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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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Negative numbers in contemporary primary school mathematics
Skálová, Tereza ; Slezáková, Jana (advisor) ; Jirotková, Darina (referee)
The aim of this thesis is to deal with teaching of negative numbers in mathematics in lower primary school. The thesis brings an overview of exercises related to negative numbers, which are available in textbooks dedicated to lower and upper primary school. Main part of the thesis is devoted to three different experiments - pupils experiment, teaching experiment and parlour game. The pupils experiment analysis the successes and troubles of pupils attending 4th and 5th class when filling out the worksheets focused on various models of negative numbers. Furthermore, the teaching experiment based on a questionnaire survey describes comments of lower and upper primary school teachers in regards to implementation and usefulness of negative numbers. Parlour game experiment demonstrates the ability of pupils to grasp mathematical phenomenon by playing a game. Key words: additive operations with negative numbers experiment models of negative number: thermometer, floor, surface environment Stepping environment Stairs word problems board game negative numbers
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How children solve word problems in mathematics containing traditional and non-traditional gender content
Nováková, Veronika ; Smetáčková, Irena (advisor) ; Páchová, Anna (referee)
The goal of my thesis is to find out how school children react to word problems in mathematics that defy traditional distinction of gender roles in a typical household. This Bachelor Thesis compares in which word problems (with traditional or nontraditional gender content) children score higher and whether boys/girls in 2nd or 6th grade are more successful in solving them. It also differentiates if there are any noticeable differences between girls and boys. The research was carried out by mixed methodology and I used sequential progression of data. Firstly, I handed out the forms, then came the investigation of previously mentioned forms which granted me a better insight on the research of this particular phenomenon in the field. After the quantitative collecting of data came the qualitative investigation using half-structured interviews.
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Students' problem posing as an indicator of mathematical culture of lower secondary students
Bureš, Jiří ; Novotná, Jarmila (advisor) ; Hošpesová, Alena (referee) ; Zhouf, Jaroslav (referee)
TITLE: Studentsʼ problem posing as an indicator of mathematical culture of lower secondary students AUTHOR: Mgr. Jiří Bureš DEPARTMENT: Department of Mathematics and Mathematical Education SUPERVISOR: Prof. RNDr. Jarmila Novotná, CSc. ABSTRACT: This thesis is focused on studentsʼ problem posing as an indicator of mathematical culture of lower secondary students. The theoretical background consists of research on problem posing, word problems in mathematics, mathematical culture and the Theory of didactical situations in mathematics. The goal of the thesis is to analyse links between problem posing and studentsʼ mathematical culture through the analysis and description of the posed problems. The thesis consists of two parts, theoretical and research part. In the theoretical part, there are the main findings about studentsʼ problem posing and some approaches to the concepts of word problems and mathematical culture, and the main concepts of the Theory of didactical situations used in the thesis. The research part starts with the analysis of the pre-experiment, which constitutes the basis for creation and characteristics of the conception of mathematical culture of problem posing. These parts are followed by the analysis of the main experiment, which provides the complete description of the posed problems...
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Word problems with topics from chemistry
Poulová, Anežka ; Novotná, Jarmila (advisor) ; Čapek Adamec, Martin (referee)
The thesis is focused on verbal tasks within the subject of chemistry and consists of several parts. The introductory chapter contains a definition of the concept of verbal task, including the basic division of tasks, then the stages of solving the general verbal task and the approach to the solving of verbal tasks with chemical issue is mentioned. The second part summarizes the most common verbal tasks with chemical issue, their theoretical chemical and mathematical basis and offers various ways of how these tasks can be solved. The third part of the paper includes tasks that are an extension of the first part and serves as a sample of interesting examples (also in the terms of mathematical procedures) that are solved in chemistry. The author of the paper tries to show and compare different procedures for solutions and their influence on the efficiency and speed of calculation.
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Solving algebraic problems in history and in the classroom
Vojáček, Josef ; Kvasz, Ladislav (advisor) ; Zamboj, Michal (referee)
This diploma thesis deals with the comparison of historical solutions of word problems with student solutions. Its aim was to describe how students solve historical word problems, while looking for analogies between student and historical solutions. This intention led me to a better understanding of student solutions. The theoretical part of the thesis describes important concepts for algebraic word problems, such as a variable, algebraic expression or algebraic word problem. In the historical part I describe chronologically the development of algebra from antiquity through the Middle Ages and the Renaissance to the Baroque. In each period, I mention important mathematicians of the time and present several solved word problems. In most cases, I analyze these solutions from the perspective of today's mathematics. The theoretical part describes the research that took place at the eight-year grammar school. As part of the research, I gave students 6 historical tasks across historical periods and then analyzed the ways in which students solved problems. I found that for most of the tasks, there were solutions similar to the historical solutions among the student's solutions. Some historical methods appeared very often. An example is the use of addition instead of multiplication, or division, as used by the...
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Students' problem posing as an indicator of mathematical culture of lower secondary students
Bureš, Jiří
TITLE: Studentsʼ problem posing as an indicator of mathematical culture of lower secondary students AUTHOR: Mgr. Jiří Bureš DEPARTMENT: Department of Mathematics and Mathematical Education SUPERVISOR: Prof. RNDr. Jarmila Novotná, CSc. ABSTRACT: This thesis is focused on studentsʼ problem posing as an indicator of mathematical culture of lower secondary students. The theoretical background consists of research on problem posing, word problems in mathematics, mathematical culture and the Theory of didactical situations in mathematics. The goal of the thesis is to analyse links between problem posing and studentsʼ mathematical culture through the analysis and description of the posed problems. The thesis consists of two parts, theoretical and research part. In the theoretical part, there are the main findings about studentsʼ problem posing and some approaches to the concepts of word problems and mathematical culture, and the main concepts of the Theory of didactical situations used in the thesis. The research part starts with the analysis of the pre-experiment, which constitutes the basis for creation and characteristics of the conception of mathematical culture of problem posing. These parts are followed by the analysis of the main experiment, which provides the complete description of the posed problems...
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The Pupils' Strategies of Mathematical Word Solving Problems With Real-Life Context
Gruberová, Nicole ; Smetáčková, Irena (advisor) ; Páchová, Anna (referee)
In my thesis I concentrated on mathematical problem solving by pupils at elementary school. I lead interviews with six 3rd grade children, during which they were instructed to solve the problems as well as to share their stream of thoughts concerning their solving strategies with me. I tried to understand the ways how they solve the problems and where their mistakes stem from. My attention focused on the ways the problems were formulated and what specific words may have either helped or distracted the children while the problem solving. The special attention was paid to contextual information which children use during the solving of word problems - its attractivness as well as the way it is served to them. The information about the childrens' school results and the difference between word problems from my set and the regular ones I gained from an interview with the school teacher of the children from my research group. The research showed that the difference between intuitive and analytical way of thinking had the most crucial impact on the strategies the children chose during the word problem solving. The occurence of non-standard context as a motivator was proved, however it was not so in the case of it in a role of a cognitive help. This impact was not proved surely. Concerning the length of the...
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Non-mathematical world of mathematics textbook for 6th grade of lower secondary schools and in the area of financial literacy
Moraová, Hana ; Bendl, Stanislav (advisor) ; Hošpesová, Alena (referee) ; Voňková, Hana (referee)
The aim of the dissertation thesis is to study the non-mathematical content of textbooks of mathematics. Textbooks of mathematics are not only a pedagogical document but also a cultural artefact that is produces in a particular society with its own cultural norms. While working with a textbook of mathematics, pupils come across many images of everyday life. Yet, since the main goal of a mathematics textbook is to help pupils gain knowledge and skills in mathematics, not much attention is paid to textual (non-mathematical, cultural) content. This means that pupils almost on everyday basis visit a world that tries to awaken the illusion of being "real", of being model of reality but in fact is a model for what is perceived as normal. The question asked in the presented research is what images of everyday life pupils come across while working with Czech textbooks of mathematics and whether there are differences among textbooks by different authors in this respect. Within the frame of this research, five sets of textbooks for 6th grade of lower secondary schools and four textbooks for 9th grade (only the chapter on financial mathematics, an area closely connected to everyday life) were analysed with respect to their non-mathematical, cultural content. The method used in the research comes out of the...
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