154
Formative assessment for achieving
competency in mathematics
Jimmy Alexander Moreno Castro1
Jairo Guillermo Moreno Castro2
To reference this article / Cómo citar este artículo / Para citar
este artigo: Moreno Castro, J. A. & Moreno Castro, J. G. (2024).
Formative assessment for achieving competency in mathematics.
Revista UNIMAR, 42(2), 154-168. https://doi.org/10.31948/
ru.v42i2.3800
Received: November 30, 2023
Revised: April 11, 2024
Accepted: May 6, 2024
Abstract
The assessment of mathematical competencies is an aspect of paramount
importance for involving students in their own learning process. Formative
assessment stands out as an opportunity to improve the level of learning
achieved; however, in some contexts it is applied partially or systematically,
giving priority to summative or final assessment. The aim of this study was
to identify the processes that support formative assessment in relation to the
achievement of mathematics competencies in basic education. For this purpose,
the documentary review technique and an analysis matrix were used as a tool
to answer the following question: Which formative assessment processes are
relevant to the achievement of mathematics literacy in elementary education?
The documents were located in databases such as WoS, Scielo, Redalyc and
Google Scholar and then an analysis matrix was applied. It is concluded that
formative assessment is of extraordinary relevance for the acquisition of
mathematical competences when it applies feedback processes, such as the
identification of achievements, self-assessment and co-assessment, in which
students are recognized as the main actors of their learning process; therefore,
this type of assessment allows them to focus on the internal demand to learn,
not only in the areas of knowledge they have to master, but in all aspects of
their lives.
Keywords: basic education; student assessment; formative assessment;
competencies; mathematics competencies
1 Doctoral candidate in Educational Sciences, Universidad Metropolitana de Educación, Ciencia y Tecnología Umecit (Panamá). E-mail
address: jimmymoreno.est@umecit.edu.pa
2 Doctoral candidate in Educational Sciences, Universidad Metropolitana de Educación, Ciencia y Tecnología Umecit (Panamá). E-mail
address: jairomoreno.est@umecit.edu.pa
Review article.
Revista Unimar Julio-Diciembre 2024
e-ISSN: 2216-0116 ISSN: 0120-4327 DOI: https://doi.org/10.31948/rev.unimar
Rev. Unimar Vol. 42 No. 2 pp. 154-168
155
La evaluación formativa para el logro de
competencias en matemáticas
Resumen
La evaluación de las competencias en matemáticas es un aspecto de
singular importancia para involucrar a los estudiantes en su propio proceso
de aprendizaje. La evaluación formativa se destaca como una oportunidad
para potenciar los niveles de aprendizaje logrados; sin embargo, en algunos
contextos se aplica parcialmente o de manera asistemática, privilegiando la
evaluación sumativa o final. El objetivo del presente estudio fue identificar los
procesos que fundamentan la evaluación formativa en términos del logro de
las competencias en matemáticas en la educación básica. Para ello, se utilizó
la técnica de revisión documental y se empleó una matriz de análisis como
instrumento, a fin de dar respuesta al siguiente interrogante: ¿cuáles procesos
de la evaluación formativa son pertinentes para el logro de competencias en el
área de matemáticas en la educación básica? Los documentos se localizaron en
bases de datos como WoS, Scielo, Redalyc y Google Scholar; posteriormente,
se aplicó una matriz de análisis. Se concluye que la evaluación formativa es
de extraordinaria relevancia para el logro de competencias matemáticas al
momento de aplicar procesos de realimentación, tales como la identificación de
logros, la autoevaluación y la coevaluación, a partir de los cuales se reconoce
al estudiante como el actor principal de su proceso de aprendizaje. Por ello,
este tipo de evaluación permite a los estudiantes enfocarse en la demanda
interna de aprender, no solo en las áreas de conocimiento que requieren
dominar, sino en todos los aspectos de su vida.
Palabras clave: educación básica; evaluación del estudiante; evaluación
formativa; competencias; competencias en matemática
Avaliação formativa para alcançar a competência em
matemática
Resumo
A avaliação das competências matemáticas é um aspecto de suma importância
para envolver os alunos em seu próprio processo de aprendizagem. A
avaliação formativa se destaca como uma oportunidade de aprimorar o nível
de aprendizado alcançado; entretanto, em alguns contextos, ela é aplicada de
forma parcial ou sistemática, dando prioridade à avaliação somativa ou final.
O objetivo deste estudo foi identificar os processos que apoiam a avaliação
formativa em relação à obtenção de competências matemáticas na educação
básica. Para isso, foram utilizadas a técnica de revisão documental e uma
matriz de análise como ferramenta para responder à seguinte pergunta:
Quais processos de avaliação formativa são relevantes para o alcance da
alfabetização matemática no ensino fundamental? Os documentos foram
Revista Unimar Julio-Diciembre 2024
e-ISSN: 2216-0116 ISSN: 0120-4327 DOI: https://doi.org/10.31948/rev.unimar
Rev. Unimar Vol. 42 No. 2 pp. 154-168
Formative assessment for achieving competency in mathematics
Jimmy Alexander Moreno Castro
Jairo Guillermo Moreno Castro
156
Revista Unimar Julio-Diciembre 2024
e-ISSN: 2216-0116 ISSN: 0120-4327 DOI: https://doi.org/10.31948/rev.unimar
Rev. Unimar Vol. 42 No. 2 pp. 154-168
localizados em bancos de dados como WoS, Scielo, Redalyc e Google Scholar
e, em seguida, foi aplicada uma matriz de análise. Conclui-se que a avaliação
formativa é de extraordinária relevância para a aquisição de competências
matemáticas quando aplica processos de feedback, como a identificação
de realizações, a autoavaliação e a coavaliação, nos quais os alunos são
reconhecidos como os principais atores de seu processo de aprendizagem;
portanto, esse tipo de avaliação permite que eles se concentrem na demanda
interna de aprendizagem, não apenas nas áreas de conhecimento que
precisam dominar, mas em todos os aspectos de suas vidas.
Palavras-chave: educação básica; avaliação do aluno; avaliação formativa;
competências; competências em matemática
Introduction
The debates on curricular transformation
ask why, for what purpose, and to whom the
mission of educational systems is directed. One
of the aspects has been and continues to be
evaluation, especially when a teacher-centered
role prevails in the face of a passive student
body. This article arises from the demands of an
approach between teaching-evaluation and the
conditions to achieve quality learning. Taking
into account that in the educational systems of
Latin American countries, including Colombia, it
has been observed that despite the fact that the
evaluation model is no longer a directive process
(García et al. 2019), traditional evaluation
practices that privilege rote learning, without
considering a student-centered evaluation,
continue to be carried out.
However, the qualification and the distinction
between those who pass and those who fail take
precedence, in order to meet the bureaucratic
requirements of educational administration
(Córdoba et al. 2018). This involves a series
of contradictions: first, with the theoretical
principles of an evaluation linked to the
acquisition of competencies, through constant
help in terms of identifying and overcoming
weaknesses to optimize learning (Muñoz-
Jaramillo, 2023); second, with the integral
formation of individuals (Medina, 2022).
It also contradicts the evolution of the concept
of evaluation, to the extent that it can be
considered transcendental to assess the
different dimensions of the human being; hence
its holistic and integral character, which includes
the measurement of knowledge (knowledge or
knowing), disposition and practical or procedural
performance and the attitudes involved, as well
as the forms of understanding, reflexivity and
emotionality to respond to a given learning
situation (Uzcátegui and Albarrán, 2020).
In this regard, Bizarro et al. (2021) state that
«teachers and students have the arduous task of
transforming the traditional forms of evaluation
into a formative form of evaluation» (p. 874).
Thus, «teachers perform a new role, since the
context is the one that guides the development
of learning, and they have to promote
meaningful situations related to this context»
(Meléndez et al., 2023, p. 1106). Therefore, an
attempt has been made to abandon traditional
epistemologies and to adopt contents, methods
and techniques that favor an evaluation based
on the peculiarities of each context.
For his part, Ruiz (2021) considers that «for
many teachers, it is practically impossible
to imagine plausible forms of formative
evaluation» (p. 659). According to the results
of the Mejoredu survey (Comisión Nacional para
la Mejora Continua de la Educación, 2020), for
any educational institution to adopt this type
of evaluation, it is necessary to have training
programs for teachers, curricular definitions,
support from educational authorities to create
a collaborative culture, and for each school to
carry out research on the contextual conditions
of the students, among other aspects.
Formative assessment for achieving competency in mathematics
Jimmy Alexander Moreno Castro
Jairo Guillermo Moreno Castro
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The above points are important in all areas,
but mathematics is indispensable in the
different disciplines and areas of life; therefore,
evaluation cannot be analyzed in isolation from
other aspects of didactics, such as planning,
facilitation or, mediation and motivation.
In terms of planning, this is done from the
point of view of fulfilling a program, with
evaluation being automatic through strategies
and tools (Martínez, 2016, cited in Medina-
Zuta and Deroncele-Acosta, 2019), so that
pedagogical know-how is instrumental, far
from its formative dimension. Planning should
give meaning to meaningful and discovering
learning, in addition to having diverse strategies
for formative assessment.
As for facilitation or mediation, it should be a
practice inspired by the recognition of students,
which privileges strategies and resources aimed
at promoting the development of skills through
the appropriation of plural knowledge (Alzate-
Ortiz and Castañeda-Patiño, 2020). For this,
the teacher, as mediator, must start from an
episteme that transcends the rigid, inflexible
and not very determinant conceptions regarding
the evaluation of mathematical competences,
only for grading, without promoting motivation
and persistence to learn.
Given that the objective of this article is
oriented to identify the processes of formative
assessment relevant to the achievement of
competencies in the area of mathematics at the
basic education level, procedures of analysis and
comparison of authors were developed based
on the referential and defining understandings
of formative assessment as a resource for the
achievement of competencies. The analysis of the
results allowed us to have a well-founded basis
with regard to the identification of conditions
for reflection on the identified processes and
to reflect on the quality of education according
to Silva-Escalante (2023), who states: «the
result of the evaluation is known through the
achievement of competencies, and it is there
that the issue of formative evaluation becomes
important» (p. 14).
Methodology
The methodology considered the documentary
review technique, defined by Fernández de Silva
(2021) as «the search for existing information
that the researcher carries out on the basis
of previous research, theories or approaches
of other scientists and authors, with the aim
of clarifying the objectives, conceptualizing
the study events and orienting the research
work» (p. 32). In terms of tools, an analysis
matrix was used, supplemented by three other
matrices: registration, topic and file. The data
collection consisted of recording the authors
consulted and to be consulted, with all their
data, the location and the subject or content
of interest; the topics were listed according to
the complexity of the aspect to be studied, in
accordance with the outline of the article. A
matrix was then constructed to record the core
concepts present in the publications, in the form
of research articles, review articles and essays,
in both printed and digital formats.
The inclusion criteria were the following: i)
formative assessment in basic education and
mathematics; ii) Spanish and English language;
iii) affiliation of the journal of origin to recognized
databases; iv) abstract with at least three
elements (objective or purpose, methodological
criteria and results). Documents written in a
language other than the one required and those
without elements demonstrating completeness
and appropriateness in their development were
excluded. A total of 52 articles from indexed
journals were included (see Table 1).
Formative assessment for achieving competency in mathematics
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Jairo Guillermo Moreno Castro
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Table 1
Indexing, temporality and total number of sources selected for the study
Indexing Temporality Total
2018 to 2020 2021 to 2022 2023
Scielo 3 3 3 9
Scopus 2 3 2 7
Dialnet, Redalyc Latindex Publindex 6 5 3 14
Web of Science 2 2 2 6
Doaj 2 2
Google Scholar 5 5 4 14
Total 18 18 16 52
Background
On the subject of assessment in general, there
are statements based on its potential, as well
as judgments on the limited use of formative
assessment, especially in mathematics, where
it is a flashpoint in terms of confrontation
between teachers and students (Gómez et al.,
2022; Medina and Peralta, 2018); consequently,
there is disharmony in the classroom climate
and a high risk to the quality of education.
In basic education in Colombia, educational
institutions have autonomy in the design,
organization and application of assessment.
Decree 1290 of 2009 establishes the Institutional
System of Student Evaluation (SIEE), which
regulates the evaluation processes that must
be established in the Institutional Educational
Project (PEI), based on the Curricular Guidelines
(1998), the Basic Learning Rights (DBA) and
the Basic Competence Standards (EBC) in
Mathematics, with the aim of taking into
account the competences for a comprehensive
education, self-knowledge, social, autonomous,
critical, with basic and essential learning skills.
In the study carried out by Gómez (2019), in the
evaluation of the mathematical competences
of 299 students in an educational institution in
Colombia, no positive results were obtained in
the advanced level of the qualification in three
of the basic competences of the field: there
were a total of 141 students at an insufficient
level in the competence of communication,
representation and modeling; 281 students
were at the same level in terms of reasoning and
argumentation, and 108 in terms of presenting
and solving problems. This means that in the
field of mathematics, the teaching continues
to be traditional, without producing significant
learning in the students; that is, it is based
on learning by rote, based on computational
techniques, without understanding the meaning
of the procedures.
Faced with this situation, a study that provides
evidence on the use of formative assessment
is that of Alarcón et al. (2019), in which they
worked on formative assessment strategies for
the development of mathematical thinking in
fifth grade elementary students, who presented
difficulties in the development of Saber tests in
the components of variational thinking, modeling
processes, communication and problem solving
in two educational institutions in Colombia. The
objective was to demonstrate the follow-up of
the use of formative assessment as a tool to
develop variational thinking. Among the results,
it is highlighted that the formative assessment
allowed students to recognize their learning and
difficulties in ratio, direct proportionality and the
rule of three, thanks to the fact that they were
linked to activities that generated commitment
and motivation.
For their part, Ibarra-Sáiz et al. (2023) analyzed
the quality of learning outcomes assessment
tasks to describe the characteristics of
Formative assessment for achieving competency in mathematics
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Jairo Guillermo Moreno Castro
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Rev. Unimar Vol. 42 No. 2 pp. 154-168
assessment tasks according to the perception
of teachers and found that the most relevant
nuances that assessment should have are the
transparency and depth of the tasks, while
feedback and student participation in the
assessment processes are the least valued.
The reality described is worrying because
truthfulness and completeness are part of
formative assessment, which is called to
appease students’ ability to reflect on their own
actions and, in turn, to generate a disposition
to propositional criticism (Medina-Zuta and
Deroncele, 2019). Therefore, it is necessary
to strengthen teacher training to promote the
use of feedback and, above all, to facilitate
student participation in evaluation, which
would improve the quality of evaluation tasks
and lead to greater achievement of the desired
learning outcomes.
In the same sense, we agree with a finding
of the Latin American Laboratory for the
Evaluation of the Quality of Education (LLECE),
which distinguishes formative evaluation and
characterizes it as having great didactic value
because it «represents a particular educational
approach that seeks to give higher profile to
students, leading to more meaningful, useful
and motivating learning, giving greater value to
processes and improvement» (Organización de
las Naciones Unidas para la Cultura, las Ciencias
y la Educación [Unesco], 2021, p. 2).
Meléndez et al. (2023) conclude that in
mediation, as part of the dimensions of the
teaching and learning process, it is essential to
pay special attention to formative evaluation.
Thus, mediation is called to prioritize the
socio-emotional and motivational attention
of students, considering their experiences.
However, the stimulation of metacognitive
processes is lacking in relation to formative
assessment. The authors argue that the
main challenges relate to the need to adjust
the objectives and content established in the
curriculum in order to have an assessment
relevant to the conditions of the students.
Similarly, Medina-Zuta and Deroncele-Acosta
(2019) say that one of the problems faced by
educational institutions at the elementary and
high school levels is the need to deepen the self-
reflective capacity of teachers as an alternative
and response to the implementation of formative
assessment. For these authors, it is essential to
strengthen the self-reflective capacity and the
disposition to propositional criticism to provide
answers to the implementation of formative
assessment. This merits a paradigm shift that
leads to the promotion and improvement of
formative assessment.
Another contribution on learning assessment
in general was the study by Cáceres et al.
(2018) on the role of the teacher in learning
assessment. The authors identified gaps and
aspects to be improved in terms of adopting,
adapting, diversifying and enriching techniques
that allow assessment to become a formative
process and, therefore, enriching, permanent,
fair, grounded and participatory. They specified
the importance of evaluation for understanding
and improving student learning and the practices
developed in educational institutions.
Valdez et al. (2023), in their research on
the application of this type of evaluation
of feedback, found that through formative
evaluation, students manage to strengthen
motivation, self-evaluation, critical thinking
and personal improvement. In addition, the
regular practice of this type of evaluation
improves learning, but it must be a continuous
and participatory process.
These studies have provided a diagnosis of
the difficulties that students face in academic
performance, especially in mathematics, in
basic educational institutions in Colombia, a fact
that endangers the quality of education. They
emphasize key processes such as feedback
(Torres and San Martin, 2021), as well as student
control and participation through self-evaluation.
The results confirm the relevance of formative
assessment as an element that directs the
search for the achievement of competencies in
mathematics, because it allows identifying both
the state of progress and the difficulties that
students have in achieving significant progress
in their studies.
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Jairo Guillermo Moreno Castro
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Considerations about Formative
Assessment in Mathematics
The literature distinguishes three types of
assessment: diagnostic, summative and
formative. The first is a specific and differentiated
inquiry for each student (Díaz and Hernández,
2010), prior to the development of any
educational process; in a timely manner, before
the beginning of any instructional sequence or
segment, since its function is to identify and
use the students’ prior knowledge, taking it into
account in the design of the instructional plan.
Summative or final evaluation is used to
determine the extent to which educational
intentions have been achieved, to assign
grades, and to make judgments about the
level of learning achieved. This is considered
a traditional evaluation that allows for grading
and distinguishing who passes, the purpose of
which is to meet the bureaucratic requirements
required by the educational administration
(Córdoba et al., 2018). However, it is important
to consider that this type of evaluation, although
it has a pronounced use in basic primary and
secondary education and responds to learning
products in a global way, contributes to making
pedagogical decisions that in one way or
another affect the educational process (Díaz
and Hernández, 2010).
The relevance of formative assessment
lies in «promoting personal development,
the improvement of knowledge, skills and
preparation for the world of work [of future
professionals] » (Gallego-Arrufat and Cebrián-
de-la-Serna, 2018, p. 139), also considering
that mathematics is part of everyday life and
manifests itself in all areas of society. Thus,
diagnostic and summative assessment are very
different from formative assessment, since the
latter has positive effects; therefore, its use is
recommended as an essential part of teaching
and learning in all areas (Tamayo et al., 2023).
The Colombian Ministry of National Education
(MEN, 1998), in its curriculum guidelines, defines
formative evaluation as a renewing concept
that refers to a set of procedures that should
be permanently practiced, which should also be
understood as inherent to the educational task,
to interact the construction of their knowledge
and value systems, increase the number of skills
and perfect each of them, and that grow within
the context of a life in society.
For Valdivia and Fernández (2020), formative
evaluation refers to the cyclical process through
which students or their teachers carry out the
collection (taking and recording) and processing
(analyzing and interpreting) of information to
make a judgment about learning and thus be
able to use it as feedback. From this perspective,
«assessment should serve as a tool both for
learning and for improving teaching» (MEN,
2018, p. 56). Indeed, Muñoz-Jaramillo (2023)
points out: «The ideal end of evaluation is
a training that is systematized through the
continuous evaluation of its learners, which the
different evaluation modalities become a focal
point, and therefore, the results» (p. 88).
The above confirms that the purpose of formative
assessment in mathematics teaching and
learning is to review these situations to adapt
or adjust them for the benefit of students, to
the extent that processes such as identification
of achievement, feedback, self-assessment and
co-assessment are recognized (Pasek and Mejía,
2017). In line with this, Pellegrino (2020) states
that assessment should help to improve student
performance, but not to audit it.
For Filippi et al. (2021), «making explicit and
sharing the evaluation criteria of the activity and
of each evaluable task or milestone, and having
a synchronous or asynchronous dialogue with
students about them, will contribute decisively
to making assessment more transparent» (p.
397). To this end, it is essential to promote
understanding of the process by identifying
possible errors or limitations, but also
opportunities, potentialities and challenges that
could have an impact on the achievement of the
desired competencies.
In the educational reality, it is not possible to
avoid two aspects: first, the real meaning of
formative evaluation, because at all times there
must be an interest in highlighting and valuing
the successes or achievements that students
achieve in the construction process (Pasek and
Mejía, 2017; Barboza and Cherres, 2021).This
is due to the consolidation of learning, which
gives students the opportunity to know what
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criteria are being followed to evaluate their
achievements. The second aspect is to consider
mistakes as positive, in the sense that through
them one learns, because by identifying what
one does not know, one works to overcome it,
through internalization and responsible adoption
of different means to bridge failures.
Bizarro et al. (2021) emphasize that the purpose
of formative assessment is to improve and
motivate students’ autonomy, as it helps them to
see their own achievements and difficulties, as
well as to reflect on their mistakes. This approach
to formative assessment is fundamental to
understanding and adjusting the teaching and
learning process in the classroom.
In order for assessment to strengthen the
quality conditions in mathematics learning, it
must meet a series of characteristics, especially
the interaction between teacher and student,
so that the student internalizes his or her
achievements, but also the skills to develop
competencies (Muñoz, 2020). In this regard,
Lozano and Tamez (2014, as cited in Montenegro
et al., 2022) point out that «feedback is adapted
to the current times, in which the student is
required to develop competencies» (p. 2027)
and, with them, achieve meaningful learning
with lasting anchors for life (Morales-Aibar and
Medina-Zuta, 2020).
Another aspect of formative assessment is
flexibility, which is understood as «the ability
to adapt the teaching-learning process flexibly
according to the needs of the students» (Unesco,
2021, p. 13). Although there are systematized
and preconceived processes in this assessment,
it can change in the course of its application,
making it less rigid (Sánchez et al., 2022).
In this particular case, there is a need for a
reflective and flexible teacher who promotes
evaluation as an integral pedagogical proposal,
where the intercultural factor that enhances
the ability to know how to be and live together
stands out (Mollo-Flores and Medina-Zuta,
2020; Cruzado, 2022; Salazar, 2023). These
characteristics are of interest to obtain reliable
or truthful information about how a student
thinks, feels, or communicates, as a function
of «analyzing their practice and transforming
it into situated teaching to achieve the goal
of providing quality education» (Rocha and
De la Cruz, 2018), and capable of transferring
mathematical knowledge to everyday life.
For Unesco (2021), another quality of formative
assessment is the ability to adjust in the teaching-
learning process according to the needs of the
students. This is one of the main advantages
associated with formative assessment, which
is in agreement with Galarza-Salazar (2021),
from the perspective of formative assessment
in distance environments, and with Díaz (2018),
in science education.
In terms of the opportunities it offers to students,
its importance is even more appreciated,
«because it will not only make students’
learning much more sustainable and enriched,
but it will also help them in their performance
and motivation» (Azpilicueta, 2020, p. 5).
From the above clarifications, it can be seen
that one of the fundamental features of
formative assessment is the possibility of
providing feedback; this, applied to the field
of mathematics, is a way for each person who
participates in learning processes to awaken
the internal demand to learn, through the
shortcomings, but also through the degree of
success achieved.
Formative assessment and mathematical
literacy
Currently, in educational systems, it is imperative
to focus on the development of competencies
in the processes of all areas, especially in
mathematics and language, because «access to
knowledge, to be able to understand it, to adopt
a critical stance and to be able to transform it,
that is, to form competent citizens» (Gómez,
2019, p. 163), is a right.
It is undeniable that, historically, mathematical
knowledge has been and continues to be of
particular relevance due to the great variety of
situations and areas of life in which it is applied.
This circumstance represents a great challenge
in terms of promoting knowledge, skills and
values that are synthesized in the competencies
for achieving performances in accordance
with the demands of today’s world, as well
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as participation and sound decision making,
especially from feedback (Muñoz, 2020).
Similarly, in the curricular perspective, new
approaches and paradigms oriented to the
development of competencies have been
assimilated. «This, in turn, has implied the
reformulation of the evaluation process,
emphasizing an evaluation of a more formative
nature that takes place within the teaching and
learning process itself» (Rodríguez-Fenco and
Soplapuco-Montalvo, 2019, p. 39).
At this point, formative assessment in
mathematics, according to Torres-Corrales et
al. (2022), although it is a complex process, its
benefits can extend transversely throughout the
university education of students, from whom it
requires a lot of motivation and perseverance;
therefore, the teacher must use didactic forms
that, far from being repetitive and rote, are
dynamic, entertaining and capable of generating
their commitment to the learning process
(Orozco, 2022).
Barrientos and Borghouts (cited in Cañadas
and Santos, 2021) point out that motivation
contributes to the development of initiative,
entrepreneurship and learning to learn; it
encourages students to take greater responsibility
for their learning. Therefore, as stated by
Cáceres et al. (2018), it is essential to create
spaces that generate interest in learning; here,
evaluation performs an essential role, especially
when it takes into account transparency, depth,
feedback and participation, because credibility
and rigor are promoted, in interesting classes
that promote valuable learning for students,
that is, quality assessment tasks as factors of
formative evaluation (Ibarra-Sáiz et al., 2021).
In Colombia, both the Curricular Guidelines
(MEN, 1998) and the DBA and Basic Competency
Standards (MEN, 2006) are references for quality
expectations in terms of knowing and doing
(Gómez, 2019). In this sense, the integration
of the objectives of education in the field of
mathematics is based on the achievement
of three competencies: (a) Communication,
representation and modeling, which allows
students to analyze situations, express
themselves about these ideas and make known
in written, verbal, algebraic or graphic form, a
mathematical expression in a simple way; (b)
Problem posing and solving: The student will
have the ability to formulate problems, identify
and apply the most appropriate strategy for
the corresponding verification of the results; c)
Reasoning and argumentation: The student will
develop the ability to argue the how and why of
their approaches, strategies applied, findings,
results, formulation of hypotheses (MEN, 1998).
Orozco (2022) points out that these competencies
demonstrate three fundamental aspects,
namely: «the cognitive aspect (knowledge of the
discipline), socio-affective (understood as the
disposition and willingness to solve an internal
or external demand) and practical (the tendency
to act in a continuous, persistent and dedicated
manner) » (p. 128). These competencies can
guarantee the acquisition and development of
knowledge in a sustainable way over time.
Likewise, Córdoba et al. (2018) describe the
positive changes that manifest themselves in the
attainment of competencies when we move from
traditional assessment, which is characterized
by being summative and qualifying, to formative
assessment. It is understood that, based on the
experience, the importance of this valuation
model is recognized, which is at the service of
the learning of the learner and its consequences
in society.
From the above references, it can be affirmed
that, in the acquisition of competences,
formative assessment promotes the integral
development of the student in terms of
autonomy and independence of criteria, and,
above all, generates an improvement in the
level of learning, since the student acquires
confidence when receiving, in oral or written
form, the strengths as well as the difficulties of
his/her evidence, which allows him/her to arrive
at meaningful learning (Cáceres et al. 2018).
For Uzcátegui and Albarrán (2020), verification
is relevant as the end of any evaluation process;
however, for this it is essential to promote
changes and transformations in the forms of
teaching aimed at generating self-reflection
on one’s own thinking. Thus, formative
evaluation is seen as a new challenge for 21st
century education.
Formative assessment for achieving competency in mathematics
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Jairo Guillermo Moreno Castro
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Formative assessment, although it includes
value judgments on the student’s appropriation
of knowledge (Pomares et al., 2018), by
demonstrating the skills and abilities to
generate solutions to specific problems from a
specific knowledge, is a way that favors each
person who participates in the learning process,
arousing the internal demand to learn through
the shortcomings, but also through the degree
of success achieved. The emphasis is on how
each student performs the process, providing
individualized feedback to support students and
teachers (Niño and Bahamonde, 2019; Molina et
al., 2020).
However, one of the threats is that many
teachers are still reluctant to implement them.
According to Mola et al. (2021), the leading
role of the learner is not exercised in teaching,
because evaluations are mainly limited to
the results at the end of each educational
period, weakening aspects such as regulation
and feedback during the development of
the learning process. In this way, a teaching
process is put into play that, according to Yepes
and Gutiérrez (2022), is flexible, dynamic and
participatory, based on strategic planning and
formative evaluation, which allows accessible
and inclusive environments for meaningful
learning. Thus, it can be said that the formative
process is influenced by the performance of the
teacher, who must have sufficient academic
training, relevant materials, research on
teaching and learning, sociocultural phenomena
and the wisdom granted by teaching experience
(Mendoza et al., 2019).
Discussion
In discussing the above considerations, it
can be affirmed that formative assessment
has implications for the acquisition and
reinforcement of mathematical competences.
However, there are still some aspects to
be considered in this changing reality. In
the first place, there are several theoretical
developments that need to be analyzed and
understood, as well as contributions in the
modality of proposals to be implemented and
evaluated to what extent they contribute to
strengthening formative assessment to lead
students to be more curious about mathematical
applications, critical thinking and to expose
independent points of view.
This also leads to the formulation of concerns
for future studies: What is the epistemological
knowledge that supports the practice of
formative assessment from the voice and actions
of teachers? What proposal would support the
practice of formative assessment in mathematics
in which students and teachers navigate to build
meaningful learning? And to what extent would
teachers be willing to free themselves from
standardized curricular schemes that, while
purporting to embrace a constructivist and
holistic educational ideal, are based on rigid and
traditional forms of assessment that deny the
possibility of setting new goals based on what
has been achieved and, beyond that, on what
has not been achieved?
Conclusions
After consulting and analyzing different authors
who present their criteria on the processes related
to formative assessment on its potentialities
within the teaching-learning process, it is clear
that it is important to comply with processes
such as feedback, co-evaluation and hetero-
evaluation, since if they are not complied with,
there may be implications in the achievement of
competences in the field of mathematics.
Feedback emerges as one of the most essential
elements of formative assessment, since
it provides information on the success or
otherwise of the level of achievement, allows
self-criticism and reflection by the students,
as well as identifying their interests in terms of
what motivates them most, checking what their
concerns are, and then integrating all this into
classroom life based on the teacher’s reflection
and commitment.
Co-evaluation and hetero-evaluation are linked
to the conditions of transparency, flexibility and
the possibility for students to reflect on their own
performance, key aspects that are very relevant
in mathematics, because they require review
and analysis processes to check both the results
and the strategies used in each procedure, as
well as possible errors. According to the reality
of the mathematics learning process, students
Formative assessment for achieving competency in mathematics
Jimmy Alexander Moreno Castro
Jairo Guillermo Moreno Castro
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Revista Unimar Julio-Diciembre 2024
e-ISSN: 2216-0116 ISSN: 0120-4327 DOI: https://doi.org/10.31948/rev.unimar
Rev. Unimar Vol. 42 No. 2 pp. 154-168
are satisfied with checking whether the results
were correct or not, without considering the
reasons for the error and possible strategies for
correction and improvement.
Conflict of interest
The authors declare that they have no personal,
political, intellectual, racial, religious or other
conflicts of interest that might affect the
reliability of this publication.
Ethical responsibilities
The methodological processes performed did
not involve human subjects; therefore, no
declaration of ethics or bioethics committees or
ethical responsibilities is required.
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Contribution
Jimmy Alexander Moreno Castro: Principal
investigator. Selection and processing of
bibliographic sources, registration, analysis,
comparison of authors, writing of the text.
Jairo Guillermo Moreno Castro: Analysis
and interpretation of results, writing of
the summary, introduction, style review,
grammatical contributions, organization of
the text; contributions regarding methods,
discussion and conclusions.
The authors participated in the preparation of
the manuscript, read and approved it.
