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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 re-teach 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...
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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, pre-experiment 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
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Introducing the area of polygons, particularly by method of releasing parameter in primary schools
Kovář, Luděk ; Kloboučková, Jaroslava (advisor) ; Tůmová, Veronika (referee)
This thesis deals with the description of constructive approach to teaching mathematics in the third grade of primary school. Teaching mathematics is focused on geometry, specifically on one way of introducing the area of the scalene triangle which describes the relation between a side and its height and corresponding area. In the thesis I describe six particular lessons, their preparation, process of their realization and my own reflections. In these lessons, I analyse some cognitive phenomena as well as social relationships among pupils. Furthermore, I present a detailed examination of tasks from the final diagnostic test, in which I aim towards proving success of this method of teaching mathematics. After four years, I attempt to verify the permanency of the knowledge pupils gained in these particular lessons. I illustrate this by presenting analysis of additional exercises. The whole experimental process was led within the method of releasing parameter. Individual lessons were in accordance with given stages of this method, as described in specialised literature. I verified that the above mentioned method is applicable in teaching mathematics even in the third grade of the primary school. KEYWORDS teachingstyles, perimeter and area, square grid, polygon, method of releasing parameter
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The construction of polygons with the didactic aid
Průšová, Adéla ; Kloboučková, Jaroslava (advisor) ; Havlíčková, Radka (referee)
This thesis deals with construction of polygons with use of a didactic aid a geoboard at primary education. I have done analysis of three series of mathematics books in order to know, if they include possibility of mechanical work during construction of polygons. Based on study of professional literature related to teaching mathematics, mainly geometry at primary education, I have created patterns that can be used altogether with geoboard in mathematics. The patterns had been used in three classes thank to this I could have assess their practical use. Then I have corrected wrong instruction of patterns in order to be clear. Next I described three stages of beginning to work with geoboard that I have personally done and that are written in details in protocol. I have concluded didactic potential work with geoboard and theoretical obstacles while geoboard is using.
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Advanced Topics in Plane Geometry
Hajmová, Kateřina ; Štěpánová, Martina (advisor) ; Moravcová, Vlasta (referee)
The aim of this thesis is to introduce a series of knowledge from advanced planimetry, which can be proved using the knowledge of high school geometry. Selected theorems deal with characteristic of squares with a common vertex (Finsler-Hadwiger theorem, Theorem of Four Squares, Bottema's theorem), significant points of plane entities (Gergonne point theorem, Švrček point theorem, Simson's Theorem, Miquel's theorem), Feuerbach's circle and its relation to the Euler's line. In this thesis, there is also mentioned Reim's theorem, Napoleon's theorem, and Thebault's theorem. This thesis contains a lot of illustrations created in the Geogebra Mathematical Software, which are available online in interactive form.
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Geometric Proofs
Hanusová, Tereza ; Štěpánová, Martina (advisor) ; Halas, Zdeněk (referee)
Title: Geometric Proofs Author: Tereza Hanusová Department: Department of Mathematics Education Supervisor: RNDr. Martina Štěpánová, Ph.D., Department of Mathematics Edu- cation Abstract: This Bachelor's thesis treats such proofs of mathematical theorems in which pictures and secondary school geometry play a significant role. Its aim is to promote an unusual approach to theorem proving which enables to literally see the way they function. The proofs described include three categories: figu- rate numbers, polygons and areas of plane figures with curved boundaries. The thesis can be useful to teachers to liven up their secondary school mathematics lessons or to students of maths-oriented programmes to enrich their knowledge by an unusual approach to theorem proving. Keywords: proof, geometry, figurate number, polygon, area of plane figure 1
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Rectagles inscribed in Jordan curves.
Ye, Tomáš ; Šír, Zbyněk (advisor) ; Vršek, Jan (referee)
We will introduce quotients, which are very special kinds of continuous maps. We are going to study their nice universal properties and use them to for- malize the notion of topological gluing. This concept will allow us to define interesting topological structures and analyze them. Finally, the developed theory will be used for writing down a precise proof of the existence of an inscribed rectangle in any Jordan curve. 1
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Introducing the area of polygons, particularly by method of releasing parameter in primary schools
Kovář, Luděk ; Kloboučková, Jaroslava (advisor) ; Tůmová, Veronika (referee)
This thesis deals with the description of constructive approach to teaching mathematics in the third grade of primary school. Teaching mathematics is focused on geometry, specifically on one way of introducing the area of the scalene triangle which describes the relation between a side and its height and corresponding area. In the thesis I describe six particular lessons, their preparation, process of their realization and my own reflections. In these lessons, I analyse some cognitive phenomena as well as social relationships among pupils. Furthermore, I present a detailed examination of tasks from the final diagnostic test, in which I aim towards proving success of this method of teaching mathematics. After four years, I attempt to verify the permanency of the knowledge pupils gained in these particular lessons. I illustrate this by presenting analysis of additional exercises. The whole experimental process was led within the method of releasing parameter. Individual lessons were in accordance with given stages of this method, as described in specialised literature. I verified that the above mentioned method is applicable in teaching mathematics even in the third grade of the primary school. KEYWORDS teachingstyles, perimeter and area, square grid, polygon, method of releasing parameter
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Plane geometry teaching at secondary schools
Machovcová, Lucie ; Zhouf, Jaroslav (advisor) ; Dvořák, Petr (referee)
This work compares and evaluates several math's textbooks for secondary school where we can find schoolwork from plane geometry. The aim of this work is drawing the main advantages and disadvantages of those textbooks, evaluating whether all textbooks contain themes which are required by School Curriculum and interpretation of a questionnaire survey among teachers of mathematics. In the last chapter, it is described how a new ideal textbook of plane geometry wouldlook like. Those were taken on the grounds of gained information from my questionnaire survey. Themes which cannot be found in compared textbooks for secondary schools are a part of recently made textbook since it is not necessary to know any new terms for their understanding. Key words: geometry, teaching geometry, textbooks, polygon, circle
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