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The quantitative and qualitative rubric in
algebraic operations learning assessment in
students of eighth year of general basic
education
La rúbrica cuantitativa y cualitativa en la evaluación del
aprendizaje de las operaciones algebraicas en
estudiantes de educación general básica
Diego Tipán-Renjifo
Universidad Central del Ecuador, Quito, Ecuador
Facultad de Filosofía Letras y Ciencias de la Educación, Carrera de Matemática y Física
dmtipanr@uce.edu.ec
https://orcid.org/0000-0002-4463-2013
Edgar Cazares-Fuentes
Universidad Central del Ecuador, Quito, Ecuador
Facultad de Filosofía Letras y Ciencias de la Educación, Carrera de Matemática y Física
escazares@uce.edu.ec
https://orcid.org/0009-0006-9023-4178
Edgar Freire-LLive
Unidad Educativa Sagrados Corazones Centro, Quito, Ecuador
diegofreire@live.com
https://orcid.org/0009-0005-0631-8495
(Received on: 20/02/2025; Accepted on: 20/05/2025; Final version received on: 11/12/2025)
Suggested citation: Tipán-Renjifo, D. M., Cazares-Fuentes, E., y Freire-LLive, E. (2026). The
quantitative and qualitative rubric in algebraic operations learning assessment in students
of eighth year of general basic education. Revista Cátedra, 9(1), 128-145.
Abstract
This article analyzes the importance of designing a taxonomic rubric to assess the learning
of algebraic operations in eighth-grade students in basic general education. The manuscript
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posits as a fundamental problem the lack of application of rubrics as an assessment tool that
allows students to develop the skills, competencies, and abilities acquired in mathematics.
To address this problem, the author designs a didactic guide for designing a taxonomic
rubric that employs the Marzano and Kendall taxonomy, which focuses on mental processes
and memory related to the information students acquire. It clarifies some guidelines
regarding the principles and types of assessment, the learning cycle, and the assessment of
learning in mathematics. It explains the characteristics, elements, and types of rubrics, the
domains of learning, and the taxonomic levels with a view to achieving appropriate
assessment. This research employs a mixed-methods approach, combining qualitative and
quantitative methods, supported by various documentary and field sources, and includes a
correlational scope, thus providing an existing perspective on the problem. Relevant
findings include the deficiency in the use of rubrics due to the lack of information and
descriptors to guide the evaluation process in order to achieve a detailed learning outcome,
change the action of evaluating to valuing, experience changes in motivation and
participation, and ultimately, rediscover the desire to learn with appropriate evaluation
instruments.}
Keywords
Educational assessment, teaching guide, algebraic operations, quantitative rubric,
qualitative rubric, Marzano and Kendall taxonomy.
Resumen
El artículo analiza la importancia del diseño de la rúbrica taxonómica para evaluar el
aprendizaje de las operaciones algebraicas en estudiantes de octavo año de educación
general básica. El manuscrito plantea como problema base la falta de aplicación de rúbricas
como instrumento de evaluación que permiten a los estudiantes desarrollar las destrezas,
competencias y habilidades adquiridas en el área de la matemática. Ante este problema el
autor diseña una guía didáctica para el diseño de la rúbrica taxonómica que emplea la
taxonomía de Marzano y Kendall orientado a los procesos mentales y la memoria sobre la
información que va adquiriendo el estudiante. Aclara algunas pautas acerca de los
principios y tipos de evaluación, ciclo del aprendizaje y la evaluación del aprendizaje en
matemática. Explica las características, elementos y tipos de rúbricas, los dominios del
aprendizaje y los niveles taxonómicos con miras a alcanzar una evaluación adecuada. Es una
investigación con un enfoque cualitativo y cuantitativo que se respalda con varias fuentes
de tipo documental, de campo y un alcance correlacional así logra una perspectiva existente
de la problemática. Como hallazgos relevantes están la falencia en la utilización de la rúbrica
debido a la falta de información y descriptores que guíe el proceso de evaluación con la
finalidad de lograr un resultado detallado del aprendizaje, cambiar la acción de evaluar por
valorar, experimentar cambios en la motivación y participación, en definitiva, redescubrir
el deseo por aprender con instrumentos de evaluación apropiados.
Palabras clave
Evaluación educativa, guía didáctica, operaciones algebraicas, rúbrica cuantitativa, rúbrica
cualitativa, taxonomía de Marzano y Kendall.
1. Introduction
The level of education in Ecuador reached a turning point with the 2020 pandemic, bringing
about a radical shift in the methodology, content, and resources used for teaching. Thanks
to significant technological advancements, the renowned artificial intelligence emerged in
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2022, capable of generating concrete answers to any question in seconds. In some ways, the
development of this autonomous tool has devalued critical thinking, human judgment, and
analytical skills due to the availability of pre-processed responses.
In education, assessment has traditionally focused on the grade of a final product or result,
neglecting the development of genuine student learning. Similarly, the adaptability of digital
educational resources has changed how we learn and has also fostered a reliance on
applications that cater to the whims of completing assignments.
In Ecuador, teachers face a challenging process in applying assessment techniques,
methods, and instruments that not only measure final results but also the process involved
in achieving meaningful learning. Thus, rubrics are seen as an alternative that surpasses
traditional assessment due to the advantages the tool provides. Well-implemented rubrics
are instruments structured with clear criteria for evaluating an activity. Subject to various
descriptors, they measure the step-by-step process of each partial achievement with a
defined rating scale for each level. The final grade provides a broader perspective for
identifying strengths and weaknesses during the learning process, supported by timely
feedback. The assessment guidelines propose the regulations that must be followed in the
Teaching and Learning Process (TLP), considering assessment not as an end in itself but as
a means to improve educational processes. The goal is the student's holistic development
through appropriate support and feedback at each stage of learning, determined by the
teacher's high capacity, competence, and professionalism.
In mathematics, the usefulness of an assessment tool that values the process is essential;
currently, students arrive at the answer using any application, but they are unaware of the
process followed to arrive at that answer. For this reason, the rubric, with its taxonomic
approach, allows for the demonstration of the development of skills that the student
acquires in solving a problem or exercise. The rubric's value lies in its integration of
Marzano and Kendall's taxonomy, which focuses on the development of thinking across six
levels, emphasizing gradual learning. The incorporation of metacognition allows students
to engage in deep reflection, as do cognitive, procedural, and attitudinal processes. This
promotes the value of learning styles and leads to a more effective and meaningful
evaluation.
Methodologically, this study has applications in education globally and specifically in the
area of mathematics, encompassing the evaluation guidelines established by the Ministry of
Education of Ecuador for student learning. It presents a qualitative and quantitative
approach in a narrative, rather than experimental, manner. The method is interpretive for
understanding the problem, and the scope is correlational in predicting a result. The
research is documentary and field-based, culminating in a proposed didactic solution.
The manuscript is comprised of three sections: the first presents the theoretical framework
explaining the research topic; specifically, it provides a conceptual explanation of the
characteristics, types, and digital educational resources that generate rubrics as assessment
tools in Mathematics. The second section explains the methodology used in the research
process. The third section presents the results obtained from exploring the problem in
relation to the characteristics of the research instrument, namely the rubric, as well as its
application in learning assessment and the contribution of a guide for designing taxonomies
and rubrics in the field of Mathematics.
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2. Literature review
This research aimed to analyze the usefulness of rubrics in mathematics education. It
examined previous studies in the field of education related to the design of assessment
instruments that offer a detailed perspective on learning. The theoretical framework
addresses the study variables using information sources appropriate to the research
problem.
2.1 The rubric
A rubric is a tool used to evaluate an activity or task according to specific parameters. Fraile
et al. define it as a document that details a task according to certain evaluation criteria
corresponding to a level of quality and assigning a grade (Fraile et al., 2017, p. 1328). From
this perspective, a rubric is presented as a matrix that describes an action or set of actions
using criteria that serve as a guide for assessing progress, and a grade related to the level of
complexity can be assigned.
2.1.1 Elements of a rubric
A rubric is a matrix containing key elements for its correct application. In the process of
developing a rubric, it is essential to define the descriptors, the rating scale, and the criteria
(Gatica-Lara & Uribarren-Berrueta, 2013, p. 64). These components form three essential
parts that must be logically and coherently interconnected to facilitate the effective
evaluation of learning outcomes, as shown in Table 1.
Criteria
Concepts/Categori
es
Scales/Levels of performance
4
3
2
1
Aspects to be
evaluated
Descriptors
Evidence to be
obtained
Descriptors
Evidence to be
obtained
Descriptors
Evidence to be
obtained
Descriptors
Evidence to be
obtained
Table 1. Key elements of a rubric. Source: (Gatica-Lara and Uribarren-Berrueta, 2013, p. 62).
2.1.2 Types of rubrics
Rubrics are defined in two main groups: analytical rubrics and holistic rubrics. These differ
in their design, elements, and final results, as detailed below: Analytical rubrics offer a more
detailed perspective compared to holistic rubrics, which provide a more general overview.
Fraile et al. specify that analytical rubrics are more precise in their criteria, levels, and
qualitative descriptions, while holistic rubrics are more general and do not highlight
strengths and weaknesses (Fraile et al., 2017, p. 1328). As they explain, the application of a
rubric depends on what is being evaluated, considering either the detailed process or the
final product. If the goal is to identify strengths and weaknesses, an analytical rubric should
consider a specific overview of the process. If the goal is to assess a final activity, a holistic
rubric, which provides a comprehensive overview, should be used. Finally, the differences
between each type of rubric are described as shown in Figure 2.
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Analytical
Part of the student’s performance.
Levels of achievement focused on
improvement.
More time required to grade.
Figure 1. Differences between the holistic and analytical rubrics. Adapted from: (Gatica-Lara and Uribarren-
Berrueta, 2013, p. 62).
2.2 Taxonomic rubric criteria
The taxonomic rubric has been proposed in the field of Mathematics to clearly define the
level at which the indicators are intended to be achieved. There must be complete coherence
between this level and the verbs used to assess mathematical learning (Tipán-Renjifo,
2022). The evaluation criteria are based on levels of increasing complexity, which are
related to the taxonomy. Atonal argues that taxonomies allow for the classification of
cognitive processes involved in learning, organizing them into levels that correspond to
different degrees of mental complexity. These are structured around domains of knowledge
that include everything from basic memorization skills to higher-level processes such as
analysis, evaluation, and creation. Furthermore, the author emphasizes that the difference
between the levels lies in the degree of difficulty of the mental process required for each
one, which allows for more effective planning of learning objectives (Atonal, 2020, p. 86).
A detailed process is easy to understand when the actions to be followed are prioritized and
systematized. In education, taxonomies are key for setting objectives and developing skills
for student learning. Bloom's and Marzano-Kendall's taxonomies are the most widely used
to ensure students' appropriate cognitive development.
In assessment, congruence between what is taught and what is learned is important for the
application of an assessment instrument. Atonal explains the use of a taxonomy for
assessment, stating that taxonomic levels link innate abilities in individuals (Atonal, 2020,
p. 99). He also affirmed that during learning, progress is evident with a hierarchy of actions
to be completed, highlighting skills and competencies acquired in relation to critical
thinking, as shown in Figure 2.
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BLOM
Learning objectives:
- Remember
- Understand
- Apply
- Analyze
- Evaluate
- Create
MANZANO
Information processing
- Self-system
- Metacognitive
- Cognitive
SOLO
Understanding
-Pre-structural
-Uni-structural
-Multi-structural
-Relacional
-Extended abstract
FINK
Significant learning
-Foundational knowledge
-Application
-Integration
-Human dimension
-Caring
-Learning to learn
WEBB
Thinking complexity:- -
Rote/Memorization
-Processing
-Strategic
-Extended
ANDERSON Y
KRATHWOHL
Separates knowledge and
process:
-Factual
-Conceptual
-Procedural
-Metacognitive
Figure 2. Types of taxonomies and levels. Adapted from: (Atonal, 2020, pp. 86-92).
2.2.1 Rubric Criteria for an Evaluation
The rubric, as an assessment tool, has its own structure that allows it to focus on a specific
task. As Garcia-Valcarcel et al. mention, several criteria are related to the performance levels
that define the quality of learning to be assessed. Furthermore, these levels allow for the
establishment of clear descriptors that guide both the teacher and the student regarding
what is expected to be achieved in each phase of the assessment process (Garcia-Valcarcel
et al., 2020, p. 74). Consequently, the identification of criteria in an assessment will depend
on the desired level within the assessment context, thus fostering self-assessment and peer
assessment, which represents an achievable goal. The criteria highlighted in Figure 3 are
shown below.
Student Reflection
-Formative value
- Achievement or failure in
objectives
Construction Value
-Teacher-student
interaction
-Performance
improvement
Deep Learning
-Concrete expectations
- Quality
Figure 3. Criteria to consider in the evaluation with a rubric. Adapted from: (Garcia-Valcarcel et al., 2020, p.
75)
2.3 Principles of Evaluation
Assessment is understood as a systematic process of gathering information that allows for
the evaluation of student learning within a given educational context. To maintain its
pedagogical character, it must be based on principles that guide its purpose, structure, and
application. Sánchez-Mendiola and Martínez-González state that effective assessment
requires clarity in the objectives to be evaluated, the use of methods appropriate to the
learning context, and a variety of instruments that promote a comprehensive assessment of
performance. They also emphasize that assessment should be understood as a means to
support the continuous improvement of the educational process, not as an end in itself.
These principles are essential for promoting fair, formative assessment practices aligned
with learning objectives (Sánchez-Mendiola & Martínez-González, 2022, pp. 17–21).
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Likewise, the characteristics of educational assessment are related to student learning,
starting with the question every teacher has thought about: "What am I going to assess?"
This central axis is accompanied by appropriate techniques, strategies, and instruments
that provide a current understanding of the student's knowledge acquired in class, as
demonstrated in an assessment.
2.3.1 Evaluation criteria
Assessment criteria allow for the identification of achievement levels through clear and
objective benchmarks that guide the evaluation of learning. They act as a bridge between
educational objectives and the evidence gathered in the classroom, strengthening curricular
coherence. Furthermore, they guide pedagogical decision-making and promote the
continuous improvement of the learning process (Sánchez-Mendiola & Martínez-González,
2022, pp. 21-23). In the case of assessing algebraic operations using quantitative and
qualitative rubrics, these criteria allow for the establishment of precise descriptors that
guide both teachers and students toward the achievement of clear and measurable
mathematical competencies.
2.3.2 Evaluation indicators
Assessment indicators allow us to observe and evaluate the degree of development of a
competency or expected learning outcome through clear descriptions of student
performance. In this sense, Gatica-Lara and Uribarren-Berrueta argue that assessment
criteria, also called indicators or guides, are essential elements in rubric design, as they
reflect the processes and content deemed significant for educational achievement. These
must be accompanied by quality definitions that specify what the student should
demonstrate at each achievement level and scoring strategies that allow us to distinguish
between exemplary and emerging performance (Gatica-Lara & Uribarren-Berrueta, 2013,
pp. 62–64). Applying this structure to mathematics, and particularly to the learning of
algebraic operations, allows us to construct clear, objective, and formative rubrics that
guide both the teaching, and the assessment of student progress based on observable and
measurable evidence.
2.3.3 Types of Evaluation
In the academic sphere, assessment is an essential element of the teaching-learning process.
It not only allows for the evaluation of student results but also generates relevant
information for adjusting and improving pedagogical interventions. According to Sánchez
and Martínez, educational assessment should be conceived as a systematic, continuous
activity integrated into the learning process, fulfilling diagnostic, formative, and summative
functions. Diagnostic assessment aims to identify prior knowledge, skills, and attitudes at
the beginning of an educational cycle; formative assessment focuses on supporting learning
by providing constant feedback; and summative assessment allows for the evaluation of
achievements at the end of a unit or period (Sánchez-Mendiola & Martínez-González, 2022,
pp. 17–23). This comprehensive view of assessment is fundamental for designing and
implementing instruments such as quantitative and qualitative rubrics in mathematics, as
it facilitates a more complete and contextualized evaluation of the learning of algebraic
operations in eighth-grade students.
This perspective is especially relevant in the context of assessing algebraic operations. The
implementation of quantitative and qualitative rubrics requires continuous, flexible
evaluation focused on the student's actual learning, rather than solely on the final grade. At
the end of the educational process, there is the summative assessment, which aims to
evaluate all the knowledge acquired over a period of time. Its objective is to measure
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achievements and whether or not the learning objectives established in the respective
lesson plans were met. The final summative assessment helps inform decisions regarding
adjustments to the methodology or the overall lesson plan.
2.3.4 Evaluation Moments
Assessment in education unfolds in three fundamental phases: diagnostic, formative, and
summative. These stages fulfill specific functions within the teaching-learning process,
facilitating more effective pedagogical intervention focused on the student's needs. As
Sánchez and Martínez point out, each type of assessment has a distinct purpose and is
applied at different points in the educational process. These are represented schematically
in Figure 4, which illustrates the sequence and relationship of the three phases within the
assessment cycle (Sánchez-Mendiola & Martínez-González, 2022, p. 60).
Figure 4. Evaluation moments. Adapted from: (Sánchez-Mendiola and Martínez-
González, 2022, pp. 21-22)
2.3.5 Comprehensive Assessment in Mathematics
Comprehensive assessment in mathematics represents an approach that goes beyond
simply measuring theoretical or mechanical knowledge. This type of assessment seeks to
holistically evaluate students' competencies, considering both their conceptual
understanding and their ability to apply content in real and meaningful situations.
According to Castillo-Arredondo and Cabrerizo-Diago, a truly formative mathematics
assessment should include different levels of analysis, from identifying basic procedures to
solving complex problems, integrating logical reasoning, the use of mathematical language,
data interpretation, and the ability to transfer learning to everyday contexts. This
perspective allows for the evaluation not only of mastery of formulas and algorithms, but
also of students' ability to interpret, argue, and make well-founded decisions from a
mathematical perspective (Castillo-Arredondo & Cabrerizo-Diago, 2010, pp. 268–270). In
this sense, the comprehensive approach contributes to the development of critical thinking
and learner autonomy, key aspects for an education oriented toward performance and the
resolution of real-world problems. One of the key aspects of a comprehensive assessment
is the inclusion of activities that strengthen students' critical thinking and creativity.
Problems should be presented that are relevant to everyday life to encourage logical
problem-solving. Furthermore, the assessment allows for self-assessment and peer
assessment among students, strategies that enable them to reflect on their own learning
and receive feedback.
Summative
Final evaluation of the
process
Determines the
achievements attained
Formative
Partial assessment of the
process
Identifies strengths and
weaknesses for
improvement
Diagnostic
It is applied at the beginning
of a course or activity.
It determines the level of
prior knowledge.
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2.3.6 Assessment of Mathematics Learning
In mathematics, the assessment of learning is of vital importance and can be carried out in
various ways, such as written exams, practical tests, projects, and ongoing formative
assessments. Ongoing assessments tend to be the most widely used, offering teachers the
opportunity to identify areas for improvement or reinforcement, or to provide feedback on
student knowledge.
2.3.7 Skills assessment
In the field of mathematics, skills-based assessment has emerged as a key methodology for
evaluating learning because it focuses on measuring practical skills and specific
competencies of each student. This approach to teaching emphasizes evaluating not only
what students know, but also what they can do with the knowledge they have acquired.
Skills-based assessment aligns with the societal shift of recent years, where practical skills
and the ability to apply knowledge in everyday situations are highly valued. Thus, skills-
based assessment goes hand in hand with the needs of the job market and various
requirements of companies, which seek individuals who not only possess the knowledge,
but also know how to apply it and put it into practice when solving problems.
The fundamental or most notable characteristic is its focus on authenticity. Assessments
often involve projects, case studies, and simulations. They promote critical thinking,
problem-solving, and self-assessment—essential competencies for today's world, where
students must be able to adapt to new situations, innovate, and think critically and
objectively.
2.3.8 Competency-Based Assessment.
Competency-based assessment refers to the combination of knowledge, skills, attitudes, and
values that students need to perform in different aspects of their professional field. The shift
to competency-based assessment implies a change in how teaching and learning are
conceived and carried out. One of the main characteristics of competency-based assessment
is the authenticity of the students; assignments, tests, and everything submitted are based
on a real-world context, giving students the opportunity to demonstrate their competence
in contexts in which they operate. This increases the relevance and importance of the
learning. Furthermore, education becomes continuous and formative, providing students
with regular feedback throughout the teaching and learning process, where students are
responsible for their own progress. It also requires a more personalized approach to
teaching; teachers not only develop specific competencies but must also adapt to the
individual needs and contexts of their students.
In today's world, where technological evolution and scientific advancement are progressing
exponentially compared to previous decades, competency-based assessment is gaining
greater relevance. Educational institutions now seek to ensure that individuals not only
possess practical knowledge related to different subjects, but also that they can apply it
innovatively to problem-solving or innovation.
3. Methodology
This research has a broad scope in education and a specific focus on mathematics. It
presents an interpretive method that aims to reveal the behavior of educational
stakeholders in the learning process, guided by evaluation criteria. The study context allows
for the exploration of visible behavioral changes in the phenomenon, with the final results
presented in a positive light in the conclusions, enabling the generalization of the situation.
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The quantitative phase handles the non-experimental aspect through observation of the
existing study situation, supported by the calculation of Cronbach's alpha, data tabulation,
and the necessary numerical results. The qualitative phase employs a narrative approach
through the analysis of the collected information, providing a general and specific view of
the study situation based on the results of applying the data collection instruments.
The study variables are related within the educational field by calculating Pearson's
correlation coefficient, which determines the degree of direct or indirect association. It is
inferred that the evaluation instrument modifies the way specific content is learned, as
reflected in the final results obtained. Designing a tool that provides a better overall or
specific perspective on learning assessment will positively or negatively influence the
student, taking into account their context. Furthermore, it draws on the expertise of
students experiencing the current state of educational assessment as a primary source,
supported by a review of online documents with research validity as a secondary source,
and fieldwork through direct observation of the issues, accompanied by the application of
instruments that gather the necessary information for the study.
3.1 Population and Sample
Two hundred students from the upper sub-level of Basic General Education enrolled in the
2023-2024 academic year were considered, forming the entire population. Due to the
number of individuals, the population is considered as the sample for the information
collection process, along with the five teachers from the Mathematics area detailed in Table
2.
Stratum
Educational institution
Students
Teachers
40
1
Educational Unit Sagrados Corazones Centro
40
1
Intercultural Bilingual Community Educational Unit "Tinku Yachay"
40
1
Intercultural Bilingual Educational Unit Muyu Kawsay
40
1
American School of Quito
40
1
Educational Unit "Nelson Torres"
200
5
Total
Table 2. Population distribution.
3.2 Techniques for data processing and analysis
For collecting data from the student questionnaire, Google Forms survey management
software was used due to its ease of access via a link. Subsequently, the database of all
respondents was downloaded in Comma-Separated Values (CSV) format. Data tabulation
and pie chart creation were performed using Microsoft Excel. Finally, the results were
compiled and presented in a Microsoft Word document.
For the questionnaire for teachers, data collection was carried out through pre-scheduled
interviews. Participants' responses were recorded and later transcribed into text format.
Once all the information was gathered, the qualitative analysis software ATLAS.ti was used
in AI mode to identify words and sentences that were congruent both with each other and
with each of the questions posed. This process provided a clear and organized perspective
for the study.
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4. Results
The results of the research validate the researcher's proposal to design rubrics that align
taxonomic levels for appropriate assessment in mathematics. Using two instruments, the
current situation regarding the application of assessment tools to 8th-grade students in
basic general education is analyzed.
Figure 5 shows that 57% of students indicate that they only sporadically or never perceive
a positive attitude toward the importance of achieving learning outcomes when a rubric is
used in class. The rubric fosters the development of shared metacognitive skills between
teachers and students (Alcón-Latorre & Menéndez-Varela, 2016). Assessment should focus
on measuring what students are able to do with the acquired knowledge, building upon the
meaningful learning developed in class. Furthermore, recognizing and motivating each
partial achievement is an effective incentive for achieving overall success. Furthermore, the
rubric offers a detailed view of each phase of the learning process, considering the
completed achievements and allowing their verification in the final grades, thus favoring
the articulation between the qualitative and the quantitative.
Figure 5. Use of the rubric to assess learning achievements.
Figure 6 shows that 52% of students indicate that they are unfamiliar with or have never
used different assessment tools aligned with the learning process applied in teaching
practice. The learning process varies among students due to their different learning styles;
therefore, it is necessary to employ diverse methods to assess acquired knowledge.
However, most students have been assessed solely through traditional instruments,
considering written tests as an established tool. The variety of assessment methods
continues to expand with the use of Information and Communication Technologies (ICTs),
opening new possibilities for identifying emerging skills developed by new generations.
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Figura 6. El docente aplica los instrumentos de evaluación adecuados en el proceso de
aprendizaje.
Figure 7 illustrates the use of platforms to measure individual progress, adapting to new,
effective, and inclusive systems aligned with learning objectives. Interaction with
mathematical concepts is made accessible to all students through gamification, resulting in
more engaging and personalized teaching that increases learning effectiveness and
assessment accuracy.
Figure 7. Consistent responses regarding the design of assessment instruments with digital tools.
5. Discussion
The structural characteristics of assessment rubrics were analyzed in relation to the
guidelines established by the Ministry of Education of Ecuador. In this regard, Alcón-Latorre
and Menéndez-Varela point out that an effective rubric must be aligned with curricular
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content, learning objectives, and quality standards, thus facilitating a coherent, objective,
and transparent evaluation. Furthermore, they propose that rubric design should respond
to specific criteria that allow for a clear assessment of students' performance level for each
indicator. However, the results obtained in this study show that 37% of students believe
that teachers do not present the information contained in the rubrics clearly, visibly, and
appropriately, while 57% indicate that they do not perceive an objective assessment of their
learning achievements when evaluated using this instrument. These perceptions contrast
with those presented by Alcón-Latorre and Menéndez-Varela, who state that a well-
designed rubric should contain precise, understandable descriptors aligned with quality
criteria, which should be applied progressively throughout the learning process (Alcón-
Latorre and Menéndez-Varela 2016, pp. 3-4).
Comparing the theoretical framework and background with the results, it is evident that the
rubric was not applied correctly due to a lack of the necessary information to guide the
evaluation process. This prevented good results and generated a negative impact,
attributable to a poorly structured instrument implemented by the teacher. The rubric lacks
the characteristics of being objective, structured, and efficient from the process to the final
result, in relation to parameters that assess the construction of knowledge acquired by the
student. The lack of descriptors makes the rubric an ineffective instrument for the desired
level of achievement and fails to fulfill its function of evaluating skills and abilities during
the learning process.
The assessment of algebraic operations learning in eighth-grade students was
contextualized, considering current approaches to the use of instruments such as rubrics.
Within this framework, Buelvas et al. emphasize that formative assessment should be
geared towards reinforcing students' prior knowledge in order to develop competencies
meaningfully, allowing for more conscious and participatory learning (Buelvas et al., 2023,
p. 56). According to the results obtained in this study, 40% and 45% of students indicated a
lack of clarity regarding the assessment guidelines, demonstrating a lack of explanation on
the part of the teacher. Furthermore, 52% of respondents stated that they did not perceive
an appropriate application of assessment instruments during class. These data are
complemented by the percentages of 72% and 76% of students who stated that digital
educational resources are only occasionally or never used as part of an assessment with
differentiated formats. These results highlight the need to improve both the planning and
communication of assessment criteria in the classroom, as well as to integrate digital tools
that diversify the ways of assessing mathematical learning.
Sixty percent of students do not feel motivated during the assessment process, supported
by 50% and 41% of students who do not understand the actions taken by the teacher, such
as preparatory activities, participation, and appropriate feedback at each stage of the
assessment. Thus, 57% and 58% of students do not perceive a positive attitude from the
teacher during the learning process, but rather a focus solely on the final result. These data
are related to the guidelines for implementing learning assessment processes proposed by
the Ministry of Education in 2023, which value the teacher's role in the acquisition of skills
and abilities at each level, as reflected in an assessment. The results are indicators of
improvement in the teaching-learning process.
Comparing the theoretical framework and background with the results, there is a lack of
dialogue between teachers and students regarding changes in evaluation guidelines.
Furthermore, the diverse evaluation instruments detailed in current Ministerial
Agreements are not being used, and digital resources are underutilized during the
evaluation process. The need for evaluation remains, and the lack of motivation,
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participation, and feedback from teachers in class continues to be a source of concern.
Students observe that evaluation focuses solely on the final result, disregarding the process
they followed to arrive at a correct or incorrect answer.
Medina et al. analyze teachers' perceptions of rubric use in formative assessment and
conclude that rubrics are valued for their clarity, objectivity, and contribution to analyzing
students' academic performance. While their benefits for strengthening skills such as
critical thinking and self-reflection are acknowledged, it is also noted that their effective
application depends on teacher training and the educational context (Medina et al., 2023).
These perceptions support the use of rubrics as a teaching tool that promotes inclusive and
formative assessment, key aspects for improving the learning of algebraic operations in
mathematics.
The design of a teaching guide based on the use of rubrics as a key pedagogical resource was
proposed to facilitate the achievement of learning related to algebraic operations. In this
context, Medina et al. maintain that rubrics constitute an effective assessment tool in the
area of Mathematics; they not only allow for the evaluation of final products, but also the
formative processes through which students develop skills and abilities. The results
obtained reflect a consensus among the participating teachers regarding the usefulness of
rubrics for strengthening competencies such as critical thinking, reflection, and problem-
solving. They also underscore the need to integrate appropriate resources, continuous
feedback, and inclusive strategies that promote more equitable and contextualized
assessment within the classroom.
Comparing the theoretical framework and background information with the results,
teachers are aware of the skills students should master in mathematics, and this is reflected
in the grades. Assessment is traditional, using exercises and answers, and despite training
on assessment methods, teachers do not experiment with new assessment tools. A rubric,
however, is an instrument that provides detailed feedback on the process and final product,
which are key to mathematics. An effective rubric for evaluating the learning of algebraic
operations in eighth-grade students should combine qualitative and quantitative elements.
Qualitatively, the rubric should clearly describe the performance levels, the specific skills at
each level, and the ability to solve exercises. Quantitatively, it should assign numerical
scores to each performance level, allowing for a precise and objective evaluation.
The rubric should include criteria that consider the problem-solving process, not just the
final result, as this constitutes a comprehensive assessment of student learning. An example
of a quantitative and qualitative rubric for the assessment of learning algebraic operations
is presented.
6. Conclusions
An analysis of the structural characteristics of assessment rubrics was conducted in relation
to the guidelines of the Ecuadorian Ministry of Education. On average, 47% of teachers do
not use rubrics appropriately in assessments, according to the guidelines established by the
Ministry. The main issues affecting the structure of a rubric as an assessment tool are the
following: 37% (failing to specify the necessary information) and 57% (failing to assess
learning outcomes). This is because the rubric lacks the necessary guidance for students
during the activity, resulting in low grades that do not accurately reflect the level of
achievement of the student or group of students being assessed.
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The assessment of learning among eighth-grade students in basic general education is
contextualized, revealing that, on average, 57% of students perceive the assessment of
algebraic operations as a tedious process to be completed without any appeal. This is
evidenced by data such as: 42.5% (lack of knowledge of the assessment parameters), 52%
(lack of recognition of the assessment instruments), and 74% (lack of use of digital
educational resources) in relation to the assessment tool used. Similarly, 54% of students
perceive the teacher's activity as weak, based on data such as: 60% (lack of motivation),
46% (lack of participation in activities), and 58% (lack of perception of a positive attitude)
in relation to the environment before, during, and after an assessment. This indicates that
the assessment processes in algebraic operations are mechanical, based on solving
exercises in anticipation of a good grade, neglecting the purpose of a comprehensive
assessment that involves student participation.
A teaching guide based on rubrics was deemed beneficial for clarifying the mathematical
skills students should develop. According to teachers, these skills are primarily
demonstrated through problem-solving in traditional, standardized tests. Teaching
materials and assessments are typically created individually, without experimentation with
new assessment tools and instruments. Ongoing professional development in teaching and
learning topics provides opportunities for change in the approach and methods of
evaluating content. This study proposes the design of quantitative and qualitative rubrics
for assessing the learning of algebraic operations in eighth-grade students. It addresses the
issue of rubrics not being effectively applied in assessments due to the instrument's
structure, the specific skills being evaluated, and a lack of experience among mathematics
teachers who focus solely on correct and incorrect answers without recognizing the
student's progress as they tackle exercises or problems on tests. The assessment for
algebraic operations is mediocre without the support of digital educational resources,
which are a trend in current education, at every stage—before, during, and after—resulting
in mediocre grades and failing to fulfill the purpose of a test, which is to identify students'
strengths and weaknesses to improve the teaching-learning process.
Acknowledgment
This article is derived from the thesis entitled "Quantitative and Qualitative Rubrics in the
Assessment of Algebraic Operations Learning in Eighth-Grade Students of Basic General
Education, Academic Year 2023-2024," submitted for the Master's Program in Education,
specializing in Mathematics. I express my deep gratitude to the mathematics teachers who
generously shared their experiences and knowledge about classroom assessment
processes, contributing significantly to the understanding of the problem addressed.
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Authors
DIEGO TIPÁN-RENJIFO, a Technologist in Computer Systems Analysis, holds degrees in
Mathematics and Physics, and is a Specialist in Competency-Based Curriculum Design, with
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a Master's degree in University Teaching and Educational Administration, a Master's degree
in Artificial Intelligence, and a Specialist in Artificial Intelligence Projects.
He teaches at several universities at the Master's and undergraduate levels. He has served
as Dean and Coordinator in the field of Education. He has published several books and
research articles and presented at national and international conferences on Complex
Thinking and Transdisciplinarity. He has also worked as a consultant for the Ministry of
Education and as an evaluator of universities and higher education institutions in Ecuador
for the Council for Quality Assurance in Higher Education (CACES).
EDGAR CAZARES-FUENTES obtained his Master's degree in Educational and Social Project
Management from the Central University of Ecuador (Ecuador) in 2016. He also obtained
his Bachelor's degree in Education, specializing in Mathematics and Physics, from the same
university in 2002. Currently, he is a professor at the Central University of Ecuador, in the
Faculty of Philosophy, Letters, and Educational Sciences, in the Department of Pedagogy of
Experimental Sciences (Mathematics and Physics). He also serves as the department
director. He has dedicated his professional life to teaching Physics and Mathematics to
secondary school teachers, developing pedagogical, didactic, and methodological activities
that strengthen their graduate profile. He has also demonstrated a strong commitment to
proposing and managing various community outreach projects. In recent years, he has also
been involved in administrative management tasks as Coordinator of Outreach for the
Faculty of Philosophy, Coordinator of the Master's Program in Education with a
specialization in Mathematics, and most recently as Director of the Bachelor's Program in
Pedagogy of Experimental Sciences (Mathematics and Physics). He is the author of several
books on Physics and Mathematics with experimental applications in the laboratory, thanks
to his versatility with computer tools and Artificial Intelligence.
DIEGO FREIRE-LLIVE holds a Bachelor's degree in Pedagogy of Mathematics and Physics
and a Master's degree in Education with a specialization in Mathematics.
He currently teaches at the Sagrados Corazones Centro Educational Unit and has extensive
academic and professional experience. He has also worked in private educational
institutions, demonstrating a strong commitment to education. He has been a speaker at
seminars on quality education and a participant in several interscholastic mathematics
competitions.
Declaration of authorship-CRediT
DIEGO TIPÁN-RENJIFO: Problem statement, theoretical development, methodology,
validation, data analysis, and drafting of the first draft.
EDGAR CAZARES-FUENTES: Critical review of the content, methodological supervision,
project management, instrument design, final editing, and pedagogical recommendations.
DIEGO FREIRE-LLIVE: Data collection, fieldwork, organization of results, qualitative
analysis, and writing of results and conclusions.
Artificial intelligence usage statement
The authors report that they partially used the ChatGPT tool – GPT-4 model (OpenAI), July
2025 version – during the manuscript preparation stage, specifically for: support in the
syntactic restructuring of some paragraphs, the creation of alternative versions of titles and
subtitles, and the generation of preliminary examples that were subsequently reformulated
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manually. Artificial intelligence was not used to draft sections related to methodological
design, data analysis, interpretation of results, or academic discussion. All content
suggested by the tool was critically reviewed, verified, and modified by the authors, who
assume full responsibility for the final text, its accuracy, and its scientific rigor.