Licenciatura en Educación Básica con Énfasis en Matemáticas
URI permanente para esta colecciónhttp://hdl.handle.net/11349/43
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Ítem Un taller que implementa el sonido holofónico para la enseñanza de nociones espaciales en estudiantes con diversidad funcional visual de primer cicloMuete Cifuentes, Doris Gisella; Bernal Pérez, Sebastian Jair; Gil Chaves, Diana; Gil Chaves, Diana [0000-0003-3872-1105]The present work identified some aspects to be taken into account for the design and application of a didactic device (workshop) using holophonic sound, for the development of some spatial notions in first cycle students with visual functional diversity. Some of these aspects are: The activities should allow the participation of both students with visual functional diversity and sighted students; the holophonic sound is a strategy to stop emphasizing the sense of vision in the design of activities for the mathematics classroom; it is important to focus on the capabilities of all students, particularly low vision students, and not on what they cannot do, but on what they can do. The workshop "Let's listen to our world!" was designed and implemented in four sessions. The conclusion of the work refers to the fact that the design and application of the workshop in which holophonic sound is used, has proven to be an optimal tool for teaching and learning spatial thinking in first-cycle students, both with visual functional diversity and sighted students, since progress was evidenced in their understanding of topological notions.Ítem Menguando rezagos de aprendizaje en un territorio rural de ColombiaMoreno Ruiz, Juan Esteban; Torres Duarte, José; 0000-0001-9208-4843This study presents the experience of a university student who participated in the "Viva la Escuela" program in a rural educational institution in Colombia. The program aims to address learning gaps in rural communities through innovative pedagogical approaches. The student implemented various educational strategies, including diagnostic tests, literary gatherings, interactive groups, and school reinforcements, in order to improve academic performance and socioemotional well-being of the students. Additionally, the community was actively engaged in school maintenance activities and celebratory events. Despite encountered challenges, such as resistance from some community members and resource constraints, preliminary results show a positive impact on students' learning process and social cohesion within the school community.Ítem Derechos humanos y educación matemática para todosSanmiguel Reyes, Sebastián David; Tolosa Ricaurte, Álvaro Stiven; Guerrero Recalde, Néstor Fernando; Guerrero Recalde, Néstor Fernando [0000-0002-3982-4985]The report presents the outcomes of an internship undertaken by Mathematics Education undergraduates from the Francisco José de Caldas District University in Bogotá, Colombia. The project focused on creating educational videos and teaching capsules to impart mathematics and human rights education to students from vulnerable populations at Gabriel Mistral School in Piñalito Meta. Initially centered around videos, the project evolved towards the development of teaching capsules for future material implementations. The internship took place at the IN-JU HUELLAS Foundation, which supports children and youth from vulnerable communities, emphasizing understanding children's rights and fostering logical-mathematical thinking. Educational videos were designed for the Foundation's PazArte School program, linking rights to mathematical concepts and contextualizing learning within students' cultural and environmental challenges. The videos were transformed into teaching capsules for a more flexible and personalized implementation, aiming to enhance the sustainability and replicability of the project. The report details the processes, methodologies, and outcomes, highlighting key aspects of the project.Ítem Apoyo al proceso de inclusión de estudiantes con discapacidad al aula de matemáticas Colegio República de China I.E.D.Plazas Amaya, David Alejandro; Cortés Duque, Danna Vanessa; Fonseca González, Jaime; 0000-0002-5147-7912After a period of supporting students with disabilities in the mathematics classroom at Colegio República de China IED, strategies for teaching content associated with arithmetic, geometry, and algebra are described. Adapted resources such as the Abacus, Cuisenaire rods, the Cartesian plane, and conventional geometry kits are presented. Materials are designed, such as equation boxes, raised rulers, and tangible objects instead of two-dimensional visual representations. It is considered that, in arithmetic and algebraic aspects, understanding the decimal number system and its operations, especially in the set of integers, must be given meaning and context to the student's reality. In geometry, it is essential to adapt and design materials that provide an understanding of the mathematical object, as is done with the use of common representation systems. In conclusion, an inclusive environment is achieved as long as strategies are sought and appropriate teaching materials are designed.Ítem La geometría a través del arteAmórtegui González, Eliana; Gil-Chaves, Diana; 0000-0003-3872-1105This work addresses the difficulties encountered in teaching geometry and proposes a didactic strategy that integrates art, specifically painting and mandalas, to make it more meaningful and motivating for students. It is structured into sections including theoretical review, methodology, and results. The approach is qualitative and aims to assess students' progress in recognizing geometric figures. The results demonstrate the effectiveness of this pedagogical methodology in learning geometry through art.Ítem Una de las relaciones entre la matemática y la biología: ¡El canto de las aves y su matematización!Nope Acosta, Nathalia Alexandra; Gazón Arango, Juan Felipe; Carranza Vargas, Edwin Alfredo; 0000-0003-0777-6146This work addresses the mathematization of bird songs in Bogotá using the Freudenthal model, which consists of vertical and horizontal aspects to transform everyday problems into mathematical ones through intuition and empirical work, among others. A methodology structured in four levels: situational, referential, general, and formal, is followed, which facilitates the formalization of the mathematical components of the problem. The document details the procedures by levels and presents the mathematical model adjusted to the problem. It was found that the songs of the birds of Bogotá can be related to aspects of various disciplines such as the environment, biology, and music, demonstrating the interdisciplinarity of mathematics and its presence in everyday and unconventional contexts.Ítem Acciones docentes que posibilitan una dinámica inclusiva en la clase de matemáticas en relación con la diferencia(Licenciatura en Educación Básica con Énfasis en Matemáticas -- Tesis y disertaciones académicas) Centeno Campo, Melissa; Martínez Ramírez, Lina Natalia; Torres-Duarte, José; 0009-0006-7793-9931; 0009-0001-8728-9761; 0000-0001-9208-4843This monograph arises from the experiences as teachers in training, where gaps in mathematics learning among tenth grade students are evidenced, especially in a public school in the southeast of Bogota, associated with social problems in their environment and the differences they generate in the subjectivities of the students. The research focuses on the role of the school in the construction of difference and the search for inclusive dynamics, identifying social aspects that influence mathematical learning in order to propose inclusive teaching actions. Carried out at the Gerardo Paredes School, site A, with ninth grade students, it integrated activities such as mapping exercises and analysis of social problems with a mathematical approach. It highlights the need to rethink the connection between mathematics and the subjective differences of students, promoting critical thinking and establishing meaningful connections with real situations. It advocates an educational transformation that recognizes difference as central in this process, and highlights the importance of adopting pedagogical strategies that link mathematics with critical reflection and analysis of everyday problems, thus overcoming the limitations of the traditional curriculum to build a collaborative and enriching learning environment for all.Ítem Análisis de la práctica con diagramas en los inicios de las ideas de cálculo propuestas por Isaac NewtonMéndez Guzmán, Digson Daihier; Rico Rondón, Diego Armando; Bello Chávez, Jhon Helver; Bello Chávez, Jhon Helver [0000-0003-4370-9995]The following work is carried out as an innovation research internship, assumes a contribution to the MATTOPO research group and the research project "Diagrams in the constitution of the calculation. Contributions and reflections to teacher training" which is considered that diagrams are cognitive tools in the construction of objects or mathematical theories. The content of the two texts proposed by Isaac Newton in the construction of his calculus will be analyzed. The first, the text Methodus fluxionum et serierum infinitorum (1667), and the second, Philosophiæ naturalis principia mathematica (1687), with the English translation 'mathematical principles of natural philosophy' (2011), in order to analyze about the forms used by Newton to show its development from the use of diagrams and the incidence of these as representational tools in cognitive development. Within the analysis of the texts, the mathematical activities, the objects within the representation, the perspectives of infinity and the look from the variation and covariation that are presented and developed were taken into account. On the other hand, in this text 'Analysis in practice with diagrams at the beginning of the ideas of calculation proposed by Isaac Newton' is evidenced one of the treatments that Newton performs to his diagrams for the understanding of his calculation from tangents, lines and curves. A comparison is shown between the ways of representing the diagrams in the texts mentioned and how the diagrams have an impact on the calculation thinking.Ítem Desarrollo del pensamiento matemático a través del cuidado medio ambiental desde la teoría de la actividad con estudiantes de grado noveno de la I.E.T Bicentenario en Funza, CundinamarcaRincón Pinzón, Evelyn Alejandra; Torres Duarte, José; Torres Duarte, José [0000-0001-9208-4843]This investigative work focuses on the development of thinking mathematician related to real, social and cultural contexts, specifically, with care for the environment. This mathematics-reality relationship is approached didactically from the Theory of Activity, in this sense, the Theory of Activity seen from mathematical education, its importance and incidence within this research, as well as categories that allow us to describe in greater detail the characteristics that were taken into account. counts in all its development.Ítem Cambios de concepciones sobre la fracción en estudiantes del espacio de formación didáctica de la aritmética II de licenciatura en matemáticas de la Universidad Distrital Francisco José de CaldasGonzález García, Tania Lorena; Valero Garzón, Deissy Valentina; Fonseca González, Jaime; Fonseca González, Jaime [0000-0002-5147-7912]The research work focuses on investigating and analyzing the changes of conceptions about the fraction in students of the training space Didáctica de la Aritmética II of the Licenciatura en Matemáticas of the Universidad Distrital Francisco José de Caldas. The conceptions about fraction at the beginning of the course are partial, which represents a problem of understanding as to what a fraction is, then, the training space has among its objectives to resignify the concepts of fraction with which the students arrive and from there interest arises to analyze the changes of conception that are presented. The research methodology is qualitative with a hermetic approach, where three data collection instruments are used: essay and problem situation applied at the beginning and end of the course, and semi-structured interview in the final phase. The information collected is analyzed based on the theoretical framework proposed by Llinares and Sánchez (1997) who propose four interpretations of the fraction: part-whole and measure, ratio, quotient and operator, concluding that the conception changes are categorized into two, the first is an expansion in the fraction interpretations and the second is a deepening in one more fraction interpretations, these changes are directly related to the change of conception in the treatment of the fraction in a problem situation, since the strategies were diversified taking into account the different contexts in which the fraction appears. Finally, regarding the causes of the changes in conception, which were determined from the interview, it is concluded that there are three: argumentation, representation, and the role of the teacher.Ítem El tratamiento del número en las tareas de conteoMartínez Sanabria, María Fernanda; Bello Chávez , Jhon HelverThe idea of numbers as counting and its work in preschool is mediated by the work with the system of representations in counting tasks. In which the relationship between two specific elements is put into practice, the symbol and the object, which are necessary but not sufficient for the development of counting tasks, therefore it is necessary to establish a relationship between the abstract and the concrete entity to provide a total understanding of the principles of counting in the system of representations, this relationship alludes to what if understood through the object can be understood through internal representations. The work seeks to verify through a sequence of activities the importance of the proposed system of representations and to demonstrate if it allows in the counting tasks to develop the classification, seriation, and principles of counting for the resignification of the symbol in preschool-grade.Ítem Valoración de idoneidad didáctica de un proceso de instrucción del número racional en grado séptimoBeltrán Bejarano , Anyi Yasmile; Cadena Cordoba, Kelly Johana; Gordillo Thiriat, Wilson; Gordillo Thiriat, Wilson [0000-0002-3856-4691]In this research, the assessment of the didactic suitability of a process of instruction of the rational number in seventh grade, with a teacher from the OEA District College, for this purpose recordings of five class sessions were made in which the teacher addresses the concept of rational number, likewise, the analysis was carried out from the indicators of Didactic Suitability mentioned by Godino in the theory of the Ontosemiotic Approach knowledge and instruction in mathematics (EOS). The methodology used is qualitative, which allows an assessment of the process of teacher instruction. The assessment obtained from the instruction process in general for each suitability were the following: Epistemic Suitability: High, Cognitive Suitability: Medium, Affective Suitability: Low, Interactional Suitability: Low, Mediational Suitability: Medium and Ecological Suitability: Low. These assessments provide important aspects in the individual reflection of teaching practice since it allows improvements and changes to be made with the objective of achieving an ideal teaching-learning process.Ítem Desafíos y posibilidades para desarrollar prácticas de formación de profesores de matemáticas en la LEMA en el marco de la emergencia sanitaria (Sras-Cov-2)Ramírez Herrera, María Paula; Camelo Bustos , Francisco Javier; Camelo Bustos, Francisco Javier [0000-0002-8627-4816]This work was based on the teaching experiences of a group of Mathematics Degree teachers from the Francisco José de Caldas District University; focusing on the core of practice/intensive practice when developing its work in the training of future teachers. The development time of this document occurred between 2019 and 2021 and its objective was focused on showing the possibilities, challenges and difficulties faced by the teaching and learning processes within the framework of the pandemic decreed by COVID-19. or Sars-Cov-2. In the pandemic period, the economic and social sectors, specifically education, had to reorganize. The measures decreed by different governments, worldwide including Colombia, decide to suspend face-to-face attendance at all levels of schooling. In this context, a series of alternatives were deployed, such as: distance learning modalities, use of platforms, digital tools and flexible learning hours. Given the limited availability of counselors who could play this support role in the institutions, it is necessary to use different tools such as information campaigns, guides and support through teachers. Finally, for teachers, tools, platforms and applications are offered to help them plan classes, evaluate student work and promote collaborative work and incentives for creativity. (World Group Bank, 2022: p. 24). Within the framework of the suspension of face-to-face classes, the need to maintain continuity in learning begins to emerge, generating challenges in flexibility, compliance with the curriculum, connectivity, understanding of topics, as well as the lack of tangible materials for the acquisition of these lessons. As a point of attention for this research, it is given from the characterization of the context and the intensive practice in the health emergency, that is, two factors that influenced the mode and method for teacher training; These elements, found during the development of this and aspects related to the connectivity of the students, led to the practical sessions being carried out virtually. Thus, the work focuses on identifying challenges and possibilities to develop these training practices for mathematics teachers in the LEMA within the framework of the health emergency. This identification is achieved from interviews. On the other hand, to carry out this work, the qualitative methodology was used, taking as a fundamental axis what was proposed by Kvale (2011): "through the interviews we intend to approach the world "out there", fleeing from specialized research environments such as the laboratories, to understand, describe and explain "from the inside"; the latter with the purpose of developing the document with the chosen base group, teachers of the Mathematics Degree of the Francisco José de Caldas District University (UDFJC) and directing it to the academic space of intensive practice during the time that the preventive isolation was decreed to cause of COVID-19. The final conclusions of this investigation show the analysis based on the information collected; as well as a comparison of experiences that help to expand the panorama of those challenges that were found on the path of virtual training, this within an educational range that was reformulated as a result of the global pandemic crisis.Ítem Enseñanza del teorema de Thales basada en procesos de argumentaciónMelgarejo Herrera, Luis Enrique; Roa Martin, Harold Stevenn; Castro Cortes, Claudia CeciliaThis research in mathematical education focused on analyzing the argumentative processes of students during the learning of Thales' theorem, incorporating communicative elements throughout a teaching proposal designed for this purpose. The intention of this research centered on several key aspects. First, the construction of adapted argumentation levels for implementation in a mathematical education teaching sequence was addressed. These levels provided a clear and progressive framework that guided students from initial responses to the consolidation of solid and well-founded arguments. The designed teaching proposal focused on the learning of Thales' theorem and was implemented with the goal of promoting argumentation as an integral part of the educational process. Through this proposal, students had the opportunity to strengthen and formalize their prior knowledge, using it as a foundation for the construction of new mathematical knowledge. Furthermore, a deeper and more detailed understanding of how and why mathematical methods work was achieved, surpassing mere memorization of formulas and procedures. One of the key findings of this research was the need to actively promote argumentation in the mathematics classroom. It was identified that students were not accustomed to providing reasoned solutions, which poses a challenge to their educational development. Therefore, the importance of paying greater attention in the classroom to communicative skills was emphasized, fostering a pedagogical approach that encourages active participation, argumentative reasoning, and the application of mathematical concepts in diverse contexts. In conclusion, this research underscores the relevance of argumentation as a fundamental tool in mathematical education. It also highlights the need for teacher training that promotes meaningful mathematical learning, oriented towards deep understanding and practical application in students' everyday lives.Ítem Las matemáticas como medio para manejar eficientemente las tarjetas de créditoDíaz Arenas, Jhonatan; Cano Torres, Johan Schneideer; Carranza Vargas, Edwin AlfredoThis work developed a sequence of activities focused on mathematics with an emphasis on real financial life. It was applied to a small group of students in Bogotá, seeking to teach them key concepts such as savings, investment and the responsible use of money in different contexts. The activities were designed to be practical and relevant, allowing students to understand and apply financial concepts in their daily lives. The goal was to improve their understanding of financial mathematics and better prepare them to make informed economic decisions in the future.Ítem Memorias de la educación rural. Una experiencia narrada por un docente de matemáticas en formación en la Institución Educativa AlegríasGonzález Ferrucho, Osmar Jair; Camelo Bustos, Francisco Javier; Camelo Bustos, Francisco Javier [0000-0002-8627-4816]In this internship work carried out at the Alegrías Educational Institution, in the municipality of Aranzazu - Caldas, there are the activities that were carried out with the students of that institution, mainly with fifth grade students, through the Viva La Escuela program that implemented the Successful Educational Actions (AEE), which were executed over a period of three months.Ítem Uso del tratamiento de situaciones concretas como medio de sentido en los componentes de significado y uso en la enseñanza de números relativos en estudiantes de grado sextoSuárez Montenegro, Luis Felipe; Carranza Vargas, Edwin Alfredo; Carranza Vargas, Edwin Alfredo [0000-0003-0777-6146]The understanding of integers implies a relational management between the sense, meaning and use of the relative number, unfortunately, the basic standards of competencies in mathematics 2006 do not mention that use of the above should be made in the learning of integers in the school, therefore, it can be inferred that teachers may possibly perceive errors that students make when understanding integers. Therefore, a game is built that allows sixth grade students to give relational management to the relative number, giving it meaning in components of meaning and use.Ítem Matematización de un deporte de arte y precisiónOspina Forero, Estefani; Castro Muñoz, Laura Vanessa; Carranza Vargas, Edwin Alfredo; Carranza Vargas, Edwin Alfredo [0000-0003-0777-6146]The training process for mathematics teachers today is made up of various aspects in order to provide tools to the teacher in the framework of education, whether school or university, these components refer to disciplinary, normative, discursive and contextual pillars that allow that graduates have a perspective of the educational field and that they try to take into consideration the different variables that impact the teaching and learning process of mathematics. Hence, as mathematics teachers in training, one of the purposes set is to contribute precisely to the pillars that make up the teacher in the classroom. For this reason, this work focuses on the contextual component, referring to the various situations that life offers. daily routine brought to the school classroom, for this, a work of mathematization of the game of billiards was carried out in the three-cushion modality, with a development route framed precisely on the process of mathematization, under which three large simulations were established of which Ten models were derived to analyze behaviors of the necessary elements in billiards, focused on different game situations. This deepening arose from the interest in recognizing the school mathematics immersed in the game of billiards, which due to the nature of the context appears to be distant from the school classrooms.Ítem Actuaciones Educativas de Éxito como base para la transformación pedagógica, social y cultural de la Institución Educativa Santa Rosalía de Palermo, sede Simón Bolívar(2023-08-05)Este informe se desarrolla en el marco del programa Viva la Escuela del Ministerio de Educación, este proyecto se basa en las comunidades de aprendizaje, un modelo educativo bfundamentado en principios dialógicos que promueven una educación más inclusiva. Los antecedentes de estas comunidades muestran resultados efectivos en la transformación pedagógica y social de este proyecto institucional. Con base en lo anterior, se trabajó en Roldanillo - Valle del Cauca en la implementación de Acción Educativa de Éxito, motivando a los estudiantes a la lectura, mejorando su comprensión lectora, incluyendo a las comunidades en los procesos de formación de los estudiantes y promoviendo la diversidad y heterogeneidad en el proceso educativo. De igual manera se trabajan conceptos matemáticos que, incluidos en las Acciones Educativas, permitieron mejorar los procesos de los estudiantes en esta área. Así, el aprendizaje se logra a partir de la manipulación y construcción del conocimiento a través de grupos y trabajo colectivo, promoviendo el aprendizaje metodológico, didáctico y pedagógico.Ítem Transición del cero mediático al cero operacionalCalderon Cardozo, Andres Felipe; Melo Martinez, Nicole Stefanny; Bello Chavez, Jhon Helver; Bello Chavez Bello Chavez [0000-0003-4370-9995]For this degree work, a historical review of some civilizations that gave a treatment to the number zero was made, and at the same time the epistemological obstacles present in the conceptualization of this number were analyzed, in order to design and implement a diagnostic instrument that allows to demonstrate the obstacles present in the transition from the mediatic zero to the operational zero with first cycle school students.