Edited by: Tecnológico Superior
Corporativo Edwards Deming
July - December Vol. 6 - 2 - 2022
e-ISSN: 2576-0971
Received: October 21, 2021
Approved: February 19, 2022
Page 16-30
Inverted learning model for the online high school
mathematics class.
Modelo de aprendizaje invertido para la clase online de
Matemáticas del bachillerato
María Alejandra Saucedo James
Mayra Jacinta Moncayo Carpio
Carlos Andres Acosta Vergara
Roberto Milanés Gómez
In these times of covid-19, the Ecuadorian educational
system has been faced with the challenge of sustaining the
teaching-learning processes in the online modality. This has
demanded initiative and creativity on the part of teachers
and students in order to meet the expected results. The
present work proposes the inverted learning model
designed for the development of online Mathematics
classes, which includes students and teachers of the first
year of high school of the Vinces Educational Unit, Vinces
canton, province of Los Ríos. In order to obtain the results,
an observation guide was applied to the virtual classes, a
questionnaire to 177 students and an interview to teachers
as data collection instruments. These made it possible to
show the current reality of the teaching method, as well as
the limitations faced by educators and students in making
possible the online adaptation of the planning of the
development of the contents of the subject of
Keywords: Tics, Performance, Impact, Survey,
Agricultural Activities.
* Ingeniera en Sistemas, Universidad Técnica de Babahoyo, Babahoyo Ecuador,
msaucedoj@utb.edu.ec ORCID: 0000-0001-9595-5552
* Licenciada en Educación, Universidad Técnica de Babahoyo, Babahoyo Ecuador,
mmoncayoc@utb.edu.ec, ORCID: 0000-0002-7655-1576
* Ingeniero Comercial, Universidad Técnica de Babahoyo, Babahoyo
Ecuador,cacostav@utb.edu.ec, ORCID: 0000-0001-7755-4923
* Doctor en Ciencias Pedagógicas, Universidad de Guayaquil, Guayaquil, Ecuador,
roberto.milanesg@ug.edu.ec, ORCID: 0000-0002-6879-3559
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e-ISSN: 2576-0971
En estos tiempos de covid-19, al sistema educativo ecuatoriano se le ha planteado el
desafío de sostener los procesos de enseñanza-aprendizaje en la modalidad online. Este
ha demandado iniciativa y creatividad por parte de maestros y estudiantes a fin de
cumplir con los resultados esperados. El presente trabajo propone el modelo de
aprendizaje invertido diseñado para el desarrollo de las clases online de Matemáticas,
que incluye a educandos y docentes del primer año bachillerato de la Unidad Educativa
Vinces, cantón Vinces provincia de Los Ríos. Para la obtención de resultados se aplicó
una guía de observación a las clases virtuales, un cuestionario a 177 estudiantes y una
entrevista a docentes como instrumentos de recolección de datos. Estos permitieron
evidenciar la realidad actual del método de enseñanza, además de las limitaciones que
afrontan los educadores y educandos en posibilitar la adaptación online de la planificación
del desarrollo de los contenidos de la asignatura de Matemáticas.
Palabras clave: Tics, Desempeño, Impacto, Encuesta, Actividades Agrícolas.
Currently, information and communication technologies (ICT) have modified the social
encounters between individuals worldwide, giving rise to the emergence of new
paradigms that propose a diversity of knowledge and skills focused on the variety of
existing technologies. In this context, education is not at the margin of this, the presence
of platforms for teaching and learning, have facilitated the substantial change between
face-to-face and online in terms of academic activities, which have allowed to continue
with the educational processes in these times of pandemic, avoiding the permanent
paralysis of school actions.
The process of adaptation from face-to-face to online has revealed shortcomings in the
use of technology, especially for teachers, who have had to relearn new ways of
presenting didactic content. In this scenario, there is a need for motivated teachers and
students, willing to receive new information. This will encourage the use of ICT in
education, facilitating access to content and teaching-learning methods, in full harmony
with the individuals who handle it. The interaction between the subject and the
technology to educate requires new views on how to proceed and act in a context which
is mediated by a computer.
Thinking about online education requires first of all to look at the current pedagogical
models and dialectically deny their best contributions in order to build an educational
option in new Learning Management Systems (LMS). There are several proposals:
Blended-learning (Bartolomé and Sandals, 1998), E-learning (Elliott Masie, 1999),
Inverted Classroom (Lage, Platt and Treglia, 2000), among others that have transcended
and by their nature propose diverse pedagogical actions. Therefore, the inverted
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e-ISSN: 2576-0971
classroom offers a direct coincidence between what is developed in face-to-face classes
and what is intended to be achieved in the future, being essential its study and theoretical
According to the authors Abío et al., (2017) Llanos y Bravo (2017, p. 6) the flipped
classroom learning model or flipped classroom consists of turning the class around, the
student outside the classroom, seeks from his own autonomy the acquisition of
knowledge by accessing the contents, mainly those of audiovisual type elaborated and
selected by the teacher according to educational needs, the technological tools that
allow appropriating and expanding knowledge. Gallardo et al., (2017) expresses that this
model allows the teacher to dynamize and modernize the teaching-learning processes,
facilitating the use of classroom time aiming at achieving greater depth in the study of
disciplinary contents. (p. 96)
The inverted learning model is based on the need to match different types of learning,
the use of multimedia tools is considered as an important contribution to teaching and
an instrument of great influence to acquire knowledge, in which students actively
contribute in the elaboration of knowledge and value their own learning in a very
significant way (Park y Choi, 2017, p. 192). In addition, Mendoza (2017) highlights that
the intentional material taught by the teacher refers to the evaluation of the contents to
be taught and the resources to be used inside and outside the classroom, for a better
understanding of concepts, procedures, skills, abilities, aptitudes and values.
Fúneme (2019, p. 161) refers that the learning model aims to study the conditioning
factors of the teaching and learning process of Mathematics, in order to adequately focus
the efforts of teachers in the educational field. The central objective of mathematics
teaching is the cognitive development of students, which is correlated with the form of
instruction and the teacher's interaction in the classroom. (Holguín et al., 2016, p. 287).
Mathematics teachers should consider the interests and needs that allow them to create
an active environment of motivation, enthusiasm and attention to their class for problem
solving in a mathematical context. (Pochulu y Font, 2016, p. 15)In this context, students
should assume the acquisition of knowledge, directed by the educator, strengthening
class discussion or reflection. The teacher points out Oviedo (2018, p. 5)The teacher,
on the other hand, must assume strategies to generate student participation in class;
therefore, it is necessary to make known the evaluation strategy to be implemented to
determine the impact generated in the student population who acquire knowledge
through the classes. (Vega et al., 2015, p. 11)The evaluation is a fundamental dimension
for the fulfillment of the virtual educational process. (Jiménez, 2019).
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e-ISSN: 2576-0971
Moncada Cerón (2013) defines the concept of model as a conceptual pattern on which
is built from reality, providing elements that direct actions (p. 39). By relating this
definition to the educational level, Tünnermann (2008)(p. 39), conceptualizes the term
educational model as the concretion of each of the elements an institution possesses
(teaching, research, extension, linkage and services) in order to make its educational
project a reality. (p. 15).
For the development of this research, a literature review was carried out in different
scientific databases on the variables of study: flipped learning, online class and its related
terms based on the glossaries of the Social Sciences. Likewise, search chains with
exclusion criteria were applied in Spanish, English and Portuguese to improve the
accuracy of the results related to the research topic.
From the search conducted, a total of 15 research antecedents related to the variables,
descriptors and scope of the topic raised were collected, namely: Núñez Paz y Rodríguez
(2020); Fúneme (2019); Madrid et al., (2018);Guerrero (2019); Rahmadani et al. (2020);
Lai & Hwang (2016); Wei et al. (2020); Cevikbas y Kaiser (2020); Seitan et al. (2020);
Kumar et al. (2017); Clark (2015); Urbano (2020); Cedillo et al. (2021); Lo et al. (2018);
TARAZI, (2016).
With the literature review of the different studies and the consideration of systemic
summaries related to the inverted learning model and the online mathematics class in
the baccalaureate, it has been possible to identify that the topics studied are the
The inverted classroom as a strategy to improve performance, academics and
attitudes in mathematics learning.
Transformation of mathematics teaching through the application of the inverted
The inverted classroom, impact and effectiveness in motivation and learning for
Mathematics versus traditional teaching models.
Proposal for a didactic intervention with an inverse methodological approach to
learn inequalities.
Once the conclusive summaries of the study background have been exposed, it can be
seen that the tendency is to produce inverted classroom technologies in order to
motivate and intervene, but there is a model thinking of inverted learning as a process
for learning to teach mathematics online at the baccalaureate level, therein lies the
importance of the research.
After the introduction, this paper is organized in the following sections: literature review
on the flipped classroom learning model, the online mathematics classroom, a
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e-ISSN: 2576-0971
description of the research design, the modeling, discussion of the results obtained and
the corresponding conclusion.
The analysis offered does not dispense with a subject that contextualizes it, in the
particular case of this study we choose the subject Mathematics, which within the
common core of the curriculum is essential in the learning of students and its presence
in secondary education levels. In accordance with everything reviewed concerning the
subject, the central scientific question is posed for this article: how to model the learning
invested in the online classes of the subject of Mathematics in the students of the first
year of high school?
This research is assumed as explanatory from a high preponderance of modeling of the
processes of inverted learning applied to Mathematics classes through the face-to-face
modality, which seeks to discover the current situation on the methodology or strategies
used by teachers to achieve compliance with the teaching in online session and achieve
learning in their students; all this from a model thinking of inverted learning which
facilitates its future transformation perspective in the use of teaching of the
For the development of this research, 320 students in the first year of high school in the
specialties of Science and Computer Science Technician and 2 teachers of the subject of
Mathematics were considered as the study population. The random probabilistic
sampling was calculated using the online data processing sheet, obtaining a sample of 177
students to whom the scientific research instruments were applied.
For the collection of research data, the observation of online classes of the subject of
Mathematics was used, which allowed obtaining information for the realization of a
documentary analysis on how the teaching-learning activities are developed, determining
the role of teacher and student in the inverted learning model in the online modality.
Likewise, an interview was conducted with the teachers who teach the subject in the
first year of high school, with the purpose of determining the strategies used in the
development of their classes, in order to reach the contents and achieve assimilation.
Finally, a survey was applied to students to identify their perceptions about the learning
model used, as well as the didactic resources and assertiveness of the teacher when
interacting with the online Mathematics class.
All the instruments offered (questionnaire, observation and interview guide) facilitate
the triangulation of data for a systemic analysis, modeling the process of teaching-learning
Mathematics, through the logical procedures of thinking that facilitate the use of
modeling as a direct scientific method of research.
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