Browsing by Author "Trelles Zambrano, César Augusto"

Now showing 1 - 20 of 34

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.
Análisis de las prácticas evaluativas de los docentes de matemática del circuito 20 Distrito 1 de la provincia del Azuay en el período octubre-noviembre 2015
(2016) Cabrera Tacuri, Jenny Alicia; Trelles Zambrano, César Augusto
Research Analysis of assessment practices of teachers of mathematics at circuit 20, 1st district of the province of Azuay, in the period October-November 2015, aims to analyze assessment practices of teachers in the field of mathematics. It is developed based on a qualitative methodology, which is used as content analysis techniques in their qualitative variant, observation and interview. Math teachers about Educational circuit units 20, district 1 tenth year participate in this research. The main results were given in that assessment practices respond to traditional forms, given in focus on content, with types and maintained instruments separated from their context and social environment, without working the evaluation performance criteria and process elements learning. Furthermore, they do not consider evaluation as a pedagogical action in terms of improving learning.
Aprendizaje de la termodinámica a través del computador
(2009) Trelles Zambrano, César Augusto; Avecillas Jara, Alberto Santiago
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.
Creencias y actitudes de los estudiantes de la U.E.M. Francisco Febres Cordero hacia las matemáticas como factor de bajo rendimiento académico
(Universidad de Cuenca, 2022-04-29) Erreyes Toledo, Luis Antonio; Landi Minchalo, Johanna Patricia; Trelles Zambrano, César Augusto
The main objective of this work was to analyze the relationship between beliefs and attitudes towards mathematics and the academic performance of students of the upper basic level of the Unidad Educativa del Milenio Francisco Febres Cordero. The research design was descriptive correlational and non-experimental. The research involved 195 students in the eighth, ninth and tenth grades, who were administered a questionnaire on beliefs and attitudes about mathematics. For their academic performance, the grades obtained by the students were considered, information that was collected from the official records issued by the authorities of the educational institution. Subsequently, a comparative analysis was made between the answers to the questionnaires and the grades provided. The results obtained indicate that there is a remarkable relationship between beliefs and attitudes towards mathematics and academic performance in this area. Finally, some teaching-learning strategies were proposed that could help to reduce students' negative attitudes towards mathematics
Diseño y creación de un escape room como recurso didáctico para la enseñanza de la geometría en EGB Superior
(Universidad de Cuenca, 2023-09-01) Quichimbo Pesantez, Silvana Karina; Velecela Morocho, Angélica Lorena; Trelles Zambrano, César Augusto
The implementation of the Escape Room as a didactic resource for the teaching-learning of mathematics, especially in Plane Geometry, has been one of the best ways to attract the attention of students since the Escape Room is a game whose purpose is to improve the Motivation, attention, and cooperative work between students is also where alternatives (tracks) are presented to meet the objective and be able to escape from the game room initially receiving an invitation and later recognition in between. For the creation of the two Escape Rooms, the Ecuadorian Curriculum 2016 and the EBG Superior student textbooks were used, which allowed us to create different challenges or riddles, also for the creation of the same, different digital tools were used. (Genially and programming language); which are attached to the learning requirement of the subject, the detailed investigation was very useful because today what is wanted is to change the teaching-learning of mathematics by implementing striking technological resources. Finally, it can be deduced that the implementation of the Escape Room in the teaching of mathematics is an alternative to capture the attention, motivation, and camaraderie among students of EGB Superior.
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.
Estrategias lúdicas en la enseñanza de números enteros en el octavo año de Educación General Básica
(Universidad de Cuenca, 2023-07-11) Encalada Serrano, Lisseth Lorena; Trelles Zambrano, César Augusto
The current study implemented nine games focused on operations with whole numbers for the eighth-grade students of San Juan de Jerusalén School in the 2021-2022 academic year. An experimental group was selected to receive playful strategies while a control group did not. The validation process for the instruments, including pre-tests and post-tests, was conducted through expert judgment provided by teaching professionals who hold a fourth-level degree in Education from the University of Cuenca. The study began with the pretest and concluded with the posttest, and statistical analysis and hypothesis testing were conducted using the JAMOVI statistical package. The Shapiro-Wilk Test was utilized to determine the normality of the data, and the Levene Test was applied to verify the assumption of homogeneity of variances of the data obtained. The t-test for independent samples was utilized to make comparisons between the control and experimental group, while the t-test for paired samples was used to make comparisons between the same group but at different times (pre-test and post-test). Results indicated that the experimental group showed a significant increase in average, suggesting that playful strategies had a positive impact on the teaching of operations with integers.
Estudio de la coherencia entre los lineamientos curriculares y el tratamiento que se da a la modelización matemática en los libros de texto del bachillerato ecuatoriano
(Universidad de Cuenca, 2024-07-24) Astudillo Vidal, Juan Sebastián; Morocho Angamarca, Danny Damian; Trelles Zambrano, César Augusto
Mathematical modeling in the educational field has proven to be very useful in getting students to answer the question: What is the purpose of mathematics? In this way, a connection is established between mathematics and real-life situations. Its importance is such that it is even present in various parts of the Ecuadorian mathematics curriculum, as well as in some skills of the subject. For this reason, throughout this work, its importance, concepts, characteristics, perspectives, cycles, and everything essential about mathematical modeling will be presented. In addition, a quantitative analysis was carried out on the various activities proposed by the texts provided by the Ministry of Education (MinEduc) for high school, in order to understand the presence of mathematical modeling in these documents. The study focused on the blocks of Geometry and Measurement, and Statistics and Probability. Based on the above, this research aims to analyze the coherence between the guidelines issued by MinEduc in the curriculum documents and the presence of mathematical modeling in the textbooks of the Unified General Baccalaureate (BGU). The results were alarming, as the presence of mathematical modeling activities is minimal in MinEduc's textbooks, leading to the conclusion of a low concordance with what is proposed in the Ecuadorian curriculum and in the textbooks corresponding to BGU.
Gestión del aprendizaje por parte del profesor de matemáticas en el ámbito de la educación particular
(2016) Trujillo Valverde, Carmen Patricia; Trelles Zambrano, César Augusto
This research studies the learning management of mathematics teacher in a paid educational school framed in educational quality standards proposed by the Ministry of Education. It takes as its starting point the teacher professional performance standards to determine the characteristics of the mathematics teachers learning management have both in middle school and high school and to determine the similarities and differences between the two levels of education. Data collection is done through surveys applied to students, class visits to all teachers of mathematics and documentation review of relevant planning files of teachers, both middle school and high school. To be able to analyze the data, it was generated a tabulation system according to the three general standards that make a correct learning management possible: planning, teaching-learning and classroom climate and evaluation. The study concludes with a methodological triangulation to support the results. One of the weaknesses of teachers of middle school is the lack of use of new technological information systems in the teaching process and for high school teachers it is the low implementation of educational recovery processes. Knowledge of learning management determines the largest and true work of teachers, their work in the classroom, which is a real opportunity to improve the quality of education.
Guía didáctica para el aprendizaje de funciones cuadráticas a través de la modelización matemática
(Universidad de Cuenca, 2023-08-31) Fajardo Heredia, Juan José; Trelles Zambrano, César Augusto
Mathematical modeling in education has proven to be very helpful in achieving significant learning in students; even so, its application by teachers is still limited, even though the Ecuadorian curriculum itself mentions mathematical modeling as part of the skills within the area of mathematics. Mathematical modeling allows students to connect with real life, with the environment in which they develop, which allows them to understand the true importance of mathematics in society. For this reason, the present work develops a theoretical framework about the mentioned topic, what it consists of, cycles, approaches, and the importance of these activities for meaningful learning. In addition, through a quantitative content analysis, the different activities carried out by the students are analyzed, to know the presence or absence of mathematical modeling. Modeling is used to represent a phenomenon or event in real life through a mathematical model, said model can be a quadratic function, which represents great importance in society, so it is necessary that this topic is understood in a significant way in the students. For these reasons, with the research carried out, a didactic guide is proposed to help students in the subject of quadratic functions through mathematical modeling.
Guía didáctica para el aprendizaje de la estática y la cinemática mediante el uso del software “Interactive Physics” en el primer año de Bachillerato General Unificado
(Universidad de Cuenca, 2022-09-15) Calero Barrera, Dennis Sebastián; Orellana Morales, Tania Belén; Trelles Zambrano, César Augusto
The work presented below is focused on the study of statics and kinematics. To do so, the simulators developed in the Interactive Physics software (IP2005), which are included in the didactic guide aimed at teachers of the tenth year, were used. Based on studies, it is shown that teachers have shortcomings in the application of constructivist methods. Such deficiencies are: technological and didactic resources for the development of statics and kinematics classes. Students from the major of Experimental Science Pedagogy at “Universidad de Cuenca” completed surveys to establish which technological resources were necessary for teachers. Besides, physics educators from the before-mentioned major were interviews, where professors and pupils have proposed to use technological resources for teaching: uniform rectilinear motion, uniformly varied rectilinear motion, free fall, parabolic motion, uniform circular motion, Hooke's law and balance of forces. Therefore, due to these results, a didactic guide with constructivist methodology was elaborated. The guide was created based on virtual learning, using simulators developed and focused on each skill with performance criteria established by the Ecuadorian education curriculum
Guía didáctica para el aprendizaje del lenguaje algebraico y la evaluación de expresiones en el octavo año de educación general básica
(Universidad de Cuenca, 2022-09-06) Castro Alvarez, Dolores Nohemí; Riera Quichimbo, Franklin Eduardo; Trelles Zambrano, César Augusto
The objective of this work is the elaboration of a didactic guide for the learning of algebraic language and the evaluation of expressions. Based on a survey, carried out on eighth-year students of Basic General Education, it has been possible to identify the main difficulties presented by students of this educational level, which has allowed to have a starting point to prepare this guide. The need for the creation of this guide started in the development of the pre-professional practices carried out in the "Luis Roberto Bravo" Educational Unit when noting several difficulties and the limited use of resources in the teaching-learning process of this subject. Through the application of the survey to the eighth-year EGB students of this institution, it was possible to identify errors suggested by Radatz (1979) such as: language errors, errors of a poor mastery of skills, facts and concepts, errors of incorrect associations and the application of irrelevant rules or strategies, so it was observed that it generates inconveniences for students when it comes to solving algebraic problems For this reason, the elaboration of this didactic guide for the learning of algebraic language and evaluation of expressions is a proposal that seeks the construction of knowledge and the self-learning capacity of students, through learning strategies and collaborative work, which are found in each of the five classes to be developed
Guía didáctica para la enseñanza de la trigonometría para segundo año de bachillerato del Colegio Fray Vicente Solano mediante geogebra
(2015) Riofrío Sarmiento, Edwin Santiago; Samaniego Benavidez, Adriana Genoveva; Trelles Zambrano, César Augusto
This current work entitled: Tutorial for teaching trigonometry for the second year of Fray Vicente Solano High School through “Geogebra” emerges with the idea of applying a new constructivist methodology in the classroom, linking educational content with technology, in order to transform traditional education class dynamic. In Chapter 1 we focus on the theoretical foundations that strengthen our offer, topics such as constructivism, teaching and teaching methods needed to teach math based on the curriculum guidelines set by the Ministry of Education. In Chapter 2 results are shown and they proceed from a census to second year students (General Unified Bachelorship) and Fray Vicente Solano’s mathematics teachers; to demonstrate the interest students have to handle mathematical software and the lack of management of technological resources by teachers because of guideless. The results are presented using statistical tables and graphs. In Chapter 3 seven tutorials based on skills with performance criterion on the issue of trigonometry are produced, making a tutorial program management with detailed explanation through examples, raising activities and applying different assessment instruments to demonstrate the achievements obtained. Finally tutorial’s goal of using Geogebra software is design learning activities use to enable students to achieve skills with performance criteria proposed by the Ministry of Education for Trigonometry in second year General Unified Bachelorship and facilitate teaching – learning process, as well as to teachers providing information on new technologies that can be taught in their lesson plans and assessment tools that also allows the teacher to check the students’ achievement level.
Guía didáctica para la enseñanza virtual del cálculo diferencial dirigida a los estudiantes de tercero de bachillerato.
(2024-09-23) Morocho Farez, Daysi Maritza; Trelles Zambrano, César Augusto
This project presents the design, implementation, and evaluation of a didactic resource aimed at enhancing the learning of differential calculus in third-year high school students at CEBCI Educational Unit through the implementation of a virtual classroom design. The proposal, grounded in the APOE theory, aims to develop and implement a teaching guide for virtual instruction in differential calculus, using digital tools such as GeoGebra. Academic performance is taken as the research variable, addressing specific learning difficulties through the appropriate selection of technological tools, the design of the teaching guide, and the evaluation of its effectiveness. A quantitative, descriptive methodology was employed with two working groups from different academic years. The interpretation of results relied on the final grades from both courses, utilizing statistical descriptors through the JAMOVI program. Findings indicate a positive impact of the digital activity implementation. The structure of the work comprises four chapters addressing theoretical aspects, methodology, proposal construction, and results analysis. The main objective of the research is to contribute to the continuous improvement of teaching differential calculus in the virtual environment.
Guía metodológica para docentes enfocada en el bloque de matemáticas discretas del segundo BGU
(2015) Guallpa Erráez, Pablo Andrés; Sarmiento Plaza, Cristina Alexandra; Trelles Zambrano, César Augusto
This present graduation paper entitled "Methodological guide for teachers focused on Discrete Mathematics block of Second BGU" relates in the current curricular reform, which divides the subject of Mathematics in four parts in the Unified General Baccalaureate. The block three of Mathematics for Second year, corresponding to the "Theory of Graphs" is a new subject on high school, and there isn't an appropriate bibliography for the study of the subject, for this reason it has designed a guide book for teachers of Discrete Mathematics topic, with statements and exercises, proposed and resolved, to help teacher's work in the classroom. For the write of exercises and solving them it has been used dynamic geometry software GeoGebra, Microsoft Excel and even Google Maps, so that technology can be used on classroom and make learning process will be more dynamic and the study work will be significant. Exercises proposed on GeoGebra will be compiled for teachers, and future teachers (students) who want to access to them, they can do it. For this paper has been used the curriculum in spiral, a Jerome Bruner's idea, it says that studies plan should be since more basic contents and increase its difficulty and abstraction, so that in every moment of learning process, contents will be studied in a wider and deeper level.
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.
Informe sobre la formación inicial y continua de profesores de matemáticas en el Ecuador
(2017) Martínez Jara, Margarita Helena; Castillo Domenech, Ana Paola; Trelles Zambrano, César Augusto; Gonzáles Prado, Neli Norma; Calle Palomeque, Carmen Eulalia; Ayala Trujillo, Andrea Verónica; Rivadeneira Loor, Fredy Yunior; Auccahuallpa Fernández, Roxana; Flores Marin, Mónica Jeannette
This research aims to display the preservice and inservice mathematical teacher education condition in our country from the republic up to nowadays. The education of mathematic teachers in Ecuador has not followed a clear evolution and conceptualization path given the historical divorce between government policies and the educational reality. While evaluations of teachers in public institutions show a serious problem at the level of content mastery, government reforms aim to strengthen practical and civic education. The cognitive component of math teachers in General Basic Education is insufficient to lay a good conceptual structure for teachers in this area. There is incentive for training teachers but without proper structuring and monitoring. Iso-lated and individual efforts have failed to become a true state policy that goes beyond successive governments and achieve to give education in mathematics the place it deserves as the engine of scientific and technological transformation of the country.
Informes educación matemática: Ecuador, Perú. Capacity and networking project 2016. International commission on mathematical instruction
(2017) Flores Marin, Mónica Jeannette; Castillo Domenech, Ana Paola; Trelles Zambrano, César Augusto; Gonzáles Prado, Neli Norma; Calle Palomeque, Carmen Eulalia; Ayala Trujillo, Andrea Verónica; Martínez Jara, Margarita Helena; Rivadeneira Loor, Fredy Yunior; Auccahuallpa Fernández, Roxana
This research aims to display the preservice and inservice mathematical teacher education con-dition in our country from the republic up to nowadays. The education of mathematic teachersin Ecuador has not followed a clear evolution and conceptualization path given the historicaldivorce between government policies and the educational reality. While evaluations of teachersin public institutions show a serious problem at the level of content mastery, government reformsaim to strengthen practical and civic education. The cognitive component of math teachers inGeneral Basic Education is insufficient to lay a good conceptual structure for teachers in thisarea. There is incentive for training teachers but without proper structuring and monitoring. Isolated and individual efforts have failed to become a true state policy that goes beyond successivegovernments and achieve to give education in mathematics the place it deserves as the engineof scientific and technological transformation of the country.