Licenciatura en Educación Básica con Énfasis en Matemáticas
URI permanente para esta colecciónhttp://hdl.handle.net/11349/43
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Ítem Procesos de matematización en la comprensión de una actividad deportiva; una perspectiva desde el conocimiento del profesor de matemáticas(Universidad Distrital Francisco José de Caldas) Morales Cárdenas, Anderson Francisco; Forero Poveda, Alberto; [0000-0002-0452-7876]This monograph addresses the use of mathematical modeling in pre-service teacher education, with the hammer throw serving as the central case study. Based on the perspective of horizontal and vertical mathematization (Freudenthal, Treffers), a methodological process was developed that combined video analysis (Tracker) and simulation (GeoGebra with calculus) to characterize the mathematical activities involved. It is concluded that this approach complexifies the teacher's knowledge, enabling them to apply mathematics in decision-making and the improvement of real-world situations, thus promoting a functional and meaningful teaching practice.Ítem La Semilla de la Geometría: Cultivando Aprendizajes y Valores.Vasquez Capera Daniel Andres; Oyola Rubio Paula Esther; Castro Cortes Claudia CeciliaThis document presents the results of an internship carried out at the Fundación Buena Semilla, an organization that has supported children and youth from the Egipto neighborhood in Bogotá since 2002. The purpose of the internship was to examine the impact of implementing mathematics lessons connected to everyday life and real community problems, with the aim of fostering students’ motivation and interest in learning. The main objective was to design and implement pedagogical strategies focused on geometry to strengthen the mathematical skills of the children and adolescents at the foundation. The intervention sought to promote meaningful learning and creativity through activities rooted in their environment, while upholding the foundation’s core values. The work plan included differentiated sessions for three groups—small, medium large, and creatives—for whom lesson plans were developed with an emphasis on problem solving, the use of concrete materials, and playful activities. The contents addressed included place value, basic operations, proportionality, area, perimeter, and other applied geometric concepts. Lesson plans incorporated hands-on tasks and participatory dynamics. Evidence collected through photographs and classroom narratives shows the students’ interest and active engagement in activities such as constructing two-dimensional houses, participating in a school-store simulation, solving proportionality challenges, and exploring various geometry experiences connected to daily life. Overall, this report compiles the experience, lesson plans, results, and reflections developed throughout the process, demonstrating how a situated pedagogical approach can generate a meaningful impact on mathematics teaching and on the integral development of participants.Ítem La enseñanza de matemáticas críticas en población extra-edad: diseño y aplicación de un recurso digital para las manzanas del cuidado del Colegio Técnico José Félix Restrepo(Universidad Distrital Francisco José de caldas) León Paniagua , Luis Gabriel; Torres Duarte, José; Torres Duarte, José [0000-0001-9208-4843]This research addresses the teaching of critical mathematics to over-aged students through the design and implementation of a digital resource in the "care centers" of the José Félix Restrepo Technical School. The study focuses on understanding how digital tools, combined with critical pedagogical approaches, can foster active participation, the development of mathematical skills, and reflection on everyday problems. The results show significant progress in the appropriation of content, the strengthening of critical thinking, and learning motivation, highlighting the relevance of integrating digital teaching resources in diverse educational contexts and with students who require differentiated strategies to enhance their learning processes.Ítem Divertimate: Propuesta didáctica con un enfoque de integración entre las matemáticas y las artes plásticas, desde el referente de la pintura(Universidad Distrital Francisco José de Caldas) Rincón Pinzón , Ricardo Alfonso; Castro Cortez, Claudia CeciliaThis research aims to analyze experiences that have incorporated art as a pedagogical tool to strengthen the emotional and cognitive connection with school mathematics. It emerges from the recognition that many students experience mathematics as a distant, abstract discipline, or even as a source of anxiety. This proposal explores the transformative potential of art to reframe that relationship and, through the analysis of various activities, reveals its scope within the teaching process. Using a design-based approach with an interdisciplinary proposal that integrates visual and geometric elements, the study addresses mathematical concepts such as proportion, symmetry, spatial visualization, and geometric reasoning through an aesthetic and meaningful experience. The research phases, the design of the activities, and the implementation with 8th and 9th grade students foster the development of logical thinking, artistic sensitivity, and positive emotions toward mathematical knowledge. As a key outcome, the proposal positions the student as an active, sensitive, and reflective subject in their mathematics learning process. students as active, sensitive, and reflective subjects in their learning process.Ítem Aprender, enseñar, vivir: Docente en escuela rural(Universidad Distrital Francisco Jose de Caldas) Ochoa Prieto, Laura Tatiana; Castro Cortes, Claudia CeciliaThis report presents the pedagogical experience developed during a rural multigrade classroom teaching practicum, as part of the Initial Training Program of the "Todos a Aprender" Program (PTA FI). The practicum was carried out at the Institución Educativa Técnica Agroindustrial Leopoldo García, located in a rural area of Colombia. The main goal was to design and implement contextualized didactic strategies for teaching mathematics in a classroom with students from multiple grades. Through an interdisciplinary approach that incorporated elements from the local context, the project aimed to foster meaningful learning and strengthen students’ basic skills. This experience highlighted challenges, lessons, and transformations in the early stages of teacher training.Ítem Estudio comparativo del aprendizaje de decimales en Perú y Colombia en zonas rurales: impacto de la moneda, perspectivas docentes y análisis curricular(Universidad Distrital Francisco José de Caldas) Figueredo González , Deysi Lucero; Castro Cortés , Claudia CeciliaThis research aimed to compare the learning of decimal numbers in students from rural schools in Peru and Colombia, based on the influence of the economic context and local currency. Diagnostic tests were administered, teachers were interviewed, and a curriculum analysis was conducted in both countries. Methodologically, the study employed a mixed-methods approach and a comparative case study design, integrating quantitative and qualitative methods to obtain a more comprehensive understanding of the phenomenon. The diagnostic tests measured students' level of comprehension using a rubric with performance indicators, while the semi-structured interviews allowed for the identification of the pedagogical conceptions and strategies used by rural teachers. The instruments were designed considering the theoretical frameworks of Duval and Castaño, as well as the curriculum guidelines of Peru and Colombia, and included contextualized situations that linked decimals to real-world practices such as the use of currency, measurement, and the preparation of traditional recipes. The results show that Peruvian students perform better in calculating and ordering decimal numbers, aided by the everyday use of a currency with decimal values. In contrast, Colombian students, whose currency practically lacks cents, face a more abstract learning experience. However, difficulties in comparing decimals persist in Peru, indicating that the monetary context fosters certain skills but does not guarantee complete mastery. In conclusion, currency constitutes a significant teaching resource in the initial instruction of decimals, although it requires the support of sound pedagogical strategies to ensure lasting conceptual understanding.Ítem Métodos didácticos para la enseñanza de las matemáticas en una educaciòn flexibilizada(Universidad Distrital Francisco José de Caldas) Serpa Serpa, Juan Daniel; Beltrán Casallas, Julián Santiago; Torres Duarte , José; Torres Duarte, José [0000-0001-9208-4843]Flexible education emerges as a response to the need to guarantee access to diverse populations who encounter obstacles in adjusting to conventional schedules. At the José Félix Restrepo IED in Bogotá, this modality allows people of different ages and backgrounds to resume or complement their studies, which generates heterogeneous groups with varied backgrounds and knowledge. In this scenario, teaching mathematics represents a challenge for both students and teachers, as it requires strategies that respond to different rhythms, motivations, and ways of learning, even more so when it is developed during the evening shift from 6:00 pm to 10:00 pm. The purpose of this work is to analyze the teaching methods applied in this model, identifying the challenges and opportunities it offers, while recognizing the role of mathematics not only in academic development, but also in understanding the environment from personal, economic, and professional perspectives.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.