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...

Made available in DSpace on 2016-04-27T16:57:46Z (GMT). No. of bitstreams: 1 EDM - Danilo S Christo.pdf: 629300 bytes, checksum: 0ef0463bceff1c7bfe0b4f7fdda99796 (MD5) Previous issue date: 2006-10-31 / Students difficulties in writing and interpreting algebraic language, particularly in comprehending the meaning of variable have been discussed by such researchers as Kieran, Küchemann, Arcavi and others. In this research, we evaluate a teaching proposal in which it is aimed at explaining established relations between elements of circumstances of proportionality and generalizable arithmetic expressions. This analysis of regularity eases the algebraic language teaching through a dynamic approach in which the notion of dependence among the circumstantial variables is emphasized. This proposal was applied to a sixth grade group of a public primary school in São Paulo city. The analysis of the obtained results allows us to verify the teaching proposal s efficiency for attaining the objectives of this research and provides tools for training teachers / Dificuldades dos alunos na escrita e interpretação da linguagem algébrica e, em particular, na compreensão do significado de variável, têm sido discutidas por pesquisadores como Kieran, Küchemann, Arcavi, entre outros. Nesta pesquisa, avaliamos uma proposta de ensino na qual busca-se descrever as relações estabelecidas entre os elementos de situações de proporcionalidade com as expressões aritméticas generalizáveis. A análise dessas regularidades favorece o ensino da linguagem algébrica, em uma abordagem dinâmica em que se enfatiza a noção de dependência entre as variáveis envolvidas na situação. A proposta foi desenvolvida em uma sexta série do ensino fundamental de uma escola municipal da cidade de São Paulo. A análise dos resultados obtidos permite-nos constatar a eficiência da proposta de ensino para a consecução dos objetivos visados nesta investigação e fornece subsídios para a formação de professores

The study investigated errors made by Grade 9 learners when simplifying algebraic expressions. Eighty-two (82) Grade 9 learners from a rural secondary school in Limpopo Province, South Africa participated in the study. The sequential explanatory design method which uses both quantitative and qualitative approaches was used to analyse errors in basic algebra. In the quantitative phase, a 20-item test was administered to the 82 participants. Learners’ common errors were identified and grouped according to error type. The qualitative phase involved interviews with selected participants. The interviews focused on each identified common error in order to establish the reasons why learners made the identified errors. The study identified six (6) common errors in relation to simplifying algebraic expressions. The causes of these errors were attributed to poor arithmetic background; interference from new learning; failure to deal with direction and operation signs; problems with algebraic notation and misapplication of rules. / Mathematics Education / M. Ed. (Mathematics Education)