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Relevance of the prioritized curriculum with
emphasis on competencies: teachers'
perspectives on the teaching of mathematics
in Bachelor of Science
Pertinencia del currículo priorizado con énfasis en
competencias: perspectivas docentes sobre la enseñanza
de matemáticas en Bachillerato en Ciencias
Jhon Lima-Yarpaz
Unidad Educativa Fiscal Atahualpa, Quito, Ecuador
Área de Matemática
jjlima@uce.edu.ec
https://orcid.org/0009-0002-8330-5178
Ana Arias-Balarezo
Universidad Central del Ecuador, Quito, Ecuador
Facultad de Filosofía, Letras y Ciencias de la Educación, Representante Nacional en
Ecuador del Comité Interamericano de Educación Matemática (CIAEM)
alarias@uce.edu.ec
https://orcid.org/0000-0002-2317-9600
Franklin Molina-Jiménez
Universidad Central del Ecuador, Quito, Ecuador
Facultad de Filosofía, Letras y Ciencias de la Educación, Carrera de Pedagogía de las
Ciencias Experimentales Matemáticas y Física
femolina@uce.edu.ec
https://orcid.org/0000-0002-2374-2192
(Received on: 27/05/2025; Accepted on: 15/06/2025; Final version received on: 25/07/2025)
Suggested citation: Lima-Yarpaz, J., Arias-Balarezo, A. & Molina-Jiménez, V. (2025).
Relevance of the prioritized curriculum with emphasis on competencies: teachers'
perspectives on the teaching of mathematics in Bachelor of Science. Revista Cátedra, 8(2),
55-76.
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Abstract
This article analyzes the relevance of implementing the prioritized curriculum in the
teaching and learning of mathematics among second-year science baccalaureate students
during the 2023-2024 academic year. This article focuses on the development of
communication, mathematical, digital, and socioemotional competencies, as defined by the
Ministry of Education. This research, based on teachers' perceptions of their classes and
their use of the mathematics textbook provided to students, focuses on qualitative and
quantitative approaches. The research combines documentary analysis with a field study,
conducting surveys with teachers from 22 educational institutions in Quito. A worksheet
was used for text analysis. The results show a high level of contextualization and relevance
in the implementation of the curriculum, as well as a significant promotion of mathematical
and socioemotional competencies. However, the development of digital competencies
shows a medium level of integration. Regarding the text analysis, it was determined that the
limit of a function is not studied. It is concluded that, although there is an effort to
incorporate these competencies into the teaching-learning process, it is necessary to
strengthen training in the use of digital tools and improve textbooks to ensure more
effective implementation of the prioritized curriculum.
Keywords
Communicational competencies, digital competencies, mathematical competencies, socio-
emotional competencies, prioritized curriculum.
Resumen
El presente artículo analiza la pertinencia de la aplicación del currículo priorizado en la
enseñanza y aprendizaje de las matemáticas en estudiantes de segundo año de bachillerato
en Ciencias durante el año lectivo 2023-2024, con énfasis en el desarrollo de competencias
comunicacionales, matemáticas, digitales y socioemocionales, definidas por el Ministerio de
Educación, con base en la percepción de los docentes en el desarrollo de sus clases y en la
utilización del texto de Matemática entregado a los estudiantes. La investigación, de enfoque
cualitativo y cuantitativo, combina el análisis documental con un estudio de campo, a través
de la aplicación de encuestas a docentes de 22 instituciones educativas de la ciudad de Quito
y para el análisis del texto se empleó una ficha de análisis de contenido. Los resultados
evidencian un alto nivel de contextualización y pertinencia en la implementación del
currículo, así como un fomento significativo de las competencias matemáticas y
socioemocionales. No obstante, el desarrollo de competencias digitales presenta un nivel
medio de integración. En cuanto al análisis del texto se determinó que no se estudia el límite
de una función. Se concluye que, aunque existe un esfuerzo por incorporar estas
competencias en el proceso de enseñanza-aprendizaje, es necesario fortalecer la formación
en el uso de herramientas digitales y mejorar los libros de texto para garantizar una
implementación más efectiva del currículo priorizado.
Palabras clave
Competencias comunicacionales, competencias digitales, competencias matemáticas,
competencias socioemocionales, currículo priorizado.
1. Introduction
The education system faces global challenges, including the need to adapt education to
technological advances, constant social change, and the inclusion of universal values that
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promote peace and coexistence (Delors, 1996). Furthermore, the education system must
shift from a traditional approach based on the accumulation of knowledge to one that
fosters the development of skills, as proposed by various studies on curricular
modernization (Castillo and Gamboa, 2012; Egido, 2022). In this context, mathematics
education also faces significant difficulties, especially in the teaching of abstract concepts
such as the limit of a function. This concept, fundamental to differential and integral
calculus, presents cognitive and emotional barriers that hinder its learning (Blázquez and
Ortega, 2000; Socas, 2007). In Ecuador, for example, PISA assessment results have shown
low performance in mathematics, underscoring the need for a change in pedagogical
methods and teaching curricula to improve educational outcomes (El Comercio, 2018;
OECD, 2023).
This article stems from a thesis whose objective was to analyze the relevance of the
prioritized mathematics curriculum, with an emphasis on communication, mathematical,
digital, and socio-emotional skills, among second-year science students during the 2023-
2024 school year. It also seeks to evaluate teachers' perceptions of the relevance and
contextualization of this curriculum in their classes. To this end, the following research
questions have been posed:
What is teachers' perception of the implementation of the prioritized curriculum in
relation to communication, mathematical, digital, and socio-emotional
competencies with second-year high school students in the context of mathematics
learning?
How do teachers perceive the relevance and contextualization of the prioritized
curriculum in their mathematics classes?
What methodology should be used to evaluate the concept of the limit of a function
in the mathematics textbook for second-year high school students based on the
Ministry of Education's communication, mathematical, digital, and socio-emotional
competencies?
This study is not only relevant for students and teachers but also has practical value, as it
seeks to generate proposals that improve the learning of key concepts in mathematics, such
as limits, which are fundamental to the exact sciences and other areas such as physics,
engineering, and economics. The research also contributed to the continuing education of
teachers, enabling them to implement teaching activities and improve their performance in
the classroom.
The structure of this document is as follows: introduction, theoretical foundation, design of
this research (approach, types, and level of research), data collection techniques and
instruments, validity and reliability of the instruments, analysis and discussion of results.
And finally, conclusions summarizing the findings obtained.
2. Theoretical foundation
2.1 Ecuadorian educational model
Ecuador's educational model is a "set of principles and approaches that guide the
implementation of teaching and learning processes, based on a contextualized and flexible
educational offering, to improve educational quality" (Ministry of Education, 2023a, p. 4). It
is also considered "a framework that clarifies the meaning and paradigm of education;
however, it allows institutions to generate innovative, relevant, and meaningful educational
actions for their stakeholders" (Ministry of Education, 2023b, p. 5). The term "protagonists"
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refers to the students who interact inside and outside the educational institution with their
teachers, peers, authorities, and families. These interactions "return to individuals the
ability to discover, explore, inquire, and learn from one another through collaboration,
cooperation, and the relationships established between stakeholders" (Ministry of
Education, 2023b, p. 8). This model has a constructivist approach in which students are the
permanent builders of their own knowledge through interaction with their family, social,
and cultural environment. To achieve this, students must actively participate in their
learning, developing critical and problem-solving skills by working in teams (Ministry of
Education, 2023b, p. 10).
2.2 Educational quality
For the Ministry of Education of our country, educational quality allows for the co-
responsible participation of the entire educational community, the autonomy of school
management, and the relevance and flexibility in learning for the comprehensive training of
competent citizens who achieve their life plans and contribute to the development of
society, based on democratic, sustainable, equitable, and inclusive practices (2023b, p. 9).
From this definition, it can be highlighted that the quality of education, in addition to
focusing on students' academic achievements, also focuses on forming their values,
emotions, attitudes, and skills to face the challenges of society. It is important to emphasize
that the quality of education is an object in constant change and improvement; therefore, it
requires adaptation as the needs and challenges of society evolve (Ministry of Education,
2023b, p. 9).
2.2.1 Relevance
The relevance of education implies that it must be meaningful to all people, regardless of
their social or cultural context, abilities, and interests. This way, everyone can embrace the
content of culture, both global and local, and develop themselves as subjects in society,
developing their autonomy, self-governance, freedom, and identity (Blanco et al., 2008, p.
13). Along these same lines, for the Ecuadorian Ministry of Education, relevance in
education constitutes one of the characteristics that the Organic Law on Intercultural
Education attributes to the concept of educational quality. It is, therefore, a principle of
education that seeks to ensure the quality of the educational process received by students,
guaranteeing "an education that responds to the needs of their social, natural, and cultural
environment at the local, national, and global levels" (Organic Law on Intercultural
Education, 2015). “For the educational offer to be relevant, the curriculum and teaching
methods must be flexible to adapt to the needs and characteristics of the students and the
diverse social and cultural contexts” (Blanco et al., 2008, p. 13).
2.3 Ecuadorian curriculum
A curriculum is an educational project of each country with the aim of promoting the
development and socialization of a new generation. The curriculum ensures the minimum
conditions necessary to maintain continuity and coherence in the realization of pedagogical
intentions, guaranteeing quality teaching and supporting the learning process (Ministry of
Education, 2016, p. 4). “A curriculum is a document that guides and directs the learning
process. Its content includes the knowledge, skills, and attitudes that the student is expected
to learn at each stage of their educational path” (Ministry of Education, 2021, p. 5).
2.4 Prioritized curriculum with emphasis on competencies
The prioritized curriculum with an emphasis on communication, mathematical, digital, and
socio-emotional skills is a document created with the aim of providing a quality education
that adapts to the reality and needs of each educational institution and each student after
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the Covid-19 pandemic. Applying these skills helps provide a quality education and
contributes to the comprehensive development of students and improves their ability to
cope with situations that arise in their daily lives (Ministry of Education, 2021, p. 5).).
2.4.1 Competencies of the prioritized curriculum
For the Ministry of Education (2021), communication skills (CC), mathematics (CM), digital
skills (CD), and socio-emotional skills (SC) are students' ability to develop, integrate, and
utilize different levels of interrelated knowledge, skills, procedures, aptitudes, and attitudes
(pp. 7-9). Communication skills are the skills that promote the comprehension and
production of texts, effective communication, and thus improve social interaction. Students
must be able to speak relevantly and fluently. They must also understand a text when
reading or listening to it and produce texts that can be written or oral so that the recipient
can understand them. Reading is a source of information and study that allows for
intellectual and human growth and allows for the development of "reflection, critical
thinking, complex thinking, awareness, creativity, and the construction of new knowledge"
(Ministry of Education, 2021, pp. 7-8).
Mathematical competencies are skills that promote critical, logical, and rational thinking
when making decisions based on ethical and moral values. Students must be able to perform
basic operations and use mathematical symbols with different numerical sets. They must
also be able to solve everyday problems and express them in a reasoned, logical,
argumentative, and communicative manner, integrating different types of knowledge.
Furthermore, they will be honest, fair, ethical, and respectful members of a democratic,
equitable, and inclusive society. Finally, mathematical competencies go hand in hand with
the 21st-century competencies of "problem-solving, decision-making, and critical thinking"
(Ministry of Education, 2021, p. 8).
Digital competencies are the knowledge and skills that foster the development of
computational thinking, the responsible use of technology, as well as creating, sharing,
communicating, collaborating, and providing solutions in digital environments. Students
must be able to identify, define, and solve problems that arise in digital environments and
that can lead them to educational, cultural, political, and economic environments through
critical thinking. Furthermore, students cease to be technological consumers and become
analysts and creators, people who manage technology appropriately, consciously, and
responsibly. Digital competencies enable autonomous participation in the learning process
(Ministry of Education, 2021, pp. 8-9).
Socio-emotional competencies are the knowledge, capacities, skills, and attitudes that
enable the understanding and appropriate management of personal emotions versus the
emotions of others. Students must be able to self-regulate their emotions, respect the
emotions of their peers, collaborate and work as a team, make responsible decisions, and
handle situations that challenge them in their learning process in a constructive and ethical
manner. Furthermore, these competencies allow the development of “life skills proposed by
the World Health Organization: self-knowledge, empathy, assertive communication,
interpersonal relationships, decision-making, problem and conflict resolution, critical
thinking, management of emotions and feelings, management of tension and stress”
(Ministry of Education, 2021, p. 9).
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2.5 Learning theories associated with Mathematics
2.5.1 APOE
The Action-Process-Object-Schema (APOE) theory, for Arias (2019), is a cognitive model
that is part of advanced mathematical thinking and through reflexive abstraction as a
constructive mechanism allows the construction of mental objects. This theory describes
how students understand mathematical concepts by applying the mental constructs of
Actions, Processes and Objects, whose interaction with each other are organized into a
Schema. These mental constructs are developed from the following mental mechanisms:
internalization, coordination, inversion, generalization, encapsulation and/or
decapsulation. The process that students follow to understand a mathematical concept,
based on the APOE theory, begins with the manipulation of physical or mental objects
constructed to form actions, which are internalized to form processes that are encapsulated
and form objects. Objects can be de-encapsulated in the processes from which they were
formed. Finally, actions, processes and objects can be organized into schemes that, if treated
as objects and circumscribed in the organization of other more advanced schemes, it is
concluded that they have been thematized into a mathematical object (Arias, 2019, pp. 83-
84).
3. Research design
This research employs a mixed-methods approach, combining quantitative and qualitative
techniques to analyze the relevance of the prioritized curriculum with an emphasis on
competencies in the teaching of mathematics. From a quantitative perspective, a survey was
conducted among teachers about their classes, and the results were statistically analyzed to
draw general conclusions. According to Ulloa et al. (2017), “quantitative research offers us
the possibility of generalizing the results more broadly; it gives us control over the
phenomena and a perspective on their counting and magnitude” (p. 171). In parallel, a
qualitative approach was incorporated, as it allows for greater interpretive depth when
analyzing the contents and activities of the Ministry of Education's official textbook for the
2023-2024 school year using an analysis sheet. This approach provides “dispersion,
interpretive richness, contextualization of the environment, details, and unique
experiences” (Ulloa et al., 2017, p. 171).
The level of research is descriptive, as it details the characteristics of the curriculum and
describes how students learn mathematical concepts from the perspective of
communication, mathematical, digital, and socio-emotional competencies. As Hernández et
al. (2014) state, this type of research seeks to "specify the properties, characteristics, and
profiles of people, groups, communities, processes, objects, or any other phenomenon that
is being analyzed" (p. 92). Furthermore, the study is based on documentary and field
research. Information was collected from books, scientific articles, and testimonies from
mathematics teachers. In the words of Arias (2012), "documentary research is a process
based on the search, recovery, analysis, critique, and interpretation of secondary data […]
in documentary sources: print, audiovisual, or electronic" (p. 27), while field research
"consists of collecting data directly from the subjects under investigation […] without
manipulating or controlling any variable" (p. 31).
3.1 Research techniques and instruments
For field research, the survey technique was used with its respective instrument, the
cuestionnaire. For documentary research, the Document Analysis technique was applied
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through its instrument, Cards, as well as the content analysis technique using record tables
as an instrument (Arias, 2012, p. 68).
3.1.1 Description of the questionnaire
The questionnaire of this research aimed to collect the perspective of mathematics teachers
on the promotion of communication, mathematical, digital and socio-emotional skills in the
development of their classes and was applied to 112 teachers through an online survey
consisting of a questionnaire with eight items and a total of 29 subitems. The scale of
possible responses is structured as follows: 5. Always (100%), 4. Almost always (75%), 3.
Sometimes (50%), 2. Almost never (25%), 1. Never (0%).
3.1.2 Description of the record
The worksheet used in this research aimed to analyze specific content from two
mathematics textbooks for second-year high school students in relation to the competencies
of the prioritized curriculum. This worksheet applied the mathematics textbook analysis
methodology (MALTM), proposed by Acaro (2020), which consists of three stages: 1)
reference data from the textbook, 2) general outline of the textbook, 3) conceptual analysis.
In total, the worksheet had 44 items and a scale with two possible answers: Yes or No. The
value of "Yes" is three points and that of "No" is one point. The score is obtained by adding
the score obtained (PO), multiplying it by one hundred (100) and dividing it by the sum of
the ideal score (PI).
3.2 Validity of the instruments
The criterion used for instrument validation was expert validation. The questionnaire and
the form were validated in terms of their structure, mathematical content, didactic aspects,
and item wording. Table 1 presents the expert validators of the questionnaire, and Table 2
presents the expert validators of the form.
Expert
Area
Workplace
MSc. Cinthya Veloz
Mathematics
U.E.M. San Francisco de Quito.
MSc. Ruth Gonzáles
Spanish Language and Literature
U.E. Pedro José Arteta.
MSc. Edwin Lozano
Research and Psychology
Central University of Ecuador.
Cuadro 1. Expertos que validaron el cuestionario
Experto
Área
Lugar de Trabajo
PhD. Ana Lucía Arias
Mathematics
Central University of Ecuador.
MSc. Franklin Molina
Mathematics
Central University of Ecuador.
MSc. Lucia Goyes
Pedagogy
Central University of Ecuador.
Table 2. Experts who validated the form
3.3 Reliability of instruments
According to Hernández et al. (2014), “the reliability of a measuring instrument refers to
the degree to which its repeated application to the same individual or object produces
consistent and coherent results” (p. 200). This means that the results obtained must be the
same in successive repetitions. To calculate the reliability of the questionnaire, a survey was
administered to 21 master's students in Mathematics. Based on the results obtained, it was
decided to calculate Cronbach's alpha coefficient, a numerical value that can vary between
zero and one. The value obtained of 0.91 indicates that the instrument has high reliability.
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4. Results
This section is divided into two sections. The first analyzes and interprets the results
obtained from the application of the questionnaire to 112 Mathematics teachers from 73
public, municipal, and private educational institutions, as well as the information collected
from the application of the form to analyze Mathematics textbooks for second-year high
school students during the 2023-2024 school year. The second section discusses the results,
considering the theoretical constructs, background, and objectives of this research. In order
to qualify the numerical results obtained from the application of the questionnaire and the
form, a qualitative description was established as shown in Table 3.
Number of respondents
Percentage of respondents
Qualitative description
De 103 a 112
De 92 % a 100 %
Muy alto
De 90 a 102
De 80 % a 91 %
Alto
De 72 a 89
De 64 % a 79 %
Medio
De 50 a 71
De 44 % a 63 %
Bajo
De 0 a 49
De 0 % a 43 %
Muy bajo
Cuadro 3. Cualificación de los resultados numéricos para el cuestionario y la ficha
4.1 Analysis and interpretation of the questionnaire results
The analysis of each item included statistical column graphs and frequency tables to extract
the most significant findings, highlighting the highest values of each sub-item and was
qualitatively assessed as established in Table 3. In addition, for the interpretation of the
information, the meaning of the results obtained was explained, relating them to the
objectives and guiding questions of this research.
4.1.1 Relevance of the prioritized curriculum
To analyze the relevance of the prioritized curriculum, mathematics teachers were asked
about the way they teach their classes. The question was whether Mathematics teachers
consider their classes contextualized and relevant through the following actions: relating
mathematical content to everyday situations and other subjects; adapting lessons to
students' needs and interests; and connecting the content learned in class to their
sociocultural environment.
Figure 1 presents the results regarding mathematics teachers' perspectives on the
contextualized delivery of their lessons, considering several key elements to analyze the
relevance of the prioritized curriculum in the area of Mathematics. Of the 112 teachers
surveyed, 62 indicated that they always relate mathematical content to everyday situations
and other subjects (subitem 1.1); 42 teachers responded that they do so almost always, and
8 that they do so sometimes. Regarding the adaptation of lessons to students' needs and
interests (subitem 1.2), 55 teachers stated that they do this always; 50 almost always; and
7 sometimes. Finally, regarding the connection between the content learned and the
students' sociocultural environment (subitem 1.3), 47 teachers indicated that they do this
always; 56 almost always; 8 sometimes; and 1 teacher stated that they never do this.
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Relates mathematical
content to everyday life
situations and other
subjects
Adapt math classes to
students' needs and
interests
Links the content learned
in class with their
sociocultural
environment
Always
Almost Always
Sometimes
Almost never
Never
Figure 1. Perspective of the relevance of the prioritized curriculum. Adapted from: (Lima, 2024, p. 59).
These values show that, in this research according to the 112 teachers surveyed, the level
of contextualization and relevance in the application of the prioritized curriculum in the
teaching and learning process of mathematics is very high, since in all sub-items between
103 and 112 teachers surveyed, that is, between 92% and 100%. In addition indicate that
they always or almost always conduct their mathematics classes connecting learning and
educational actions with the realities, needs and aspirations of the student to guarantee an
education that responds to the needs of their social, natural and cultural environment,
contributing to the fulfillment of the right of students to receive a quality education.
4.1.2 Communication skills
To analyze the development of communication skills in Mathematics, teachers were asked
whether they believe they foster these skills through the following actions: developing oral
and written expression skills related to mathematics topics; improving reading
comprehension and information production related to mathematics; communicating
problem-solving processes using mathematical language in an orderly and coherent
manner; and promoting reflection and creativity in academic activities.
Figure 2 shows teachers' perspectives on the application of communication skills in the
classroom, highlighting specific actions that teachers are expected to promote. Of the 112
teachers surveyed, 45 indicate that they always develop oral and written expression skills
related to mathematics topics (subitem 2.1); 57 do so almost always, 8 sometimes, and 2
almost never. Regarding improving reading comprehension and information production
related to mathematical content (subitem 2.2), 43 teachers state that they always do so; 53
almost always, 14 sometimes, 1 almost never, and 1 never. Regarding the communication
of problem-solving processes through orderly and coherent mathematical language
(subitem 2.3), 76 teachers state that they always do so; 31 almost always, 4 sometimes, and
1 almost never. Finally, in relation to the promotion of reflection, critical and complex
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thinking, awareness, and creativity in academic activities (subitem 2.4), 64 teachers
respond that they always do so, 42 almost always, and 6 sometimes.
Develop oral and
written expression
skills related to
mathematical topics
Improves reading
comprehension
and information
production skills
related to
mathematics
Communicates
problem-solving
processes using
mathematical
language in an
orderly and
coherent manner
Promotes
reflection and
creativity in
carrying out
academic
activities
Always
Almost always
Sometimes
Almost never
Never
Figure 2. Application of communication skills. Adapted from: (Lima, 2024, p. 64).
These values show that, in this research according to the 112 teachers surveyed, the extent
to which teachers promote communication skills in the teaching and learning process of
mathematics is high, since in all sub-items between 90 and 102 teachers surveyed, that is,
between 80% and 91%, indicate that they always or almost always conduct their classes
encouraging oral and written expression, comprehension and production of texts and the
resolution of mathematical problems, with the aim that students are able to speak with good
enunciation, in an orderly and coherent manner, make correct use of the language and listen
carefully, analyze a text when reading or listening to it and produce written or oral texts in
a comprehensive way.
4.1.3 Mathematical skills
To analyze the development of mathematical competencies, teachers were asked how they
foster them in the classroom. Teachers considered that these competencies were promoted
through the following actions: explaining and applying mathematical concepts in solving
exercises; proposing logical-mathematical reasoning problems of varying complexity
related to everyday situations; and encouraging critical thinking and mathematical
reasoning in decision-making, both inside and outside the classroom.
Figure 3 presents the results related to the application of mathematical competencies in
classroom teaching. The data obtained show that, of the 112 teachers surveyed, 91 indicated
that they always explain and apply mathematical concepts in solving exercises (sub-item
3.1); 19 do so almost always, and 2 do so sometimes. Regarding the formulation of logical-
mathematical reasoning problems of varying complexity, linked to everyday life situations
(sub-item 3.2), 71 teachers indicate that they do it always, 33 almost always, 7 sometimes
and 1 almost never. Finally, regarding the promotion of critical thinking and mathematical
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reasoning in decision-making (sub-item 3.3), 81 teachers indicate that they do it always, 25
almost always and 6 sometimes.
Explain and apply
mathematical concepts in
solving exercises
Proposes logical-
mathematical reasoning
problems of varying
complexity related to
everyday life situations
Encourages critical
thinking and
mathematical reasoning
in decision-making, both
inside and outside the
classroom
Always
Almost always
Sometimes
Almost never
Never
Figure 3. Application of mathematical skills. Adapted from: (Lima, 2024, p. 66).
These values show that, in this research according to the 112 teachers surveyed, the extent
to which teachers promote mathematical skills in the teaching and learning process of
mathematics is very high, since in all sub-items between 103 and 112 teachers surveyed,
that is, between 92% and 100%, respond that they always or almost always conduct their
classes encouraging the explanation and application of mathematical concepts, the posing
of problems with varying complexity and encourage critical thinking and reasoning, so that
students are able to correctly use mathematical operations, use their symbols with number
sets, solve problems of everyday life and express them in a reasoned, logical, argumentative,
communicative way, and integrating different knowledge.
4.1.4 Digital skills
To analyze the development of digital competencies in mathematics, teachers were asked
how they integrate the use of technologies into their teaching practices through the
following actions: creating digital mathematical content by identifying problems, defining
them, and proposing solutions; using ICTs as tools to facilitate mathematics learning;
explaining how to ethically and responsibly use information obtained in digital
environments on mathematics-related topics; and selecting appropriate educational
platforms to promote meaningful, interactive, and contextualized learning.
Figure 4 presents the results related to the application of digital competencies in
Mathematics. The data show that, of the 112 teachers surveyed, 40 indicate that they always
create digital mathematical content, identifying problems, defining them, and proposing
solutions (subitem 4.1); 49 do so almost always, 18 do so sometimes, 4 almost never, and 1
never. Regarding the use of ICT for learning mathematics (subitem 4.2), 38 teachers state
that they do so always, 47 almost always, 22 sometimes, and 5 almost never. Regarding the
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responsible use of information obtained in digital environments on mathematical topics
(subitem 4.3), 45 teachers respond that they always explain it, 44 almost always, 20
sometimes, and 3 almost never. Finally, in relation to the selection of appropriate
educational platforms to achieve meaningful learning (subitem 4.4), 44 teachers indicate
that they always do so, 47 almost always, 15 sometimes, and 6 almost never.
Create digital
mathematical content
by identifying
problems, defining
them, and proposing
solutions.
Use ICT as tools to
facilitate the
learning of
mathematics
Explains how to
ethically and
responsibly use
information
obtained in digital
environments
Select appropriate
educational
platforms to
promote
meaningful,
interactive and
contextualized
learning
Always
Almost always
Sometimes
Almost never
Never
Figure 4. Application of digital skills. Adapted from: (Lima, 2024, p. 68)).
These values show that, according to the 112 teachers surveyed, the extent to which
teachers promote digital skills in the teaching and learning process of mathematics is
medium, given that in all sub-items between 72 and 89 teachers surveyed, that is, between
64% and 79%, always or almost always conduct their classes promoting the creation of
digital mathematical content, the responsible use of ICTs and the selection of appropriate
platforms for learning Mathematics so that students are able to identify, define and solve
problems that arise in digital environments and that can lead them to educational, cultural,
political and economic environments, through critical thinking, ceasing to be technological
consumers and becoming analysts and creators, people who handle technology
appropriately, consciously and responsibly.
4.1.6 Socio-emotional skills
To analyze the development of socioemotional competencies in Mathematics, teachers were
asked how they integrate them into their teaching practices. In this question, consider that
you foster these competencies through the following actions: you promote teamwork and
collaboration among peers to solve mathematical problems; you guide students in
controlling their emotions when faced with challenges related to mathematics in the
classroom; you encourage the prevention of all types of violence and psychosocial risks
inside and outside the classroom; and you promote self-awareness, empathy,
communication, and tension and stress management.
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Figure 5 shows the results related to the application of socioemotional competencies in
mathematics. Of the 112 teachers surveyed, 74 indicate that they always promote teamwork
and collaboration among peers to solve Mathematical problems (subitem 5.1); 35 do so
almost always, 2 do so sometimes, and 1 teacher never does this. Regarding guidance for
controlling emotions when faced with challenges in the classroom related to mathematics
(subitem 5.2), 63 teachers stated that they do it always, 42 almost always, and 7 sometimes.
Regarding the prevention of all types of violence and psychosocial risks inside and outside
the classroom (subitem 5.3), 82 teachers indicated that they always encourage it, 22 almost
always, and 8 sometimes. Finally, regarding the promotion of self-knowledge, empathy,
communication, and stress management (subitem 5.4), 77 teachers responded that they
always do it, 31 almost always, 3 sometimes, and 1 never includes these actions in their
classes.
Promotes teamwork
and collaboration
among classmates to
solve mathematical
exercises
Guides students in
controlling their
emotions when
faced with
classroom
challenges related
to mathematical
topics.
It motivates the
prevention of all
types of violence
and psychosocial
risks inside and
outside the
classroom.
It promotes self-
knowledge,
empathy,
communication, as
well as tension
and stress
management.
Always
Almost always
Sometimes
Almost never
Never
Figure 5. Application of socio-emotional competencies. Adapted from: (Lima, 2024, p. 71)).
These values show that, in this research, according to the 112 teachers surveyed, the extent
to which teachers promote socio-emotional competencies in the teaching and learning
process of mathematics is very high, because in all sub-items between 103 and 112 teachers
surveyed, that is, between 92% and 100%, always and almost always conduct their classes
encouraging teamwork and collaboration, self-knowledge, empathy, guiding the control of
emotions and motivating the prevention of violence, with the aim of contributing to the
socio-emotional development of their students in the context of learning mathematics..
4.2 Analysis and interpretation of the results of the form
The textbooks analyzed in this study were: Student Textbook for 2nd Year of High School
Mathematics (Alfa), provided free of charge by the Ministry of Education, and the book,
Culture and Mathematical Ingenuity (Beta), published by Santillana. Both textbooks were
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used during the 2023-2024 school year, and their content related to the limit of a function
was analyzed, obtaining results in the three stages of the MALTM methodology.
4.2.1 First stage: reference data from the textbook
The following characteristics are observed in the Mathematics textbooks: it lists the
author(s), the publisher, the year of publication, the place of publication, the availability of
free textbooks, and the Ministry of Education's curriculum certification.
Table 4 shows that the Alfa textbook meets all six items in the first stage, giving it a score of
18. The Beta textbook, on the other hand, meets four items, but since it is neither free (item
5) nor certified by the Ministry of Education (item 6), it obtained a score of 14.
The results obtained in this research show that the Alfa textbook, by meeting all the
evaluated items, is an option aligned with the official curriculum and equitably accessible to
students, obtaining 18 points. In contrast, the Beta textbook, since it is neither free nor
certified by the Ministry of Education, obtained 14 points, suggesting that, although it may
be a complementary resource, it is not officially validated for use in the public education
system. This highlights the importance of certification and accessibility in the selection of
teaching materials.
Ítem
Alfa book
Beta book
Yes
No
PI
PO
Yes
No
PI
PO
3
1
3
1
1
x
3
3
x
3
3
2
x
3
3
x
3
3
3
x
3
3
x
3
3
4
x
3
3
x
3
3
5
x
3
3
x
3
1
6
x
3
3
x
3
1
Subtotal
18
18
Subtotal
18
14
Table 4. Reference data for mathematics textbooks
4.2.2 Second stage: general outline of the textbook
The following characteristics are observed in the mathematics textbooks: they present the
general objective, the author's objective(s), the general objectives of the national
curriculum, a table of contents, a profile of the Ecuadorian high school graduate, the didactic
organization of the units, icons to identify specific activities, knowledge assessment
guidelines, the technological resources used, a bibliography, and the topic to be analyzed is
included in the content. Table 5 shows that both textbooks analyzed achieve a PO of 22 out
of 30. From items 7 to 16, the textbooks agree on the aspects they include and those they
omit. However, there is a difference in item 17, which does not have an assigned score.
However, it is determined that the Alpha textbook does not address the limit of a function,
while the Beta textbook does.
The results obtained in this research indicate that both textbooks have a similar didactic
structure and meet most of the criteria analyzed. However, a key difference is that the Alfa
book, published by the Ministry of Education, does not address the limit of a function, while
the Beta book, published by Santillana, does. Since both texts are aimed at second-year high
school students, this difference is significant, as the limit of a function is a fundamental
concept in the mathematics curriculum. This suggests that, although the Alfa book is the
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official material, it may not be sufficient to address all the required content, highlighting the
importance of complementing teaching with other resources.
Ítem
Alfa book
Beta book
Yes
No
PI
PO
Yes
No
PI
PO
3
1
3
1
7
x
3
1
x
3
1
8
x
3
1
x
3
1
9
x
3
1
x
3
1
10
x
3
3
x
3
3
11
x
3
1
x
3
1
12
x
3
3
x
3
3
13
x
3
3
x
3
3
14
x
3
3
x
3
3
15
x
3
3
x
3
3
16
x
3
3
x
3
3
Subtotal
30
22
Subtotal
30
22
17
Si
No
Si
No
x
x
Table 5. General outline of mathematics textbooks
4.2.3 Third stage: conceptual analysis
The following activities are observed in Mathematics textbooks to promote the application
of the prioritized curriculum competencies.
Communication skills (CC) include readings with examples and appropriate language;
spaces for writing texts or summaries; and materials that stimulate reflection, critical and
complex thinking, awareness, creativity, and the construction of new knowledge in
students. Additionally, activities are included in which students communicate problem-
solving processes through the effective use of language, both oral and written, with
relevance and fluency.
Mathematical skills (MC) include activities to use and relate real numbers and their
operations; employ formal mathematical language; work with different forms of
representation (numerical, graphical, algebraic, and verbal); encourage logical and
reasoned reasoning; relate mathematics to different contexts of everyday life; and promote
awareness, responsibility, and critical analysis in the context of mathematical processes.
Digital skills (CD) include activities that enable the development of computational thinking.
Activities to identify, define, and solve problems through the responsible use of
mathematics-related software; activities in which students analyze and build mathematical
knowledge through the use of ICTs (presentations, videos, web pages, simulators); and
activities aimed at promoting digital responsibility.
In socio-emotional competencies (SC), activities are presented to promote self-knowledge,
empathy, assertive communication, emotional management, collaboration, positive
relationships, decision-making, as well as problem-solving and conflict management from a
socio-emotional perspective.
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Table 6 shows that the Alpha book does not address the topic of the limit of a function, while
the Beta book does, albeit partially. The latter obtains a score of 3 in items 19, 20, and 21,
which focus on communication skills; in two of the six items related to mathematical skills;
in items 33 and 35, which address digital skills; and in items 39, 41, 42, and 43, which refer
to socio-emotional competencies, achieving a PO of 49 out of 81. In the other items, like the
Alfa book, it does not meet the assessed aspects. Thus, the Alfa book achieves a PO of 9 out
of 81.
Competencies
Ítem
Alfa book
Beta book
Yeas
No
PI
PO
Yes
No
PI
PO
3
1
3
1
CC
18
X
3
1
x
3
1
19
X
3
1
x
3
3
20
X
3
1
x
3
3
21
X
3
1
x
3
3
22
X
3
1
x
3
1
23
X
3
1
x
3
1
24
X
3
1
x
3
1
25
X
3
1
x
3
1
26
X
3
1
x
3
1
CM
27
X
3
1
x
3
1
28
X
3
1
x
3
1
29
X
3
1
x
3
3
30
X
3
1
x
3
3
31
X
3
1
x
3
1
32
X
3
1
x
3
1
CD
33
X
3
1
x
3
3
34
X
3
1
x
3
1
35
X
3
1
x
3
3
36
X
3
1
x
3
1
CS
37
X
3
1
x
3
1
38
X
3
1
x
3
1
39
X
3
1
x
3
3
40
X
3
1
x
3
1
41
X
3
1
x
3
3
42
X
3
1
x
3
3
43
X
3
1
x
3
3
44
X
3
x
3
1
Subtotal
81
27
Subtotal
81
49
Table 6. Curriculum competencies prioritized in mathematics textbooks
The conceptual analysis of communication, mathematical, digital, and socio-emotional
competencies in the Alpha and Beta textbooks reveals that, although both textbooks have
similar subscores, the Beta textbook outperforms the Alpha textbook in several aspects.
Beta includes more activities that encourage reflection, critical thinking, the creation of
reading-based texts, different forms of representation (numerical, graphical, algebraic, and
verbal), logical and reasoning, the development of computational thinking, the analysis and
design of mathematical content using ICT, as well as assertive communication,
collaboration, positive relationships, and decision-making.
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However, both textbooks are significantly lacking in activities related to the curriculum
competencies. This suggests that neither textbook fully meets the curriculum's objectives
in terms of competency development, especially in the context of the boundary topic of a
function.
4.2.4 Level of Compliance with Curriculum Competencies Prioritized by Mathematics
Textbooks
In this research, the compliance level is considered a percentage obtained from the
evaluation of specific content in a mathematics textbook using the MALTM methodology. To
obtain this value, the score obtained (SO) is added, multiplied by one hundred (100), and
divided by the sum of the ideal score (IS). Table 7 shows the results obtained from the
application of the worksheet to mathematics textbooks for second-year high school
students. In order to qualify the numerical results obtained from the application of the
worksheet, for this research, the same qualitative description of the questionnaire (Table
3) is considered. It was determined that the Ministry of Education textbook (Alfa) obtained
a compliance level of 52%, which is evaluated as low, while the Santillana Publishing House
textbook (Beta) obtained a level of 66%, which is evaluated as medium.
Ítem
1 al 44
Alfa book
Beta book
PI
PO
PI
PO
Total
129
67
129
85
Percentage compliance level
100%
52%
100%
66%
Qualitative description
Low level
Medium level
Table 7. Qualification of numerical results for the record
These values highlight the need to design teaching activities that enable the achievement of
the competencies of the prioritized curriculum in the Ministry of Education's textbook for
the second year of high school. Likewise, in the textbook used by private institutions (Beta),
there is a need to improve and enhance activities in order to further promote the
communication, mathematical, digital, and socio-emotional competencies of the prioritized
curriculum.
4.3 Discussion of the results
The research evaluated the contextualization and relevance of the curriculum in second-
year high school mathematics teaching, revealing that between 92% and 100% of the
teachers surveyed relate the content to everyday life and other subjects, adapting their
lessons to students' needs and interests. This finding confirms a strong ownership of the
prioritized curriculum, in line with Barrios (2016), who emphasizes the importance of a
structured and contextualized curriculum to promote meaningful learning. However, it is
important to reflect on how this contextualization translates into concrete learning
outcomes, given that adaptation to varied contexts can present challenges to the
uniformity of educational quality.
Regarding the development of communication skills, teachers report fostering these skills
in a range between 80% and 91%, promoting oral expression, reading comprehension,
and the use of mathematical language. While teacher perceptions are positive, studies
such as Toalombo (2021) and the INEVAL (National Institute of Statistics and
Censuses)'s "Being a Student 2023" report show real deficiencies in students' verbal
skills, which could indicate a discrepancy between teacher perceptions and student
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performance. This gap raises the need to investigate additional factors such as teacher
training, applied pedagogical strategies, and the classroom environment that impact
communication development in mathematics.
Analysis of the development of mathematical competencies shows that between 92% and
100% of teachers encourage the explanation of concepts, problem-solving, and critical
thinking—essential practices for logical reasoning. However, the low achievement levels
reported by INEVAL suggest that these efforts, although relevant, may not be sufficient
to overcome learning challenges. This invites critical reflection on the effectiveness of
the methodologies employed and the possible impact of external factors such as
infrastructure, resources, and institutional support. Regarding digital skills, there is
evidence of medium use of technological tools (64% to 79%), revealing a significant area
for opportunity. Although it is worth noting that a considerable proportion of teachers use
ICTs responsibly and recognize their importance, the average level of digital integration
indicates the need to strengthen teacher training and support for more effective
implementation of technologies that enhance mathematical learning.
Regarding the development of socio-emotional skills, this is perceived as a strengthened
aspect, with 92% to 100% of teachers promoting teamwork, emotional control, and
violence prevention, key aspects for comprehensive learning. This commitment coincides
with Mina et al. (2023), who identify socio-emotional skills as the most accessible for
teaching practice. However, it is important to explore how these skills impact academic
performance and student motivation in the long term.
To conclude this discussion of results and with the aim of evaluating the fulfillment of
communication, mathematical, digital, and socio-emotional competencies in
Mathematics textbooks for second-year high school, specifically in the concept of the
limit of a function. When comparing the results obtained with those of Acaro (2020), who
analyzed textbooks for first and third years of high school, it is concluded that the official
texts of the Ministry of Education, for the most part, present the dynamic conception of
the limit. In contrast, the Santillana publishing house textbook for second-year high
school shows both a dynamic and metric conception. In this analysis, the Maya publishing
house textbook (2023) for second-year high school does not address the topic of the limit
of a function, resulting in low compliance with the established indicators. On the other
hand, the Santillana (2023) textbook for second-year high school shows an average level
in the application of communication, mathematical, digital, and socio-emotional
competencies. With these results it can be seen that the mathematics textbooks for second
year of high school, with respect to the application of communication, mathematical,
digital and socio-emotional skills of the prioritized curriculum, have on average a low
level.
5. Conclusions
This research demonstrated that second-year science teachers perceive a contextualized
and relevant application of the prioritized curriculum in teaching Mathematics. This
contextualization favors the integration of content with everyday life and other subjects,
promoting more meaningful and inclusive learning, regardless of the type of educational
institution.
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One of the main contributions of the study is confirming that teachers promote the
development of communication, mathematical, and socioemotional skills at high levels,
which suggests a clear appropriation of the prioritized curriculum's approaches. However,
the integration of digital skills still presents challenges, highlighting the need to strengthen
teacher training in the pedagogical use of technologies. The analysis of textbooks, especially
on the topic of the limit of a function, reveals that, although there has been partial progress,
compliance with the prioritized curriculum criteria is still limited. This highlights the need
to review and update teaching materials to ensure adequate coverage of the established
content and skills. As a future line of research, comparative studies between teacher
perceptions and student performance in mathematics are recommended to verify the real
impact of the prioritized curriculum. It would also be valuable to analyze curriculum
implementation at other educational levels and areas of knowledge, as well as to delve
deeper into the design of innovative teaching strategies that effectively integrate digital
skills.
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Authors
JHON LIMA-YARPAZ earned his Master's degree in Education, majoring in Mathematics,
from the Central University of Ecuador in 2025. He earned his Bachelor's degree in
Educational Sciences, majoring in Mathematics and Physics, from the Central University of
Ecuador in 2021.
He currently teaches Mathematics and Physics at the Unified General High School at the
Atahualpa Fiscal Educational Unit. He has participated in international scientific events,
speaking and leading workshops on the teaching of Mathematics, reflecting his commitment
to education and research. He earned the Outstanding Teacher certificate at his institution,
awarded by Education District 17D02-Calderón in recognition of his dedication,
professionalism, and excellence in teaching.
ANA ARIAS-BALAREZO obtained her PhD in Educational Research from the University of
Alicante (Spain) in 2019. She earned her Master's degree in Educational and Social Projects
from the Central University of Ecuador in 2003. She earned her Bachelor's degree in
Educational Sciences, Specializing in Mathematics and Physics from the Central University
of Ecuador in 1995. She worked as a professor of Mathematics and Statistics at the Simón
Bolívar Experimental School and as a professor of Mathematics and Director of the
Pedagogy of Experimental Sciences, Mathematics, and Physics program at the Faculty of
Philosophy, Letters, and Educational Sciences at the Central University of Ecuador.
She is currently Dean of the Faculty of Philosophy, Letters, and Educational Sciences at the
Central University of Ecuador. Her main research interests are focused on the teaching of
Mathematics. She has been a speaker and workshop leader at national and international
events and is the author of a wide range of books on Mathematics.
76
Licencia Creative Commons Atribución 4.0 Internacional (CC BY 4.0)
Revista Cátedra, 8(2), pp. 55-76, July - December 2025. e-ISSN:2631-2875
https://doi.org/10.29166/catedra.v8i2.7916
FRANKLIN MOLINA-JIMÉNEZ earned his Master's degree in University Teaching and
Educational Administration from the Universidad Tecnológica Indoamérica (Ecuador) in
2011. He also earned his Bachelor's degree in Educational Sciences, specializing in
Mathematics and Physics, from the Central University of Ecuador in 1995. He collaborated
as an Algebra professor at the University of the Armed Forces (ESPE).
He is currently a full professor of Physics and Mathematics and Physics Didactics in the
Pedagogy of Experimental Sciences, Mathematics, and Physics program at the Faculty of
Philosophy, Letters, and Educational Sciences of the Central University of Ecuador. He has
also collaborated as a lecturer in the Geometry and Research modules of the Master's
program in Mathematics Education offered by the Faculty of Philosophy, Letters, and
Educational Sciences of the UCE (Ecuador University of Ecuador). His main research
interests are focused on the teaching of physics and plane geometry. He won first place in
the competition organized by the Quito Municipal Education Secretariat and the Fidal
Foundation in the ICTs applied to the teaching-learning process category. He is the author
of book chapters on physics and plane geometry, papers, and articles published in several
journals.
Declaration of authorship-CRediT
JHON LIMA-YARPAZ: data collection, conceptualization, methodology, formal analysis,
writing, and editing.
ANA ARIAS-BALAREZO: research supervision, formal and conceptual review of the draft
and original writing, validation, methodology, formal analysis, and writing.
FRANKLIN MOLINA-JIMÉNEZ: conceptualization, validation, methodology, formal
analysis, review of the draft and original.
