
Development of understanding of equality of 2nd and 3rd grade pupils.
Routa, Miroslav ; Jirotková, Darina (advisor) ; Kvaszová, Milena (referee)
The topic of the thesis is the development of understanding of equality in pupils of the 2nd and 3rd year of primary schools. The thesis is based on research conducted within the project Teachers' Understanding of the Causes of School Failure and the Effectiveness of Educational Interventions, in which more than 600 pupils participated. Using the results of the aforementioned research, I will analyse the most common errors and the causes from which the errors may have developed. Thanks to the results from two didactic tests in mathematics in two consecutive years with the same pupils, I can observe where the perception of equality has shifted in one year. My next goal will be to find out, by analyzing textbooks and hypothesizing about the mathematical notations used, whether my conjectures about the reasons for the incorrect solutions are correct. Based on the results of the research, it seems that the choice of textbooks that students use to learn from has a significant impact on their understanding of equality. In order to test this hypothesis, I will conduct a detailed analysis of the textbooks of all publishers used for teaching in the researched classes. A mapping will be carried out of situations in which pupils encounter equations and other tasks that promote understanding of equality. The...


The effect of Singapore mathematics on the mathematical selfefficacy of elementary school pupils
Šulcová, Pavla ; Jančařík, Antonín (advisor) ; Jirotková, Darina (referee)
This diploma thesis partly follows from the research of Smetáčková and Vozková who developed a Czech mathematical selfefficacy questionnaire. It examines the student's mathematical selfefficacy, i.e. the student's belief about his ability to successfully work on solving mathematical problems, depending on gender, year and the type of word problems used. It is also dedicated to teaching, describing solutions and student strategies for solving word problems in the form of two types of Singaporean problems  What number makes sense and What question can you answer. It describes the mathematics teaching in Singapore, which is repeatedly placed in the top ranks in international testing. 53 pupils in the 4th and 5th year of elementary school participated in the research lasting 5 weeks. The students filled out a mathematical selfefficacy questionnaire at the beginning and end of the research. During the research, the 4th graders were presented with 8 Singapore type problems What question can you answer, and the 5th graders were presented with 10 traditionaltype or Singaporetype problems What number makes sense. Hypotheses were tested with a twosample Ftest. No difference in mathematical self efficacy was demonstrated for boys and girls. The 4th grade students rated as more mathematically...


Concpet building process in geometry using the game OWL
Gandžalová, Tereza ; Jirotková, Darina (advisor) ; Kvaszová, Milena (referee)
The main topic of this thesis is the conceptual process in the field of geometry, more specifically the process of pupils' cognition of geometric objects during the didactic game Owl. The research of the thesis is focused on pupils of younger school age 911 years old. The aim of the thesis is to map pupils' ideas about geometric objects, their accompanying phenomena and relations between them through experiments, the tool of which is the Owl game and its modifications. The didactic game Owl is described in detail in the theoretical part of the thesis. Here, the theoretical background for the design of the experiments and the analysis of the pupils' discussions are also presented and the terms used in the practical part are defined. These backgrounds include the terms concept and conceptual process, the stages of development of geometric language, the theory of levels of understanding and the theory of generic model, and last but not least the levels of geometric thinking of the author Van Hiele. In the practical part, I focus on the description of the methodology and the characteristics of both the overall group and the individual pupils in it. Besides, the paper includes a breakdown of the activity plan of each experiment with their expected outcomes for each group. This is followed by the...


Development of geometrical concepts in primary school pupils
Löbel, Miroslav ; Jirotková, Darina (advisor) ; Slezáková, Jana (referee)
The thesis examines the development of pupils' understanding of geometric concepts during the transition from primary school grade 1 to grade 2. In the theoretical part, the theoretical background of the introduction of geometric concepts at the 1st grade, their anchoring in the RVP ZV and the line of building concepts in two series of mathematics textbooks are presented. At the end of the first part, didactic environments that are suitable for building the concepts of circumference and content are presented. The second part of the thesis contains research aimed at finding out at what stage of the process of understanding geometric concepts pupils are at when they move to Grade 2. The research was carried out by means of a didactic test in four 6th grade classes, and the results are translated in the form of tables. After the test, the selected pupils were interviewed to find out what previous knowledge and skills led them to solve the problems. A sample of pupils was used to attempt to reteach the skills, which will be tested again in a second round of testing after three months of teaching; the result is again presented in the form of tables. Finally, the fulfilment of the aims of the thesis is evaluated. KEYWORDS geometry, polygon, area, circumference, schema building, cognitive process of the...


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 conceptforming 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...


Solving word problems of the unfinished strategy type by pupils of the secondary school
Šinkorová, Jana ; Jirotková, Darina (advisor) ; Slezáková, Jana (referee)
The aim of the work was to test methodological materials created within the TAČR TL03000469 project "Support of the integration of mathematical, reading and language literacy in primary school pupils". The focus is on promoting word problems that combine mathematical, reading, and language skills in elementary school students. The pilot test was conducted in three 2nd grade elementary school classes, and three NEStype tasks were tested: "I think of a number", "Supermarket", and "Birthday Party II". Based on worksheets, questionnaires completed by the students, transcripts of the recorded group discussion, and a thorough analysis of the followup, I have concluded that the ability to successfully solve word tasks does not depend on the age of the student. Rather, it is related to the "readiness" to solve tasks, to the ability to read comprehensibly, to understand the relationships in the task, and to numerical competence. The essential component is cooperative work in a group, where individuals are enriched by discussing the problem together. Their communication often leads from a misunderstanding of the task to a correct solution. The result of the work is the description of methodological recommendations, examples of analyzing solution including their group discussions, and several specific...


Mapping of the trial and error method in solving problems in structural environments Spider web and Exhibition grounds
Kučerová, Lucie ; Havlíčková, Radka (advisor) ; Jirotková, Darina (referee)
The aim of this diploma thesis is to observe and describe the use of the trialanderror strategy in two didactic environments from the Hejné method among pupils in the second and third year of primary school, who are educated using the usual method of teaching mathematics. The theoretical part deals with the definition of heuristic strategies, their classification and a closer description of some selected heuristic strategies. The key chapter is devoted to the description of the trialanderror strategy and its inclusion among the solving strategies. It also deals with the problematic attitude of teachers and the wider public towards this strategy. At the end of the chapter, the advantages of its use in solving mathematical problems are included. The next chapters deal with work with mistakes, the child's experiment not only in teaching, and thus follow on from chapter 1.3. Chapter 1.7 describes Hejné's method of teaching mathematics and the didactic environments with which this method works and which are important for the practical part. At the end of the theoretical part, I define the distribution of the curriculum in the second and third years, which influence the students' approaches to solving. In the practical part, the research methods of unstructured observation and the method of verbal...


Didactic potential of game Ubongo in teaching mathematics at primary school
Váchová, Michaela ; Slezáková, Jana (advisor) ; Jirotková, Darina (referee)
This diploma thesis seeks the possibilities of using the board game UBONGO in teaching mathematics at elementary school. This thesis focuses on manipulative activities of pupils during the game and its goal is to explore what are pupils learning through the game. The theoretical part describes the basis for the research, thus content of mathematics and geometry curriculum in FEP BE, child's developmental stages in terms of learning, play with emphasis on the board game, lightly examines motivation and is inspired by tasks which are in geometrical environment Parkety and utilize prof. M. Hejný's method. The practical part of the diploma thesis contains the preparation of graded tasks, which are formed from the board game UBONGO in order to implement qualitative research. Didactical potential of the game is verified by performing series of graded tasks, preexperiment and experiment with elementary school pupils. The course of the experiment is described together with all steps, strategies and findings, which pupils learn through playing the game. At the end of the diploma thesis is an evaluation of the fulfillment of individual objectives. KEYWORDS Planar geometry, 2 D, manipulation, game, Ubongo, motivation, learning, polyomino, polygon, gradation, strategy


Games in primary school geometry
Myšková, Markéta ; Jirotková, Darina (advisor) ; Slezáková, Jana (referee)
5 Abstract This diploma thesis is called The Games in Primary School Geometry and it describes the benefits of the games in teaching geometry as a teaching method for acquiring and strengthening geometric knowledge. The goal of the thesis is to submit the set of didactic games which are suitable for teaching geometry and point out interesting cognitive and interactive phenomena identified in the communication among pupils and a teacher in the role of an experimenter. The work consists of a theoretical and practical part. The first one explains the key terms related to the game in geometry, for example: the learning process, teaching methods, didactic game, motivation, communication, spatial and geometric imagination. Literature concerning the fields of pedagogy, psychology and mathematics was used to elaborate the topics of the thesis. The practical part contains a set of game suggestions for teaching geometry. I chose a few of the games and used them when teaching the pupils of the 4th class of the basic school. The course of each game is commented on and described in details. The conclusion contains the selfreflection and I set the topics for my future work as a teacher. Keywords: didactic game, teaching methods, learning process, terminology, game strategy.


Didactic game as a way to open the world of geometry
Malcová, Michaela ; Jirotková, Darina (advisor) ; Tůmová, Veronika (referee)
The aim of this thesis is to explore thinking processes of pupils when solving problems of geometric manipulative environment Parquets. I elaborated this environment Parquets and stated characteristic tasks. I have also described, in what mental schemes of mathematical concepts solving tasks may contribute. I made use of pupil's life experiences with the game Ubongo in the presentation of the environment for them. The diploma thesis is presenting the ideas of the constructivist approach to teaching mathematics. Necessary relevant theoretical concepts are defined in the theoretical part. The experiment with third grade, who attended the Math's club is the basis of this diploma thesis. Video recordings were transcribed in the form of a written report and these were analyzed in the aim of diagnosing and describing phenomena that are related to discussions of pupils, their cooperation within the group and the development of mathematical experience, knowledge, skills and abilities of the student, but also the personality and social competences. In the analysis I also pay attention to the role of the experimenter, who was also in the role of a teacher. In conclusion, I made recommendations that could improve the lesson.
