Edited by: Tecnológico Superior Corporativo
Edwards Deming
January - March Vol. 6 - 2 - 2023
e-ISSN: 2576-0971
Received: December 12, 2022
Approved: May 02, 2023
Page 26-41
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
In these times of covid-19, the Ecuadorian educational
system has been challenged to sustain 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 Mathematics.
Keywords: Inverted classroom, inverted learning, online
classroom, virtual classroom, Baccalaureate, Mathematics.
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.
* Ingeniera en Sistemas, Universidad Técnica de Babahoyo, E-mail:
msaucedoj@utb.edu.ec ORCID: 0000-0001-9595-5552
* Licenciada en Educación, Universidad Técnica de Babahoyo
mmoncayoc@utb.edu.ec, ORCID: 0000-0002-7655-1576
* Ingeniero Comercial, Universidad Técnica de Babahoyo
cacostav@utb.edu.ec, ORCID: 0000-0001-7755-4923
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e-ISSN: 2576-0971
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: Aula invertida, aprendizaje invertido,
clase en línea, clase virtual, Bachillerato, Matemática.
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 and 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 developed and
selected by the teacher according to the educational needs, the technological tools that
allow appropriating and expanding knowledge. Gallardo et al. 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 flipped 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 a
highly influential tool for acquiring knowledge, in which students actively contribute to
the elaboration of knowledge and value their own learning in a very significant way (Park
and 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 the 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 interaction of the teacher 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 and Font, 2016, p. 15), students should
assume the acquisition of knowledge, directed by the educator, strengthening class
discussion or reflection. The teacher points out Oviedo (2018, p. 5)., for his part 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 population of students 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. (Jimenez, 2019).
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). Relating this definition
to the educational level, Tünnermann (2008)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.
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e-ISSN: 2576-0971
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 carried out, a total of 15 research precedents related to the variables,
descriptors and scope of the proposed topic were compiled, namely: Núñez Paz and
Rodríguez (2020); Fúneme (2019); Madrid et al.;Guerrero (2019); Rahmadani et al.
(2020); Lai & Hwang (2016); Wei et al. (2020); Cevikbas and Kaiser (2020); Seitan et al.
(2020); Kumar et al. (2017); Clark (2015); Urban (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
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
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 posed for this article is: how to model the learning
invested in the online classes of the subject of Mathematics in students of the first year
of high school?
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e-ISSN: 2576-0971
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 by means of 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 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.
Table 1. Availability of technological equipment for the development of the online class.
Totally agree
Strongly disagree
It can be seen that more than 70% of the students have technological equipment for the
development of the virtual session, 20% do not have this resource. In the courses
observed, a great majority of them connect to the online class, being highlighted by the
teachers, those who do not have technological resources, look for options to connect.
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e-ISSN: 2576-0971
Table 2. Digital resources sent by the teacher to review the class topic
Totally agree
Strongly disagree
It is evident that more than 80% of the students receive didactic material from the
professor, while 12% indicate that they do not have access to it. In the observations
made, it is evident that the teacher sends the material at the end of the class online, but
in his opinion not all students can receive it due to different difficulties regarding
accessibility to a technological device.
Table 3. Review of class material by the student at home
Totally agree
Strongly disagree
It was determined that more than 60% of respondents review the