a didactic game called Tandemat which I have created as a complement for the teaching of mathematics at secondary schools. The goal of the thesis is to find out and describe the potential of this game for the teaching of mathematics at this school level. First, the importance of games in our lives and also in teaching is mentioned. Next, some resources concerning games in the teaching of mathematics are described. The core of the thesis consists of the game Tandemat which I have elaborated and which is inspired by the popular game Activity. The results of the pilot studies of the game with the preliminary name Aktivity which were realized at elementary school and university helped to improve the game into its present version Tandemat. This has been tested by five groups of pupils in four classes of a secondary grammar school. The experiments were recorded and the acquired data were analyzed using the method based on the grounded theory approach. Moreover, a questionnaire was administered to pupils, concerning their grades in mathematics and the Czech language and their remarks on the game itself. The results of the analyses, observations and questionnaires show the potential and the limits of...

 

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 socalled 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, qualitativequantitative 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 decisionmaking process of the respondents were described. These are, for instance, differences in the categorization of examples and non...


Approaches to the deduction of formulas for measure in geometry in Czech mathematics textbooks
Procházková, Anežka ; Vondrová, Naďa (advisor) ; Zamboj, Michal (referee)
This bachelor's thesis aims to analyse selected mathematics school books published in the Czech Republic and summarize different approaches to calculating the area, volume and surface area in geometry. The thesis has been divided into two sections. The first section focuses on geometry, geometric measure and geometric figures, defining and explaining key terms related to the measure in geometry. The section also summarizes key information on the geometric figures addressed in the second section of the thesis. The second section includes different approaches to formula derivation, as used in Czech mathematics school books for lower secondary schools. The approaches are described in ways comprehensible to both teachers and pupils. The second section has been divided according to the geometric figures introduced in the first section, dealing with the area of a triangle, parallelogram, trapezium and circle, as well as the surface area and volume of a cube, cuboid, general prism, pyramid, cylinder, cone and sphere. The final section also explores Cavalieri's principle, which was used in some of the investigated approaches.


Expressions with variables with the help of agebraic tiles
Konrádová, Lenka ; Vondrová, Naďa (advisor) ; Novotná, Jarmila (referee)
The diploma with the help of algebraic tiles thesis focuses on teaching expressions with variables in the eighth grade in middle school. It is divided into theoretical and experimental parts. A particular chapter is devoted to an analysis of selected textbooks. First of all, the aim of this thesis was to analyse mathematics textbooks from the perspective the algebraic expressions. Some knowledge acquired thanks to the textbook analysis was used for my own educational experiment, whose preparation, realisation and assessment were the second objective of this thesis. The theoretical part provides a look at expressions with variables in curricular documents. Thereafter the pillars of teaching algebraic expressions are presented. This part is completed by the classification of errors made by students in relation to the topic. An analysis of selected textbooks follows the theoretical part. The core of this thesis is the experimental part, where teaching is based on constructivist principles. The preparation of the course explains the manipulation of the algebra tiles used during the lessons. After the teaching experiments, we may conclude that the application of algebra tiles helps students get into the environment of algebraic expressions, improves the understanding of the rules of manipulations with...


Reeducating university students' mechanical knowledge in mathematical analysis
Šmídová, Kristýna ; Vondrová, Naďa (advisor) ; Kvasz, Ladislav (referee)
The topic of this thesis is the didactics of mathematical analysis. The thesis describes selected observations from the reeducation in an individual tutoring environment of for mal knowledge of university students in the field of calculus. The aim of the thesis is to describe what formal knowledge appeared, to describe and evaluate selected reeducation interventions and on this basis formulate appropriate methodological recommendation. In the first chapter we deal with the contradiction between definition and concept concept of students, we outline how to convey to students the purpose of definitions and we suggest how to teach students to work with definitions properly, including understanding quan tified propositions. In the second chapter we present the theory of process and concept together with the generic model theory. In the third chapter we explain the methods of work with students and the methods of the analysis of videos from tutoring. In the fourth chapter we analyze cognitive processes of the concept of sequence limits. KEYWORDS reeducation, individual tutoring, mechanical knowledge, calculus, definitions, quantified proposition, infinity, sequence, limit 1

 