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- Title
LOS MODOS DE PENSAMIENTO SINTÉTICO Y ANALÍTICO EN LA COMPRENSIÓN DEL CONCEPTO DE BASE EN EL ESPACIO VECTORIAL R²: UN ESTUDIO DE CASOS EN UN CONTEXTO UNIVERSITARIO.
- Authors
Parraguez, Marcela; Vera-Soria, Guadalupe
- Abstract
An investigation on the understanding of the concept of basis in the vector space R² in university students is presented, based on the model of Sierpinska's modes of thought. The objective of the research was to describe how the process of constructing the meaning of the act of understanding the base concept for R², when three ways of thinking the Basis in vector space R² are articulated: through the synthetic-geometric-Basis of R², the analytical-arithmetic-Basis of R² and the analytical-structural-Basis of R². The documents derived from interviews carried out with six students from the Engineering area, who previously tackled activities for the exploration of the concept of basis for R² in a graphical-algebraic environment, were organized according to the comprehension operations that it was possible to highlight during the process of abstraction of mental operations to describe the act of understanding the concept of basis for R² synthesis, generalization, discrimination or identification. Subsequently, a hermeneutical analysis of the meanings that these students assigned to the notions of linear combination, generating set and linear independence, was indicative that some relationships, such as linking the idea of generating with a continuous variation of linear combinations in R², or recognizing that there is not a single way to generate the R² vector space, are key elements to achieve the understanding the notion of Basis for R² as a conceptual system.
- Subjects
VECTOR spaces; COMPREHENSION; COLLEGE students; ENGINEERING students; GENERALIZATION; EMOTION recognition
- Publication
Paradigma, 2020, p600
- ISSN
1011-2251
- Publication type
Article
- DOI
10.37618/paradigma.1011-2251.2020.p600-635.id813