Matemáticas y Física-Tesis de Pregrado

Permanent URI for this collectionhttps://dspace-test.ucuenca.edu.ec/handle/123456789/156

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Guía didáctica para el aprendizaje de progresiones aritméticas y geométricas en BGU
(Universidad de Cuenca. Facultad de Filosofía, Letras y Ciencias de la Educación, 2025-10-30) Durán Sánchez, Kelly Stacy; Mocha Cárdenas, Jonnathan Bolívar; Bravo Guerrero, Fabián Eugenio
The objective of this research is to develop a teaching guide that facilitates the learning of arithmetic and geometric progressions. Learning these topics not only requires memorizing formulas but also requires reasoning to solve problems. A mixed methodology was implemented within this research: quantitative and qualitative. This was done to take advantage of the benefits offered by these methods and achieve better data analysis. The quantitative methodology was used with a 14-question survey to 64 second-year high school students (BGU). Meanwhile, the qualitative approach involves a six-question interview with three mathematics teachers. The study conducted for this work revealed a deficit in knowledge of these topics. Most students did not recognize these concepts and also expressed that they require different teaching methods to improve their learning process. Therefore, this teaching proposal is being developed. It seeks to implement learning methods with an approach that fosters understanding, connection to the real world, practice, and the development of skills such as critical thinking.
Análisis de las metodologías empleadas en el refuerzo pedagógico de matemáticas dirigido a estudiantes de noveno año de Educación General Básica
(Universidad de Cuenca. Facultad de Filosofía, Letras y Ciencias de la Educación, 2025-10-22) Ordoñez Ochoa, Yeleny Alexandra; Rubio Ortiz, Paulina Rebeca; Trelles Zambrano, César Augusto
This study aims to analyze the methodologies used in academic reinforcement classes within the subject of mathematics for 9th grade students (12-year-olds) of Basic General Education (K-12) and their influence over the academic performance of the students. Given the current legislative and recent research, the importance of pedagogical reinforcement classes as a strategic tool to optimize educational results and confront the current challenges of education is emphasized. The research employs a mixed-methods approach design that enables the discovery of the most effective teaching strategies and implementation challenges through both qualitative and quantitative data collection. The research reveals that search-based active, participatory, and student-centered methodologies, along with comprehensive teacher training and tailored pedagogical strategies, significantly enhance students’ understanding and achievement in mathematics. During the research in classrooms, challenges like limited class time and discrepancies between planned activities and actual implementation were identified, emphasizing the need for ongoing teacher training and the use of different strategies and resources. Overall, strategically applied reinforcement methods are essential for enhancing learning in mathematics and promoting educational equity.
Propuesta de etnomodelación utilizando herramientas de albañilería como un recurso didáctico para el aprendizaje de la geometría
(Universidad de Cuenca. Facultad de Filosofía, Letras y Ciencias de la Educación, 2025-10-30) Sarmiento Quezada, Valeria de los Ángeles; Calle Palomeque, Carmen Eulalia
This thesis explores the application of ethnomodeling using masonry tools such as the plumb line, the leveling hose, and the square as a strategy to innovate the learning of geometry. This research addresses the need to bridge institutional learning with local knowledge by integrating everyday cultural practices where these construction tools become valuable educational resources for teaching mathematics. Through a mixed content analysis, the perspectives of students (via surveys) and the community of masons (via interviews) are examined to assess their interest in mathematical ethnomodeling, which is highly effective for connecting a mathematical model of a real-world situation with the mathematics practiced by community members. As a result of this research, a magazine titled "Ethnoconstructors" is proposed to assist and guide students in enhancing their understanding of geometry.
El Movimiento Rectilíneo Uniforme y su enseñanza: un estudio comparativo de la Inteligencia Artificial en la planificación curricular
(Universidad de Cuenca. Facultad de Filosofía, Letras y Ciencias de la Educación, 2025-10-31) Calva Narváez, Aylin Antonella; Loyola Delgado, José Antonio; Quezada Matute, Tatiana Gabriela
Lesson planning is an essential but demanding task in the teaching work, especially in topics such as the Uniform Rectilinear Movement (URM), which require pedagogical structure and conceptual clarity. This research analyzes the use of ChatGPT and Gemini artificial intelligence chatbots as support tools to develop micro-curricular lesson plans based on the URM, in order to evaluate their effectiveness, relevance, and applicability in the Ecuadorian educational context. The study was conducted in three stages: a systematic literature review (2020–2024) The research was developed in three stages: a systematic review of literature (2020-2024) under the PRISMA methodology; the elaboration of lesson plans through a prompt designed with the Iterative Methodology for the Generation of Didactic Prompts (IMGDPro), using criteria from the Ministry of Education; and expert validation of an instrument using Aiken’s V coefficient, which was later applied to secondary and higher education teachers with experience in physics. The results shows that both chatbots should generate valid lesson plans, with a clear structure and activities aligned with the curriculum. ChatGPT shows greater consistency in evaluation criteria and didactic clarity, while Gemini highlighted for it´s sequencing. Teacher’s perceptions were positives, recognizing the potential of it tools as complementary resources, although they underlined the importance of human pedagogic criteria for its proper use. It is concluded that AI chatbots should be valuable allies in educational lesson planning, provided that they are used as a complement to professional teaching knowledge and are adapted to the needs of the classroom.
Guía Didáctica sobre la Enseñanza de Campos Eléctricos para la Carrera de Pedagogía de las Ciencias Experimentales
(Universidad de Cuenca. Facultad de Filosofía, Letras y Ciencias de la Educación, 2025-10-27) Aucay Cevallos, Luis Fernando; Rojas Rojas, Marco Alejandro
The present study aims to elaborate a didactic proposal that allows teachers to develop their classes on electric fields in a creative manner, using the Challenge-Based Learning (CBL) strategy. The teaching of electric fields is of paramount importance as it is immersed in different areas such as technology, engineering, and nanotechnology. Furthermore, electric fields are constantly evolving, requiring continuous familiarization. The study was conducted under a qualitative approach, where the technique used was interviews, for which a seven-question questionnaire was developed to facilitate data collection. The sample consisted of three physics teachers from the Experimental Sciences Pedagogy Program at the University of Cuenca. The information gathered allowed for an understanding of the limited use of concrete material by the teachers, but they showed openness to using a proposal that facilitates the utilization of concrete resources. Finally, a proposal is elaborated that contains three classes based on Challenge-Based Learning, which seeks to achieve a significant improvement in the understanding of the fundamental concepts of electric fields, as well as an increase in students' interest and motivation towards the subject.
Enseñanza Lúdica de operaciones básicas de matrices
(Universidad de Cuenca. Facultad de Filosofía, Letras y Ciencias de la Educación, 2025-10-27) Sicha Chillogalli, Kelyn Susana; Yunga Jiménez, Jonnathan David; Trelles Zambrano, César Augusto
Mathematics is considered by most students to be a tedious and difficult subject, especially when studying advanced concepts and topics they don't understand, such as matrices. The study of matrices is fundamental since their concepts are used in different branches, due to their ease of representing information and the efficient management of their data. Therefore, this work is a didactic proposal designed for teaching basic matrix operations. This proposal includes different educational games that teachers can use to reinforce their students' knowledge. Additionally, it explains how to use each game and the accessible material needed to carry it out. The objective of this didactic proposal is to provide mathematics teachers with playful tools that allow them to develop their classes in a more dynamic and engaging way, thus encouraging greater student participation. Through the use of playful strategies, the aim is to capture students' attention, facilitate learning through play, and reinforce the content covered in class, promoting a different and more positive view of mathematics.
Enseñanza de la Física y Aprendizaje Colaborativo: estrategias para manejo de grupos
(Universidad de Cuenca. Facultad de Filosofía, Letras y Ciencias de la Educación, 2025-10-24) Maldonado Naula, Jorge Andres; Coello Apolo, Juan Diego
This research arose in response to the need for guidance on group management strategies among students in the Pedagogy of Experimental Sciences: Mathematics and Physics program. The methodology used was mixed. Regarding the quantitative aspect, given that managing the classroom environment is a broad topic, the study was defined through a survey, which revealed that the greatest difficulty encountered is when carrying out group activities. The theoretical basis of this research provides important concepts on the management of discipline. The teacher's attitude and role in the teaching-learning process were considered, as well as the importance of collaborative work, since it is a significant part of teaching physics. This information was systematized through a thorough review to identify effective strategies. Subsequently, regarding the qualitative aspect, interviews were conducted with teachers to understand how they manage discipline in the classroom. The results were analyzed using artificial intelligence tools and complemented by a detailed manual review. Finally, the triangulation technique was applied, comparing the results obtained from the theoretical review and the interview analysis. Based on the similarities between the two sources, 14 effective strategies for managing discipline in collaborative work emerged.
Caracterización de la argumentación por estudiantes de bachillerato en la resolución de problemas matemáticos
(Universidad de Cuenca. Facultad de Filosofía, Letras y Ciencias de la Educación, 2025-10-25) Peñaloza Mejía, Daniela Lissette; Quizhpilema Zhagui, Jennifer Alexandra; Trelles Zambrano, César Augusto
This study characterizes the mathematical argumentation employed by second and third-year high school students during problem-solving. Through a mixed-methods approach, with an emphasis on qualitative analysis, classroom observations of the four core teachers involved in this research were analyzed, along with teacher interviews one conducted with a focus group of 15 teachers and the same interview conducted at different times with the four core teachers and assessments involving intra and extra-mathematical problems administered to a sample of 142 students. The results show that students most frequently rely on argumentation based on algorithms, memorization, and intuition, while contextualized or interdisciplinary arguments are uncommon. Furthermore, a discrepancy was identified between teachers’ conceptions of argumentation and their classroom practices, which affects the quality of students' reasoning. The study concludes that the development of mathematical argumentation is influenced by factors such as teaching practices, curriculum, assessment type, and student motivation. Promoting a classroom environment that values justification, debate, and critical thinking is essential to strengthening this competency.
Explorando Circuitos Eléctricos con el apoyo de Material concreto: Evaluación de una propuesta didáctica
(Universidad de Cuenca. Facultad de Filosofía, Letras y Ciencias de la Educación, 2025-10-24) Chalco Paute, Julio Javier; Guamán Fajardo, Ana Gabriela; Rojas Rojas, Marco Alejandro
This research analyzed the academic impact of implementing teaching guides with concrete materials on electrical circuits in the second year of high school at the Guillermo Mensi Educational Unit during the 2024-2025 period. The study adopted a quantitative approach and worked with two groups: experimental and control. The independent and dependent variables were the teaching guides with concrete materials and academic performance, respectively. Students in the experimental group worked with the proposed approach, while the control group followed the traditional approach. Data collection involved a pretest and posttest on knowledge of electrical circuits, which were validated by expert judgment. The data were subsequently processed and analyzed using statistical tests of normality, homogeneity of variance, and comparison of means, which allowed for the analysis of results between the experimental and control groups. The Student t-test, with a p-value less than 0.05 (p < 0.05), indicates significant improvements in the academic performance of the experimental group. The study shows that the implementation of teaching guides with concrete materials facilitates the understanding and application of topics such as Ohm's law and electrical circuits, indicating that the approach used fosters effective learning.
Propuesta constructivista para el aprendizaje de matemáticas en personas con escolaridad inconclusa
(Universidad de Cuenca. Facultad de Filosofía, Letras y Ciencias de la Educación, 2025-10-25) Guamán Parra, Mónica Priscila; Jácome Guzmán, Marco Vinicio
This research is framed within the field of Youth and Adults Education (EPJA) and aimed to design a didactic proposal based on the constructivist approach, focused on strengthening mathematics learning in adult learners with incomplete schooling who are entering the first year of the Intensive Baccalaureate program. A mixed-methods approach was adopted, combining quantitative and qualitative techniques. A diagnostic test and the Honey-Alonso Learning Styles Questionnaire (CHAEA) were applied to a population of 20 students; in addition, semi-structured interviews were conducted with three mathematics teachers and one student from each level (first and second year of the program). The results revealed insufficient mastery of fundamental mathematical content, particularly in basic operations, powers, and equations, as well as a predominance of reflective and theoretical learning styles. Based on the diagnostic findings, a contextualized leveling guide was developed, structured around the constructivist approach and supported by Problem-Based Learning (PBL) methodology. This proposal seeks to promote meaningful learning, enhance logical-mathematical thinking, and contribute to the development of autonomy, motivation, and self-confidence in adult students, within an inclusive, flexible, and learner-centered educational model.
Una propuesta didáctica de aprendizaje de campos eléctricos de tercero de Bachillerato mediante Gamificación
(Universidad de Cuenca. Facultad de Filosofía, Letras y Ciencias de la Educación, 2025-10-28) Juela Zumba, Raúl Agustín; Guachún Lucero,Freddy Patricio
In this degree work, a proposal was developed for the application of gamification as a pedagogical method for teaching electric fields to third-year high school students. The learning guide integrates playful elements such as points, training sessions, challenges, and rewards, with the aim of increasing student motivation and engagement. Based on a quantitative evaluation of the students, results indicated that they needed an alternative non-traditional learning method. The relevance of these results lies in the evidence that gamification can be an effective tool for improving the learning of complex concepts in science, suggesting its potential implementation in the educational curriculum to enhance interest and academic performance in physics.
Lenguaje Matemático: Estrategias Comunicativas Para la Enseñanza
(Universidad de Cuenca. Facultad de Filosofía, Letras y Ciencias de la Educación, 2025-10-22) Lazo Cuzco, Nelly Elizabeth; Bernal Reino, Juan Carlos
This degree work presents as a proposal a set of ten communicative strategies for mathematics teaching centered on mathematical language, aimed at mathematics teachers. From a qualitative approach with a comparative scope, techniques such as classroom observation and interviews with mathematics teachers were applied, with the purpose of identifying the most effective communicative strategies and the limitations present during teaching. As a result, progress is evidenced in participation and dialogue in classes, although difficulties persist related to classroom organization, content contextualization, and the development of linguistic and argumentative skills. Therefore, a set of communicative strategies is proposed through practical sheets to be applied without requiring additional time or complex resources, thus promoting more participatory, reflective, and communicative teaching. The objective was to provide teachers with strategies that strengthen the teaching of mathematical language and facilitate interaction, reflection, and knowledge construction by the student. In conclusion, these strategies respond to the real needs of the classroom, the promotion of horizontal communication, and the use of diverse languages (verbal and non-verbal) that are important for improving the understanding of mathematical language.
Propuesta de enseñanza mediante las TIC para el tema de ondas en el tercero de Bachillerato General Unificado
(Universidad de Cuenca. Facultad de Filosofía, Letras y Ciencias de la Educación, 2025-10-27) Jimbo Uday, Christian David; Rojas Rojas, Marco Alejandro
Physics teaching, from its beginnings to the present, has been carried out in classrooms through a mechanical process where the main factor is the memorization of concepts and their formulas, without taking into account the applications presented for each environment, as well as the teacher's role, who is responsible for creating educational environments that allow the correct application of TIC for each moment of the class, since it is important that each knowledge acquired is assimilated by the student. This research focuses on the development of a teaching proposal that addresses the topic of waves through the use of TCI for third year of high school, due to the existence of various digital tools that have been developed in recent years for the benefit of education. To develop the proposal, information was gathered by adapting a methodology with a qualitative approach through the interview technique with teachers at the Ciudad de Cuenca High School. The information collected was necessary to identify difficulties in teaching Waves and the need to create a teaching guide with the support of simulators. The literature review highlights the importance of using ICT as a complement to the teaching process. It also greatly assisted in the creation of a teaching guide that meets the demands of today's education.
Recursos didácticos para el aprendizaje de la Hidrostática en la Carrera de Pedagogía de las Ciencias Experimentales de la Universidad de Cuenca
(Universidad de Cuenca. Facultad de Filosofía, Letras y Ciencias de la Educación, 2025-10-27) Ortiz Vásquez, Boris David; Calle Flores, Jordan Steven; Guachún Lucero, Freddy Patricio
In this degree work, a didactic proposal is presented for the learning of Hydrostatics based on Problem Based Learning (PBL), specifically focused on the following topics: Pascal´s Principle, Application of the principle of communicanting vessels and the Siphon Principle for the third cycle students during the period March 2024 – August 2024. In order to analyze the relevance, a study with a quantitative approach of descriptive scope was carried out, through the application of a survey to students of Pedagogy of Experimental Sciences: Mathematics and Physics. As a results, it was obtained that students wish to carry out laboratory practices on Hydrostatics due to the abstraction of some topics and the complexity involved in understanding them. Also that didactic resources would be a great resource to optimize learning and achieve a better conceptualization of all topics. Based on the answers of these surveys, it can be considered that Problem-Based Learning and the development of didactic resources are ideal strategies to addres Physics topic, because students translate theory with reality.
Guía didáctica para la enseñanza de la probabilidad condicional e independencia de sucesos en Bachillerato General Unificado (BGU) enfocada en la toma de decisiones
(Universidad de Cuenca. Facultad de Filosofía, Letras y Ciencias de la Educación, 2025-10-22) Mejia Pillco, Erick Adrian; Bravo Guerrero, Fabián Eugenio
This study addresses the issue of teaching conditional probability and independence of events in the Ecuadorian educational context, specifically the scarcity of innovative didactic resources. The Organic Law of Intercultural Education emphasizes the need for innovative educational methodologies, justifying this research. Through a comprehensive analysis of the current curriculum and interviews with teachers, the time and resource limitations that hinder a deep understanding of these mathematical concepts were identified. To address these deficiencies, a didactic guide and a physical resource accessible to teachers were designed and created, integrating digital tools and interactive activities. The didactic guide is structured to facilitate the teaching of conditional probability and independence of events through innovative pedagogical methods that promote active learning. It includes simulations, practical applications, and interactive examples that allow students to experiment with the concepts dynamically. This approach aims not only to improve students' understanding but also to increase their interest and engagement with the subject matter. The created physical resource is designed to be easily used in the classroom, providing teachers with a practical and effective tool for teaching these complex concepts. By integrating this resource into the educational process, it aims to overcome current limitations and promote probability teaching that is both comprehensible and relevant to students. The implementation of this guide and didactic resource represents a significant step towards a more innovative and effective mathematics education in Ecuador.
Guías virtuales de prácticas de laboratorio virtuales para el aprendizaje de circuitos eléctricos
(Universidad de Cuenca. Facultad de Filosofía, Letras y Ciencias de la Educación, 2025-10-24) Vásquez Gutiérrez, María Fernanda; Sumba Tigre, Christhian David; Guzñay Padilla, Sonia Janneth
Esta investigación aborda la problemática de la enseñanza de circuitos eléctricos en entornos educativos con limitaciones de recursos, tiempo y seguridad en laboratorios físicos. El estudio explora, desde un enfoque cualitativo y descriptivo, las percepciones de doce docentes de física sobre el uso de simuladores virtuales, destacando su potencial para facilitar la comprensión conceptual, la experimentación autónoma y la superación de barreras logísticas. Mediante un cuestionario de doce preguntas abiertas, se analizaron cuatro ejes temáticos: conocimiento de simuladores, impacto en el aprendizaje, condiciones institucionales y perspectivas sobre guías didácticas. Los resultados revelan un consenso favorable hacia los laboratorios virtuales como complemento híbrido (no sustituto) de las prácticas físicas, resaltando la necesidad de guías didácticas con retroalimentación automatizada para fortalecer el autoaprendizaje. Se concluye que estas herramientas, cuando se implementan con planificación intencional y adaptación al contexto sociocultural, transforman al estudiante en protagonista de su aprendizaje y redefinen el rol docente como facilitador. La investigación aporta un modelo de guía didáctica que estructura la experimentación virtual, vinculándola con aplicaciones reales para lograr aprendizajes significativos.
Percepciones de docentes de matemáticas sobre el impacto de la pandemia de COVID-19 en los aprendizajes y sus repercusiones en la actualidad
(Universidad de Cuenca. Facultad de Filosofía, Letras y Ciencias de la Educación, 2025-10-24) Villa Vera, Lilian Estherina; Guiracocha Guiracocha, Michelle Alexandra; Bravo Guerrero, Fabián Eugenio
This research analyzes the effects of the COVID-19 pandemic on mathematics learning from the perspective of teachers who experienced this process first hand. Several recent studies and reports warn about learning gaps generated during virtual education, which continue to affect the academic development of students today. Addressing this issue not only allows us to understand what happened, but also to better prepare ourselves to face similar situations more effectively in the future. To this end, a review of literature related to the topic was conducted, and then a qualitative approach was adopted to collect information through interviews with teachers from an educational institution in the city of Cuenca, Ecuador. The responses obtained were analyzed through the content analysis technique, in order to identify patterns, categories and key elements that led to the proposal of strategies to improve learning according to the context. The main findings reveal technological limitations and curricular reduction during the pandemic, as well as learning lags and lack of family support that persist in the face-to-face environment. Based on these results, strategies are proposed in three areas: strengthening family support, promoting the appropriate use of emerging technologies and linking mathematical learning with the student's reality. These actions seek to contribute to the improvement of the educational process in a context still marked by the consequences of the pandemic.
Propuesta didáctica para el aprendizaje de la óptica geométrica a través de la experimentación virtual
(Universidad de Cuenca. Facultad de Filosofía, Letras y Ciencias de la Educación, 2025-10-23) Granda León, Elian Ernesto; Guachún Lucero, Freddy Patricio
In this degree project, a didactic proposal using virtual simulators is presented, designed to facilitate the learning of concepts of geometric optics, specifically reflection and refraction on spherical surfaces and lenses. It is aimed at students of the Pedagogy of Experimental Sciences program at the University of Cuenca, with the objective of fostering active and meaningful learning, all within a constructivist approach. For its development, a mixed-method methodology was employed through a ten-question survey administered to fourth-cycle students of the Pedagogy of Experimental Sciences program. The results made it possible to identify their perceptions, needs, and interests regarding the use of digital tools in the teaching of Physics. Based on these data, a structured guide of four interactive classes was developed using the PhET Colorado simulator, focused on reflection in plane and curved mirrors, as well as the analysis of converging and diverging lenses. Consequently, this proposal seeks to enrich the educational process through the observation, manipulation, and analysis of optical phenomena in virtual environments.
Guía de prácticas de laboratorio para la enseñanza de la estática en segundo de bachillerato
(Universidad de Cuenca. Facultad de Filosofía, Letras y Ciencias de la Educación, 2025-10-22) Vélez Tuapante, Luis Armando; Guachún Lucero, Freddy Patricio
Physics teaching in high school presents multiple limitations, including a lack of resources, limited use of laboratory materials, and a lack of time to address the content. Teaching statics in particular requires teaching resources that connect theory with real-life experiences to facilitate understanding. This thesis presents a proposal for laboratory practices whose primary purpose is to provide a practical guide for teachers, facilitating the implementation of experimental resources that enhance the understanding of statics concepts. It also seeks to foster an active and participatory approach in the classroom, overcoming traditional difficulties in teaching this subject. Qualitative research based on interviews with physics teachers demonstrates the relevance and structure of the proposal for its intended audience. Challenges were identified such as a lack of materials, limited use of guides, and a poor connection between theory and practice. The results show that the pedagogical use of the laboratory contributes significantly to improving the understanding of statics, promotes meaningful learning, and develops scientific skills.
Uso de material didáctico para la enseñanza de los campos electromagnéticos en el Bachillerato General Unificado
(Universidad de Cuenca. Facultad de Filosofía, Letras y Ciencias de la Educación, 2025-10-22) Yadaicela Morocho, Christian Hernan; Guachún Lucero, Freddy Patricio
This study addresses the persistent difficulty faced by students in the Bachillerato General Unificado in understanding abstract physics concepts, particularly those related to electromagnetic fields, whose invisible nature and theoretical complexity hinder learning. A qualitative descriptive approach was adopted, using semi-structured interviews with teachers from various educational levels to explore their perceptions of the use of didactic materials in physics teaching. The results showed that didactic materials are key pedagogical tools to facilitate meaningful learning, promote student engagement, and connect content with real-life situations. In response, an educational proposal was developed consisting of four instructional guides, each accompanied by concrete materials, structured according to the 5E inquiry-based learning model. These guides aim to enhance active knowledge construction, collaborative work, and critical thinking development through experimentation. It is expected that this proposal will not only improve the understanding of electromagnetic fields but also strengthen students' motivation and autonomy throughout their educational process.

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