2010
DOI: 10.1016/j.laa.2009.06.034
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Construction of the vector space concept from the viewpoint of APOS theory

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Cited by 47 publications
(15 citation statements)
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“…Numerous frameworks explicitly include a theoretical analysis as an initial step in their research cycle, as is the case of the APOS theory (Arnon et al, 2014), whose theoretical analysis culminates in the socalled preliminary genetic decomposition. This is a hypothetical model of the mental structures and mechanisms that a student may need to build a specific mathematical concept: numerical sequence (Bajo, Gavilán-Izquierdo, & Sánchez-Matamoros, 2019), linear transformation (Roa-Fuentes & Oktaç, 2010), derivative (Borji, Alamolhodaei, & Radmehr, 2018), vector space (Parraguez & Oktaç, 2010), eigenvectors and eigenvalues (Salgado & Trigueros, 2015); among others. In these works, the authors carry out their theoretical analyses based on one or more data sources: researchers' mathematical understanding of the concept, their experiences as teachers, prior research on students' thinking about the concept, historical perspectives on the development of the concept, and/or an analysis of text or instructional materials related to the concept (Arnon et al, 2014).…”
Section: Methodsmentioning
confidence: 99%
“…Numerous frameworks explicitly include a theoretical analysis as an initial step in their research cycle, as is the case of the APOS theory (Arnon et al, 2014), whose theoretical analysis culminates in the socalled preliminary genetic decomposition. This is a hypothetical model of the mental structures and mechanisms that a student may need to build a specific mathematical concept: numerical sequence (Bajo, Gavilán-Izquierdo, & Sánchez-Matamoros, 2019), linear transformation (Roa-Fuentes & Oktaç, 2010), derivative (Borji, Alamolhodaei, & Radmehr, 2018), vector space (Parraguez & Oktaç, 2010), eigenvectors and eigenvalues (Salgado & Trigueros, 2015); among others. In these works, the authors carry out their theoretical analyses based on one or more data sources: researchers' mathematical understanding of the concept, their experiences as teachers, prior research on students' thinking about the concept, historical perspectives on the development of the concept, and/or an analysis of text or instructional materials related to the concept (Arnon et al, 2014).…”
Section: Methodsmentioning
confidence: 99%
“…The definitions of APOS theory are (a) Action is a transformation of mental objects to obtain other mental objects and a person is said to experience an action if the person is focusing his mental processes on the effort to understand a given concept; (b) Process is when an action is repeated, then a reflection of action takes place, thus come into a process phase and a person is said to experience a process of a concept if the thinking is limited to the mathematical idea encountered and characterized by the presence of the ability to perform reflection to the mathematical idea; (c) Object is a person who already has the object conception of a mathematical concept, if he has been able to treat the idea or concept as a cognitive object that includes the ability to act on the object, and provide a reason or explanation of its nature and has been able to deconstruct an object into a process whereby it the natures of the object will be used; (d) Scheme is a schema of a particular mathematical material that is a collection of actions, processes, objects, and other schemes that are connected so that form an interrelated framework within the mind of a person, with scheme indicator that is if the person has the ability to construct examples of a mathematical concept in accordance with the natures of the concept. Accordingly, students are required to have the ability to integrate the use of computers, learning in small groups, mathematics connection and creative thinking to understand a mathematical concept [18,22].…”
Section: A Apos Theorymentioning
confidence: 99%
“…Existen numerosas investigaciones que ofrecen evidencias sobre las dificultades que muestran los estudiantes para comprender y aprender diferentes conceptos de álgebra lineal, en tópicos como transformación lineal (Roa-Fuentes y Parraguez, 2017), coordenadas de vectores (Parraguez, Lezama y Jiménez, 2016), base de un espacio vectorial (Arnon et al, 2014), combinación lineal (Parraguez y uzuriaga, 2014), espacios vectoriales sobre cuerpos finitos (Weller et al, 2002), espacios vectoriales sobre un cuerpo (Parraguez y Oktaç, 2010), entre otros. Investigadores franceses (dorier, 1995) nos hablan del obstáculo del formalismo.…”
Section: Introductionunclassified