Resumo

PARRAGUEZ, Marcela  e  OKTAC, Asuman. Development of a vector space schema. Paradígma [online]. 2012, vol.33, n.1, pp.103-134. ISSN 1011-2251.

We apply APOS theory and the Intra-Inter-Trans triad with the aim of explaining the development of a vector space schema. We characterize the levels of the development of this schema, starting from a genetic decomposition, which is the result of a theoretical analysis that indicates a possible way with which students can construct the vector space concept. Based on this theoretical analysis we designed a semi-structured interview with the purpose of verifying the viability of the mental constructions predicted by the preliminary genetic decomposition. Interview questions were designed in such a way as to obtain relevant information about the development of a vector space schema. This interview was applied to a group of students majoring in mathematics. Analysis of the results obtained from the empirical data allows a refinement of the initial theoretical analysis and a better characterization of the levels of a vector space schema. This theoretical analysis, in addition to being a learning model, serves as a didactic tool pointing to teaching strategies for the vector space concept.

Palavras-chave : APOS theory; Schema; Intra-Vector Space Level; Inter-Vector Space Level; Trans-Vector Space Level.

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