Edited by: Tecnológico Superior Corporativo
Edwards Deming
January - March Vol. 6 - 2 - 2023
e-ISSN: 2576-0971
Received: January 09, 2023
Approved: May 14, 2023
Page 15-25
E-activities for the identification and use of
immediate integration formulas.
E-actividades para la identificación y uso de las fórmulas de
integración inmediata
Segundo Bienvenido Camatón Arízabal
Marco Vinicio Añazco Maldonado
Janine Noemí Cueva Palacios
Yefferson Ricardo Litardo Mieles
The present research work proposes the theory of
conceptual fields as a means to reach the use and
recognition of the formulas of immediate integration;
because through the development of the four essential
characteristics of the cognitive schemes, implicit in the e-
activities, it is sought to facilitate the teaching-learning
process in this part of Integral Calculus. In this way, a
research with a quasi-experimental design is carried out,
which recognized the veracity of the facts with
correlational hypotheses and a test directed to the
students; confirming that the theory of conceptual fields
does influence the understanding and association of the
recognition and use of the formulas of immediate
Keywords: Immediate integrals, conceptual fields,
El presente trabajo de investigación propone a la teoría de
campos conceptuales como un medio para llegar al uso y
el reconocimiento de las fórmulas de integración
* Magister en Enseñanza de la Matemática, Universidad de Guayaquil
segundo.camatona@ug.edu.ec https://orcid.org/0000-0001-8327-2869
Magíster en Investigación Operativa, Universidad de Guayaquil
marco.anazcom@ug.edu.ec https://orcid.org/0000-0003-1022-6487
Licenciada en Pedagogía de las Matemáticas y la Física, Unidad Educativa San
Antonio de Padua, janine.cuevap@ug.edu.ec, https://orcid.org/0000-0002-
Licenciado en Pedagogía de las Matemáticas y la Física Unidad Educativa
Comandante Antonio José de Sucre , yefferson.litardom@ug.edu.ec
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e-ISSN: 2576-0971
inmediata; pues a través del desarrollo de las cuatro
características esenciales de los esquemas cognitivos,
implícitas en las e-actividades, se busca facilitar el proceso
de enseñanza-aprendizaje en esta parte de Cálculo Integral.
De esta forma se efectúa una investigación con diseño
cuasi-experimental que reconoció la veracidad de los
hechos con hipótesis correlacionales y un test dirigido a
los estudiantes; confirmando que la teoría de campos
conceptuales si influye en la comprensión y asociación del
reconocimiento y uso de las fórmulas de integración
Palaras clave: Integrales inmediatas, campos
conceptuales, esquemas.
Today's society has evolved in all possible areas, among them we can highlight the school,
where specifically the teaching-learning process has sought the necessary mechanisms
to reach perfection, especially through theories that propose the student as the main
actor of the educational system; thus, changes are observed in the different branches of
science. In spite of the fact that for Mathematics there are always the greatest difficulties,
here the Theory of Conceptual Fields has been highlighted, which pretends that students
come to understand the object of study as a whole, visualizing it through real situations.
This is stated by Pabón et al. (2020) who show that the use of conceptual fields oriented
with other tools and methodological strategies allows the assessment of the student's
formative processes, enabling them to generate a significant context in the analytical and
systematic capacity of understanding Integral Calculus (pp.179).
However, one part is the research, which leads us to listen or read a number of steps
that sound very good together, and a very different one is to propose it in the classroom,
because in the classroom this theory is very little applied, as Mateus-Nieves (2021) says,
(Scagnoli, 2006)(Scagnoli, 2006), who mentions that "the lack of a deep conceptual
teaching can be evidenced, due to the fact that the most used approach is the mechanical
del Mastro & Monereo, (2014). All this has repercussions on the student's learning, who,
not internalizing what is being executed, will present difficulties during their studies to
reach the Third level, even more so in the moments when they must implement them
in everyday life situations.
Definitely, the object of study must be internalized regardless of the profession to be
exercised in the future, that is, it should not matter whether the trainee is going to
become an engineer or a teacher; since, if we speak specifically of the integration
formulas, both must have mastery of them, in the case of the engineer for its execution
during the calculation of irregular areas or a teacher to exemplify to his students how
to implement it.
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e-ISSN: 2576-0971
To this end (Romero, 2016), (Capraro et al., 2010), (Caballero-Montañez & Sime-Poma,
2006)The updating of knowledge on the part of the teacher is indispensable, since this
way he can be informed of new methods, activities, strategies, teaching techniques that
facilitate or allow the improvement of learning.
From this point of view, the problem that arises can be described from two perspectives:
on the one hand, the analysis of the theory of conceptual fields in the use and
identification of the formulas of immediate integration in the future mathematics
teachers of the pedagogy career of experimental sciences of Mathematics and Physics
belonging to the University of Guayaquil and on the other hand, the scarce relevant
information on the methodology of conceptual fields that motivates the use of such
methodology in the use and identification of formulas of immediate integrals, not only
as a concept but as a complex cognitive scheme (conceptual-procedural).
In order to verify if the Theory of Conceptual Fields helps students to use and implement
the formulas of immediate integration, a correlational research with quasi-experimental
design was carried out, for which we proceeded to form the research groups with the
students of the career of pedagogy of experimental sciences of Mathematics and Physics
at the University of Guayaquil Cycle I 2022-2023 and being defined the parallels 4-5 A2
as experimental group with a total of 19 members; while courses 4-6 C2 were
designated as the control group, with a total of 22 students.
Thus, it is defined that the experimental group will implement the instructional sequence
designed with e-activities, while the control group will only be taught a regular class, as
shown in Table 1.
Table 1. Variables Scheme
Experimental group
Control group
x: Instructional sequence with e-activities based on CBT on the immediate
integration formula with powers
: Successful identification and use of the formula.
: Success in identifying and using the formula, which to this group the
instructional sequence will not be applied.
Therefore, to collect the data, a test was applied to each research group, which was
composed of a questionnaire of 10 questions, valued at one point each; these questions
were based on what was taught through the e-activities and the regular class,
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e-ISSN: 2576-0971
respectively. The data collected were analyzed with the help of descriptive statistics,
thus giving the study a quantitative approach.
It is worth mentioning that the e-activities were planned and developed based on the
information found through the literature review; in addition, the structure and platforms
used were incorporated based on this research. Also, the relevant stages of the
Conceptual Fields Theory were defined.
The following is a description of the e-activities developed for the experimental group,
which allow students to manipulate the object of study and thus achieve the use and
application of the immediate integration formulas:
Integral Calculus Course
Unit 1. Immediate Integrals
Topics covered
- Algebraic Immediate Integrals
Expected learning. Objective
Apply the algebraic immediate integration formula that
relates power to the properties of integrals to solve
specific exercises.
2 hours
1. Learning situation
20 minutes
Display instruction
The frequent use of the calculus of a variable is based fundamentally on the problem of
calculating the area enclosed by the graph defined by a function.
It is often used in economics through statistical analyses, which are closely linked to
functions that have powers within their composition.
If it is stated that integration is the inverse operation of derivation, how could the
following integral be solved
𝒅𝒙 ?
Describe at least 2 steps that you consider necessary to solve the integral with their
Cross-cutting artifacts
Instructions for use
Padlet or Forum
Students should access the following link to access
the Padlet (an interaction wall)
https://padlet.com/jannyest30/sw5shf8k00ye20h4 , in
the case of teachers who have a virtual classroom,
they can do the same through a forum.
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e-ISSN: 2576-0971
2. Context of the problem
25 minutes
Instruction screen
It is important to keep in mind that to solve this type of exercises we must not only
calculate its primitive, but also analyze the integral; which allows us to apply the most
appropriate method to solve. Therefore, we can analyze what type of integral it belongs
to in order to solve it, through the following steps:
1. Check if it is immediate integral
2. Check if it is almost immediate
3. Check that the exponent is a number and not the same variable
4. Check that the differential refers to the same variable of the function.
Cross-cutting artifacts
Instructions for use
Google Sites
Celeriti Game
It is a blog created with the information that the
student needs, where they will have the availability of
a previous game to remember the previous concepts
seen in the previous section, this web site is available
at the following here
For the game, students should go to the following link
matematicas/generalidades-de-calculo-integral and
complete the activity.
3. Operational Invariants
25 minutes
Display instruction
To start solving the exercise, it is vital to recognize the terrain first.
So we must list the elements, properties, concepts that we will use to solve it.
Therefore, we will exercise our knowledge trying to decipher which is the rule that the
algebraic immediate integrals with powers comply with, which will be done through the
following activity by accessing the following link https://es.educaplay.com/recursos-
Transversal artifacts
Instructions for use
The student must enter the game with the link, which
will be provided by the teacher and the student will
enter to find the formula that allows us to solve
algebraic immediate integrals.