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Construction of elementary pupils' geometric schemas via motivating learning environments
Kloboučková, Jaroslava ; Jirotková, Darina (advisor) ; Coufalová, Jana (referee) ; Novák, Bohumil (referee)
Title: Construction of elementary pupils' geometric schemas via motivating learning environments Author: Jaroslava Kloboučková Department: Department of mathematics and mathematics education Supervisor: doc. RNDr. Darina Jirotková, Ph.D. Abstract: The aim of the dissertation is to discuss teaching geometry as integral part of mathematics education at the primary school level. The thesis also documents a longitudinal teaching study which was initiated in 2010 and which gives us a base for discussion of some fundamental questions regarding the process of learning geometry for pupils in their early school years. The main objective here is to attempt to answer the following four didactic questions: In which way do pupils learn about geometrical objects? How do they share their geometrical knowledge, experience and discoveries with one another? How much (at what level) are they able to understand mathematical concepts that the official curricular documents (the Czech Framework for Education Program) place in later years of schooling? What phenomena are they able to grasp and describe using their mother tongue? The theoretical framework focuses on the learning process and the typology of mathematical problems in geometry. Four specific engaging environments (Cube Buildings, Origami, Wooden Sticks, and Tiles) and...
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Mathematical Environments Mazes and Cycle Path with Primary School Pupils
Bartoňová, Jana ; Slezáková, Jana (advisor) ; Kloboučková, Jaroslava (referee)
The diploma thesis deals with the mathematical environments Mazes and Cycle Paths. The first part is concerned with the definition of two opposite educational styles, transmissive and constructivistic. Within the constructivistic educational style it is also focused on schema-oriented education and on defining its principles for teaching mathematics by Hejný's method. It also introduces a new term genetic constructivism - its author proves that Hejný's mathematics and its didactic environments are embedded in ancient history. This diploma thesis gives an answer to the question of why the environments Mazes and Cycle Paths belong to the teaching of mathematics, and therefore, on what mathematical basis it stands. It is for this reason that it provides insight into the fundamentals of graph theory. It is focused on the historical aspect of terms maze and cycle path and charts exercises in Hejný's textbooks of mathematics from environments Mazes and Cycle Paths. The aim of research is to expand the collection of exercises from these two environments, to chart pupils' solving strategies and identify effective teaching methods in accordance with the schema-oriented education, which has been studied in seven experiments. The last part of this diploma thesis presents a didactic game, which is focused on...
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Comparison of mathematical problem solving strategies of primary school pupils
Wasilewská, Eliška ; Jirotková, Darina (advisor) ; Kloboučková, Jaroslava (referee)
The aim of this dissertation is to describe the role of educational strategy especially in field of the teaching of mathematics and to compare the mathematical problem solving strategies of primary school pupils which are taught by using different educational strategies. In the theoretical part, the main focus is on divergent educational strategies and their characteristics, next on factors affected teaching/learning process and finally on solving the problems. The empirical part of the dissertation explores the effect of educational strategy on problem solving strategies of third graders of primary school by using the method of experiment that includes a didactic test and interviews with selected pupils. The result of the dissertation is providing the evidence of influence of educational strategy on mathematical problem solving strategies. KEYWORDS Educational strategy, teacher, pupil, mathematical problem solving, experiment.
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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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Financial literacy and its inclusion in the curriculum of practical primary schools
Löffelmannová, Anna ; Kloboučková, Jaroslava (advisor) ; Tůmová, Veronika (referee)
The theoretical part of the diploma work defines intellectual disabilities, as well as the possibilities of counselling and educating of pupils with mental disabilities. Further, the thesis discusses education and re-education of pupils with diagnosed mental retardation. It outlines the inclusion of financial literacy into the curricular documents intended for pupils with a mental disability across educational areas with emphasis on mathematics. The thesis introduces materials and their parameters suitable for the inclusion of financial literacy at practical primary schools. The practical part covers experimental education of individual thematic topics of financial literacy at practical primary schools. The carried out initial diagnostics of pupils at a selected practical primary school focused on percentages, simple interest and a family budget. This diagnostics had a general character, as was also verified. Furthermore, the thesis presents a detailed record from own executed teaching with regard to four monitored pupils, including their casuistry. After the completion of the teaching, its success was assessed. The work can be used not only by teachers at practical primary schools but also at ordinary primary schools, because it contains a series of graded tasks that lead to the development of...
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Pupils' strategies for solving additive algorithms
Khanová, Alžběta ; Kloboučková, Jaroslava (advisor) ; Slezáková, Jana (referee)
This thesis deals with the strategies that pupils use for solving additive tasks. The theoretical part focuses on younger-school ages, the transformation of education in the 20th century and the addition operation. The practical part describes a series of experiments realized in mathematics lessons with pupils from the 1st elementary school. During the experiment, pupils have met the environment of the hundred board. I compared pupils's numerical strategies for solving additive algorithms, after the end of the experiment. Also I compared results between pupils, who were part of the experiment and are taught by textbooks from "Nakladatelství Fraus" with pupils who did not participate in the experiment and are taught by textbooks from "Nakladatelství ALTER".
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Fostering of spatial imagination of students using three projections - different approaches in Czech and Danish Education
Petráková, Barbora ; Kloboučková, Jaroslava (advisor) ; Jirotková, Darina (referee)
TITLE: Fostering of spatial imagination of students using three projections - different approaches in Czech and Danish Education SUMMARY: This master thesis is focused on description of different conception of teaching geometry in chosen czech and danish mathematics textbooks and on the possibilities of fostering the spatial imagination at elementary school. On example of one particular class from an elementary school in Prague, we will take an inside view of the advantages and disadvantages of using three projection in mathematics education and its influence on development of spatial imagination. In this class, a diagnostic interview was taken to determine the level of spatial imagination development and in order to find out, how these children can work with three projections. KEY WORDS: pupils of primary school age, spatial imagination, three projections, conceptions of geometry teaching
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Concepts from graph theory in primary school mathematics curriculum
Mutinová, Tatiana ; Kloboučková, Jaroslava (advisor) ; Slezáková, Jana (referee)
Concepts from graph theory in primary school mathematic curriculum Ing. Tatiana Mutinová, 2014 Abstract This diploma thesis is focused on graph theory, especially on the concepts that are used in primary school mathematic curriculum. Furthermore it shows the reasons why it is necessary to include these graph concepts in young pupil's education. In the theoretical part, basic terms and definitions from chosen parts of graph theory are mentioned and few examples demonstrate how the applications of graph theory can help with solving real-life situations. The practical part summarized the current use of some graph theory concepts in primary school mathematic curriculum. This part also includes the demonstration of the graded series of problems and the sheets of exercises that could be usable in introducing and practising of some graph concepts. The experiment with mosaics, that was carried out within this diploma thesis, is an illustration how to connect mathematical and non-mathematical world and how to integrate research activities in young pupil's education. Key words: mathematics, graph theory, graph vertex, degree of graph vertex, edge of graph, problem of two colours, child of primary school
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Building of Arithmetical Triads in Two Mathematical-didactical Environments: Neighbours and Coloured Triples
Otradovcová, Dana ; Jirotková, Darina (advisor) ; Kloboučková, Jaroslava (referee)
The thesis attends to the mathematical charts constructing of additive triad of pupils on 1st grade of the primary school by means of two mathematical - didactic settings "The Neighbours" and "The Coloured Trio". They occure in mathematical textbooks created by prof. RNDr. Milan Hejný, CSc., RNDr. Darina Jirotková, Ph.D., PhDr. Jana Slezáková, Ph.D. and their colleagues and which are published by Fraus. In my thesis I shall attend to the theoretical pieces of knowledge in the given mathematical area as well as to the reasons for the creation of the new mathematical teaching concept after the czech educational reform. Mathematical tasks from the two appointed settings will be handed in to the pupils to be solved. The pupils will encounter such tasks for the first time. It shall be observed how they are able to cope with the given tasks and if they will be able to infiltrate the problem of the tasks or to invent their own tasks. Further on the thesis shall attend to the means of solutions of similar tasks by the students of The Pedagogical Faculty of the Univerzita Karlova and to the analysis of their comments on the tasks.
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