The new outcomes based education (OBE) in the form of the Revised National Curriculum Statements (RNCS, 2002) advocates for the use of contexts in the teaching and learning of mathematics. The motivation for this advocacy is the expectation of the promotion of understanding of the subject. Such expectations however cannot be achievable without consideration of factors such as what contexts are appropriate for use in the teaching and learning of mathematics, how the contexts have to be used in order to promote understanding and more importantly how are teachers involved in this process. The study explores the ways in which a Grade 7 teacher selects contexts in the learning support materials or in any other source for use in order to promote understanding of the concept of variable among learners. It draws on socio-cultural theories and is underpinned by the notion that understanding of a concept presupposes and is presupposed by the formation of the concept. The research method employed was a case study and data was mainly collected through interviews as well as materials that were availed by the teacher. The following three key issues emerged from the study and were taken up for discussion: a) what does it take to make the transition from context to mathematics in terms of the promotion of the understanding of the concept of variable? b) to what extent were the materials selected by the teacher adequate to deal with issues of transition from context to mathematics in terms of the promotion of the understanding of the concept of variable? and c) what possibilities were available for the teacher to use context in order to promote understanding of the concept of variable? This study further explores the extent to which the notions of mathematisation and transition from context to mathematics may be used as the means by which the selection and use of contexts in the learning and teaching of the concept of variable may facilitate the promotion of understanding of the concept variable.

Physical experiments have a great potential in mathematics lessons. Students can actively discover how mathematical concepts are used. This paper shows results of research done how students got to know the different aspects of the concept of variable by doing simple physical experiments. Further it will be shown what other concepts could be touched by the same treatment.

Physical experiments have a great potential in mathematics lessons. Students can actively discover how mathematical concepts are used. This paper shows results of research done how students got to know the different aspects of the concept of variable by doing simple physical experiments. Further it will be shown what other concepts could be touched by the same treatment.

Made available in DSpace on 2016-04-27T16:58:55Z (GMT). No. of bitstreams: 1 Rosania Maria da Silva.pdf: 1668777 bytes, checksum: 69484135dcc7276b463fc0748a8ce902 (MD5) Previous issue date: 2009-05-22 / Secretaria da Educação do Estado de São Paulo / This report refers to a case study that aimed to check the understanding and usage of the variable for students of eighth grade, in questions that involving their symbolization, interpretation and manipulation. Thus, we used a tool called the theoretical and methodological the three uses of variable model (3UV), presented by Trigueros and Ursini (2001). This model relates the skills necessary to understanding the three main uses of the variable in school algebra: unknown number, general number and variables in functional relationship. As a methodological tool it was used to design a questionnaire to identify the meanings and uses of the variable by seventeen students of a public school in the city of São Paulo. Besides the application of the questionnaire, which was attended by an observer, were used in audio recordings and semi-structured interviews as tools for collecting information. The set of data was analyzed taking as references the Model 3UV and aspects that, according Caraça (1954) summarize the concept of variable: the symbolic and substantial. The results show the difficulty of symbolization, especially when it should be variable of roles in general number or functional relationship. The interpretation, these students, when questioned, citing the variable as a representative of any values, but not always referring to all that it represents, but also its coefficient. In procedures for manipulation, indicating a lack of interpretation of the variable in algebraic sentences, showing the predominance of the use of algorithms for the resolution and lack of understanding of the solutions obtained, even when used correctly. The results also show that the symbolic and substantive issues stand out, separately, depending on what the question requires / Este relatório se refere a um estudo de caso que teve por objetivo verificar a compreensão e os usos da variável por alunos de oitava série, em questões que envolvem sua simbolização, interpretação e manipulação. Para tal, foi utilizada uma ferramenta teórico-metodológica denominada Modelo dos três usos da variável (3UV), apresentada por Trigueros e Ursini (2001). Tal modelo relaciona as habilidades necessárias ao entendimento dos três principais usos da variável na álgebra escolar: incógnita, número genérico e variáveis em relação funcional. Como ferramenta metodológica foi utilizado na elaboração de um questionário para identificar os significados e usos da variável por dezessete alunos de uma escola da rede estadual da grande São Paulo. Além da aplicação do questionário, que contou com a presença de um observador, foram utilizadas gravações em áudio e entrevistas semi-estruturadas como instrumentos de coleta de informações. O conjunto de dados obtido foi analisado tomando como referências o Modelo 3UV e os aspectos que, segundo Caraça (1954) sintetizam o conceito de variável: o simbólico e o substancial. Os resultados mostram a dificuldade de simbolização, principalmente quando deve ser por variáveis nos papéis de número genérico ou em relacionamento funcional. Quanto à interpretação, esses alunos, quando questionados, citam a variável como representante de quaisquer valores, porém, nem sempre se referindo ao conjunto que ela representa, mas também ao seu coeficiente. Em procedimentos de manipulação, indicam a falta de interpretação da variável nas sentenças algébricas, mostrando o predomínio do uso de algoritmos para a resolução e a falta de entendimento das soluções obtidas, mesmo quando foram utilizados corretamente. Os resultados também apontam que os aspectos simbólico e substancial se destacam, separadamente, dependendo do que requer a questão