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Learning linear and quadratic functions
through the use of artificial intelligence in
higher education students
Aprendizaje de función lineal y cuadrática mediante el
uso de la inteligencia artificial en estudiantes de
educación superior
Bryan Carrera-Arias
Universidad Técnica Particular de Loja, Quito, Ecuador
Facultad de Filosofía Letras y Ciencias de la Educación, Maestría de Pedagogía de las
Ciencias Experimentales Matemática
bdcarrera2@utpl.edu.ec
https://orcid.org/0009-0002-8693-6434
(Received on: 24/09/2025; Accepted on: 1/11/2025; Final Version received on: 16/06/2025)
Suggested citation: Carrera-Arias, B. (2026). Learning linear and quadratic functions
through the use of artificial intelligence in higher education students. Revista Cátedra, 9(2),
144-161.
Abstract
This article analyzes the integration of Artificial Intelligence (AI), based on Deep Learning
and Machine Learning, for teaching linear and quadratic functions in higher education. The
main objective is to evaluate the impact of AI on academic performance, comparing it with
the traditional method and measuring student acceptance using a Likert scale. The research
adopted a quantitative approach with a quasi-experimental design, working with a sample
of two groups (40 students in section A and 41 students in section B). Data collection
involved a satisfaction survey, a diagnostic assessment, and a final evaluation using
dichotomous questionnaires. The results were analyzed using descriptive and inferential
statistics (Student's t-test, after verifying normality) with the SPSS statistical software. The
analysis determined that, while positive perceptions and areas for improvement in
mathematical understanding were identified, the AI-based model did not significantly
improve grades compared to the traditional method. However, a greater interest from
students was evident through the use of AI, generating greater motivation and active
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participation, feedback, favoring the interaction of content for learning the subject of
Mathematics.
Keywords
Machine learning, artificial intelligence, mathematics, academic performance.
Resumen
Este artículo analiza la integración de la Inteligencia Artificial (IA), fundamentada en el Deep
Learning y Machine Learning, para la enseñanza de funciones lineales y cuadráticas en
educación superior. El objetivo principal es evaluar la incidencia de la IA en el rendimiento
académico, comparándola con el método tradicional y midiendo el nivel de aceptación
estudiantil mediante el uso de la escala de Likert. La investigación adoptó un enfoque
cuantitativo con un diseño cuasiexperimental, trabajando con una muestra de dos grupos
(40 estudiantes paralelo A y 41 estudiantes paralelo B). Para la recolección de datos se
empleó una encuesta de satisfacción, evaluación de diagnóstico, evaluación final mediante
el uso de cuestionarios dicotómicos. A su vez los resultados fueron analizados mediante el
uso de la estadística descriptiva e inferencial (prueba t-student, previa verificación de la
prueba de normalidad) mediante el software estadístico SPSS, determinaron que, si bien se
identificaron percepciones positivas y áreas de mejora en la comprensión matemática, el
modelo basado en IA no mejoró significativamente las calificaciones en comparación con el
método tradicional. Sin embargo, se evidenció un mayor interés por parte de los estudiantes
mediante el uso de la IA, generando mayor motivación y participación activa,
retroalimentación, favoreciendo la interacción de contenidos para el aprendizaje de la
asignatura de Matemática.
Palabras clave
Aprendizaje automático, inteligencia artificial, matemática, rendimiento académico.
1. Introduction
It is essential to ensure that students receive an education adapted to their needs, based on
the right to academic inclusion, comprehensive support, and equitable access to technology.
However, limitations persist in teacher training regarding active methodologies and the
availability of innovative resources. Specifically, there is a lack of curricular integration of
Machine Learning and Deep Learning models, meaning that AI has not yet been consolidated
as a tool for strengthening academic performance. In this context, the main objective of this
research is to evaluate the impact of AI on the learning of linear and quadratic functions in
higher education, as well as to determine the level of student satisfaction after its
implementation in the classroom.
According to De León De Hernández, the modernization of mathematics teaching through
the use of AI is a necessity in the current educational context. In this sense, the author
maintains that the right to education is fundamental for the development of children and
adolescents, making it essential to incorporate diverse learning technologies, including
artificial intelligence, into academic training processes (De León De Hernández, 2024). It is
important to adapt pedagogical strategies to the students' circumstances. In accordance
with this approach in Ecuador, classrooms are part of the inclusive education model
promoted by the Ministry of Education, which establishes the guidelines for the
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development of this modality that fosters the development of multiple intelligences in
students (Ministry of Education of Ecuador, 2021).
Soledispa et al. argue that one of the main challenges in higher education is the teaching of
mathematics, given that this discipline requires continuity, abstraction, and constant
practice of each student's analytical and critical thinking. Furthermore, with the
modernization of learning through the use of artificial intelligence, and despite efforts to
guarantee equitable education, the implementation of specific strategies for teaching
mathematics in these environments remains a challenge (Soledispa et al., 2024, p. 8). In this
context, the main objective of this research is to evaluate the impact of using artificial
intelligence in the classroom by comparing it with traditional teaching methods, as well as
to establish a student satisfaction scale that allows for assessing students' perceptions of
the implementation of this new technological methodology in the teaching-learning process.
Consequently, this research adopts a quantitative approach with an explanatory scope,
employing hypothetico-deductive reasoning. Within this framework, technological tools
were used to collect numerical data through satisfaction surveys and evaluation
questionnaires (midterm and final), integrating Artificial Intelligence models, specifically
Machine Learning and Deep Learning, into the teaching of linear and quadratic functions.
The study has a comparative-explanatory scope, seeking to analyze the differences in
academic performance between the experimental and control groups. The study's relevance
lies in its ability to statistically measure the impact of technological innovation on the
understanding of mathematical concepts. This allows us to determine whether the use of AI
overcomes learning difficulties in the university environment and to identify significant
differences in academic averages.
The article is structured as follows. The second part presents the theoretical background, a
brief review of other research related to the application of artificial intelligence in
mathematics education, and theoretical frameworks that explain a conceptual approach to
the didactic resources used for learning mathematics with concepts from Machine Learning
and Deep Learning. The third section details the research methodology, describing the
approach, type, level, and design adopted. It also explains the process of administering the
surveys and dichotomous evaluation questionnaires, concluding with an analysis of the
reliability of the collected data. The fourth section presents the results derived from the
descriptive and inferential statistical analysis. The parametric t-test was applied to analyze
possible significant differences in academic performance when comparing the traditional
method with the use of AI in the classroom. Finally, the fifth session presents the conclusions
of the study, where the integration of AI in educational institutions is discussed and the need
to strengthen the learning of Mathematics under a comprehensive pedagogical approach
that transcends the use of the technological tool is emphasized.
2. Theoretical Background
In Mexico, following the research of Quiroz-Rosas (2023), it is important to point out that
the integration of AI into mathematics education demonstrates how technology has become
a fundamental support for human development, advancing rapidly in various areas of
knowledge. Education is no exception; digital methodologies provide strategies and
techniques that optimize the teaching-learning process, offering distinctive features such as
adaptive learning and assessment. Among these tools, Script stands out, which solves
complex mathematical problems by interpreting handwriting on mobile devices and
offering real-time feedback with a step-by-step guide, as does Photomath, an application
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that uses the device's camera and an integrated scientific calculator to display detailed
procedures and final results.
In Ecuador, the research of Tóala-Zambrano (2024) highlights that the use of AI simulators
in mathematics education is a valuable tool, providing practical, dynamic, and engaging
methods for experimenting with concepts such as the notion of number, thus facilitating
their understanding through contextualization. The author emphasizes that AI has high
potential to accelerate the achievement of global educational goals by reducing access gaps,
automating management processes, and optimizing learning methodologies. According to
the study's findings, the implementation of AI tools fostered a more dynamic and effective
teaching model, adapted to the individual progress of students in the early years of
Information Technology and Telematics programs. Furthermore, it was observed that
students developed additional technological skills that strengthen their academic and
professional profiles. Consequently, Tóala-Zambrano underscores the importance of
designing policies that guarantee equitable access to AI, the implementation of which
should be led by faculty across various university disciplines.
From Peru, and referencing the research of Rubina-López et al. (2025), it is important to
note that AI has significantly transformed the landscape of higher education, especially in
mathematical problem-solving. Thanks to its ability to process large volumes of data and
provide real-time feedback, AI has fostered the development of advanced tools that
facilitate the understanding of complex concepts. The study concludes that technologies
such as Intelligent Tutoring Systems (ITS) are innovative resources that strengthen
teaching and learning processes in mathematics. Adaptive learning platforms and machine
learning algorithms are highly effective, offering flexible solutions that allow students to
overcome the challenges of advanced mathematics. These tools stand out for their
personalization capabilities, adjusting both the content and the pace of learning to the
specific needs of each student, which positively impacts academic performance and
promotes more efficient teaching.
2.1 Theoretical Framework
2.1.1 Mathematics in our culture
Based on the manuscript by Rivas-Díaz et al., it is important to note that mathematics
constitutes a fundamental language for the development of science and technology.
Mathematical work has required the construction of a system capable of representing
complex reasoning and mental processes through symbols. In this sense, the symbolization
of mathematical objects, which was initially limited to concepts associated with number and
extension, has been progressively refined to translate increasingly advanced cognitive
tasks. According to the authors, this language is based on the determination and verification
of the relationships between the created symbols, which provides the precision and rigor
necessary for the progress of other scientific disciplines (Rivas-Díaz et al., 2024, p. 10).
Furthermore, analyzing the manuscript by Heredia-Arias et al., it is important to suggest
that mathematics is a rather playful activity, making it crucial to stimulate students through
games, which can be intelligent systems that have accompanied humankind in a better
cognitive learning process through graphs. However, over time, this practice has required
powerful tools based on information technologies for its development and resolution that
facilitate the understanding of a mathematical object in class (Heredia-Arias et al., 2024, p.
3).
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2.1.2 Influence of computers on learning mathematics
Addressing the manuscript by Machuca-Almeida et al., it is important to point out that the
emergence of computers in the second half of the 20th century generated a technological
revolution that has become integrated into all aspects of contemporary culture. This
influence is strongly evident in our immediate environment, from the processing of banking
data and business planning to the robotization of production and the control of air
navigation. In the field of mathematical research, the influence of the computer has been
decisive; an emblematic example is its fundamental role in the proof of the Four Color
Theorem. This demonstrates the capacity of digital processing to solve problems of high
numerical complexity, providing solutions that were previously unattainable (Machuca-
Almeida et al., 2025, p. 12).
2.1.3 Programming Language
Analyzing the U.S. Department of Education's manuscript, it is important to note that the
most widely used programming languages in education are those known as high-level
languages. These allow for the development of programs using an accessible and user-
friendly syntax, without requiring the user to master binary code or the machine's internal
processes. Among the historically most used general-purpose languages are LOGO, BASIC,
FORTRAN, and PASCAL, which were selected for their ability to enhance cognitive skills
such as design and problem-solving. Under this approach, learning was not limited to
acquiring coding techniques; rather, learning the specifics of a language was considered
secondary to the development of higher-order thinking skills. In this way, programming
became established as an effective means for learning mathematics (U.S. Department of
Education, 2023, p. 112).
2.1.4 Artificial Intelligence
Reading Mohamed, it's important to note that AI refers to systems that exhibit intelligent
behavior by analyzing their environment and executing actions with a degree of autonomy
to achieve specific goals. This conceptualization refers to systems that demonstrate
intelligent behavior, analyzing their environment and undertaking actions with a degree of
autonomy to achieve specific objectives. This term is well-received by the scientific
community. First, it distinguishes AI from the simple use of algorithms and digital
technology in general, and second, it includes deep learning, also known as transversal
learning (Mohamed, 2021, p. 22).
conceived as the development of systems capable of solving complex tasks using a set of
AI was reduced to the simple execution of algorithms by a computer, which could not be
considered intelligent. Because of this, AI began to be associated with the development of
systems capable of solving problems considered intuitive for humans. However, problems
such as recognizing objects in images or words in voice recordings are difficult to reduce to
a set of formal rules.
Furthermore, according to González-Jiménez (2024), it is important to note within the
which are mathematical models or computations composed of interconnected numerical
manipulating the connections between neurons, the networks can be made to exhibit the
desired behavior to be useful in solving complex problems, including classification and
regression problems.
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In this sense, Figure 1 provides a concise visualization of the relationship between artificial
intelligence, machine learning, and deep learning. As can be seen, AI constitutes a broad
field that seeks to imitate human thought and action processes, while machine learning is
based on previous experiences to generate predictions. Deep learning, in turn, employs
neural networks with input data, hidden layers, and output data, demonstrating how
artificial neural connections process information to solve specific problems. Therefore, the
image complements the theoretical explanation by graphically showing how neural
networks are structured within the learning processes of artificial intelligence.
Figure 1. Supervised Learning Diagram using Artificial Intelligence. Artificial Intelligence System. Source:
(González Jiménez 2024)).
2.1.5 Machine Learning
Studying Estrada-Oviedo's manuscript, it is important to note that data science is an
eminently interdisciplinary field of knowledge, integrating methodologies and techniques
from mathematics, statistics, and computer science. Its objective is to obtain useful
information or new knowledge from enormous amounts of data that can be complex or
inconsistent, dynamic, from multiple sources, and structured or unstructured. Within data
science, we find machine learning and deep learning, which also fall under the field of AI
(Estrada-Oviedo, 2025, p. 17).
In both cases, the goal is to build models capable of solving problems using a training
dataset; that is, the aim is for the system to develop autonomous learning capabilities. This
learning is primarily classified as supervised and unsupervised. Simbaña-Nauñay, for his
part, explains that supervised learning starts with a set of pre-labeled data, which allows
the model to know in advance the possible values and expected solutions for the problem
posed. In contrast, unsupervised learning does not have these pre-labeled data, so the
system must independently identify underlying patterns and structures in the data
(Simbaña-Nauñay, 2025, p. 118).).
2.1.6 Deep Learning
In the analysis of the manuscript by Castillo Del Pezo et al., it is important to highlight that
the design of artificial intelligence algorithms for feature extraction has the fundamental
purpose of distinguishing the factors of variation that explain the observed data and, in turn,
excluding those that are irrelevant to the process of modeling and interpreting the
information. These factors affect each unit of information; therefore, if the factors of
variation are modified, the observed data also change. An example of this is found in voice
recordings, where the speaker's age, sex, and accent influence the data obtained. In this
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context, deep learning emerges as a solution to the problem of factors of variation,
introducing representations expressed in terms of simpler ones. This allows the computer
to identify complex concepts from elementary levels of abstraction. For example, when
determining whether an image contains a car, the technique does not track elements such
as wheels from the beginning; The process begins by identifying basic concepts such as
straight lines to build more complex structures (corners or contours) and, finally,
consolidate the concept of a car (Castillo Del Pezo et al., 2024).
2.1.7 Cognitive Learning
Addressing the manuscript by Bolaño-García and Duarte-Acosta, it is important to point out
that metacognition structures, or rather, the knowledge that people construct about their
own cognitive functioning. This involves mental operations of monitoring and regulation
that individuals exert over their daily dynamics, allowing them to distinguish the awareness
of their mental processes from personal content, beliefs, and motivations. These skills are
essential for monitoring and regulating one's own thinking. In this sense, linking
metacognitive strategies with learning allows us to diagnose the causes of academic
performance in relation to educational quality. It also facilitates the design of techniques
that promote autonomous and independent learning, ensuring that the process does not
depend exclusively on the teacher. This approach is especially beneficial when the student
is able to plan, regulate, and evaluate their own learning, applied in this case to the study of
linear and quadratic functions (Bolaño-García and Duarte-Acosta 2025, p. 43).
3. Methodology
This section describes the quantitative approach of the research, which employs a quasi-
experimental design with two working groups: a control group and an experimental group.
The total sample consisted of 81 students selected through simple random probability
sampling, ensuring the representativeness of the data. The control group (Parallel A)
comprised 40 students, while the experimental group (Parallel B) had 41 participants.
Furthermore, for the statistical analysis, Hernández-
criteria for the Shapiro-Wilk normality test independently for each group; this statistic was
selected because the size of -Sampieri
et al., 2014, p. 312). After confirming the normal distribution of the grades, the parametric
Student's t-test for independent samples was used to compare the academic performance
of the traditional method versus the innovative AI-based model.
3.1 Research Approach and Design
This research adopts a quantitative approach, based on the collection and analysis of
numerical data obtained through satisfaction surveys and evaluation questionnaires. This
methodological procedure allowed for the testing of both null and alternative hypotheses
to determine the validity, significance, and consistency of the results obtained.
Likewise, hypothesis testing is a fundamental aspect of the research process, since the use
of descriptive and inferential statistics enables the objective interpretation of the data and
informed decision-making regarding the phenomenon under study. This facilitates the
measurement of academic performance and the comparison of the traditional method with
the new, innovative AI methodology and its academic impact.
According to Arias, the quasi-experimental design allows for the comparison of a previously
established control group with an experimental group. This design allows the verification
of one of the null hypothesis (Ho) or alternative hypothesis (Hn) on the impact on grades
with the use of the artificial intelligence technological tool, through the analysis of the Type
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and Level of Research. The research adopts an explanatory approach, based on the technical
measurement of academic performance and the determination of the influence of artificial
intelligence use in the experimental group, compared to the control group.
A quasi-experimental design is also employed, which allows for the analysis of the influence
of the independent variable on the dependent variable. The research has a longitudinal
focus, as data collection was carried out at two points in time: an initial diagnostic
assessment and a final assessment, with the purpose of comparing the results obtained
before and after the intervention.
variations in grades in the two AI courses after the pedagogical intervention with the use of
Machine Learning and Deep Learning templates (Arias, 2012, pp. 58-60).
3.2 Population and Sample
The population consists of 102 first-year higher education students majoring in Business
Administration, divided into four sections at the Ibarra Higher Technological Institute. A
simple random sampling method was used to determine the sample size, resulting in a
sample of 81 students (45 men and 36 women) with an average age of 19 years. The
following method was used to determine the sample size:
N = population size
e^2 = squared sampling error
Z^2 = squared confidence level
pq = population variance (constant of 0.25)
Ecuación 1
For the organization of the groups, a quasi-experimental design was implemented using
simple random sampling, resulting in a sample of 81 students. The groups were organized
as follows: the Control Group (Group A), consisting of 40 students, received instruction
using the traditional method. The Experimental Group (Group B), consisting of 41 students,
received instruction using the innovative methodology that integrates the use of AI
(Machine Learning and Deep Learning).
To ensure the validity of the study, the instruments were validated by five academic experts
in higher education. Inclusion criteria included legally enrolled students with a minimum of
80% regular attendance at scheduled sessions, voluntary participation, and attendance at
individual and group workshops. Exclusion criteria included students who did not complete
the final summative assessment or the satisfaction survey, including those who submitted
blank instruments. Finally, students with advanced knowledge in programming languages
(Java, Python) or development environments (TensorFlow) oriented to Machine Learning
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and Deep Learning were excluded, in order to avoid bias in measuring the impact of the
intervention.
3.3 Research Technique and Instrument
In this research, a survey was used as the technique to determine the level of satisfaction
with the use of artificial intelligence (AI) in the topic of linear and quadratic functions among
higher education students. The instrument used was a dichotomous questionnaire with
questions on subtopics such as quadrants of the Cartesian plane, increasing and decreasing
functions, the quadratic formula, and concave and convex parabolas. An open-ended
questionnaire with exercises was also used, where students developed solutions both
manually and using the AI system. This was key to measuring the academic performance of
higher education students.
First, the survey technique (ordinal qualitative variable; student satisfaction) was used to
measure the perceptions of the 81 students who received technological intervention
through the use of AI in the classroom. Regarding the instrument, the satisfaction survey
was administered after the AI classes concluded. The items consisted of five Likert scale
questions structured as follows: strongly agree, agree, neutral, disagree. The cognitive
process, in turn, facilitated the evaluation of the use of the AI-powered templates in terms
of mathematical problem comprehension, graphical representation, feedback, and self-
learning. Furthermore, to assess academic performance, a pretest (diagnostic assessment)
and a posttest (final assessment) were administered to both the experimental and control
groups to compare performance before and after the intervention.
Secondly, an assessment questionnaire (academic performance variable) was used to
measure the understanding of mathematical concepts. The instrument was used for
summative assessment on the topic of linear and quadratic functions. The items consisted
of ten questions with mathematical problems involving linear and quadratic functions,
including subtopics related to the Cartesian plane, increasing and decreasing functions, the
general formula of the quadratic function, manual problem-solving with verification, and
structured academic support clues within the AI-powered templates. Regarding the
cognitive process, this was developed through the resolution of mathematical problems
related to linear and quadratic functions, combined with methods of logical and abstract
reasoning, reading comprehension, and decision-making. In this way, cognitive skills
oriented towards the analysis, interpretation, and solution of mathematical problems were
strengthened..
3.4 Descriptive Statistics
It is important to mention that the descriptive analysis is structured around the ordinal
qualitative variable corresponding to the satisfaction survey, using frequency tables based
on the Likert scale (strongly agree, agree, neutral, disagree). Pie charts and bar graphs were
used to represent the results, allowing for better visualization of the frequencies obtained.
The median was also considered as a measure of central tendency, as it allows for
identifying the central value of the averages achieved by each group: control and
experimental (Maureira, 2025).
To determine the impact of AI use on student averages, a quantitative numerical variable
was used to assess learning of linear and quadratic functions, recording the grades of the 81
students (section A and section B). The research focuses on the use of measures such as
central tendency and the mean for both courses in terms of student averages, for both the
control and experimental groups. That is, essential characteristics of the dependent and
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independent variables are presented by observing the total number of subjects structured
as a sample, using percentages of valid and missing data.
3.5 Inferencial Statistics
The inferential statistics used in this research allow for comparing differences between
groups within the studied sample by calculating the significance level (p-value) of the
average scores of students in both groups (control and experimental) to determine the
impact of using artificial intelligence compared to the traditional method. For the main
experiment, a quantitative (numerical) variable was used, focusing on the data distribution
and the significance level, which means that student scores are symmetrically clustered
around the course mean. The categorical or ordinal component mentioned in previous
sections was limited exclusively to the descriptive analysis regarding students' perceived
satisfaction with the use of AI in the classroom, but not to verifying the hypothesis of
academic performance.
To validate the impact of using artificial intelligence, the parametric Student's t-test was
applied, which allows for comparing the means between the control and experimental
groups. According to Gordillo-Armijos, this procedure requires that the data have a normal
distribution, considering that the values tend to cluster around the mean or average of the
course. Likewise, the significance level is expressed as a value between 0 and 1. In
experimental studies, the most commonly used alpha levels are 0.05 and 0.01. In this sense,
when the p-value is less than 0.05, the null hypothesis is rejected and the alternative
hypothesis is accepted; whereas, if the p-value is greater than 0.05, the null hypothesis is
not rejected, indicating that there is no statistically significant difference between the
groups analyzed (Gordillo-Armijos, 2021, p. 52).
3.6 Results of Descriptive and Inferential Statistics
Question 1 is worded as follows: Does using Machine Learning software to graphically
represent a linear function help you understand the class topic by fostering logical thinking?
Figure 2. Percentages of responses in the acceptance of the template for graphical representation of the linear
function.
According to the results, among the students of the Higher Education Institute, 37.14%
strongly agree, 22.86% agree, 20% are neutral, and 20% disagree regarding the application
of the machine learning template in the graphical representation of linear functions.
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Furthermore, it can be interpreted that 60% of the students in the entire course agree with
the use of AI-powered templates to improve the learning process for linear and quadratic
functions by fostering cognitive skills.
Question 2 is formulated as follows: Does using machine learning software in the graphical
representation of quadratic functions help you understand the exercises proposed in class?
Figure 3. Percentages of responses in the acceptance of the template for graphical representation of the
quadratic function
According to the results, among the students of the Higher Education Institute, 22.86%
strongly agree, 28.57% agree, 34.29% are neutral, 11.43% disagree, and 2.86% strongly
disagree. It is important to note that 34.29% of the class is neutral. Furthermore, the results
indicate that 22.86% of the class strongly agrees with the application of the machine
learning template for the graphical representation of the quadratic function. This
perception demonstrates that the tool facilitates the understanding of the exercises
developed in class, particularly those related to the algebraic determination of the parabola
from two points located on the Cartesian plane. However, it is considered necessary to
implement feedback processes to improve the template in those areas where students
experience the greatest difficulties, with the aim of strengthening the teaching and learning
process.
Question 3 is worded as follows: Does applying Deep Learning to the feedback boxes in the
template help you develop cognitive skills such as logical reasoning?
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Figure 4, Percentages of responses in the acceptance of feedback boxes in the Deep Learning template
According to the results, among the students of the Higher Education Institute, 25.71%
strongly agree, 28.57% agree, 31.43% are neutral, 11.43% disagree, and 2.86% strongly
disagree. Furthermore, it can be interpreted that 54.28% of the students have a high
acceptance of the application of Deep Learning in solving linear and quadratic function
exercises using the feedback strategy. However, 45.72% of the students are skeptical about
the application's potential to improve their learning, indicating the need for timely feedback
during class time to help them solve algebraic expressions.
Question 4 is formulated as follows: Does entering values of the linear function into the
Machine Learning template help you develop the algebraic solution of the equation of a line?
Figure 5. Percentages of responses in the acceptance of income values in the quadratic function in the Machine
Learning template
Regarding the results, 14.29% of students strongly agreed; 40% agreed; 28.57% were
neutral; 11.43% disagreed; and 5.71% strongly disagreed. These data show that 54.29%
have a favorable view of using the Machine Learning template to determine the equation of
a line in a linear function. However, the 28.57% of neutral responses reflect the need to
strengthen support through demonstration classes and feedback in the areas of greatest
difficulty.
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Question 5 is worded as follows: Did the deep learning template, by allowing peer feedback
comments, help you understand the topic of linear and quadratic functions?
Figure 6. Percentages of responses in the acceptance comments on the quadratic function in the Deep Learning
template
Regarding the results, 11.43% of the students strongly agreed; 45.71% agreed; 28.57%
were neutral; 11.43% disagreed; and 2.86% strongly disagreed. These data show that
57.14% of the students have a favorable view of peer discussion as a feedback strategy for
solving linear and quadratic function exercises. However, the 28.57% of neutral responses
reflect the need to strengthen pedagogical support to consolidate learning. It is important
to emphasize that a high percentage of the class was skeptical, so personalized feedback
was necessary in areas such as the algebraic solution of a concave and convex parabola.
3.7 Normality Test
It is important to mention that the Shapiro-Wilk test was applied to assess normality,
considering that the sample consisted of more than 30 and fewer than 50 students. The
experimental group yielded a significance value of 0.138, while the control group yielded a
significance value of 0.225. Since both values exceed the established significance level ( =
0.05), it is determined that both the experimental and control groups exhibit a normal
distribution in their scores, as shown in Table 1..
Normality Test
Table 1. Normality test of the control and experimental groups using the SPSS statistical software.
3.8 T-Test for independent samples
It is important to mention that the parametric t-test for independent samples was used,
given that there was a control group and an experimental group where the scores passed
the normality test and the data were numerical. A p-value of 0.843 was obtained with a two-
way p-value, given the significance level of =0.05. The difference between the means was
0.267 units, and the difference in the standard error was 1.34 units. Furthermore, in the
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interpretation of the results, the null hypothesis was accepted, which states that there is no
significant difference in the students' scores. Therefore, it was determined that academic
performance did not show a statistically significant improvement after the application of
artificial intelligence as a learning method, through the use of machine learning and deep
learning templates.
In this sense, the results demonstrate that there is no significant difference between the
means of the two working groups at the Higher Education Institute. The control group
obtained an average of 8.25 points, while the experimental group reached an average of 8.52
points, which shows that, although there is a slight numerical difference between both
averages, this is not statistically significant.
Independent Samples Test
P of a
factor
Two-
factor P
Table 2. T-test for independent samples using SPSS statistical software
4. Discussion of Results
Quiroz-Rosas's research indicates that, although students recognize the transformative
support that AI provides, many do not feel fully prepared to effectively integrate it into their
teaching practices. The implementation of AI in education raises concerns about the
potential for dehumanizing the educational process, as well as the possible excessive
dependence this technology generates (Quiroz-Rosas, 2023, p. 18). In accordance with this,
the present research shows that while Deep Learning and Machine Learning templates,
consisting of continuous feedback charts, had a high acceptance rate among students
(66.71% of the course), there is too much dependence on the solution software.
Consequently, students did not develop broader cognitive skills in reasoning and critical
and analytical thinking, resulting in poor integration into the pedagogical learning process.
Torres-Torres's research shows that the arithmetic mean of the experimental group was
7.71, while the control group obtained an arithmetic mean of 6.22. In turn, the standard
deviation of the experimental group is 2.40 units and that of the control group is 1.66 units.
A significant difference in the standard deviation between the performance of the
experimental and control groups is observed (0.74). Therefore, it can be concluded that the
experimental group, which used AI in the development of the classes, had higher academic
performance than the control group (Torres-Torres, 2024, p. 35). In contrast, this research
used the parametric Student's t-test for independent control and experimental groups with
a p-value of 0.843 units, indicating that there is no significant difference between the means
of the groups. The control group obtained a mean of 8.25 units and the experimental group
8.52 units, demonstrating that there is no significant difference in the averages.
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5. Conclusions
Students at the Higher Education Institute showed high acceptance of the application of
artificial intelligence in the study of linear and quadratic functions. The results demonstrate
that in the satisfaction survey, 57.14% of the sample was in favor of using AI in the
classroom, while skepticism remained low or in the minority. It is important to note that
more than half of the students found the feedback process helpful; peer discussions
encouraged students to solve linear and quadratic function exercises. It is important to
emphasize that a high percentage of the students were skeptical, so feedback was needed in
specific areas such as the algebraic solution of concave and convex parabolas, and, in linear
functions, the input of limits of an increasing function to solve the proposed exercises.
This research determined that there is no significant impact of AI application compared to
traditional teaching methods. This was corroborated by the parametric t-test for
independent samples (control and experimental groups), where the scores met the
normality test requirements. The statistical analysis yielded a p-value of 0.843 with a two-
way p-value, given a significance level of =0.05, leading to the confirmation of the null
hypothesis that there is no significant difference in student grades. Therefore, their
performance does not improve when using AI with Machine Learning and Deep Learning
templates as a learning method. Furthermore, there is no significant difference in the mean
scores of either group of students at the Higher Education Institute.
This study highlights an important dichotomy: despite high acceptance among higher
education students of AI as a teaching tool, it does not influence academic performance, as
students' grades do not surpass those obtained with the traditional method. Detailing the
opportunity to integrate artificial intelligence methodology into lesson planning, which
requires high pedagogical feedback, this study integrates various skills within multiple
intelligences to develop abstract and logical reasoning skills in proposed and developed
exercises, along with assessments, highlighting difficulties in the areas of increasing and
decreasing functions. As a future line of research, the need arises to delve deeper into the
design and implementation of a hybrid teaching model that incorporates AI-supported
diagnostics to address learning difficulties with functions. In this regard, it is pertinent to
explore how teachers can leverage AI-generated feedback systems to focus their
pedagogical intervention on the most complex areas, such as the algebraic solution of
complex parabolas or the incorporation of the concept of limits.
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Authors
BRYAN CARRERA-ARIAS obtuvo el título de Ingeniero Electrónica y Redes de
Comunicación, Universidad Técnica del Norte (Ecuador) en 2017. Ha concentrado su
formación de posgrado en el ámbito de la docencia en matemáticas, obteniendo el título de
Magíster en Educación Enseñanza de la Matemática mención Docencia Matemática de la
Universidad Particular de Loja (Ecuador) en 2025. Además, posee varios Diplomados
Superiores, incluyendo la Enseñanza de la Matemática en GeoGebra, con Khan Academy, y
con Matlab y Wólfram, todos enfocados a diferentes niveles educativos.
Actualmente, se desempeña como docente en el área de Pedagogía de las Ciencias
Experimentales Matemática e Informática en el Instituto de Educación Superior ITISI, y
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colabora en la Facultad de Filosofía Letras y Ciencias de la Educación de la Universidad
Central del Ecuador. Su experiencia se complementa con la autoría de diversos libros y
artículos científicos, reflejando su compromiso con la investigación y la innovación
pedagógica. En los últimos años se ha concentrado en la investigación de metodologías
activas para el aprendizaje de la matemática. Al igual que la aplicación de conceptos y
desarrollo de software con Inteligencia Artificial para la evolución de las inteligencias
múltiples en los estudiantes.
Statement on the use of artificial intelligence
The authors declare that they used the ChatGPT tool GPT-4 model (OpenAI), June 2025
version, exclusively to support language improvement. None of the scientific content,
results, analyses, or interpretations were generated by artificial intelligence. All material
was written, reviewed, and validated by the author, who is responsible for its accuracy and
rigor.
