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Browsing Doctorados by Subject "510"
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Item Aprendizaje de las ecuaciones diferenciales desde un enfoque cualitativo(Universidad Antonio Nariño) Caicedo Parra, Edinson; Chacón Guerrero, Gerardo AntonioThis work arises due to the importance of modeling through differential equations both in the basic sciences and in the humanities and social, which is extremely relevant, since since Newton managed to develop the calculus, and more importantly, to model the laws of classical mechanics using differential equations, they became an important resource for the modeling and problem solving.Item Avances en la caracterización del desarrollo del pensamiento matemático en los estudiantes de ingeniería en un contexto realista del cálculo multivariado en temas relacionados con superficies(Universidad Antonio Nariño) Acosta Solarte, Pablo Andrés; Cruz Ramírez, MiguelThe research was carried out with students of Technology in Industrial Mechanics at the Francisco Jose de Caldas District University.The students were in the multiva- ´riate calculus class. The research proposed to advance in the characterization of the development of mathematical thinking when some topics of course through realistic contexts are developed.Item Avances en la caracterización del pensamiento combinatorio(Universidad Antonio Nariño) Anzola Caldas, José Ciro; Falk de Losada, MaryThis research is based on the analysis of the manifestations of mathematical thinking that arise during the solution of significant problems, mathematical and contextual, within the framework of the analysis combinatory, and the corresponding construction of meanings of the concepts implicit in them with the aim of characterizing and consolidating a way of thinking that was called combinatorial thinking. The study was carried out with an experimental design in two phases, one under action research and the other using elements of the grounded theory, which implied the design of a didactic unit consisting of eight activities based on the basic principles of counting, an instrument that was implemented and developed with first-year engineering students in the Problem Solving course.Item Avances en la caracterización del pensamiento geométrico a través de la resolución de problemas trigonométricos no rutinarios(Universidad Antonio Nariño) Pinzón Cardozo, Margarita; Chacón Guerrero, Gerardo AntonioThe objective of this research project is to contribute to characterization of geometric thinking, based on existing studies in current literature on teaching and learning trigonometry. Authors such as Bressoud (2010), Altman and Kidron (2016) and Gomes (2013) show that there is a dichotomy between triangular and circular trigonometry; insufficient knowledge in geometry and algebra, as well as lack of familiarity with straightedge and compass constructions, do not allow for solid comprehension when learning trigonometry.Item Avances en la caracterización del pensamiento matemático: relaciones y aportes mutuos entre la solución de problemas de competiciones y la teoría sobre competencias(Universidad Antonio Nariño) Rangel Luengas, Juan Samuel; Falk de Losada, MaríaThis qualitative approach research is supported by quantitative methods and mathematics education as a design science with the purpose of bringing together two different reference frameworks: the theory on competencies on the one hand and mathematical competitions that focus on the solution of challenging problems on the other hand, by contrasting PISA-type and Olympiad-type problems.Item Avances en la caracterización del pensamiento vectorial a través de la resolución de problemas(Universidad Antonio Nariño) Galindo Rivera, Oscar Andrés; Falk de Losada, MaríaThe objective of this present research is to show some advances in the characterization of Vector Thinking through problem solving in Engineering students at the Universidad Antonio Nariño. Eight activities were designed, which were implemented to 35 students. In these activities, a set of nonroutine or challenging problems are proposed for which students offer solution strategies, where five modes of thought that characterize the Vector Thinking involved in them come to light.Item Caracterización de las relaciones y fronteras entre el pensamiento divergente y la creatividad. Un estudio a través de la resolución de problemas geométricos con estudiantes de secundaria(Universidad Antonio Nariño) Chávez Castiblanco, Carlos Fernando; Rojas Velázquez, Osvaldo JesúsThis research seeks to characterize divergent thinking, underlying the resolution of geometric problems with multiple solutions, through the analysis of a system of activities applied with high school students in the city of Bogotá, exploring the relationships between divergent thinking and creativity through fluency, flexibility and originality. The research is approached from a mixed approach with an action research design applying methods of analysis-synthesis, participant observation, content instruments, besides being consistent with psychometric and pragmatic trends of creativity.Item Creencias epistemológicas de docentes de matemáticas en formación y en servicio. un estudio de casos para proponer cambios en los programas de formación(Universidad Antonio Nariño) Vesga Bravo, Grace Judith; Falk de Losada, MaryThis research aimed to analyze and describe the epistemological beliefs that have mathematics teachers in training and in service about mathematics, its teaching and learning, understand how they were structured and how they are transformed, to propose elements that must be consider in training programs aimed at achieving more productive beliefs towards teaching and learning mathematics.Item El desarrollo del pensamiento matemático a través de la heurística de lakatos en la construcción de demostraciones y en la resolucion de problemas de la matemática discreta(Universidad Antonio Nariño) Cortes Amaya, Jader Wilson; Falk De Losada, MaryThe objective of this study was to analyze the impact generated by the Lakatos heuristic method in mathematics education. Specifically, important results were obtained when considering said heuristics along with solving challenging problems as a methodology in a mathematics course discrete for systems engineering and mathematics undergraduate students. were achieved results regarding the implication of heuristics in the development of mathematical thinking, in the student attitude, in the construction of mathematical demonstrations and as an effective tool for problem solving.Item Estrategia didáctica basada en la resolución de problemas para la enseñanza y aprendizaje de los intervalos de confianza en estudiantes de ciencias económicas(Universidad Antonio Nariño) Camargo Forero, Marleny; Bolívar Díaz, NicolásOne of the most relevant skills for data analysis in inferential statistics is related to the interpretation and application of confidence intervals, since they are useful for estimating unknown parameters. This research addresses the problems observed in economics students of the Antonio Nariño University (UAN) regarding the erroneous understanding of the concept and lack of interpretation of this statistical object.Item Hacia la generación de oportunidades de aprendizaje de calidad para cada estudiante en la clase de matemáticas en contextos rurales(Universidad Antonio Nariño) Rojas Sevilla, Sandra Patricia; Gerardo Antonio Guerrero Chacón, Gerardo AntonioResearch advances in the field of Mathematics Education in recent decades have been prolific and high quality (Kaiser, 2019). It is observed, a plethora of studies devoted to improving the learning of school mathematics, with the purpose of contributing research that favors the advancement of the field and at the same time are closer to the classroom and aim to directly impact the practice by example (Kilpatrick, 2018; Schoenfeld (1994; 2014; 2016; 2020); Skovsmose, 1999; Valero & Skovsmose, 2012; Cai et al., 2020; Cai et al., 2019b; Cai et al., 2019; Cai, et al., 2019a; Dröse & Prediger, 2020; Prediger et al., 2015; Predicter, 2019; Schoenfeld et al., 2018; Ernest, 2010; Li et al., 2020).Item Un modelo didáctico para el aprendizaje del algebra lineal centrado en el razonamiento plausible en carreras de ingeniería(Universidad Antonio Nariño) García Hurtado, Orlando; García Pupo, MauroThis thesis proposes a methodological strategy for teaching linear algebra for engineering students centered on conjecturing and plausible reasoning, concepts developed by Polya (1966) and Lakatos (1978), and is based on formulating and adapting interesting problems whose design admits a didactic model and a methodological procedure for the generation of conjectures mediated by technology and geometric visualization as fundamental factors in the construction by students of the main concepts that characterize this discipline. This work is motivated by the inadequacies that students in these fields manifest in the learning of linear algebra which lead to this research and inform its design.Item Modelo didáctico para el desarrollo del pensamiento matemático a través de la modelación matemática en situaciones de riesgo ambiental(Universidad Antonio Nariño) González González, Ana Elizabeth; Rojas Velázquez, Osvaldo JesúsModelling has become one of the general processes of mathematical activity that allows enhancing mathematical thinking. For its part, mathematical thinking contributes to the development of logical reasoning, creativity, and allows the articulation of knowledge of different types and from different areas. In this sense, mathematics can help minimize environmental risks and use this didactic resource to motivate students towards their study.Item Modelo pedagógico inclusivo para la enseñanza aprendizaje de la matemática a través de la resolución de problemas en niños de grado quinto con trastorno por déficit de atención e hiperactividad(Universidad Antonio Nariño) Zabaleta Mesino, Randy; Rojas Velázquez, Osvaldo JesúsA robust process of teaching and learning mathematics in the fifth grade is important to provide solid knowledge and skills to students, specifically those with a diagnosis of Attention Deficit Hyperactivity Disorder (ADHD). In these students, among other difficulties, concentration in the lessons taught in the classroom is limited, which has a negative influence on the understanding of the fundamental concepts of mathematics, affecting the learning of these at their schooling level.Item Modelo pedagógico para la formación de los docentes de matemáticas de la educación básica primaria usando como herramienta el laboratorio de matemáticas(Universidad Antonio Nariño) Romero Huertas, Alfonso; Falk de Losada, MaríaThe purpose of this research was to build a continuous training model for practicing teachers at the basic primary education level who work in the area of mathematics in the Department of Cundinamarca’s schools, using the laboratory as a tool through which is strengthened the disciplinary and pedagogical knowledge of the content in the area in question.Item El razonamiento repetido en el aprendizaje de la matemática(Universidad Antonio Nariño) Quintero Suica, Diana Isabel; Guerrero Chacón, Gerardo AntonioConsidering the importance of repeated reasoning in the mathematics classroom as a way of consolidating learning, this research seeks to advance in the description, explanation, and enrichment of the processes underlying this reasoning (internalization; organization and reorganization; and retention of knowledge), within the framework of the principle of repeated reasoning postulated by the DNR.Item Sistemas Dinámicos No Lineales a Partir de Series de Tiempo para el Análisis y Control de Pilas de Combustible(Universidad Antonio Nariño) Cruz Cardozo, José Laureano; Gutiérrez Salamanca, Rafael María; Hernández Duarte, Andrés IgnacioThis work presents a procedure for constructing models of nonlinear dynamic systems that exhibit deterministic chaos behaviors based on time series data. The procedure involves extracting information from the time series to reconstruct the dynamic system in phase space, using second-order equations and three variables. We implemented this procedure in Python as a software and tested it on the well-known Lorenz system, extensively studied in chaos theory.Item El teorema de bayes en el proceso de formación de los estudiantes de medicina. una herramienta para su actuación profesional(Universidad Antonio Nariño) Pérez Duarte, Luis Fernando; Monterrey Gutiérrez, Pedro Agustín; Rojas Velázquez, Osvaldo JesúsBayes' theorem is dealt with in Biostatistics courses in Medical Careers, but its presentation follows the guidelines of Statistics books and in general it is not linked to the problems of medical practice in the context of Information-Based Medicine. Evidence. In this sense, the improvement of the subject of Probabilities is imposed, in the course of Biostatistics in Medicine. In the research, a didactic model is implemented to strengthen the teaching-learning process of Bayes' theorem, in the medical students of the Antonio Nariño University, within the framework of applications to diagnostic tests in the context of Medicine Based on the evidence. With the didactic proposal based on the model, it is possible to: increase the number of students who correctly use Bayes' theorem and the total probability; create conceptual networks to improve skills in the use of probabilities; facilitate the creation of mechanisms where students formulate heuristics to solve practical problems in the context of medicine and prepare students to improve clinical decisions, based on a knowledge of the possibilities of applying Bayes' theorem in the process of clinical diagnosis.Item Transición de la matemática de la escuela secundaria a la de la universidad a través del énfasis en la solución de problemas matemáticos(Universidad Antonio Nariño) Peña Moreno, Renne Andrés; Sánchez Lamoneda, RafaelIt is well known that the transition between high school mathematics (predominantly procedural) and university mathematics (structured by definitions, theorems and proofs) demands a profound change in the ways of understanding and thinking in mathematics which few students manage to avoid without shocks. Several studies show that the student often confronts the new demands by trying to memorize definitions and proofs without appropriating new theories and not knowing how to take advantage of new ways of thinking mathematicallyItem Valoración del alcance de la teoría de las representaciones semióticas de Duval para caracterizar el pensamiento matemático mostrado por estudiantes que participan en los exámenes de olimpiadas colombianas de matemáticas(Universidad Antonio Nariño) Guerrero Morales, Lexander; Falk de Losada, MaríaRaymond Duval's theory of semiotic representations constitutes a semiotic approach to Mathematics Education that proposes explaining complex phenomena such as the cognitive functioning of Mathematical Thinking and comprehension in mathematics, starting only by taking into account such representations and their transformations.