Examinando por Autor "Vergel Causado, Rodolfo"
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Ítem Un acercamiento a los procesos de objetivación y subjetivación en el contexto de tareas histórico-culturales del logaritmo: una experiencia con estudiantes de grado novenoChaparro Rueda, Pedro Elías; Vergel Causado, RodolfoThe essence of the research is the simultaneous identification and description of the processes of objectification and subjectivation that arise when students face tasks in the sense of a historical-cultural reflection of the logarithm. The methodological treatment of the problem is concerned with an informed design of tasks and sets in motion a multimodal analysis strategy, part of the conceptualization of mathematical thought as a historical-cultural entity; More detailed information about the ways students are done logistically. The idea of semiotics that underlies the work of degree emphasizes the processes of communication and meaning among students.Ítem Un acercamiento a los procesos de objetivación y subjetivación en el contexto de tareas sobre razones trigonométricas: una experiencia con estudiantes de grado novenoGuerrero Osorio, Yeison Andrés; Sáenz Martínez, Paola Catterine; Vergel Causado, RodolfoThe research work focuses on documenting the processes of objectification and subjectivation from the Objectification Theory (OT) proposed by Luis Radford, these processes emerge from the interaction between teacher and students during the mathematical activity to return to the trigonometric ratios object in other object of conscience and thought. In order to take this study, we take the identification and description of semiotic media that emerge in the mathematical activity in solving tasks with the intention of updating knowledge was taken into account. In addition, the document proposes a possible characterization of trigonometric thinking from the (OT) that provides inputs for further research.Ítem La actividad argumentativa que emerge en estudiantes de grado noveno en torno a la demostración en geometríaArevalo Vanegas, Camilo; Vergel Causado, RodolfoA job with the use of problem situations that promote mathematical argument in the classroom from a context of socialization and building expertise to determine whether it is possible to promote the argumentative activity is proposed, will be developed by a group of ninth graders from school Forests Sherwood private, located in the municipality of Chia. The research will analyze the argumentative schemes emerging in the demonstration activity of students; taking the argument as justification and validation of statements made during the demonstration process, thus identifying and describing patterns that emerge in the process. With reflective elements to be determined, it is expected that a teacher can consider or infer more assertive criteria for assessing the knowledge that a student uses when faced with a problem-solving process; reflections on teaching demonstration in geometry and analysis schemes argument underlying the demonstration activity.Ítem Análisis didáctico a un proceso de instrucción del método de integración por partesMateus Nieves, Enrique; Vergel Causado, Rodolfo; Vasco Uribe, Carlos EduardoThis is a systematic didactic analysis that analyzes a process of instruction of the method of integration by parts. It is a qualitative research based on the case study and focused on a particular educational context. The observation methodology used was the description of class sessions. We apply the ontosemiotic approach of mathematical cognition as a theoretical framework and develop the proposed analysis categories. Specifically, the notion of didactic suitability (description, explanation and evaluation) of the mathematical instruction processes. This analysis shows an X-ray of what happened in the classroom and why. It is important to recognize that the relationship between the relationship of teaching and the meanings assigned to mathematical objects that institutionalize are not disconnected from the context in which they develop given the implication that it has in the evolution and construction of meaning implemented ; for that reason we propose to do less formal teaching processes where other techniques are included, such as the incorporation of Tics among others. This research in which we tried to look at the role of context in the processes followed by a teacher chosen to institutionalize the construction of meaning of the method of integration by parts (MIP) can be a guide for other teachers interested in improving their pedagogical practices and be replicated in other objects of basic, medium or higher level, typical of the teaching of mathematics.Ítem Una aproximación a la caracterización de la analiticidad a partir de tareas sobre transformación de lenguaje natural a lenguaje algebraico en un contexto variacionalDíaz Guarín, Mónica Andrea; García Leguizamón, Jimena; Vergel Causado, RodolfoThis research addresses the characterization of algebraic thinking that is proposed from the theory of objectification, specifically in one of its components: analyticity. This links the sense of the indeterminate and its semiotic expression. Likewise, the productions of a group of seventh grade students are interpreted when addressing tasks of transformation from natural language to algebraic language in a variational context, making an approximation of the characterization of the analytic component. The semiotic means of objectification present in his written, verbal and gestural productions are described; Generalization types are established and which of them correspond to algebraic productions are defined, describing the nature of the analytic component. This research is qualitative and interpretive-descriptive and uses multimodal analysis as a methodological framework. The results show that the productions made by the students correspond to two types of generalization: some of an arithmetic nature and others, of an algebraic nature. The description of the nature of analyticity is deepened from the semiotic means that emerge when solving tasks, emphasizing the way they are present in the generalization process.Ítem Características del cambio y la variación asociadas al uso de recursos semióticos en la generalización de patrones figurales: una experiencia con estudiantes de grado octavoContreras Griego, Andres Alberto; Vergel Causado, RodolfoThe following study documents the identification and description of the characteristics of change and variation associated with the use of semiotic resources that emerge in the productions of eighth grade students in generalization tasks on sequences of figural patterns. In this sense, it is approached through elements of the Theory of Objectification (Radford, 2006b, 2018a, 2020a) by means of a multimodal analysis of human thought (Radford, Edwards and Arzarello, 2009), where, based on them, three tasks of figural sequences were designed, created, adapted and implemented with aspects of the cultural context of the Guajiro people, such as weaving and corn cultivation. The analysis of the results shows the emergence of the use of semiotic resources of objectification through corporeal actions (indexical gestures, perceptual activity, rhythm and speech), mediated by written and spoken signs (key words and phrases, mathematical and alphanumeric symbols, linguistic resources, spatial, temporal and mode deictics), and artifacts (iconic figural representation of the weaving, tables and calculator), with which they identify the intervening variables thanks to the multimodal (multisemiotic) activity with the great richness and multiplicity of the coordinated and reduced use of not only cognitive but also physical and perceptual resources, through multiple forms of expression and representation and allows them to encounter characteristics of change and variation such as: (i) what changes and remains constant; (ii) recognition of variation; (iii) quantification of change; (iv) identification of intervening variables; (v) the field of variation or the universe of each variable; (vi) covariation relationships at the factual, contextual and symbolic level of generalization between intervening quantities as processes of objectification.Ítem Caracterización de la subitización perceptual y conceptual en niños de grado primero, a través de una serie de tareas bajo el enfoque de trayectorias hipotéticas de aprendizajeBarrera Gómez, Rocío del Pilar; Vergel Causado, Rodolfo; Pontón Ladino, TeresaAt present in mathematics education, many research in these area focus in the teaching and learning the mathematics in all level of education, begins in low grades until university grade and post-doctoral. For these research in specific, I postulate the methodology that it is deep into in field of interpretation research, making teaching experiments, the objective of these it is analyze the learning in context, through the Trajectory Hypothetic of Learning perspective, or THA how contribution in development of Mathematics knowledge. The THA it is an instrument or tool to make possible the advance and evaluation the process mathematics linking with numerical senses development, that kids appropriate since childhood, schooling and all theirs lives. Between these first mathematics process, found to deep the Subitizacion, which have been studding for researches Clements and Sarama (2015) with kids in first levels of schooling or childhood. The research of these authors can show five arithmetic trajectories for the development of numeric senses, which restart in the subitizacion trajectory for these research, look into with kids the first grade between six and seven years in schooling of primary school of a public school. In the trajectory hypothetic learning of subtizacion or THAS its characteristic for process mathematic how perpetual or conceptual where observe the development and production mathematic through the sequence of work that have to address.Ítem Comprensión de enunciados de problemas multiplicativos: algunas dificultades semiótico-cognitivasLondoño Morales, Yerry; Vergel Causado, RodolfoIn this paper, the difficulties that arise in the understanding of multiplicative problem statements are identified and described from a semiotic-cognitive perspective. For this, this work is structured in two stages. In the first stage, the representative statements of the field of statements of multiplicative problems are determined. In the second stage, a series of observations is made to the 6th grade students of the Colegio Entre Nubes School District Educational Institution of the city of Bogotá, with respect to how they understand these problem statements and how their understanding varies when making modifications to these statements. The modifications to the representative statements of the field of statements of multiplicative problems had two versions: With respect to the first version, the representative statements were modified in relation to the linguistic marks or with the intention of varying the background that can arise in the student to the Read the problem statement. With respect to the second version, figurative or iconic auxiliary representations were added to the representative statements with the objective of demonstrating the incidence of these representations in the comprehension of a multiplicative problem statement. The results of this work show that the difficulties in understanding sentences of multiplicative problems are due to the incidence that has: a) the factors of the variation of the wording of the statement, since these determine the way in which the cognitive content is explained of the multiplicative problem statements (Duval, 1999b); b) the indiscriminate use of auxiliary representations that support the multiplicative problem statement, since these representations make sense and are meaningful in the understanding of these statements if and only have been intended for teaching students; c) the interpretations made by students from the cultural background when reading a problem statement, since the interpretations they make of the statements open a gap between the meaning and content thought by the author of the statements and understood by the student; and d) the linguistic marks in the statement, given that the linguistic marks can attribute to an enunciation of mathematical problem an intention to mobilize elements of the conceptual structure (Pontoon, 2012). These results lead to affirm that the understanding of multiplicative problem statements occurs when the student achieves the capacity to understand and make any change in the representation register, that is, to be able to face the cognitive complexity of the conversion ( Duval, 2016).Ítem Desarrollo del pensamiento variacional en estudiantes de grado novenoGómez Ospina, Oscar Mauricio; Vergel Causado, RodolfoThe objective of this work is to study the characteristics present in the development of the variational thinking associated to the change and variational processes in a group of ninth graders. Some tasks taken from national and international literature were adapted and applied with the aim to foster the variational thinking in this group from the change and variational processes. Likewise, the evidenced processes in the classroom intervention were described with the purpose of systematizing the development and variational thinking processes in the ninth graders, give feedback and promote the pedagogical action the classrooms of our country.Ítem Dificultades, conflictos y obstáculos en las rácticas educativas universitarias de iniciación al cálculo diferencial —PEUC— en estudiantes de ingenieríaNeira Sanabria, Gloria Ines; Vergel Causado, Rodolfo; Vasco Uribe, Carlos EduardoThis research focuses on identifying, describing, characterizing and explaining the difficulties, conflicts and obstacles that can be inferred from the study of some university educational practices of the initial work in the differential calculus in first semester students of Engineering, how they emerge, and what possible causal relationships could be established for its explanation, initially configuring a comprehension framework for the conceptualization of some theoretical constructs related to the notion of obstacle. The theories of Brousseau, Sierpinska, Artigue, Godino, Radford and D'Amore, as well as the studies of Sfard on reification, and of Tall on conceptual image ("concept image") and procept ("procept") were used. . The research is qualitative, descriptive-interpretative; The type of study is exploratory, with the case study method, in which non-participant observation and structured task-based interviewing were used.Ítem La dimensión gestual en la generalización de patrones en estudiantes de cuarto grado de educación primariaMoreno Giraldo, Gustavo Adolfo; Vergel Causado, RodolfoThis document documents the identification and characterization of the gestures used by fourth grade students of primary basic education of the Monseñor Manuel María Camargo Gymnasium, as a support to the process of algebraic generalization of patterns. For this, this work is based on the framework of the cultural theory of objectification and takes as a methodological framework multimodal analysis (Arzarello, 2006). Taking into account the theoretical and methodological framework, four tasks associated with figurative sequences with tabular support are designed. The implementation and analysis of the results of the proposal show that students reach an algebraic generalization of factual type that is evidenced by gestures such as: indexical, figural, formulaic and algorithmic imagination. The present investigation reveals that in the process of objectification of knowledge students can employ various semiotic means of objectification, not only the written discourse but also the gesture and the oral discourse.Ítem Elementos de la heurística de Arquímedes identificados en estudiantes de grado noveno en la comparación de magnitudesCastañeda Moncada, Carlos Andrés; Vergel Causado, RodolfoThe research work developed within the framework of the Master's Degree in Education of the Universidad Distrital Francisco José de Caldas is presented. It was developed in the second semester of 2016, with twelve ninth grade students, the main interest of this degree work was to recognize if students approached a model of thought spontaneously, from the design and application of a sequence of six activities that incorporated elements of Archimedes' heuristics, in the comparison of magnitudes supported by physical experimentation and dynamic geometry. The methodology in which this work was framed was in qualitative research from Denzin & Lincoln (1994). As a result of the research, identification and description of students' heuristics was achieved where it was possible to demonstrate approximations to the elements of Archimedes heuristics in the comparison of magnitudes, relating the actions of students within five strategies that were highlighted in the development of activities. Finally, it could be concluded that the design and implementation of the sequence of activities was structured from two elements of Archimedes heuristics, the mechanical hypotheses and the compositional hypotheses, the former placing emphasis on experimentation from notions and propositions of static that appeared spontaneously in the implementation of activities. The second ones allowed the students to put into play the composition of areas by strings or parallel lines under some elements of euclidean geometry.Ítem La emergencia del pensamiento algebraico en adultosAlméciga Ruiz, Hasbleydy Lizeth; Vergel Causado, RodolfoIn this document, a characterization of the emergence of algebraic thinking is carried out, taking into account as population object of study adults of the eleventh grade of non-formal education. All of them seen from the objectification processes mobilized by the students in the middle of the activity, in which the linear figurative patterns are tasked with tabular support.Ítem La evaluación desde la teoría cultural de la objetivación : una experiencia con estudiantes de grado octavoBautista Albornoz, Sandra Yamile; Cardozo Limas, Juan Carlos; Vergel Causado, RodolfoActually, newest dynamics in classroom and new points of view in front of teaching and learning, require in addition some moderns ways of evaluate, better, to assess. Despite of interest for improve the educational practicing, the evaluation is one of the aspects that show more resistance to change. Some authors consider the evaluation as touch stone in scholar curriculum, what means that if we change the others components but we leave quiet the evaluation system used by teacher, we can wait changes in the classroom because nothing new going to happen (Moreno, 2014). Following this perspective, will be important to ask ¿why is not the same to assess and to qualify? is clear, ¿what do we assess?, ¿which will be a right method of assessment that would take into account all the aspects in the classroom? ¿What would be assessed: a thematic comprehensions, a way of thinking and interaction in the classroom, or the way that the student approximate to the object that want to apprehend in a determinate context? Those questions evoke a wide context, in as much as these can be analyzed in different point of views. Our interest is oriented to theory cultural of objetivation, theory that make as priority the learning gotten from the sociocultural interaction, from the touch with other and from all the artifacts put in a community, that engaged with the knowledge in itself for thinking and being in mathematics. We star from conception down this perspective, is necessary a new stance in front to valuation practices in the classroom in as much a technical evaluation as this has been done distance of assess teaching, the way how students interact with others for make a situations solutions and concepts that born in this line when is observed all the process linked through classwork that are relational with learn algebra.Ítem La Evaluación desde la teoría cultural de la objetivación : una experiencia con estudiantes de grado octavo.Cardozo Limas, Juan Carlos; Bautista Albornoz, Sandra Yamile; Vergel Causado, RodolfoActually, newest dynamics in classroom and new points of view in front of teaching and learning, require in addition some moderns ways of evaluate, better, to assess. Despite of interest for improve the educational practicing, the evaluation is one of the aspects that show more resistance to change. Some authors consider the evaluation as touch stone in scholar curriculum, what means that if we change the others components but we leave quiet the evaluation system used by teacher, we can wait changes in the classroom because nothing new going to happen (Moreno, 2014). Following this perspective, will be important to ask ¿why is not the same to assess and to qualify? is clear, ¿what do we assess?, ¿which will be a right method of assessment that would take into account all the aspects in the classroom? ¿What would be assessed: a thematic comprehensions, a way of thinking and interaction in the classroom, or the way that the student approximate to the object that want to apprehend in a determinate context? Those questions evoke a wide context, in as much as these can be analyzed in different point of views. Our interest is oriented to theory cultural of objetivation, theory that make as priority the learning gotten from the sociocultural interaction, from the touch with other and from all the artifacts put in a community, that engaged with the knowledge in itself for thinking and being in mathematics. We star from conception down this perspective, is necessary a new stance in front to valuation practices in the classroom in as much a technical evaluation as this has been done distance of assess teaching, the way how students interact with others for make a situations solutions and concepts that born in this line when is observed all the process linked through classwork that are relational with learn algebra.Ítem Evolución de fórmulas corpóreas en procesos de generalización de patrones en estudiantes de cuarto grado de educación primariaSuárez Mendoza, Diana Pahola; Olarte Zabala, Christian Arturo; Vergel Causado, RodolfoThis research proposal addresses the teaching-learning of algebra in primary education, prior to the alphanumeric language and from the pattern generalization as an enhancing tool. From a sociocultural perspective of mathematics education, and supported by the multimodal methodology, the evolution of corporeal formulas is investigated, as an indication of algebraic thinking, towards more sophisticated forms in the generalization of pattern sequences. The analysis is made from the three problems of generalization (epistemological, phenomenological and semiotic), supported by the idea that the gestures, movements and signs evidence forms of algebraic thought that have intentions in front of a work of pattern generalization.Ítem Formas de pensamiento aditivo en estudiantes de tercero de primaria (8-9 años): una aproximación desde la teoría de la objetivaciónPantano Mogollón, Óscar Leonardo; Vergel Causado, Rodolfo; Radford Hernández, LuisThe research entitled Forms of additive thinking in third grade students (8-9 years old): an approach from the Theory of Objectification characterizes forms of additive thinking that appear, are produced, through the encounter with historical-cultural arithmetic knowledge in the joint labor that emerges between third grade students of Primary Basic Education and the teacher in the process of solving additive tasks in the naturals. These forms of thinking are produced through sensitive and material forms of perception, gestures, corporeality, symbolization, discursivity and use of artifacts.Ítem Formas de pensamiento algebraico temprano en alumnos de cuarto y quinto grados de educación básica primaria (9-10 años)Vergel Causado, Rodolfo; Vasco Uribe, Carlos EduardoThe possibility of promoting the development of algebraic thinking in the early years of schooling is an issue that increasingly generates more interest for research in mathematics education. In particular, generalization of patterns is considered one of the most important ways of introducing algebra in school. However this necessarily demand develop an enlarged perspective on the nature of school algebra, consider a dialectical relationship between forms of algebraic thinking and ways of solving the problems of generalization pattern, which introduces a problem in terms of the constitution of algebraic thinking in young students. In this process of generalization of patterns we must consider that acts of knowledge by students include different sensory modalities, such as tactile, perceptual, the kinesthetic, etc., which become integral parts of cognitive processes. This is what has been called in the international context (Arzarello, 2006) the multimodal nature of human cognition. We are therefore faced with the need to recognize all those discursive situations (oral and written), gestural and procedural evidencing in student attempts to build explanations and arguments on general structures and mindsets, and their arguments and explanations are supported by individuals or situations into concrete actions. In epistemological terms, we are suggesting ways of conceptualizing, knowing and thinking can not be adequately described only in terms of discursive practices. It is important to consider the cognitive, physical and perceptual students mobilize resources when working with mathematical ideas. These resources or modalities include symbolic and oral communication as well as drawings, gestures, manipulation of artifacts and body movement (Arzarello, 2006; Radford, Edwards & Arzarello, 2009).Ítem Formas de pensamiento algebraico temprano en alumnos de cuarto y quinto grados de educación básica primaria (9-10 años)(Universidad Distrital Francisco José de Caldas) Vergel Causado, RodolfoÍtem Generalización de patrones: una forma de desarrollar el pensamiento algebraicoRamírez Orozco, Sandra Milena; Vergel Causado, RodolfoIn the present work the processes of generalization (arithmetic-algebraic) developed by the eighth grade students of the Colegio Entre Nubes Sur Oriental IED, when confronted with tasks of generalization of patterns of sequence sequences, in order to enhance algebraic thinking. The tasks proposed were intended to analyze the student's way of changing, ie, how to increase or decrease the terms of the sequence, in other words, the spatial and numerical structure; which leads them to conjecture the form of the following terms; Finally, formulate a procedure that allows establishing the pattern of behavior, through a joint activity in different working groups, based on the Cultural Theory of Objectivation, in which learning is defined as "social processes of making of critical conscience in which different semiotic means put in play by the students (language, gestures, symbols, artefacts, etc.) are involved " (Miranda, Radford, & Guzmán, 2013)