Scientia et Technica Año XXVIII, Vol. 28, No. 04, octubre-diciembre de 2023. Universidad Tecnológica de Pereira
The aforementioned motivated to give a proposal to develop
educational innovation actions as proposed by (Leal, Rojas,
Ortiz, & Monrroy, 2020) which is achieved through the
transformation of academic activities and not only the
incorporation of new resources so "innovating means opening
horizons, generating an investigative interest, enjoying the
pleasure of inquiring, discovering, proposing, evaluating, but
above all of inventing. It is about advancing in a critical stance
towards existing postulates, because only when it becomes a
subject of reflection, research and questioning is it possible to
innovate" (Salcedo, 2016, as cited in Leal, Rojas, Ortiz, &
Monrroy, 2020) on the other hand "despite the ethereal nature
of the term, pedagogical innovation alludes to the
systematisation and recognition of transformative practices and
as such is an opportunity to make visible and recognise
pedagogical practices according to the needs of the context"
(Gómez 2016, as cited in Leal, Rojas, Ortiz, & Monrroy, 2020).
This is how the incorporation of the mathematical software
SageMath (SageMath, 2022) is proposed, of which we have the
manual (Bard, 2014) and for the specific application of this
software to Linear Algebra with the book (Hefferon, 2021).
We consider this SageMath software as a TAC (Technology of
Learning and Knowledge) since we intend to guide and focus
the Information and Communication Technology (ICT) for
educational uses together with an active methodology in order
to improve the teaching-learning process in the classroom as
suggested by (Unir, 2021), (Lozano, 2011), (Moya, 2013),
corresponding to the need raised in the conclusions of the
conference (Maya & Pino, 2019) to innovate in Engineering
education and attending to multidisciplinarity from the
teaching-learning of mathematics and in particular for the study
of some topics of the subject Linear Algebra, such as solutions
of systems of linear equations and geometric interpretation in
the plane and in three-dimensional space, given the difficulties
of students to face the study of these topics as stated in
(Rodriguez, 2011), (Avilez, Romero, & Vergara, 2016),
(Rosales, 2010).
SageMath is a free program, which can be used as an online or
desktop application, and also allows working with the Python
programming language, which is used in some of the activities
of this project at a basic level, to create small routines and
provide solutions to application problems where conceptual
knowledge of Linear Algebra is required, thus managing to
incorporate them in a transversal way to programming skills
that this academic programme promotes as considered by
(Bravo, Cedeño, Coello, Coello, & Guerrero, 2019).
This proposal seeks to close the gap between the way current
students learn and the traditionally implemented methodology,
highlighting the importance of the implementation of
technological tools in the study of linear algebra and how they
contribute to an interactive didactic between teachers and
students, obtaining results such as: low retention in the course
which is evident in the results obtained, better use of teacher-
student meetings, as well as greater receptivity on the part of
the latter towards the subject.
To implement this idea, a guide was created in pdf format
containing the topics corresponding to the subject of Linear
Algebra with applications focused on the Systems Engineering
programme. This guide, as the topics are developed, presents
instructions on how to use SageMath by means of concrete
examples.
Initially, the software is used to perform numerical calculations
and simplify problem solving. As the course progresses,
routines are implemented through functions created in Python,
under the SageMath environment, which challenge the student
to apply their basic programming knowledge and create
routines to solve problems in Linear Algebra. Engaging the
student in a learning environment characterised by problem
analysis, exploration, discovery, conjecture and verification of
results.
The designed guide includes workshops to enhance the
student's ability to analyse, demonstrate, verify, interpret,
conjecture and apply the different concepts of linear algebra.
This paper presents the results of this didactic research, in the
teaching and learning of some concepts of Linear Algebra, at
the end statistical data are presented that allow us to identify the
impact on the academic performance of students when the
subject of Linear Algebra is developed with the support of
SageMath in the academic periods from 2014 to 2022.
II.
METHODOLOGY
For the development of this work, qualitative research is chosen
as a method, since, through it, a problem is studied that allows
the collection and analysis of direct data of reality in this case
of the solutions proposed by the students through the Sage-
Math software, and activities that allow to observe more
frequent errors in the resolution of the proposed problems. Then
an interpretation is made with the students' notes in the course
of six semesters.
According to Belloch, the stages of evolution in the use of
technological resources by teachers are: access, adoption,
adaptation, appropriation and invention (Belloch, 2012), this
work has been developed in an evolutionary way in the first
three stages, since it was necessary to train in the use of the
mathematical software SageMath, identify activities with this
software for the punctual support in the subject of Linear
Algebra aimed at systems engineering students and finally the
technology has been integrated with the previous knowledge of
programming that students have for the teaching-learning
process of this subject.
In methodological terms, the students are guided by the teacher
in the study of topics related to the solution of systems of linear
equations and proposed problems that require the creation of
functions in the Python programming language under the
SageMath environment to obtain possible solutions. For this
study, a problem is identified as an activity that requires
different complex cognitive processes to work together to find
the mechanism that allows them to be solved, mediated by the
technological-computer resource: SageMath software that
enhances students' ability to discern the correct information and
generate the environment to solve the problem, which cannot
be solved automatically and requires relating diverse
knowledge, on the other hand they do not necessarily have a
single solution path, allowing them to generate and modify
knowledge while developing skills and abilities by practising
what they have learnt, awakening their interest and motivation.
This work seeks to provide challenges and strategies in the
teaching of Linear Algebra, which, as in (Andrews, Berman,