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Back and forth between science and reality: Mathematical modelling in tasks with a science context (didactic experiment)
Šmíd Ridzoňová, Ráchel ; Havlíčková, Radka (advisor) ; Vondrová, Naďa (referee)
Mathematical modelling is part of the focus of the educational area "Mathematics and its applications" in the Czech national curriculum and is also a widely studied topic abroad. However, it does not receive much attention in Czech research. This thesis aims to introduce the concept to Czech readers and test the connection of mathematical modelling with science topics and the implementation of modelling tasks in the 5th grade of primary school. The thesis presents mathematical modelling as solving process of a complex problem with a real context in steps (0) undertanding the problem, (1) creating the real model, (2) mathematization, (3) mathematical operations, (4) interpretation of the result and (5) validation of the solution. Modelling competence, the modelling probem, and the relationship to word problems are also described. The chosen qualitative research method of didactic experiments explores the application of a holistic and analytical approach to teaching, identifies the difficult steps of modelling for 5th- grade students, and provides insights into cross-curricular relationships and organizational forms in the teaching of modelling. The research findings positively demonstrate that incorporating modelling tasks into regular lessons and linking them to science topics is possible but...
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Teaching word problems using teaching materials "Comparison"
Hrúzová, Eva ; Vondrová, Naďa (advisor) ; Novotná, Jarmila (referee)
This paper focuses on the implementation of methodological materials based on concept cartoons for teaching word problems at the lower level of secondary school. The theoretical part of the work deals with the description of word problems and their teaching in schools, including the role of the teacher and the constructivist approach. It also addresses the concept of concept cartoons, which is used as the basis for implementing methodological materials. In the practical part, these materials are implemented over five teaching hours in the seventh and eight grades. The results indicate that the implementation of methodological materials using concept cartoons in teaching word problems at the lower secondary school level was succesful, and students evaluated this new teaching approach positively. One of the main benefits of using concept cartoons, based on the experience from teaching experiment, is that they createa non-threatening learning environment where students do not experience the fear of failureThis is because mistakes and difficulties in solving problems are attributed to fictional cartoon character. Additionally, the use of concept cartoons encourages discussion and interaction among students, as there is often more than one correct solution to a given problem. This approach helps to...
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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 NES-type 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 follow-up, 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...
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Pupils' solutions of word problems with fractions and percentages
ADAMCOVÁ, Hana
This diploma thesis deals with a topic of mathematics, namely word problems with fractions and percentages. Specifically, this work deals with students' solutions to such word problems. The work acquaints the reader with how selected word problems with fractions and percentages are solved by pupils in the 9th grade of primary schools. It introduces the readers to the various numerical procedures chosen by the students. Some procedures occurred more frequently, others only rarely. Each word problem is supplemented by a graph, which shows the success of students in solving the word problem. The work also includes photographs of students' solutions for the reader's better idea. At the end of the chapter, some word problems are processed using the Concept Cartoons method. The work shows mainly close connections between fractions and percentages. And especially on how primary school students look at the problem from their point of view.
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Worksheets for teaching mathematics at secondary school from selected topics
ONDRÁČKOVÁ, Kamila
The main aim of the thesis is to verify the pupils knowledge in arithmetic on the basis of worksheets at lower-secondary schools and selected grammar schools. The theoretical part of the thesis is focused on the knowledge that each pupil should already know. The practical part contains 4 working sheets intended for pupils of the sixth, seventh, eighth and ninth grades of lower-secondary school and for the pupils of equal corresponding grade of grammar schools. The results with detailed solution of the work sheets is listed in the appendix of the thesis. The practical part includes is the results of the research which show the pupils´ differences of knowledge of the selected schools.
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Teacher's approach to language and situational context of mathematical word problem
Viktorová, Martina ; Havlíčková, Radka (advisor) ; Macháčková, Jana (referee)
The focus of this thesis is to investigate how the elementary school teachers work with mathematical word problem from the perspective of language and situational-contextual level of word problem. Furthermore it is focused on the teachers' work approach to the word problem and identification of phenomena oriented to one of cognitive modes - paradigmatic and narrative described by J. S. Bruner (1986) and O. Chapman (2006). The main research method of this thesis is based on observing how the teachers work with the word problem in class and interviewing them as well as pupils. In the theoretical part of the thesis the mathematical word problem is determined, and it is focused on the word problem on the level of language and context. The cognitive functioning of pupil is described as well as the two problem solving approaches - narrative and paradigmatic by J. S. Bruner, and their application during solving the word problem according to O. Chapman's elaboration. Furthermore the definition of word problem and specification of non-standard word problem in curriculum document FEP BE is described. The practical part is based on qualitative research. The research is designed to provide objective information about the teachers' approach to the word problem and teachers' way of working with language and...
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Ways and strategies of 10-12 years old pupils when solving selected type of word problems
Strnádková, Ivana ; Jirotková, Darina (advisor) ; Hejný, Milan (referee)
Title: Ways and strategies of 10-12 years old pupils when solving selected type of word problems Abstract This Diploma thesis is focused on word problems that, to some extent, make pupils troubles with their solution. In the first theoretical part there are word problems that the work deals with. These are word problems with ant signal, dynamic, complementary, graphic and their characteristics. The next section is about the strategy of solving word problems and work with mistakes. The second part is focused on experiment of all types of word problems that are described in the theoretical part. This experiment is analysed according to strategies of pupils' and teachers' solutions. Those strategies are later described and commented in detail. Key words word problem, solving strategy, mistake, source of mistake, grasping of word problem
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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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Solving strategies for word problems that can be solved with equations
Chromá, Stanislava ; Novotná, Jarmila (advisor) ; Pilous, Derek (referee)
The aim of this work is to get acquainted with the issue of solving word problems by means of equations, to state and to analyse various ways of solving them. The thesis also includes the comparison of strategies for solving word problems that are selected by students who have been already taught the given type of the equation, and students who have not yet mastered these procedures. The introductory part of the work deals with word problems in general. There the terms such as the word problems, procedures, methods and strategies used for solving word problems are specified. In the next part of the text, the basic types of equations are characterized. For each type of the equation, one typical word problem was selected and it was experimentally found out which solving strategies were used by students most often. Keywords: word problem, algebraic equation, non-algebraic equation, system of equations
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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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