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Understanding of algebraic expressions by pupils of higher primary schools
Jelínek, Patrik ; Kvasz, Ladislav (advisor) ; Vondrová, Naďa (referee)
This master's thesis focuses on the understanding of algebraic expressions by higher primary school pupils. The objective is twofold. First, to determine, based on the quantita- tive evaluation of research data, the most common mistakes pupils make under the headings of generalization, algebraization, interpretation, geometrization, & manipu- lation; and then second, to compare the introduction of algebraic expressions in different mathematics textbooks. Beyond this, a theory is also appended. Including several research results, literature review also delves into several activities effective in enhancing pupils' understanding of algebraic expressions, as well as an illustration of their typical errors associated to the aforementioned headings. The second part of the thesis then consists of the two-part textbook analysis: First, a qualitative analysis of authors' reasoning when validating modifications of algebraic expressions, and then a quantitative analysis of the algebraic tasks concerning the headings (i.e., the creation of a task overview). The third part of the paper finally evaluates the author's research. With the test sample of 207 pupils selected from the last years of compulsory education, two additional objectives were set out - first, to find out which tasks (according to said...
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Teaching algebraic expressions using algebra tiles
Kuchaříková, Gabriela ; Vondrová, Naďa (advisor) ; Novotná, Jarmila (referee)
The primary goal of this thesis is to prepare and carry out an education programme on algebraic expressions with variables for eight grade primary school students. This is so they can understand the basic principles of operations with simple algebraic expressions. The secondary goal was to determine whether this education method can also be applied in an online environment, which became a necessity during the Covid-19 pandemic. The theoretical chapter of the thesis covers the introduction of the symbolic language of algebra and the ways of understanding a letter (variable). It contains the definition of basic algebraic terminology in a primary school environment as well as an analysis of select textbooks. Additionally, student work levels with algebraic expressions and a categorization of students' mistakes in operations are used as supplementary grounds for the experimental chapter of the thesis. Finally, the two types of algebra tiles are presented. The experimental chapter of the thesis is aimed at the propaedeutics of algebra tiles via operations with integers, at teaching variable expressions using algebra tiles and at expanding the method of teaching expressions in primary school (Vieta's formulas, completing the square). This chapter's sections cover the respective expression operations and...
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Pupils' Problems and Mistakes when Manipulating Algebraic Expressions
Bílek, Vladimír ; Vondrová, Naďa (advisor) ; Žalská, Jana (referee)
The thesis focuses on mistakes and problems in manipulations with the algebraic expressions occurring to pupils at the second level of Elementary school. The thesis is divided into a theoretical and experimental part. The theoretical part contains description of manipulations with algebraic expressions, selected results of international comparative surveys, and an analysis of related foreign research. Analysis of three series of textbooks, according to which pupils involved in the experimental project are taught, is essential for understanding of possible origins of their mistakes. The classification of mistakes in manipulations with algebraic expressions is included. At the core of the work is the experimental part aiming to identify problems and mistakes of pupils when manipulating and working with algebraic expressions. The participants of the research consisted of six third-grade pupils of an eight-year Grammar school (13-14 years old) and eight ninth-grade pupils of an Elementary school (14-15 years old). Test used for my experiment came from the GA ČR project Critical parts of mathematics in primary school. The investigation was carried out individually with each pupil by the method of monitoring clinical interviews over the solution of the test tasks. The obtained data was qualitatively...
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Pupils' Problems and Mistakes when Manipulating Algebraic Expressions
Bílek, Vladimír ; Vondrová, Naďa (advisor) ; Žalská, Jana (referee)
The thesis focuses on mistakes and problems in manipulations with the algebraic expressions occurring to pupils at the second level of Elementary school. The thesis is divided into a theoretical and experimental part. The theoretical part contains description of manipulations with algebraic expressions, selected results of international comparative surveys, and an analysis of related foreign research. Analysis of three series of textbooks, according to which pupils involved in the experimental project are taught, is essential for understanding of possible origins of their mistakes. The classification of mistakes in manipulations with algebraic expressions is included. At the core of the work is the experimental part aiming to identify problems and mistakes of pupils when manipulating and working with algebraic expressions. The participants of the research consisted of six third-grade pupils of an eight-year Grammar school (13-14 years old) and eight ninth-grade pupils of an Elementary school (14-15 years old). Test used for my experiment came from the GA ČR project Critical parts of mathematics in primary school. The investigation was carried out individually with each pupil by the method of monitoring clinical interviews over the solution of the test tasks. The obtained data was qualitatively...
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