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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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Problem posing for limits of functions
Prskavcová, Pavla ; Pilous, Derek (advisor) ; Kvasz, Ladislav (referee)
Title: Problem posing for limits of functions Author: Pavla Prskavcová Department: Department of Mathematics and Mathematical Education Supervisor: Mgr. Derek Pilous, Ph.D. The aim of the thesis is to describe methods of limit problems solving and of posing new problems that are solvable by those methods. The first part of the thesis contains the necessary theory (definitions and theorems). In the second part of the thesis there are described the standard methods used for evaluating containing limits. The third part suggest ways of posing problems solvable by using elementary methods, based on the analysis of methods describes in the se- cond part of the thesis (without usage of the differential calculus). Keywords: limit, problem solving, problem posing, elementary function.
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Interpretation of calculations in word problems - looking for a question
Legová, Tereza ; Vondrová, Naďa (advisor) ; Jančařík, Antonín (referee)
Title: Interpretation of calculations in word problems - looking for a question Author: Tereza Legová Department: Department of Mathematics and Mathematical Education Supervisor: prof. RNDr. Naďa Vondrová, Ph.D., Department of Mathematics and Mathematical Education Abstract: This thesis deals with an exploratory study of the introduction of modified word problems into the teaching of mathematics. The modification of the classical word problem consists in setting the context of the word problem and calculation. The task of pupils is to find out what we get by the given calculation, what question the calculation answers and substantiate their claims. The aim of the thesis was to describe how pupils think in solving this type of problem. Specifically, it investigated what strategies pupils elect and what difficulties arise in solving. The theoretical part of the thesis is a search of literature on the topic of solving word problems and their possible implementation in teaching. The practical part is divided into two phases. A test consisting of three problem contexts was given to pupils. The aim was to determine the meaning of the three given calculations for the each context. Before solving the test, a sample problem was discussed with the pupils. In the first phase, interviews were conducted with six pupils...
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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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Problem posing for limits of functions
Prskavcová, Pavla ; Pilous, Derek (advisor) ; Kvasz, Ladislav (referee)
Title: Problem posing for limits of functions Author: Pavla Prskavcová Department: Department of Mathematics and Mathematical Education Supervisor: Mgr. Derek Pilous, Ph.D. The aim of the thesis is to describe methods of limit problems solving and of posing new problems that are solvable by those methods. The first part of the thesis contains the necessary theory (definitions and theorems). In the second part of the thesis there are described the standard methods used for evaluating containing limits. The third part suggest ways of posing problems solvable by using elementary methods, based on the analysis of methods describes in the se- cond part of the thesis (without usage of the differential calculus). Keywords: limit, problem solving, problem posing, elementary function.
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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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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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Problem solving and problem posing (not only in teacher training)
Hošpesová, A. ; Tichá, Marie
Problem solving we can support by problem posing. The paper shows the different possibilities of problem posing (to a given calculation, to the given data or results, to given structure) and their illustrations through problems posed by students and teachers. It is outlined that problem posing can be understood as a goal of education, training and diagnostic tool and as a source of motivation.
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