Browsing by Author "Trelles Zambrano, César Augusto"

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Análisis al reconocimiento y valoración de la Etnomatemática en libros de matemática de EGB Superior
(Universidad de Cuenca. Facultad de Filosofía, Letras y Ciencias de la Educación, 2025-10-17) Bacuilima Guanga, Paola Nayeli; Fernández Tenezaca, Jéssica Paulina; Trelles Zambrano, César Augusto
Ethnomathematics, proposed by Ubiratan D’Ambrosio, acknowledges the diverse ways in which cultures approach mathematics, a crucial aspect in a culturally diverse country like Ecuador. However, its integration into the educational system remains limited, as evidenced by this study, which analyzes the inclusion of ethnomathematics in General Basic Education textbooks (ages 11-14). Using a mixed quantitative-qualitative methodology, 2,167 activities, 18 projects, and 383 interdisciplinary sections from eighth, ninth, and tenth-grade textbooks were evaluated, classifying the exercises into 18 categories to identify cultural content. The results showed that 98.11% of the exercises lacked cultural influence, and only 1.89% incorporated ethnomathematical elements, highlighting a significant gap between the Ecuadorian curriculum, which promotes interculturality, and the textbooks in use. To address this limitation, the study includes interviews with a master mason and a market vendor, representatives of distinct cultural groups, whose practices served as the basis for designing a teaching guide. This guide proposes contextualized mathematical activities, integrating practical knowledge and connecting learning with the students' sociocultural environment.
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.
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.
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.
Information and communication technologies, contrasting teacher - student assessments in high schools within Cuenca, Ecuador
(2019) Trelles Zambrano, César Augusto; Gonzáles Prado, Neli Norma; Mora Oleas, Janeth Catalina
The purpose of this study is to diagnose the management and use of Information and Communication Technologies (ICT) as well as mathematical software in the teaching and learning of mathematics. A survey was provided to 64 mathematics teachers from different high schools in the city of Cuenca, Ecuador and their 381 students. A relational research approach was employed to collect and compare the data of the two educational participants, the teacher and the learner. According to the results of the study, most teachers reported that they use ICT to motivate learning and improve the assimilation of concepts. The students however, do not confirm that those technologies are being used at the levels mentioned by their teachers. GeoGebra is a Dynamic Program for the Teaching and Learning of Mathematics. This software is better known and used for teaching in private education than in public education.
Método singapur en la enseñanza de las cónicas en segundo año de bachillerato
(Universidad de Cuenca, 2024-07-11) Pastuizaca Guamán, Nelson Romeo; Trelles Zambrano, César Augusto
In recent years, a deficiency has been evidenced in the high school students of the Víctor León Vivar educational center located in the city of Nabón, Ecuador, mainly in the subject of mathematics and, specifically, in the topic of conic sections. For this reason, in the search for improving the quality of education and the teaching-learning process, the Singaporean educational system was found as a reference model in this research. In this research we intend to design a didactic guide based on the Singapore model, which seeks to improve the academic performance of students, as well as to promote problem-solving skills of students and provide teachers with a tool for better planning. We will work with students in the second year of high school, who, being separated into two different parallels, will be treated separately, the first will be considered the control group and the second the experimental group. In the first instance, a pretest is applied to each of the groups as a diagnosis to be taken as a starting point; followed by the teaching stage where the control group maintains the process with the educational texts of the Ministry of Education, while the experimental group uses the proposed didactic guide. Finally, an academic evaluation is made to each of the groups in order to determine their understanding of the concepts taught by the teacher. It is determined that the experimental group obtained a better academic achievement demonstrated with a better understanding of the concepts, better communication and satisfaction of the students compared to the control group that maintained the performance of the last times.
¿Qué, cómo y para qué leen los futuros docentes de Matemática y Física?
(Universidad de Cuenca. Facultad de Filosofía, Letras y Ciencias de la Educación, 2025-11-19) Matute Fárez, Katherine Pamela; Trelles Zambrano, César Augusto
This research analyzes the reading habits of university students enrolled in the Experimental Sciences Teaching program at the University of Cuenca, using a mixed-methods approach that combines quantitative and qualitative techniques. The study explores variables such as reading frequency and duration, types of materials read, reading preferences, motivation, attitudes, resource accessibility, and environmental influence. Data were collected through a questionnaire administered to 222 students and a focus group interview with a selected group. The results show a predominantly academic reading practice, limited leisure reading, and a strong influence of the educational and family context. It is concluded that although students recognize the importance of reading, their habits are conditioned by academic demands and access limitations. The discussion is framed within a sociocultural perspective on reading, which views this practice as a situated construction mediated by social, institutional, and personal factors.