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Changes in pupils' understanding of models of fractions
Hillebrandová, Eliška ; Janda, David (advisor) ; Kvasz, Ladislav (referee)
Fractions are a dreaded topic not only for students but also for teachers. The reason is that it is a breakthrough subject in primary schools, without which one cannot successfully continue in further studies. Therefore, in the first chapter of this thesis we will focus on understanding fractions through visual models (discrete and continuous - chocolate, circle, line segment, rectangle) that can be commonly found in textbooks aimed at teaching fractions. In the second chapter, using action research tools, we investigated how students' understanding changed over time following the interventions. The research consisted of two pilot tests and three iterations of the test over a two-month period in three seventh grade classes in a Prague elementary school. Specifically, the test focused on part-from- whole and whole-from-part search for the following three models: the discrete ordered model, the fraction-as-part-of-an-area model in a lattice network, and the number axis model. All results were graphically processed using tables, boxplots and we relied on statistical tests. In the third chapter, we summarized these results in detail and also pointed out the shortcomings of the research and how they can be addressed. It showed that there was a positive change in students' understanding of fraction...
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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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Inquiry based mathematics education: case of fractions
Podhajská, Kristýna ; Tichá, Marie (advisor) ; Novotná, Jarmila (referee)
The theoretical part deals with approaches to teaching, especially constructivistic, instructivistic and transmissive approach. The goal of this part is to compare the approaches and evaluate them considering the permanency of knowledge and active engagement of students. Simultaneously it aims at evaluating the approaches from the point of their of the mechanical knowledge. The charter dealing with inquiry based mathematics education is focused on teaching related to constructivistic approach. The next chapter describes tool called concept cartoons, which can be used as a mean to research. The theoretical part is focused on the topic of fraction, especially fraction interpretation and models and fraction representation. The second part of the thesis describes a survey realized at basic school. I narrowed the problem to fraction interpretation and representation according to survey of student's work. The next part of research is based on this analysis. Trying to accomplish the aims and find the answers to questions of the survey I chose strategy inspired by action research, because the main goal of the research was to improve and enhance my teaching knowledge and skills. The survey was processed qualitatively. The making of the thesis helped me make it clear, why the topic of fractions is so...
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Inquiry based mathematics education: case of fractions
Podhajská, Kristýna ; Tichá, Marie (advisor) ; Novotná, Jarmila (referee)
The theoretical part deals with approaches to teaching, especially constructivistic, instructivistic and transmissive approach. The goal of this part is to compare the approaches and evaluate them considering the permanency of knowledge and active engagement of students. Simultaneously it aims at evaluating the approaches from the point of their of the mechanical knowledge. The charter dealing with inquiry based mathematics education is focused on teaching related to constructivistic approach. The next chapter describes tool called concept cartoons, which can be used as a mean to research. The theoretical part is focused on the topic of fraction, especially fraction interpretation and models and fraction representation. The second part of the thesis describes a survey realized at basic school. I narrowed the problem to fraction interpretation and representation according to survey of student's work. The next part of research is based on this analysis. Trying to accomplish the aims and find the answers to questions of the survey I chose strategy inspired by action research, because the main goal of the research was to improve and enhance my teaching knowledge and skills. The survey was processed qualitatively. The making of the thesis helped me make it clear, why the topic of fractions is so...
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Creating images of fraction at the elementary school
Siblíková, Marta ; Tichá, Marie (advisor) ; Macháčková, Jana (referee)
This thesis "Creating images of fraction at the elementary school" is divided into theoretical and practical part. The theoretical part defines the subject matter of fractions in curriculum, deals with a mathematical literacy concept and introduces basic conceptions related to fractions and propaedeutic of fractions at the Primary School. The practical part consists of a preparatory research and a consequential research. The goal of the preparatory research is fractions knowledge mapping on Primary School pupils comparing to an expert knowledge acquired in the theoretical part. The consequential research focuses on confirming results of the preparatory research, respectively preferring the circle model off other models. It also checks if pupils get acquainted with other models (line segment, rectangle, and set of discrete objects). Key words Fraction, propaedeutic, models, representation, primary education, curricula.
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Rational numbers for the future teachers on primary school
SVITÁKOVÁ, Jana
This thesis presents comprehensive study material relating the subject of rational numbers for students trained to be teachers at primary school. I am mainly concentrating on qualities of racional numbers and their methodology in the theoretic part. I am checking the level of school knowledge in the subject of racional numbers in the operative part. I was concentrated on pupils at 2nd and 4th classes of Primary School in Choustník and on students of the pedagogical faculty at South Bohemia University in České Budějovice. Task collection for students trained to be teachers at primary school and also for teachers in profession is part of my thesis.
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