Licenciatura en Educación Básica con Énfasis en Matemáticas
URI permanente para esta colecciónhttp://hdl.handle.net/11349/43
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Ítem Proyecto de aula para abordar algunos aspectos del pensamiento variacional(Universidad Distrital Francisco José de Caldas) Guzmán González, Andrea Lizeth; Gil Chaves, DianaThe classroom project is designed to develop variational thinking in mathematics with fifth-grade students at Colegio República de China. It proposes an inclusive approach that addresses the diversity of the student body, including students with visual impairments and Autism Spectrum Disorder (ASD). The construction of the project follows a qualitative methodology and is organized into four main phases: diagnosis and contextualization, theoretical foundation, design and planning, and the preparation of the final report.The project’s design integrates the use of Information and Communication Technologies (ICT) and Learning and Knowledge Technologies (LKT), along with principles from Universal Design for Learning (UDL) and the Individual Plan for Reasonable Accommodations (PIAR). All of this aims to create a flexible, collaborative, and inclusive environment that promotes meaningful and active learning.Ítem Estrategias de prevención y seguimiento de la deserción en la Licenciatura en Matemáticas(Universidad Distrital Francisco José de Caldas) Moreno Hernández, Julián David; Gil Cháves, DianaThis internship report presents the development of strategies aimed at preventing, promoting, and monitoring student dropout rates during the first semesters of the Bachelor's Degree in Mathematics at the Francisco José de Caldas District University. This strategy is coordinated with the Sinde+ research group and is part of the program's high-quality accreditation process. Using a mixed-method inquiry instrument applied generally to the student community, academic, socioeconomic, and emotional factors that could influence retention were identified, including difficulties maintaining study habits, academic load, work responsibilities, and stress management. The results reflected the complexity of the dropout rate phenomenon and highlighted the need to strengthen institutional support mechanisms, implement academic and emotional guidance strategies, and consolidate comprehensive actions that promote retention, well-being, and successful training among future mathematics teachers.Ítem Desafíos y oportunidades en la implementación de estrategias colaborativas, grupales y/o cooperativas en el núcleo de pensamiento matemático avanzado en la Licenciatura en Matemáticas (LEMA)(Universidad Distrital Francisco José de Caldas) Cerquera Gambino , Chayanne; Gil Chaves, Diana; Gil Chaves, Diana [0000-0003-3872-1105]This study analyzes the challenges and opportunities that arise from implementing collaborative, group, and cooperative strategies within the core of Advanced Mathematical Thinking in the Bachelor’s Degree in Mathematics (LEMA) at Universidad Distrital Francisco José de Caldas. It begins with the need to understand how collective work dynamics influence learning, knowledge construction, and the development of professional competencies in future mathematics teachers. Through the analysis of different theoretical approaches and teaching experiences, the study identifies the strengths of cooperative work in fostering active participation, critical reflection, and shared responsibility among students. Likewise, it acknowledges the limitations related to lesson planning, process assessment, and the articulation between individual and collective roles. Finally, the study proposes pedagogical guidelines aimed at strengthening collaborative practices in initial teacher education, enhancing both social and academic skills.Ítem Números que viajan, realidades que cambian: Experiencia virtual de enseñanza matemática en comunidades de Arauca, Norte de Santander y Meta(Universidad Distrital Francisco José de Caldas) Romero Mora , Heidy Natalia; Guerrero Recalde, Néstor Fernando; Guerrero Recalde,Néstor Fernando [0000-0002-3982-4985]This report documents an internship focused on Critical Mathematics Education (CME) in rural areas of Norte de Santander, Meta, and Arauca affected by armed conflict. The project, aimed at children aged 8 to 12, sought to redefine mathematics as a language for understanding and questioning social reality, moving beyond the view of mere numbers and formulas. Through a virtual learning space, real-life situations were connected to fundamental rights (identity, equality, mutual respect) and emotional management. The methodology employed was Participatory Action Research. Following an initial characterization, virtual interventions were designed and implemented, intertwining human rights and mathematical content, fostering social justice as a principle for reflection. Analysis, based on various systematization tools, demonstrated that linking mathematics with the social environment strengthens comprehension, critical analysis, and citizenship. The internship confirms that virtuality acts as a pedagogical bridge, allowing the cultivation of innovative and deeply human educational experiences in territories marked by adversity.Ítem Lo inclusivo de lo abstracto: Apoyo en la enseñanza de las matemáticas a estudiantes con discapacidad visual(Universidad Distrital Francisco José de Caldas) Erazo Quintero, Gabriel Andrés; Díaz Yara, Edgar Samir; Fonseca González, Jaime; Fonseca González, Jaime [0000-0002-5147-7912]The present report is the result of an internship work to obtain the Bachelor's Degree in Mathematics, in accordance with Agreement 012 of 2022 of t Francisco José de Caldas District University. The internship was carried out at the I.E.D. República de China, located in Engativá, Bogotá, D.C. The internship responded to the need for address mathematics learning in students with visual impairments. Support was mainly provided to those students who needed a abjusts of the mathematical learnings when the processes in class did not fully meet their needs. The adaptation and teaching process, and the methods, involved studying the different guidelines available in the field of typhlology. This work was designed at the direct participation of two interns during mathematics classes for students with visual impairments, compiling the theoretical bases, the different strategies used, and the significant results that they left for the interns' teaching work.Ítem Matemáticas y criptografía: posibilidades y desafíos en el aula(Universidad Distrital Francisco José de Caldas) Arismendy Gil, Caren Johana; Orjuela Forero, Steven; Peña Acuña, Fredy; Peña Acuña, Fredy [0000-0002-6880-8124]This research aims to demonstrate the potential of cryptography as an educational tool that fosters and promotes a contextualization of algebra, in addition to highlighting the importance of effective pedagogical support, understanding that we are social beings who construct knowledge in a community. Methodologically, four encryption methods were implemented for the proposal, based on a position of progressive advancement in their complexity. The ciphers we used were: one-to-one cipher, Caesar cipher, affine cipher, and Hill cipher. It should be noted that these methods were selected due to their practicality for discussing mathematical concepts such as functions, modular arithmetic, and linear transformations, providing a close and useful context, such as the protection of information in digital communications.Ítem Integración de recursos manipulativos y artísticos para el fortalecimiento de competencias básicas matemáticas y pensamiento variacional en contextos vulnerables(Universidad Distrital Francisco José de Caldas) Méndez Soto, Luz Helena; Torres Duarte, José; Torres Duarte, José [0000-0001-9208-4843]This report documents the process of pedagogical intervention developed during the internship as a degree modality at the Fundación Nueva Vida Generación Exitosa, Ciudad de Suba, Bogota, as a qualification for the Bachelor’s degree in Mathematics from the Francisco José de Caldas District University. The intervention focused on strengthening basic mathematical skills and variational thinking in students aged 5 to 13 years belonging to the School Reinforcement program of the Foundation. Significant difficulties in learning abstract mathematical concepts, low motivation towards the mathematical discipline and limited application of knowledge in real contexts were identified as central problems. The pedagogical proposal implemented integrated manipulative resources (plasticine, pompons, legos) and artistic expressions (music, juggling) from theoretical approaches Freirean, Ausubeliano and variational thinking. During 16 weeks, innovative didactic sequences were developed which included: construction of musical instruments ("marimbotella") to model patterns of change, projects of statistics applied to entrepreneurship, and geometrical activities with concrete materials. The intervention demonstrated that art-mathematics articulation transforms student perception, facilitates conceptual understanding and develops skills transferable to entrepreneurship.Ítem Cultivando el ser: relato de una experiencia sobre educación ambiental a través de la matemática escolar en la Institución Educativa de Yati(Universidad Distrital Francisco José de Caldas) Forero Roa , Mayerly; Guerrero Recalde , Néstor Fernando; Guerrero Recalde, Néstor Fernando [0000-0002-3982-4985}This document systematizes a pedagogical experience developed at the Yatí Educational Institution, Magangué (Bolívar), within the framework of the Tutoring Program for Comprehensive Learning and Training (PTAFI 3.0). The experience integrated support for environmental education with the teaching of school mathematics, under the approach of comprehensive training and CRESE (Citizenship, Reconciliation, Socio-Emotional, Anti-Racist, and Climate Action) education. Through an action research methodology, environmental and pedagogical problems affecting the teaching-learning process were diagnosed, including inadequate solid waste management and traditional practices in mathematics teaching. Contextualized activities were implemented in support of the institution's established environmental project, which promoted critical reflection, environmental ownership, and the strengthening of mathematical competences. The results demonstrate progress in environmental awareness, student participation, and the development of significant mathematical skills linked to local realities.Ítem Propuesta de inclusión en la enseñanza de las matemáticas en el Colegio Técnico José Félix Restrepo(Universidad Distrital Francisco José de Caldas) Pineda Ramos, Jaime Andrés; Ramos Romero, Jojhan Armando; Torres Duarte, José; Torres Duarte, José [0000-0001-9208-4843]The Francisco José de Caldas District University, the José Félix Restrepo I.E.D. Technical School, and the curriculum project for the Bachelor's Degree in Mathematics, reached an agreement to carry out an internship aimed at generating teaching strategies for students with visual and cognitive disabilities related to mathematics. This process is established through mentoring in various mathematics classes, providing support so that our students can more easily understand the mathematical object being taught. The ideal is to create an environment that establishes equal opportunities and fosters equitable participation among the student community, so that each student can enjoy a quality education. This is where we discuss a proposal for inclusion in the teaching of mathematics, which seeks to address each of the students' educational needs. Teaching resources will be used to assist with this process and make it easier for students to understand the mathematical object they want to develop. It is worth noting that each of these processes is developed individually, as there are several students with different difficulties. In the educational field, the inclusion of people with disabilities is perhaps of the utmost importance, as it is expected to develop social integration in the best possible way. The inclusion of people with disabilities affects how they interact and act in society. Likewise, it must be guaranteed that they have the same rights and opportunities regarding participation in everyday situations, being clear about their abilities and desires, as this is important to achieve this integration with people with this condition (Martínez, 2012). (Zúñiga, 2012) the issue of inclusive education is aimed at or seeks to meet basic learning needs. An internship has been proposed as a degree thesis, which aims, as previously stated, to provide educational support to people with visual and cognitive disabilities. This document consists of a work plan, which establishes an introduction that allows us to justify the development and process of the internship, as well as each of the elements implemented during that period, thus fulfilling the voluntary agreement signed with the institution and the university.Ítem Matemática crítica y educación: una propuesta pedagógica integradora desde la práctica en territorios excluidos(Universidad Distrital Francisco José de Caldas) Moreno Vargas, David; Peña Carrero, Daniel Ricardo; Guerrero Recalde , Néstor Fernando; Guerrero Recalde, Néstor Fernando [0000-0002-3982-4985}This undergraduate research project stems from a pedagogical experience developed in territories affected by conflict and social exclusion, within the framework of an internship at the IN-JU Huellas Foundation. From the perspective of Critical Mathematics Education, it proposes an integrative pedagogical strategy that connects social reflection with mathematical thinking. Using the Participatory Action Research (PAR) approach, several learning modules were designed and implemented around topics such as equality, volume, exponentiation, and three-dimensional figures, aiming to strengthen students’ autonomy, argumentation, and social awareness. The results show that playful activities, collaborative work, and contextualized learning promote mathematical understanding and the formation of critical individuals capable of connecting mathematics with their social reality.Ítem Autovaloración de la faceta mediacional de la idoneidad didáctica en la enseñanza de la noción de elipse: un estudio de caso(Universidad Distrital Francisco José de Caldas) Martínez Vargas, José Yecid; Torres Duarte , José; Torres Duarte, José [0000-0001-9208-4843]This thesis arose from the need to assess my own teaching practice regarding the teaching of the ellipse in its analytical interpretation. To do so, I drew on the Ontosemiotic Approach to Mathematical Knowledge and Instruction (OSI), which offers tools for analyzing didactic suitability from different perspectives. The study focused particularly on the mediational aspect, with the aim of understanding how material, technological, and semiotic resources influence the construction of meanings in the classroom.Ítem Mercado y finanzas: construcción de conceptos matemáticos desde la creación y gestión de emprendimientos(Universidad Distrital Francisco José de Caldas) Argumedo González , José Mario; Saiz Mosquera , Yuli Paola; Castro Cortés, Claudia CeciliaThis report illustrates the work carried out at the Buena Semilla foundation, focused on the implementation of various projects aimed at strengthening mathematical learning by creating and managing projects, thus providing social, recreational, and pedagogical support to approximately twenty-nine children aged five to eleven who belonged to the 'semillitas' group, and thirty young people aged twelve to seventeen who were part of the 'medianos y creativos' group. Throughout the internship, participatory support was provided in activities, celebrations, and pedagogical days to the community of the Egipto neighborhood, which allowed us to acquire skills for our future teaching profession, highlighting the importance of social commitment, thereby strengthening teamwork and continuous training in different educational fields.Ítem Diseño y validación de un material didáctico (libro) para aulas multigrado en contextos de población multi-edad: un enfoque inclusivo y flexible(Universidad Distrital Francisco José de Caldas) León Rodríguez, Kevin David; Torres Duarte, José; Torres Duarte, José [0000-0001-9208-4843This thesis aims to design and validate a didactic material (book) for multigrade classrooms in night school contexts with multi-age populations, from an inclusive and flexible approach. The research, qualitative and applied in nature, was conducted through a participatory action research methodology, involving students and teachers throughout the process. The material was implemented and evaluated in sixth and seventh grade night classes, showing improvements in the learning of basic operations, fractions, and decimals, as well as in students’ autonomy and participation. The results and teacher feedback confirmed the relevance of the resource, while highlighting the need for adjustments in sequencing and conceptual accuracy. This work contributes to the strengthening of inclusive and context-based pedagogical practices, addressing the challenges and particularities of night education in Colombia.Ítem Explorando las matemáticas a través del tacto y la escritura braille: Pasantía inclusiva para niños con discapacidad visual en el colegio José Félix Restrepo I.E.D(Universidad Distrital Francisco José de Caldas) Huertas Pinto, Andrés Estiven; Torres Duarte, José; Torres Duarte, José [0000-0001-9208-4843]This thesis documents an internship carried out at Colegio José Félix Restrepo I.E.D., with the aim of promoting inclusive education in the field of mathematics for students with visual impairments. This initiative arises from the need to break down the barriers these students face due to the visual nature of mathematical content. The project is based on the use of multisensory strategies that combine touch and Braille writing, allowing students to meaningfully access mathematical concepts. The work includes the design and implementation of adapted materials such as Cuisenaire rods, abacuses, tactile Cartesian planes, Braille books, geoboards, and technological tools such as Braille printers, screen readers, and magnification software.Ítem Geometría elíptica con estudiantes de educación media(Universidad Distrital Francisco José de Caldas) Piraján Parra , Juan David; Ortiz Mancera , GabrielThis thesis aims to introduce high school students to elliptic geometry as an alternative to traditional Euclidean geometry. To achieve this, a sequence of activities supported by digital resources such as GeoGebra and manipulative materials was designed and implemented, enabling students to explore concepts such as geodesics, spherical triangles, and trajectories on curved surfaces. The proposal challenged students’ prior conceptions, broadened their understanding of non-Euclidean geometries, and fostered critical reasoning, problem-solving, and geometric thinking from new perspectives.Ítem Proyecto Piemsa Plantea, identifica, estructura, matematiza, sorprende y aprende(Universidad Distrital Francisco José de Caldas) Bedoya Montoya , Brayan; Yaya Pulido, Miguel Alexander; Peña Acuña, Fredy; Peña Acuña, Fredy [0000-0002-6880-8124]This thesis presents PIEMSA project, a didactic proposal based on problem-solving and focused on entrepreneurship, implemented with 401A and 401B students at Colegio Técnico José Félix Restrepo. Through six phases—Plantea, Identifica, Estructura, Matematiza, Sorprende y Aprende—students created simulated companies presented at a Math Fair.The project aimed to strengthen mathematical skills in real-life contexts, addressing concepts such as costs, income, and profit. It also promoted critical thinking, creativity, and teamwork. The methodology, grounded in meaningful and contextual learning, positioned students as active participants in their own learning process.The results show improvements in conceptual understanding and practical application of mathematics, effectively connecting the subject with the school’s broader educational goals in entrepreneurship.Ítem Educación matemática en el contexto del aula hospitalaria(Universidad Distrital Francisco José de Caldas) Téllez Suns, Julián David; Castro Cortés , Claudia CeciliaThis report describes the internship carried out in the hospital classroom of Clínica Infantil Colsubsidio, with the aim of supporting the learning process of hospitalized students, particularly in the area of mathematics. To achieve this, a flexible curriculum based on the Basic Learning Rights (DBA) was implemented, tailored to the specific needs of each student. The experience focused on designing meaningful activities that connected academic content with human experience, offering each student a personalized teaching process—something difficult to achieve in a conventional classroom. Despite challenges such as limited time, frequent transfers, and unavoidable medical interruptions, significant progress was made thanks to formative assessments designed for each individual case. The work required constant communication with the students’ home institutions and highlighted that, beyond improving administrative procedures and coordination between the university and external entities, empathy, sensitivity, and the ability to reflect on one’s own practice are essential to respond effectively to the situations that arise in this context. It was especially valuable to work in an environment of respect and solidarity, where no major conflicts occurred and many gestures of collaboration were present. This experience led me to reflect that teaching is not merely about mastering a subject area, but about adapting, listening, and being willing to learn alongside the students. Therefore, I recommend streamlining internship procedures, strengthening socioemotional development in teacher training, and ensuring continuous support for interns—not only academically, but also personally. Ultimately, this internship was an opportunity to bridge theory and practice in a real-world setting, and to grow not only as an educator, but also as a human being.Ítem Viva la escuela – Aportando en la escuela rural(Universidad Distrital Francisco José de Caldas) Escobar Suárez, Erly Andrey; Mancera Ortiz, GabrielThis document presents the experience gained during the internship carried out within the framework of the Tutoring Program for Learning and Comprehensive Training – PTA/FI 3.0, a more updated version of the Viva la Escuela program. The objective of the internship focused on designing a center of interest oriented toward mathematics, taking into account the context and priorities of the students at the Eliseo Pinilla Rueda school. Within the framework of the PTA/F project, with the support of the teachers and administrators of the institution where the internship took place, the Eliseo Pinilla Rueda school, and with the guidance and assistance of the director of the thesis for this document, a proposal for the development of a center of interest was developed and subsequently implemented. The project was specifically aimed at a group of seventh-grade students. Initially, elements such as the students' interests, their context and that of their families, and the institutional environment were identified. As a result of this diagnosis, poultry production was selected as a relevant and pertinent theme for the development of the center of interest, given its relevance and pertinence to the community. The methodological proposal considered defined phases and moments. Initially, different characteristics of the institution's environment, the students, and the community in general were identified through observations, interviews, and casual conversations with students, teachers, and other people around the school. In a later stage, the focus of interest was developed, anticipating different scenarios: one in which the implementation of the focus of interest was not possible for specific reasons; another in which the intern or trainee could propose a focus of interest; and a third in which the school already had a focus of interest and the intern or trainee would adjust to it. Finally, in the final stage, an analytical and reflective interpretation of the experiences and results obtained throughout the experience was carried out. Throughout the experience, taking advantage of poultry production as the theme of the center of interest, an effort was made to link concepts such as proportionality, reason, basic measures of central tendency, and data organization. In addition to documenting the successes and measures taken during the experience to ensure the project's objectives were met, the document addresses various challenges that arose and presents critical reflections based on observations and experiences during the process.Ítem Diseño de una propuesta para jóvenes y adolescentes privados de la libertad haciendo uso de la educación matemática crítica(Universidad Distrital Francisco José de Caldas) Orozco Torres, Andrés Camilo; Mancera Ortiz, GabrielThis project addresses the importance of education as a fundamental right, and the role of mathematics as a tool for social transformation, particularly in the context of juveniles and teenagers deprived of their liberty. The goal is to propose guidelines for developing educational initiatives that support the learning process of these individuals from the perspective of critical mathematical education. To achieve this, a theoretical framework is established, which includes the knowledge areas of mathematics, technology, and reflection as proposed by Skovsmose; learning environments and their dimensions in critical mathematical education; and mathematical modeling from a socio-critical perspective. The methodology used is qualitative research, acknowledging its characteristics and approaches. In this regard, the study gathers information through a review of specialized literature on education proposals for incarcerated youth, supplemented by a semi-structured interview with an expert in the field. Finally, the research suggests that future educational initiatives for this population should recognize the laws that guarantee the right to education for incarcerated youth, along with various other considerations that will be discussed later.Ítem Construcción de máquinas simples para la enseñanza y aprendizaje de las matemáticas con base en el enfoque en STEM(Universidad Distrital Francisco José de Caldas) Carreño Rivera , Laura Valentina; Vinasco Aguilar , Julián Felipe; Castro Cortés , Claudia Cecilia; Castro Cortés Claudia Cecilia [0000-0002-4224-2580]This paper recounts the experience gained during an internship at the DCM Social Mission Foundation, where an educational proposal was developed focused on teaching mathematics through workshops on simple machines. Throughout the process, significant learning took place on both a professional and personal level, highlighting commitment, adaptation, and the ability to respond to the challenges involved in working with a multi-age group. The plans served as a fundamental guide for organizing activities by topic and month, allowing key content to be addressed in a structured way, although the need for greater flexibility and attention to diversity was also evident. The experience highlighted the value of building more inclusive activities, recognizing the individual abilities of students. In addition, interpersonal bonds were strengthened inside and outside the classroom, understanding the importance of getting to know students beyond the academic space. Finally, the relevance of settings such as the foundation is recognized, as they offer valuable alternatives for the use of free time, contributing to the comprehensive development of children and young people. This experience reaffirms the importance of non-conventional educational spaces and leaves us, as future teachers, with a broader, more sensitive, and committed view of the transformative role of education.