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Indirect Proportion - Pupils' Strategies, Textbook Analysis and Teachers' Didactic Practices
Reichmann, David ; Vondrová, Naďa (advisor) ; Novotná, Jarmila (referee)
1 Abstract The goal of the diploma thesis was to identify and describe didactic practices of selected experienced mathematics teachers, used in the teaching of indirect proportion, to make an analysis of the most used textbooks from the point of view of teaching indirect proportion, to select suitable problems which diagnose pupils' knowledge of indirect proportion and to identify pupils' strategies and their mistakes in solving them. Indirect proportion is first described from the point of view of curricular documents and of Czech pupils' results in this area in both national and international surveys. The pupil's knowledge gaining process is characterised from the point of view of didactic constructivism. Next, ways and conceptions of teaching indirect proportion as provided by selected primary textbooks are given. The content analysis of textbooks was made and compared to results of similar studies. Next, the thesis deals with some results of international research on proportional thinking and solving strategies for problems on proportion which are then used as a starting point of my own research on pupils' strategies for problems on indirect proportion. The next part of research consists of semi-structured interviews with experienced teachers, observations of their lessons and analysis of their pupils'...
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Systems of linear equations at the primary school - pupils' problems and teachers' views
Kliner, Jiří ; Vondrová, Naďa (advisor) ; Jančařík, Antonín (referee)
The goal of the diploma thesis was to describe critical moments for solving systems of linear equations at the primary school. First, various methods of solving systems of two linear equations with two unknowns are summarized, the history of systems of linear equations is briefly outlined and the theme is described from the point of view of curricular documents. Based on the review of literature, the critical moments and types of mistake made by pupils are described. My own research used the mixed research strategy, where the main strategy was qualitative and the secondary strategy was quantitative. The research consisted of semi-structured interviews with four mathematics teachers, the preparation and realization of a questionnaire for primary school pupils and the creation, realization and analysis of a didactic test. The main results of the thesis consists of the description of the most frequent pupils' problems when solving systems of linear equations, the didactic analysis of textbooks and teachers' views of the topic and its teaching. Keywords: linear equations and their systems, pupils' problems, mistakes, semi-structured interviews, didactic test Powered by TCPDF (www.tcpdf.org)
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Word problems at the Waldorf secondary schools
Daniel, Radovan ; Vondrová, Naďa (advisor) ; Jančařík, Antonín (referee)
The theoretical part of the diploma thesis contains didactic analysis of word problems, that is the definition of a word problem, classification of word problems from various perspectives and methods of solving word problems, according to czech specialists in didactics of mathematics. The second part describes the teaching of mathematics at the secondary Waldorf schools with an emphasis on teaching in main lesson blocks. The core of the work lies in the experimental part which consists of two sections. The first section describes the preparation, implementation and evaluation of educational experiments on the subject of word problems. The educational experiment was conducted in the first class of the Waldorf lyceum in Prague in the academic year 2014/2015. All days of the main lesson block are described. Part of the reflection of the teacher and an observer who participated in the entire main lesson block is the part of thesis. The practical part continues with the pupil's solving strategies analysis. Pupils wrote a didactic test with word problems once before the teaching experiment and once after it. The analysis of each problem is following, in which the interesting phenomena that emerged in the pupils' solutions are explored. The conclusion summarises the main points of the research conducted...
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Pupils' difficulties in solving selected word problems from TIMSS research
Matěka, Petr ; Vondrová, Naďa (advisor) ; Novotná, Jarmila (referee)
Pupils' difficulties in solving selected word problems from TIMSS research. (Diploma Thesis.) Abstract The theoretical part of the diploma thesis describes international comparative surveys, namely PISA and TIMSS, and analyses results of Czech pupils. Some areas are distinguished in which our pupils were unsuccessful and from them, the area of word problems and their mathematisation was selected for further work. Next, a solving strategy is characterised and some relevant research from this area is given. The core of the work lies in the experimental part whose goal was to find out what strategies pupils use when solving selected problems from TIMSS research and why they fail in them, via the analysis of pupils' written solutions complemented by interviews with them. Causes of failure of our pupils in these problems in TIMSS 2007 are looked for in mistakes pupils make, while it is also followed in what phase of the solving process they appear. The participants of research were pupils of Grade 9 of a primary school who solved three selected word problems from TIMSS research. Their written solutions were complemented by interviews with the experimenter focused on their mistakes and lack of clarity of the solutions. Four pupils participated in a pilot study. The atomic analysis of their solutions confirmed...
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Developing activity and creativity in teaching fractions in grades 6 to 7
Svobodová, Lenka ; Tichá, Marie (advisor) ; Novotná, Jarmila (referee)
TITLE: Developing activity and creativity in teaching fractions in grades 6 to 7 AUTHOR: Bc. Lenka Svobodová DEPARTMENT: Department of Mathematics and Mathematical Education SUPERVISOR: Mgr. Marie Tichá, CSc. ABSTRACT: The thesis consists of a theoretical and an empirical part. The theoretical part looks at the cognitive process of pupils and possible ways of their motivation during fractions teaching. Furthermore, it outlines causes of lack of understanding of fractions and re-education interventions. The empirical part is based on a qualitative research whose main objective was to determine how the pupils are able to solve fractions exercises independently and creatively and what mistakes they make. Various methods of data collection were used, such as interview with teachers on issues of fractions teaching in elementary schools, non- standardised test with fractions exercises and additional interview with the tested pupils. This part also describes the preparation of the research, the research itself and its results KEYWORDS: fractions, interpretations, representations, models, misunderstandings, mistakes, teaching approaches
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Critical areas of mathematics at the primary school - analysis of teachers' didactic practices (linear equations)
Nováková, Anežka ; Vondrová, Naďa (advisor) ; Jančařík, Antonín (referee)
Kritická místa matematiky na základní škole (Analýza didaktických praktik učitelů - lineární rovnice) Critical Areas of Mathematics at the Primary School (Analysis of Teachers' Didactic Practices - Linear Equations) Abstract The goal of the diploma thesis is to describe didactic practices used by primary teachers when teaching linear equations, seen as one of the critical moments of primary school mathematics. First, semantic and structural models of linear equations and ways of teaching linear equations as suggested by selected textbooks for primary schools are described. Next, on the basis of literature review, pupil' problems and types of mistakes they make in this area are given. My research consisted of semistructured interviews with five experienced mathematics teachers and observations of their lessons. The interviews and observations were transcribed and the transcriptions were analysed by techniques of grounded theory. It was found out that the teachers use common didactic practices as well as their own which they develop. The practices, models which the teachers use when teaching linear equations, approaches to introducing equivalent operations, as well as a list of critical places within linear equations are the main results of the work. Keywords: Linear equations, models, pupils' problems,...
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Fractions - Some Difficulties of Pupils and Teaching Approaches of Teachers
Vejmelková, Eliška ; Vondrová, Naďa (advisor) ; Novotná, Jarmila (referee)
(anglicky) Fractions are one of the critical areas of mathematics at the primary school. The aim of this diploma thesis is to describe didactic practices used when teaching fractions (focusing in particular on additive operations with fractions) and find out what strategies are used by pupils at selected tasks focusing on fractions, what difficulties are an obstacle in their successful solutions and what images of fractions the pupils have. The theoretical part contains considerations about the teaching and learning of mathematics, the overview of the historical development of the concept of fraction and operations with fractions and also selected research related to fractions. The practical part begins with the analysis of the textbooks where their semantic and structural models used for fractions are identified as well as ways of teaching operations with fractions. My own research consists of semi-structured interviews with five experienced teachers (one of whom is not qualified) on the topic of teaching fractions, the difficulties of pupils with fractions and of clinical interviews with three pupils from different primary schools. Interviews with the pupils were focused on the solution of the diagnostic tasks in the field of fractions. Transcripts of both interviews were analyzed by techniques...
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New Generation of Open-Source Tool Stranger Strings
Kňazík, Matej ; Dobeš, Petr (referee) ; Herout, Adam (advisor)
Cieľom tejto bakalárskej práce je opísať vývoj webovej aplikácie s názvom Stranger Strings. Projekt si ponechal svoje meno po internom firemnom nástroji, avšak vo všetkom ostatnom prešiel kompletnými zmenami. Účel Stranger Strings sa pozmenil, kód bol od základu prepísaný a celý projekt bol zmenený na open-source. Rovnako bolo redizajnované aj užívateľské prostredie za účelom rozšírenia cieľovej skupiny užívateľov. Táto práca podrobne popisuje tento proces a tiež vysvetľuje, akú úlohu zohralo užívateľské testovanie pri identifikácii hlavných problémov aplikácie. Výsledkom tejto práce je open-source nástroj na analýzu lokalizácie, ktorý pomáha užívateľom zlepšovať jej kvalitu.
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Mistakes of Czech Learners of German in Writting
Nováková, Veronika ; Nečasová, Pavla (advisor) ; Švermová, Dagmar (referee)
The following thesis deals with the topic "Mistakes of Czech Learners of German in Writing." The goal is to find out and describe the mistakes made in various German niveaux - specifically A1, A2 and B1. At the same time, it aims to introduce a new classification of mistakes and their symbols for correction that are easy to use and understandable for both the teachers and the learners. The connection between the type of the mistake and the level of German's niveau is also examined. In other words, the question is whether some of the mistakes are connected to the student's level of language or whether the mistakes in question are to be found everywhere. Firstly, the topic of mistakes and writing competence is introduced. The subsequent practical part is concerned with the experiment, in which 75 pupils from two grammar schools took part. They were given a standard examination writing assignment from German as a foreign language on levels A1-B1. The individual writing assignments are corrected, and the results are given in a well-arranged table according to the level of language. Furthermore, it is described closely with respect to the types of the mistakes. Last but not least, the mistakes are analyzed with respect to their abundance. The experiment showed that some expressions are used incorrectly...
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Expressions with variables in primary mathematics
Pokorný, Antonín ; Vondrová, Naďa (advisor) ; Pilous, Derek (referee)
The thesis is focused on the teaching of variable expressions at the eighth grade of elementary school and is divided into the theoretical, preparatory and experimental part. The theoretical part contains a short description of the objectives of the teaching of variable expressions. This section is complemented by the selected results of international comparative research and the classification of mistakes which pupils make in connection with the topic. An important part is the analysis of selected textbooks according them the teaching of variable expressions at the primary schools takes place. In the preparatory part there are presented the selected tasks of generalization which are recommended by the curriculum materials, but are not included in the textbooks. Component of the preparatory part is the presentation of algebra tiles environment. The core of the thesis is the experimental part aiming to compare the results of teaching of variable expressions in two differently taught groups. The first group was taught according to the textbook. In the second group the teaching was based on patterns of algebra tiles. The research of teaching results is focused on pupils' difficulties and the most frequent mistakes. The results indicated that the environment of algebra tiles helps to reduce number of...
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