Detalhes bibliográficos
| Ano de defesa: |
2009 |
| Autor(a) principal: |
Lucas, Anderson Barros
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| Orientador(a): |
Coelho, Sonia Pitta |
| Banca de defesa: |
Não Informado pela instituição |
| Tipo de documento: |
Dissertação
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| Tipo de acesso: |
Acesso aberto |
| Idioma: |
por |
| Instituição de defesa: |
Pontifícia Universidade Católica de São Paulo
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| Programa de Pós-Graduação: |
Programa de Estudos Pós-Graduados em Educação Matemática
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| Departamento: |
Educação
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| País: |
BR
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| Palavras-chave em Português: |
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| Palavras-chave em Inglês: |
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| Área do conhecimento CNPq: |
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| Link de acesso: |
https://tede2.pucsp.br/handle/handle/11391
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Resumo: |
The research problem in this work is related to questions raised since the beginning of our professional experience, having reached the status of a research issue during the Postgraduate Studies Program in Mathematics Education of PUC-SP, particularly in the research group named TecMEM (Technologies and Means of Mathematical Expression). Despite the large number of studies on the theme "Functions", we have felt the need to specify the ways in which this issue might be related to the theme "Equations". To accomplish this task, we have proposed the following question: When addressing the various types of functions taught during High School, which are and why are there conceptual discontinuities that lead to erroneous conclusions about the roots of these functions? Supported by previous research on the topic, we have developed an instrument that was applied to twelve students in the second year in High School to diagnose, for example, which knowledge these individuals mobilize to distinguish an equation of a function given by an algebraic expression or, also, to what extent this distinction influences the understanding of the graphs produced by these functions. We have focused on 1st and 2nd degree equations and linear and quadratic functions. For the analysis of the protocols, we have based our analysis on the Theory of Semiotic Representation Records by Raymond Duval and on the methodology of content analysis, identifying the main discontinuities in the natural language records. As one of the most important results obtained in our investigation, we verified that, when looking for roots for a given function, the participant subjects of the research treated her as an equation, trying to solve her and to find one or more values for her independent variable, that in the case was treated as unknown. We highlight the need to encourage school activities addressing conversions between the semiotic representation records required for the understanding of the concepts involved, that encourage students to recognize similarities and differences between those two mathematical objects, which consensually belong to the list of central ideas to be taught in Algebra |
