|
Article |
Modelación matemática y actitudes hacia su aprendizaje
en educación básica: una revisión bibliográfica
Paúl Enrique Álava Valeriano[*]
Arturo Damián Rodríguez Zambrano*
Abstract
This article presents an exhaustive review of how
conventional mathematics instruction creates emotional barriers, such as apathy
and stress. The objective of this study is to analyze, through a review of the
scientific literature, the impact of mathematical modeling on students’
attitudes in general basic education. A representative sample of 15 scientific
articles published between 2015 and 2026 was selected. Data were collected from
high-impact databases such as SciELO, Redalyc, Dialnet, and Google Scholar
using structured search strings and recorded in a matrix for data extraction
based on specific inclusion criteria. The findings show that mathematical modeling
reduces emotional barriers, promotes collaborative work, and stimulates the
development of mathematical communication—provided that the activities are
based on real-world contexts relevant to the students— . It is also emphasized
that teacher guidance is important for the implementation of the proposed
activities. The conclusion reached is that mathematical modeling is more than a
teaching technique; it is a pedagogical approach that transforms the relationship
with this discipline and the prejudices held about it by making students the
protagonists of their own learning.
Keywords: mathematical modeling, attitudes toward mathematics,
elementary education, meaningful learning, affective dimension.
Resumen
En este artículo se realizó
una búsqueda exhaustiva sobre como la enseñanza convencional de las matemáticas
genera barreras emocionales, como la apatía y el estrés. El presente estudio
tiene como objetivo analizar a través de la revisión de la literatura
científica, el impacto que tiene la modelación matemática en las actitudes de
los estudiantes en el nivel de educación general básica. Se eligió una muestra
representativa de 15 artículos científicos publicados entre 2015 y 2026. La
recolección de la información se realizó mediante bases de datos de alto
impacto como SciELO, Redalyc, Dialnet y Google Académico, mediante el uso de
cadenas de búsquedas estructuradas y se registró en una matriz para la
extracción de datos bajo criterios de inclusión específicos. Los hallazgos
muestran que la modelación matemática disminuye las barreras emocionales,
favorece el trabajo colaborativo y estimula el desarrollo de la comunicación
matemática, en caso de que las actividades se basen en contextos reales y
cercanos al estudiante, también se destaca que el acompañamiento del docente es
importante para el desarrollo de las actividades propuestas. Se llega a la
conclusión de que la modelación matemática es más que una técnica de enseñanza,
es un enfoque pedagógico que transforma la relación de esta disciplina y el
prejuicio que se tiene sobre esta al convertir a los estudiantes en
protagonistas de su propio aprendizaje.
Palabras clave: modelación matemática, actitudes hacia las matemáticas, educación
básica, aprendizaje significativo, dimensión afectiva.
Introduction
Currently, mathematics faces a major challenge: the
development of students with negative attitudes, apathy, and anxiety toward the
subject. The literature warns that this systematic rejection arises at a very
early age. Thus, children are raised under the false premise that this
discipline is a purely abstract, complicated burden reserved for a select few.
One possible cause lies in the fact that teaching
practices focus on traditional instruction rather than a constructivist model,
placing greater emphasis on the memorization of procedures and the presentation
of contexts that are meaningless to the student (Mancilla et al. 2026) .
Attitudes toward mathematics can be understood as
affective and cognitive dispositions that determine how students relate to the
discipline, including their level of confidence, motivation, and interest in
mathematical tasks. Savaşlı & Serin (2025) , through the application of the Attitudes Toward
Mathematics Scale (ATMS), demonstrated that these dispositions are measurable
and modifiable: fourth-grade students who participated in mathematical modeling
activities showed a statistically significant improvement in their attitudes
compared to those who received traditional instruction, demonstrating that the
affective dimension of mathematics learning responds directly to the type of
pedagogical experience offered to them.
From this perspective, mathematical modeling emerges
as a solid teaching strategy for general basic education. This methodology is
understood as a process in which students use mathematical tools to understand,
represent, and propose solutions to real-world problems in their environment.
In this regard, Donnet et al. (2024) explain that modeling serves as a bridge to real
life and enables students to respond to everyday challenges.
From a didactic perspective, a strategy is
understood as an organized set of pedagogical actions aimed at facilitating
learning by connecting mathematical content to real-life situations. In this
regard, Moreno Reyes et al. (2016) structure the modeling process into five sequential
stages: understanding the problem, simplifying it, mathematizing it, applying
the model, and interpreting the results.
This cycle demonstrates that modeling is not a
spontaneous activity, but rather a pedagogical process that, when properly
guided, fosters critical thinking, autonomy, and a greater interest in
mathematics.
Similarly, Asempapa (2017) notes that “mathematical modeling facilitates
students’ problem-solving efforts and collaboration, in addition to fostering
their mathematical thinking and learning” (p. 25).
Although various authors highlight the benefits of
mathematical modeling, the literature analyzing how this methodology impacts
affective and attitudinal dimensions in elementary education is scattered. Part
of the literature focuses on evaluating academic performance or the conceptions
of pre-service teachers (Rivera & Gallegos, 2009) .
In this context, there is a need to investigate
alternatives for transforming the teaching–learning process in mathematics and
promoting an active role for students that allows them to apply problem-solving
to real-world contexts.
This narrative review seeks to bridge that gap by
offering an organized synthesis of the existing evidence on the impact of
mathematical modeling on the attitudes of elementary school students. Most of
the available studies focus on measuring academic performance or teachers’
conceptions, leaving the students’ affective dimension in the background.
The objective of this narrative review is to analyze
the existing scientific literature on the impact of mathematical modeling on
the attitudes of students in general elementary education. To guide this search
and help bridge that gap, three main questions were proposed: What are the most
common attitudes students exhibit when participating in mathematical modeling
activities? Which elements specific to this methodology directly influence
these attitudes? And which teaching strategies or innovations are most
effective when implementing modeling to foster a positive attitude toward
learning?
Systematizing these findings is innovative and
important for Ecuadorian education. Applying mathematical modeling starting in
elementary school helps build a positive relationship between students and the
subject, thereby reversing stress, apathy, and demotivation toward mathematics.
Materials and Methods
This research was conducted using a narrative review
design in mathematics education. This methodological approach allows for the
comprehensive identification, analysis, and organization of scientific
knowledge; this design was chosen for its ability to integrate studies
employing diverse methodologies.
The review included qualitative, quantitative, and
mixed-methods articles to provide a broader perspective on the study. This
approach is ideal for addressing dimensions such as the affective and
attitudinal, which are not always quantifiable; therefore, a narrative approach
allows for the capture of classroom experiences.
To collect the information, an exhaustive search was
conducted using academic databases. Priority was given to high-impact,
open-access platforms to ensure the reliability of the sources. The main
databases consulted were SciELO, Redalyc, Dialnet, and the Google Scholar
search engine. These search engines were chosen due to their ease of access and
extensive scientific information at both the global and Latin American levels
(see Figure 1).
The literature review was conducted using the
following search string: “mathematical modeling” OR “ ” “mathematical modeling”
OR “mathematical modeling” AND “positive attitudes” OR “attitudes toward
mathematics” OR “positive attitudes toward mathematics” OR “mathematical
attitudes” AND “basic education” OR “students” OR “elementary students” OR
“educación básica” (see Figure 1).
Figure 1.
Data Collection Process
This search string allowed for the interrelation
between the main variable—mathematical modeling—and the affective dimension of
students in basic education. Additionally, a filter was applied to ensure that
the collected information was up-to-date; priority was given to scientific
articles and book chapters published between 2015 and 2026 to ensure that the
review presents the most recent information and innovations.
In order to select literature related to the topic,
inclusion criteria were established. The search was limited to studies
conducted in basic education that analyzed how mathematical modeling influenced
the development of students’ attitudes, such as stress, interest, and
motivation. Furthermore, the decision was made to exclude from the sample those
studies focused on college students, pre-service teachers, or those that
measured only students’ numerical performance.
In the first phase, search engines yielded a large
number of articles that were discarded after reviewing their titles and
abstracts. The relevant studies proceeded to a full-text review, during which
articles that did not meet the established criteria were definitively excluded.
Through this process, it was possible to identify
recurring patterns related to students’ attitudes toward mathematical modeling
activities, as well as the pedagogical factors that influence those attitudes.
To finalize the literature review, the selected articles were organized into a
matrix to facilitate data extraction.
This design aimed not only to organize information
but also to construct a robust explanatory framework, thereby establishing a
connection between theories of mathematical modeling and how these theories
relate to the attitudes students develop toward mathematics.
Similarly, the matrix made it possible to identify
various teaching strategies used by teachers to implement modeling in the
classroom and promote more active and meaningful student participation in
mathematics learning.
Results
The results of the narrative review were organized
around three research questions. Table 1 presents a synthesis of the selected
studies, followed by an analysis of the findings for each question.
Table 1. Summary of selected studies on mathematical modeling
and attitudes in elementary education.
|
Title and Author(s) |
Year |
Method |
Participants |
Country |
|
Interactions
and Contributions. Form of Participation... (Parra-Zapata
and Villa-Ochoa) |
2016 |
Qualitative
(Observation and interviews) |
27
fifth-grade students |
Colombia |
|
Fermi
Problems and Modeling Eliciting Activities... (Toalongo et
al.) |
2024 |
Mixed (Case study) |
24 sixth-grade students |
Ecuador |
|
Modeling for
the Development of Mathematical Competence... (Miñarro
Fernández and Montejo-Gámez) |
2023 |
Qualitative
(Classroom experience) |
24
sixth-grade students |
Spain |
|
Solving
multiplication problems through modeling... (Tambaco
Quintero et al.) |
2025 |
Mixed
(Descriptive-exploratory) |
15 elementary school
teachers |
Ecuador |
|
A
Mathematical Modeling Activity in Elementary School... (Trelles et
al.) |
2022 |
Qualitative
(Multiple case study) |
7 sixth-grade
students |
Spain |
|
Standardizing
the practice of modeling- ... (Olarte García) |
2020 |
Qualitative (Descriptive
study) |
30
fifth-grade elementary school students |
Colombia |
|
Modeling as a
learning strategy for solving... (Malusín Carabajo et al.)
|
2025 |
Mixed
(Pre-experimental) |
35
fourth-grade elementary students |
Ecuador |
|
Contributions
to reflection on reality... (Martínez-Novoa) |
2025 |
Qualitative (Case
studies) |
38 eighth-grade students |
Colombia |
|
The Effect of
Mathematical Modeling Activities... (Savaşlı and Serin) |
2025 |
Quantitative
(Quasi-experimental) |
Fourth-grade
elementary students |
Turkey |
|
Dengue as a
Context: Working on Statistical Concepts... (Ocampo-Arenas
and Gaviria-Quintana) |
2022 |
Qualitative (Classroom
experience) |
Fifth-grade elementary
students |
Colombia |
|
Learning
Mathematics Through Modeling... (Hitt and Quiroz Rivera) |
2017 |
Qualitative
(Case Study) |
60 high
school students |
Canada |
|
Energy
expenditure during physical activities... (Parra-Zapata
et al.) |
2017 |
Qualitative (Classroom
experience) |
42 seventh-grade students
|
Colombia |
|
The
development of modeling skills... (Carrasco Mancilla et
al.) |
2026 |
Qualitative
(Case studies) |
Two
fifth-grade teachers |
Chile |
|
Mathematical
Modeling as a Bridge Between the Classroom... (Donnet et
al.) |
2024 |
Qualitative (Case study) |
High school students |
Argentina |
|
Stop
Swallowing Lies: Modeling a Study... (Jiménez Echavarría) |
2022 |
Qualitative
(Classroom experience) |
Third-grade
elementary students |
Colombia |
Impact of Mathematical Modeling on
the Affective Dimension
The reviewed articles show that in traditional
educational settings, children develop emotional barriers toward mathematics,
thereby creating feelings of insecurity, stress, and boredom, as they perceive
the subject as merely abstract content. Along these same lines, indicates that when students were asked about the
topics covered in class, they struggled to explain them and stated that this
subject was boring for them and only for gifted individuals.
This apathy toward mathematics often leads to what Villa-Ochoa (2015) refers to as “shortcut” attitudes stemming from
factors such as students’ reactions to highly structured problems, resulting in
teachers lowering the quality of their texts and failing to take full advantage
of the resources that modeling can provide.
However, when working with this methodology—by
providing the necessary scaffolding and a well-structured instructional
sequence—an immediate emotional shift occurs: students’ passivity gives way to
a willingness to work. In this regard, Parra-Zapata & Villa Ochoa (2016) demonstrate that mathematical modeling provides
spaces that foster dialogue and reflective participation, thereby leading
students to reflect on their own reality.
Martínez Novoa (2025) points out that when students are engaged in
real-world contexts, they internalize knowledge, strengthen collaborative work,
and even begin to develop a more technical language, making them feel more
confident in what they are learning without feeling misled.
Parra-Zapata et al. (2017) demonstrate that connecting mathematics to
students’ interests transforms their attitude toward the subject. By engaging
in a modeling activity—such as calculating the energy expenditure of
cycling—the students were able to mathematically understand their own routine.
This confirms that using a personal context is not secondary but rather the
indispensable driving force for achieving a change in attitude.
The literature highlights that students are able to
understand mathematical modeling activities, even if they have no prior
experience. In this regard, Toalongo et al. (2024) point out students’ ability to adapt to this
methodology, as well as the ease with which they interact with one another,
exchange ideas, and relate their prior knowledge to the problem at hand.
Similarly, Miñarro & Montejo (2023) highlight that one of the competencies students
developed most during the application of modeling was mathematical
communication, which is of utmost importance for understanding the assigned
task and for peer collaboration.
In this regard, the quasi-experimental study by Savaşlı & Serin (2025) provides concrete evidence by using psychometric
scales to measure changes in students’ attitudes. They found a clear
improvement in the group that worked with modeling, compared to those who
received traditional instruction. These results suggest that applying this
approach helps transform the classroom environment and enables students to take
on a more confident and active role in their own learning.
In conclusion, the literature confirms that the
implementation of mathematical modeling in elementary and middle school
classrooms across different countries and grade levels transforms the
educational environment, in which students become active agents of their own
learning, reinforcing positive attitudes and the ability to collaborate with
their peers.
Instructional Design and Teacher Mediation
A review of the literature makes it clear that what
truly motivates students is the connection between mathematics and real-world
problems. However, these approaches are not always implemented in the
classroom, as noted by Asempapa (2017) : “Teachers fear that students will be unable to
solve modeling tasks due to the high cognitive demands.”
For this reason, it is essential to emphasize the
teacher’s role in this process. Mancilla et al. (2026) assert that close guidance and just-in-time support
prevent students from becoming frustrated by challenging mathematical
situations, ensuring that young people do not lose confidence in their
abilities.
Breaking down this barrier is necessary if we want
to change the classroom environment. Olarte (2020) highlights in his research that students perceive
mathematics as “difficult and only for geniuses”; however, when problems are
related to everyday situations, motivation increases.
In fact, the emotional benefits of applying
mathematical modeling are evident. Quintero et al. (2025) state that approaching multiplication through
modeling completely changes students’ perspective, as they lose their fear of
making mistakes and become actively engaged with the problem.
Consequently, students’ attitudes can be reinforced
over the long term if modeling is introduced from the earliest stages of
education. In this regard, Malusín Carabajo et al. (2025) agree that presenting modeling as a learning
strategy in elementary education sparks a participatory interest that prevents
future aversion to mathematics.
In conclusion, the way in which mathematical
modeling is implemented directly contributes to the development of students’
attitudes, especially when the teacher promotes active communication during the
activities. Similarly, it fosters confidence in expressing ideas, thereby
strengthening participation during the learning process, as noted by Miñarro & Montejo (2023) .
Innovative Strategies for Building Mathematical
Confidence
To foster a positive attitude toward mathematical
modeling, the literature emphasizes that the key innovation lies in how
activities are designed. Olarte (2020) suggests that replacing traditional textbooks with
materials featuring real-life problems is an effective strategy and can serve
as the most beneficial starting point for students.
Along the same lines, notes that the activities implemented must be
realistic or applied to real-life situations so that students can develop a “ e
sense of reality”; this is why the implementation of mathematical modeling
activities is an innovative strategy and must be carried out in a realistic
context.
In a study conducted by Jiménez (2022) with third-grade students, the students analyzed
the sugar content in the items in their lunchboxes. The students examined
labels, organized statistical data, and interviewed a nutritionist. The process
culminated in the creation of a television commercial in which they
communicated their findings and proposed healthy alternatives. Beyond the
mathematical content, the students developed a critical perspective on what
they consumed. This demonstrates that when mathematics addresses something real
and relevant to their lives, students take on an active role without the need
for external explanations.
One strategy that ties into modeling is the
incorporation of public health topics. In a study conducted by Ocampo et al. (2022) , the researchers found that using the spread of
dengue fever to teach statistical concepts was highly effective. Because it was
a situation affecting their community, the students understood the real-world
value of the data they were analyzing.
Similarly, Trelles et al. (2022) implemented a mathematical modeling activity using
real COVID-19 data, in which students had to predict the number of infected
people based on a data table; the activity demonstrated that students were able
to express their predictions even without prior experience. This suggests that
strategies linked to students’ real-world experiences strengthen the
development of confidence and engagement in their learning.
Table 2.
Innovative Strategies for Applying Mathematical
Modeling in the Classroom
|
Innovative Strategy |
Context of Application |
Author(s) |
Observed Impact |
|
Public Health |
Dengue Transmission |
Ocampo et al. (2022) |
Understanding
the true value of data. |
|
Current Data |
COVID-19 Predictions |
Trelles et al. (2022) |
Developing predictions
without prior experience. |
|
Text Substitution |
Everyday Problems vs.
Books |
Olarte (2020) |
Greater sense
of reality and motivation. |
After analyzing the findings, we can confirm that
modeling positively transforms the classroom, regardless of the country or
grade level. However, a reasonable question arises: almost all studies involve
brief experiences limited to a single instructional unit. This leads us to
wonder whether this enthusiasm is fleeting or whether we are truly fostering a
lasting change in children’s relationship with mathematics.
To resolve this uncertainty, the way forward is
through longitudinal studies. We need to understand whether continued exposure
to this method succeeds in consolidating these positive attitudes over the
years. Only then will we know if modeling can be the definitive antidote to
math anxiety, which often persists throughout a student’s entire academic
career.
Another vital point is the role of the teacher, who
acts as the primary driver of attitudinal change. However, the current
literature does not clearly show how to prepare teachers for this challenge in
our Latin American context. As suggested by Mancilla et al. (2026) , there are severe gaps in initial teacher training
that we must address so that this methodology becomes a regular practice and
not just an isolated experiment.
On the other hand, we need to broaden our
perspective. While the information we have from Ecuador, Colombia, and Spain
provides an excellent foundation, we still need to discover what is happening
in the rest of the region. It would be ideal to have much larger and more
rigorous studies, similar to the work by Savaşlı and Serin (2025) , to help us measure this emotional change in
completely diverse classrooms.
Finally, we cannot ignore the fact that every
classroom is a world of its own, shaped by its environment. Factors such as
gender, socioeconomic status, or the gap between rural and urban contexts could
completely alter a student’s response. Including these variables in the future
research agenda will allow us to design strategies that are far more inclusive
and attuned to the human reality of our students.
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Mathematics Education, 10 (1), 16–29.
https://doi.org/10.26711/007577152790002
Donnet, Y., Scaglia, S., & Cruz, M. F. (2024). Mathematical
Modeling as a Bridge Between the Secondary Classroom and Real Life:
Contributions to Thinking About the Production of Meaning. Bolema: Bulletin of Mathematics
Education, 38 , e230038.
https://doi.org/10.1590/1980-4415v38a230038
Jiménez, A. M. (2022). Stop Eating Lies: Modeling a Study on Added Sugar
Consumption in School Lunches. Antioquia Research
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Malusín Carabajo,
J., Tigre Matute, C., & Ortiz Aguilar, W. (2025). Modeling as a Learning Strategy for Solving
Mathematical Problems in the Fourth Grade of Elementary School. Sinergia Académica, 8, 558–586.
Mancilla, J. C.
C., Mardones, M. I. V., & Santander, P. A. R. (2026). The development of modeling skills in
teaching large numbers. Educational Research Notebooks, 17 (1).
https://doi.org/10.18861/cied.2026.17.1.4189
Martínez Novoa, A. M. (2025). Contributions to the
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and Didaxis: TED, 57 , 121–137.
https://doi.org/10.17227/ted.num57-20051
Miñarro, J. M.,
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Ocampo, M. C., Quintana, L., & Gaviria-Quintana, L.
(2022). Dengue as a Context: Exploring
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Olarte, J. (2020). Standardizing the practice of
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Bachelor of Science in Education
Master’s Degree in Pedagogical Innovation,
Eloy Alfaro Secular University of Manabí (ULEAM)
https://orcid.org/0009-0000-7918-521X
Doctor of Education
Office of Graduate Studies, Cooperation,
and Relations, Eloy Alfaro Secular University of Manabí (ULEAM)
arturo.rodriguez@uleam.edu.ec
https://orcid.org/0000-0002-7017-9443