Detalhes bibliográficos
| Ano de defesa: |
2019 |
| Autor(a) principal: |
Paias, Ana Maria
 |
| Orientador(a): |
Ag Almouloud, Saddo |
| Banca de defesa: |
Não Informado pela instituição |
| Tipo de documento: |
Tese
|
| Tipo de acesso: |
Acesso aberto |
| Idioma: |
por |
| Instituição de defesa: |
Pontifícia Universidade Católica de São Paulo
|
| Programa de Pós-Graduação: |
Programa de Estudos Pós-Graduados em Educação Matemática
|
| Departamento: |
Faculdade de Ciências Exatas e Tecnologia
|
| País: |
Brasil
|
| 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/22519
|
Resumo: |
An obstacle is knowledge, a conception and it is not a difficulty or lack of knowledge, uncertainty or chance. This knowledge produces appropriate responses in a particular context, but it generates erroneous answers out of this context, being unforeseeable errors. The objective of this work is to identify which epistemological and / or didactic obstacles are present in the teaching and learning processes of the mathematical power object. It was a basic study with a qualitative approach. Initially, potentiation was discussed as a representation record of the mathematical power object. A study of the mathematical power object was developed, based on the cognitive and epistemological approaches. The cognitive approach contemplated the cognitive analysis, in which it was made an appreciation of certain questions of the diagnostic instrument applied in Paias, with semantic congruence analysis of these questions. The epistemological dimension was developed by a historical study and the elaboration of the epistemological model of reference, based on Chevallard. An ecological analysis was performed that identified habitats and power niches, through documents such as PCN, PCNEM + and BNCC. A study was carried out with researches that approach the power theme in Brazil and outside the country. From the data, the analysis was made, identifying the following obstacles. The epistemological obstacles are: inability of the perception of potentiation, as a representation record of the mathematical power object; rupture of the power definition for unnatural exponents; understanding the zero exponent as nothing, heterogeneity of meaning in conversions and induction of multiplication when the exponent is 1 understanding that the base is multiplied only once. As for the didactic obstacles identified are: discontinuous generalization; Exiguity in the proposals of problems related to the mathematical power object; inadequate use of conventions; the existence of mathematical symbols in the calculation of powers and the conflict of the bad example, comprehensiveness in the application of power properties , triviality in the conversions presentation between natural and algebraic language registers and suppression of power with rational fraction in some textbooks |
