Cognitive Construction of the R² Vector Space

Jara, Miguel Rodríguez; Parraguez, Marcela; Gaismán, María Trigueros

doi:10.12802/relime.18.2113

Cited by 4 publications

(2 citation statements)

References 24 publications

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“…El conjunto solución en este caso, puede ser generado por un subconjunto finito de sus elementos. También es desde el análisis o depuración de estos conjuntos generadores mediante los conceptos de combinación lineal e independencia lineal que se logra establecer el conjunto mínimo de elementos que puede formar un conjunto generador y aproximarnos así a los conceptos de base y dimensión (Parraguez, 2009).…”

Section: Euler Y Una Histórica Primer Mirada Cualitativa a Los Sistem...unclassified

Enseñanza del álgebra lineal a partir de una mirada cualitativa de los sistemas de ecuaciones lineales

Guzmán

2023

Prax. Educ. Pedagog.

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Se presenta una reflexión a partir del trabajo de Leonhard Euler: “Sobre una aparente contradicción en la teoría de las líneas curvas”, mostrando la proximidad de esta obra con algunos de los principales conceptos del álgebra lineal. Se aplica una aproximación documental, no exhaustiva, para señalar, tanto en el contexto histórico de las matemáticas, como en el salón de clases, cómo la aparición de nuevos métodos de solución (algoritmos) pueden tener un efecto retardante en la construcción de nuevos conocimientos, y por último,se caracteriza y presenta el obstáculo epistemológico llamado “El paradigma de la solución”.

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Section: Euler Y Una Histórica Primer Mirada Cualitativa a Los Sistem...unclassified

Enseñanza del álgebra lineal a partir de una mirada cualitativa de los sistemas de ecuaciones lineales

Guzmán

2023

Prax. Educ. Pedagog.

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“…Focusing on the Latin American context, studies such as that of Bianchini et al (2019) offer a review of the research studies on the teaching and learning of linear algebra in undergraduate engineering programs; their findings however do not include the study of SLE, namely because the topic is not always considered to be fundamental in linear algebra but rather it is seen as a tool to solve linear algebra problems. The authors' analysis shows that the studies carried out have focused on promoting the learning of other topics, namely the concept of vector spaces and associated concepts, such as basis of a subspace (Parraguez, 2009), linear transformations (Silva, 2016), theorems on the matrix of a linear transformation (Roa-Fuentes & Parraguez, 2017), and eigenvalues and eigenvectors (Salgado & Trigueros, 2015), all considered as highly abstract for most undergraduate students who take a linear algebra course (Costa & Rossignoli, 2017).…”

Section: Previous Studies On Teaching and Learning Of Linear Algebramentioning

confidence: 99%

Undergraduate Students’ Learning of Linear Algebra Through Mathematical Modelling Routes

Ramírez-Montes

Henriques

Carreira

2021

Can. J. Sci. Math. Techn. Educ.

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Mathematical modelling has acquired relevance at all educational levels in the last decades since integrating this activity in instruction provides significant contexts for improving students' learning, including in linear algebra courses that have a notable presence in many undergraduate courses from different fields, including engineering and sciences. This paper reports a study aiming to characterize the distinct modelling routes performed by Costa Rican undergraduate students when solving a mathematical modelling task involving the concept of system of linear equations (SLE). In analysing those modelling routes, it was possible to identify their learning of linear algebra concepts and their modelling competencies as well as the associated difficulties that students faced. Data collection included participant observation, with audio recording of the students' discussions, their written work on the task and digital files of their work with technology. The results show that non-linear routes are associated with a greater mobilization of students' knowledge on SLE concepts and with their development of modelling competencies. The results also highlight the need to improve the students' competency of validating results, an important step that they did not take, and suggest the need to make technology relevant to the students' work on modelling tasks.

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Mental constructions for the learning of the concept of vector space

Trigueros,

Cabrera,

Aguilar

2024

ZDM Mathematics Education

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This study contributes to the literature on linear algebra instruction by designing and researching a teaching sequence based on APOS Theory to introduce engineering students to vector spaces. The sequence offers students multiple opportunities to understand the concept. Another contribution is the evidence that introducing prerequisite concepts—such as equality, sets, and binary operations—before tackling vector space was crucial for grasping the role of proof in determining whether a set is a vector space. The findings confirm that, as other studies have shown, vector space is challenging for students. However, the results demonstrate that students were able to face this challenge. All students showed evidence of developing an understanding of the concept, with nine achieving a clear grasp of vector space and the role of proof by the end of the experience. Additionally, the progress observed—from having difficulties with symbols to successfully proving statements involving unconventional operations—underscores the effectiveness of the teaching approach.

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Cognitive Construction of the R² Vector Space

Cited by 4 publications

References 24 publications

Enseñanza del álgebra lineal a partir de una mirada cualitativa de los sistemas de ecuaciones lineales

Enseñanza del álgebra lineal a partir de una mirada cualitativa de los sistemas de ecuaciones lineales

Undergraduate Students’ Learning of Linear Algebra Through Mathematical Modelling Routes

Mental constructions for the learning of the concept of vector space

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