https://doi.org/10.37955/cs.v5i3.150
Received November 12, 2020 / Approved April, 03 2021 Pages: 71-87
eISSN: 2600-5743
Incidence of virtual learning
environments in the development
of mathematical logical thinking
Incidencia de los entornos virtuales de
aprendizaje en el desarrollo del pensamiento
lógico matemático
MGs. Ángel Cesar Mendoza Hidalgo
Teacher at the Vicente Anda Aguirre Educational Unit, Guayaquil, Ecuador
angelc.mendoza@educacion.gob.ec, https://orcid.org/0000-0003-3088-3775
MGs. Rosana Fátima Álvarez Franco
Teacher at the Vicente Anda Aguirre Educational Unit, Guayaquil, Ecuador
rosana.alvarez@educacion.gob.ec, https://orcid.org/0000-0001-9077-0591
Abstract
This research work shows the lack of knowledge of teachers about the
use of virtual learning environments within the teaching and learning
process. The main objective of the research work was to analyze the
incidence of the use of virtual learning environments in the
development of mathematical logical thinking in academic
performance. The methodology to be used is bibliographic research,
since research has been carried out in books and publications on the
Internet to detail the shortcomings that are being experienced in the
educational establishment. The method used is the scientific method,
since it is the method of systematic study of nature that includes the
observation technique, rules for reasoning and prediction, ideas on
planned experimentation. The experimental and theoretical results
obtained are shown in the analysis table, which were analyzed and
interpreted qualitatively in order to have a more realistic view of the
results. With the conclusions it can be evidenced that, in the
Centro Sur Vol. 5 No. 3 - July September – Revista Centro Sur - eISSN: 2600-5743
72
Received January 12, 2021 / Approved May, 03 2021 Pages: 71-87
eISSN: 2600-5743
Centro Sur Vol. 5 No. 3 - July September
educational unit there is enough resource to implement a module for
the use of virtual learning environment for the development of
mathematical logical thinking.
Resumen
El presente trabajo de investigación muestra el desconocimiento de los
maestros del uso de los entornos virtuales de aprendizaje dentro del
proceso de enseñanza aprendizaje el objetivo fundamental del trabajo
investigativo fue analizar la incidencia del uso de los entornos virtuales
de aprendizaje en el desarrollo del pensamiento lógico matemático en
el desempeño académico. La metodología a utilizar es de tipo de
investigación bibliográfica, pues se ha realizado investigaciones en
libros y publicaciones en internet para detallar las falencias que se está
viviendo en el establecimiento educativo. El método utilizado es el
científico ya que este el método de estudio sistemático, de la naturaleza
que incluye la técnica de observación reglas para el razonamiento y la
predicción, ideas sobre la experimentación planificadas. Los
Resultados experimentales y teóricos obtenidos constan en la tabla del
análisis que fueron analizados e interpretados de manera
cualitativamente para tener una visión más real de los resultados. Con
las conclusiones se puede evidenciar que, en la unidad educativa existe
el recurso suficiente para implementar un módulo de uso de entorno
virtuales de aprendizaje para el desarrollo de pensamiento lógico
matemático.
Palabras clave/ Keywords
Virtual learning environments, Explanatory, Descriptive,
Evolutionary, Feasible.
Entornos virtuales de aprendizaje, Explicativo, Descriptivo, Evolutivo,
Factible.
73
Received January 12, 2021 / Approved May, 03 2021 Pages: 71-87
eISSN: 2600-5743
Centro Sur Vol. 5 No. 3 - July September
Introduction
The present research work on the incidence of virtual learning
environments in the development of logical thinking, the role of
teachers has evolved in recent years. Not only have they had and have
to catch up in the use of technologies in the classroom, but their tasks
have also changed, the teacher acts as a facilitator who encourages
students to discover principles on their own, as a specific objective we
can analyze the aspects that should be considered for the design
module of virtual learning environments for the development of
mathematical logical thinking in the Vicente Anda Aguirre
Educational Unit in the city of Milagro.
In the development of this research, it allows to determine the
incidence of the use of virtual environments in the development of
mathematical logical thinking, this work will be very productive for
students because they will learn to use tools for their academic
development. The use of technology in the classroom makes it possible
to introduce changes in the way of teaching and learning. The use of
these resources favors the acquisition of some of the most useful skills
for students in the future, but, above all, the specific needs of each
student are addressed.
That of teachers has evolved in recent years. Not only have they had
and still have to catch up with the use of technologies in the classroom,
but their tasks have also changed. The teacher acts as a facilitator who
encourages students to discover principles on their own.
Virtual education is "the educational modality that raises the quality
of teaching and learning... that respects its flexibility or availability (at
any moment, time and space) reaches its apogee with technology to
integrate the three methods asynchronous, synchronous and self-
training" (Gros & Lara, 2009).
The elements that make up a virtual classroom arise from an
adaptation of the traditional classroom to which technological
74
Received January 12, 2021 / Approved May, 03 2021 Pages: 71-87
eISSN: 2600-5743
Centro Sur Vol. 5 No. 3 - July September
advances accessible to most users are added and in which factors such
as face-to-face communication are replaced by other elements
described (Scagnoli, 2006).
Being a virtual educator will be one of the most sought after options
in the XXI century, not all educators are willing to give up their master
classes, so the virtual educator in addition to stimulating one of the
professions with more future in the new economy, if this become the
most sought after by universities and business schools (Gavilanes
Sagñay et al., 2019).
For (Mota et al., 2016) he goes ahead in his conception and states:
"virtual education is a combination of virtual reality technology,
communication networks and human beings. In the coming virtual
education will be to reach out and touch someone or an entire
population in a way that humans never experienced before".
For the present research work we consider that virtual education is a
modality of the teaching-learning process, which starts from the
virtual intelligent - imaginative of man to the point of giving an effect
to reality in the interrelation with the innovative technologies without
limit of time - space that induces constant updates and innovations of
knowledge.
Meaningful learning occurs when innovative information is connected
to a relevant pre-existing concept in the cognitive structure. This
requires that innovative ideas, concepts and propositions can be
meaningfully learned to the extent that other ideas are adequately
clear and available to the individual's cognitive structures and that
they function as an anchor point to the former.
Learning is the process through which skills, abilities, skills, behavior
or values are acquired or modified as a result of experience,
instruction, reasoning and observation; this process can be analyzed
from different perspectives and therefore there are different learning
theories.
75
Received January 12, 2021 / Approved May, 03 2021 Pages: 71-87
eISSN: 2600-5743
Centro Sur Vol. 5 No. 3 - July September
To begin commenting on this topic we would have to start by defining
technology, sociology and science which is a term in which they have
been arriving so we would say that technology is a set of scientifically
ordered technical knowledge, which allows the design and creation of
goods and services that facilitate adaptation to the environment and
satisfy both the essential needs and desires of people (Barros Bastidas
& Turpo Gebera, 2018), (Aparicioetal., 2005. p 45).
Knowledge is not an object that is passed from one to another, but is
something that is constructed through cognitive operations and skills
that are induced in social interaction. Vygotsky points out that the
intellectual development of the individual cannot be understood as
independent of the social environment in which the person is
immersed (Berríos & Omaira, 2009. 43).
Innovative communication technologies offer new means to confront
and nurture educational practice and ideas, but their value emerges to
a great extent from the way they are used in the educational process.
In this field, it is essential to investigate the student-teacher-media-
knowledge relationship in order to find adequate strategies.
This era of change affects all levels of human life; education cannot
remain unaffected; however, change does not force us to change
because not all change is good, but it demands an openness to the
possibility of change. A critical, conscious, committed openness that
demands thinking before acting and rethinking what has been done.
It is thus a knowledge independent of the teacher's classroom, of
curricula, of evaluations, of fixed schedules. It is permanently available
to students through Web sites. Not only is the teacher not the
repository of knowledge, but the student can acquire more knowledge
than the teacher.
However, there is a great distance between a click and what you want
to achieve. This ease of access to knowledge requires an innovative way
of learning, since there are no summaries, no indexes, no maps or
routes, although there are tools to search for what is requested, it is
76
Received January 12, 2021 / Approved May, 03 2021 Pages: 71-87
eISSN: 2600-5743
Centro Sur Vol. 5 No. 3 - July September
necessary to imagine an innovative way of learning and an innovative
way of teaching.
Every innovative advantage that technology offers to education,
immediately constitutes a new challenge. Every solution to a new
problem leads to a new problem; what seems to balance things out
causes a new imbalance.
The summit also established development objectives for the year 2015,
known as the "UN Millennium Development Goals", in the field of
education, including: "achieving universal primary education and
promoting gender equality and the empowerment of women.
In this last objective, one of its indicators is to eliminate gender
inequalities in primary and secondary education. The term basic
education in most countries refers to compulsory education and has
been acquiring enormous relevance, particularly since the 1950s, when
it initially referred specifically to primary education. At the
international level, coverage and quality objectives have been
established for basic education.
At the World Conference on Education for All, the need to guarantee
universal access with an "Expanded Vision" to meet the basic learning
demands of every child, young person and adult was raised, as well as
the possibility and the responsibility of respecting and enriching the
common linguistic and spiritual heritage of all members of a society.
This agreement of the world conference seems to us fundamental to be
taken into account as a starting point for the actions that have been
carried out in the field of education since this year and as a precedent
in the recent history of educational reforms at the national and
international level.
It is based on abstract thinking, which a student at this educational
level is able to develop, according to Piaget, because it is located in the
stage of abstract thinking that provides the ability to deduce,
77
Received January 12, 2021 / Approved May, 03 2021 Pages: 71-87
eISSN: 2600-5743
Centro Sur Vol. 5 No. 3 - July September
synthesize, interpret and analyze phenomena and abstract situations
such as mathematical logical thinking.
It is the teacher's job to make children feel part of the group,
interacting professionally with children through guidance,
monitoring, guidance and evaluation in the learning process. In this
regard (Abreu et al., 2018) state that the teacher in his professional
practice, usually shares learning experience with children who show or
are in the beginning of some kind of learning problems hindering their
normal academic development and social coexistence.
For (Moinelo et al., 2017) at present the vast majority of contemporary
technologies and scientific work are supported, directly or indirectly,
in mathematical results, such is the situation that today we speak of
mathematization of sciences as an expression of the process of
increasing penetration of mathematical methods and products in the
different branches of human knowledge. This transforming process
has been accentuated in the teaching of this discipline, in which the
objectives aimed at the mastery of large volumes of mathematical
knowledge are replaced by those that propose a professional with an
integral form that allows him to successfully undertake the specific
activity that society requires of him. This means that the teaching-
learning process must be achieved so that students internalize the
meaning and the process of construction of mathematical processes.
El Salvador for many years has observed that the teaching of
mathematics in Salvadoran schools has been focused on the
development of programs presented in the educational reform of
nineteen ninety-eight, with the presentation of the National Education
Plan 2021, it "highlights the change of humanistic and socially
committed education programs, in the area of mathematics as such, is
modified in terms of its structure, proposed objectives, teaching
methodologies, curricular activities, achievements and goals,
competencies to be achieved, among others".
78
Received January 12, 2021 / Approved May, 03 2021 Pages: 71-87
eISSN: 2600-5743
Centro Sur Vol. 5 No. 3 - July September
In Guatemala, the CNB base curriculum has responded to a national
educational need that seeks to achieve optimal learning, so that people
can develop fully and autonomously within society. One of the greatest
challenges presented by the curriculum is "[...] to provide
opportunities for students to develop scientific ways of thinking and
acting" and the development of logical-mathematical thinking
contributes to this objective.
The educational reforms by the government of Honduras as proposals
to the commitments assumed as part of the education for all program,
known by its acronym in English as EFA (Education For All) plan,
which proposed several goals to fulfill the educational period, one of
them being to increase the academic performance of sixth grade
students in mathematics and Spanish.
Nicaragua has a national early childhood policy, "Love for the little
ones", approved in 2011, which emphasizes information for teachers
and calls for strengthening the knowledge, capacities and skills of
teachers to master early childhood and inclusive education concepts
and methodologies in order to develop pedagogical, social and human
relationships. It is also necessary to develop a training strategy for
teachers who work with children from zero to six years of age in order
to ensure that they acquire neuro-educational knowledge, skills and
abilities.
In the portal of the Ministry of Education, strategically designed for
innovation, creativity and technological updating of the community in
general; it seeks to support the development of academic, cultural,
scientific and technological activities, as well as the integration of the
educational community to collaborative spaces for the exchange of
experiences that enrich the teaching and learning processes.
(educapanama).
Inspired by new research in early mathematics, in 2009 the
government of Paraguay decided to strengthen mathematics
instruction in preschool. After considering a number of initiatives
79
Received January 12, 2021 / Approved May, 03 2021 Pages: 71-87
eISSN: 2600-5743
Centro Sur Vol. 5 No. 3 - July September
from around the world, the government opted for the "Big Math for
Little Kids," or BMLK, program.
There is growing evidence to suggest that mathematics education is a
cumulative process and that the development of pre-mathematical
skills at an early age is important for future mathematical
understanding and problem-solving skills.
The development of logical thinking in the Dominican Republic is a
project in the process of implementation that aims to develop logical
thinking at the primary level, through mathematical content and
problem solving. To this end, a diagnosis will be carried out to
determine the initial situation of the development of students'
thinking, and a didactic material will be prepared containing exercises
and problems that will contribute to the logical thinking of the
students.
The Venezuelan denominated education indicates that the profile of
the teacher must, "use different strategies for the development and
evaluations of the teaching-learning processes, in order to optimize the
time and resources available". (p60).
There are many laws and regulations under which the educational
system in Venezuela is found, these have been created with the
purpose of allowing a more active participation of both teachers and
students creating an environment of trust, creativity and responsibility
in the different areas taught in education.
After analyzing the term basic education in most countries, it refers to
compulsory education, and has been acquiring enormous relevance,
particularly since the 1950s. At first it referred specifically to primary
education. At the international level, coverage and quality objectives
have been established for basic education. This agreement of the
World Conference seems to us fundamental to be taken into account
as a starting point for the actions that have been carried out in the field
of education since that year and as a precedent in the recent history of
educational reforms at the national and international level.
80
Received January 12, 2021 / Approved May, 03 2021 Pages: 71-87
eISSN: 2600-5743
Centro Sur Vol. 5 No. 3 - July September
Materials and Methods
The methodology of this research on the incidence of virtual learning
environments in the development of mathematical logical thinking is
based on the scientific method, which is the method of systematic
study of nature that includes the technique of observation, rules for
reasoning and prediction of ideas about planned experimentation and
ways of communicating experimental and theoretical results in Latin
America. Based on the information was used the collection of indexed
articles from international journals in the database: Redalyc, Scopus,
and Scielo on the development of mathematical logical thinking with
the objective of analyzing the aspects that should be considered on the
topic to be addressed.
Results
Table 1 Mathematical logical thinking and its development in Latin
America
Country
Jomtien,
Tahiland
To ensure the right to education
for all, the following realities
persist:
- Functional illiteracy is a
major problem in all
countries, both
industrialized and
developing.
- They lack access to
technologies.
- More than 100 million
children fail to complete
the basic education cycle.
81
Received January 12, 2021 / Approved May, 03 2021 Pages: 71-87
eISSN: 2600-5743
Centro Sur Vol. 5 No. 3 - July September
Mexico
The company has not had the
capacity to respond to the
educational dilemma, so they
suggest that all the actors involved
act as soon as possible, with or
without the help of the Secretary
of Public Education (SEP), either
by convention or even by
convenience.
Peru
The type of learning disability
hinders the normal academic
development and social
coexistence, many of the teachers
are not sufficiently trained to meet
the needs of students with some
special needs, being necessary to
receive some specialization, or
insert in the curriculum of higher
education.
Cuba
It was found that there are
insufficiencies in the
conceptualization of concepts
related to formalization and
difference.
Ecuador
Within the curriculum of the area
highlighting the need for its
management from the lower
grades, since we are immensely in
an era where technology has
become an inseparable ally when
it comes to generating knowledge.
82
Received January 12, 2021 / Approved May, 03 2021 Pages: 71-87
eISSN: 2600-5743
Centro Sur Vol. 5 No. 3 - July September
El Salvador
The (MINED), is looking for a
pedagogical tool for teaching
mathematics in the classroom and
thus improve student learning.
Teachers are using a
mathematical language that
allows them to deepen their
understanding of mathematical
logic and the development of
logical thinking, with this strategy
they use logic through a game and
thus develop the mind in the use
of basic operations.
Guatemala
The curriculum is based on three
components: the individual, the
context in which he/she lives and
knowledge.
conceptual, procedural and
attitudinal.
Honduras
creativity, the ability to plan for
problem solving, establish
harmonious interpersonal
relationships, as well as other
social and emotional skills and
competencies. PESE 2018-2030
recognizes that SDG-4 and its
targets promote a model in which
learning, in all its forms and
modalities, has the capacity to
influence people's decisions to
create more just, inclusive and
sustainable societies.
Nicaragua
Specifically, the plan seeks to
define the principles of
Nicaraguan education for the next
fifteen years, promoting a
83
Received January 12, 2021 / Approved May, 03 2021 Pages: 71-87
eISSN: 2600-5743
Centro Sur Vol. 5 No. 3 - July September
participatory process for the
articulation of the educational
subsystems among themselves -
formal and non-formal - and with
the social and economic
environment.
Panama
The PISA test results report that
80% of Panamanian students do
not reach the basic level (Panama
National Report, PISA 2009).
Paraguay
In order to obtain quantitative
indicators on teaching practices,
Paraguayan students are lagging
behind in mathematics and
science Paraguay is no exception
to the overall low performance in
mathematics and science in Latin
American countries.
A large number of graduates will
not acquire sufficient knowledge
and skills to function in society.
Paraguayan students consistently
underperform their peers in other
nations in the region.
Dominican
Republic
The reports of the Secretariat of
State for Higher Education,
Science and Technology of the
Dominican Republic show that
the level of satisfaction achieved
in the teaching-learning process
of mathematics in initial teacher
training does not always meet the
expectations of those involved in
84
Received January 12, 2021 / Approved May, 03 2021 Pages: 71-87
eISSN: 2600-5743
Centro Sur Vol. 5 No. 3 - July September
it, where it is notorious that
students and graduates do not
manage to appropriate the
mathematical didactic knowledge,
in a way that allows them to be
trained with an integrative
character to ensure that students
in schools learn well and with
pleasure for mathematics.
Venezuela
always trying to motivate
students, to awaken the children's
desire to learn, and this will be
achieved through the
development of strategies applied
in class, according to the needs of
children, ensuring meaningful
learning.
After analyzing country by country in Latin America, and specifically
in Ecuador, province of Guayas, Canton Milagro, in the Vicente Anda
Aguirre Educational Unit, it can be seen that some of the teachers wish
to receive training on virtual learning environments, in order to apply
them in the classroom so that students can develop logical
mathematical thinking. While the students state that there is a need
for their teachers to use virtual environments in the classroom, which
contributes to improving the educational quality of the institution. The
educational authorities state that the virtual environment modules
should be in line with current technology, which becomes a support
material to facilitate meaningful learning where they will positively
influence the development of logical mathematical thinking.
85
Received January 12, 2021 / Approved May, 03 2021 Pages: 71-87
eISSN: 2600-5743
Centro Sur Vol. 5 No. 3 - July September
Conclusions
In the Educational Unit there are enough resources to implement a
module for the use of virtual learning environments for the
development of mathematical logical thinking. Students do not submit
homework because they do not have a place to do research and do not
give importance to the work submitted. The authorities of the
educational unit do not take steps to obtain resources for the
implementation of a module for the use of virtual learning
environments for the development of mathematical logical thinking.
Classes are routine, focused on the orthodox and are not encouraged
through didactic material for the area of mathematics, such as virtual
environments. With the analysis of Latin America, it can be observed
that teachers who teach mathematics classes are transmitted through
a routine system which does not allow students to develop
mathematical logical thinking. Students feel motivated when they hear
that their mathematics classes will be applied through virtual
environments, allowing the teacher a better teaching and therefore a
good learning.
References
Abreu, O., Rhea, S., Arciniegas, G., & Rosero, M. (2018). Object of
Study of Didactics: Historical Epistemological and Critical
Analysis of the Concept. Formación Universitaria, 11(6), 75-82.
https://doi.org/10.4067/s0718-50062018000600075.
https://doi.org/10.4067/s0718-50062018000600075
Aparicio, P. C., Blanco, N., Alvarado, M. E., Brien, Kyoung, H.,
Glenmaye, L., Yoon, D. P., Chakrabarti, B., Christensen, C. M.,
Eyring, H., Craney, C., Mckay, T., Mazzeo, A., Morris, J.,
Prigodich, C., Groot, R., Denofrio, L. A., Russell, B. S., Lopatto,
D., ... Prada, Á. R. (2005). Educación y jóvenes en conte.
Archivos Analíticos de Políticas Educativas, 17(2), 1
citation_lastpage=35,2-229.
https://www.redalyc.org/pdf/2654/265425848014.pdf.
Barros Bastidas, C., & Turpo Gebera, O. (2018). Factors influencing
the scientific production of university professors: a systematic
86
Received January 12, 2021 / Approved May, 03 2021 Pages: 71-87
eISSN: 2600-5743
Centro Sur Vol. 5 No. 3 - July September
review. Factores Que Influyen En La Producción Científica de
Los Docentes Universitarios: Una Revisión Sistemática. ,
11(22), 225-234. http://10.0.85.43/pensam.v11i21-
1.276%0Ahttps://ezproxy.uniandes.edu.co:8443/login?url=htt
p://search.ebscohost.com/login.aspx?direct=true&db=fua&AN
=141223533&lang=es&site=ehost-live
Berríos, D., & Omaira, G. (2009). Epistemological approaches
guiding 4th level research. Visión Gerencial, 3(3), 47-54.
https://www.redalyc.org/pdf/4655/465545882009.pdf
Gavilanes Sagñay, M. A., Yanza Chavez, W. G., Inca Falconi, A. F.,
Torres Guananga, G. P., & Sánchez Chávez, R. F. (2019). ICTs in
teaching and learning processes. Digital Science, 3(2.6), 422-
439. https://doi.org/10.33262/cienciadigital.v3i2.6.575.
Gros, B., & Lara, P. (2009). Innovation strategy in higher education:
The case of the Universitat Oberta de Catalunya. Iberoamerican
Journal of Education, 49, 223-245.
https://rieoei.org/historico/documentos/rie49a09.pdf
Moinelo, C., Caridad, M., Kassabb, A., & Mercedes, M. (2017).
Educational care for cognitive stimulation in people with
special educational needs . Intervention strategy. 3(4).
https://www.redalyc.org/pdf/3606/360657467012.pdf
Mota, L., Daniel, Á., & Delgado, A. (2016). Representaciones
Estudiantiles Sobre Nutrición Humana Como Modelo
Estudiantil Inicial Para Referencia Didáctica. Revista
Latinoamericana de Estudios Educativos (Colombia), 12(2),
83-108. https://www.redalyc.org/pdf/1341/134149931005.pdf
Scagnoli, N. (2006). Collaborative learning in distance courses.
Investigación y Ciencia: De La Universidad Autónoma de
Aguascalientes, 36, 39-47.
https://www.redalyc.org/pdf/674/67403608.pdf