scholarly journals A Theoretical Model for the Development of Mathematical Talent through Mathematical Creativity

2020 ◽  
Vol 10 (4) ◽  
pp. 118
Author(s):  
Zeidy M. Barraza-García ◽  
Avenilde Romo-Vázquez ◽  
Solange Roa-Fuentes
Keyword(s):  
Theoretical Model ◽  
Mathematical Creativity ◽  
Mathematical Activity ◽  
New Techniques ◽  
Mathematical Talent ◽  
Anthropological Theory ◽  
Anthropological Theory Of Didactics

This study was conducted from a perspective that adopts a broad vision of mathematical talent, defined as the potential that a subject manifests when confronting certain types of tasks, in a successful way, that generate creative mathematical activity. To analyse this, our study proposes a Praxeological Model of Mathematical Talent based on the Anthropological Theory of Didactics and the notion of mathematical creativity, which defines four technological functions: (1) producing new techniques; (2) optimizing those techniques (3); considering tasks from diverse angles; and (4) adapting techniques. Using this model, this study analyses the creative mathematical activity of students aged 10–12 years displayed as they sought to solve a series of infinite succession tasks proposed to encourage the construction of generalization processes. The setting is a Mathematics Club (a talent-promoting institution). The evaluation of results shows that the Praxeological Model of Mathematical Talent allows the emergence and analysis of mathematical creativity and, therefore, encourages the development of mathematical talent.

scholarly journals Los recorridos de estudio e investigación en la construcción de buenas prácticas docentes en los estudios de ingenieríaStudy and research course in the building of good teaching practices in the engineering studies

2020 ◽  
Vol 22 (2) ◽  
pp. 789-812
Author(s):  
Cecilio Fonseca ◽  
José Manuel Casas ◽  
Ixchel Dzohara Gutiérrez-Rodríguez ◽  
Xabier García-Martínez
Keyword(s):  
Teaching Practice ◽  
Research Process ◽  
First Year ◽  
Mathematical Activity ◽  
Good Teaching ◽  
Anthropological Theory ◽  
Considerable Portion ◽  
Teaching Of Mathematics ◽  
Anthropological Theory Of Didactics ◽  
Buenas Prácticas

ResumenEn este trabajo nos proponemos, utilizando la Teoría Antropológica de lo Didáctico y un modelo particular de Recorrido de Estudio e Investigación, articular modelos de prácticas docentes que se pueden trasladar al primer curso de las escuelas de ingeniería. Lo haremos con un ejemplo de práctica docente que recubre una parte importante del programa de Álgebra Lineal, prioriza la enseñanza funcional de las matemáticas, introduce la razón de ser de la actividad matemática siempre a partir de situaciones problemáticas, entiende la enseñanza como un proceso de investigación y asigna nuevas responsabilidades a las matemáticas, al profesor y a los alumnos.Palabras-clave: Teoría antropológica de lo didáctico, recorrido de estudio e investigación, razón de ser, enseñanza funcional de las matemáticas, buenas prácticas docentes.AbstractIn this work we provide practical teaching models that can be moved to the first year of Engineering schools, using the Anthropological Theory of Didactics and a particular Study and Research Course. We will procced with an example of teaching practice that covers a considerable portion of the Linear Algebra programme, prioritising the functional teaching of mathematics, introducing the reason for being of the mathematical activity from riddles, understanding teaching as a research process designating new responsibilities to the mathematics, to the teacher and to the students.Keywords: anthropological theory of didactics, study and research course, reason for being, functional teaching of mathematics, fine teaching practices.ResumoNeste trabalho propomos, a partir da Teoria Antropológica da Didática e de um modelo particular da Rota de Estudo e Pesquisa, articular modelos de práticas pedagógicas passíveis de transferência para o primeiro ano das escolas de engenharia. Faremos isso com um exemplo de prática de ensino que cobre uma parte importante do programa de Álgebra Linear, prioriza o ensino funcional da matemática, apresenta a lógica da atividade matemática sempre a partir de situações problemáticas, entende o ensino como um processo de pesquisar e atribuir novas responsabilidades à matemática, ao professor e aos alunos.Palavras-chave: Teoria antropológica da didática, Percurso de estudo e pesquisa, Razão de ser, Ensino funcional da matemática, Boas práticas de ensino.

scholarly journals Assessment of mediated interactivity within the scope of the Anthropological Theory of DidacticsValoración de la interactividad mediada en el ámbito de la Teoría Antropológica de la Didáctica

2020 ◽  
Vol 22 (4) ◽  
pp. 294-300
Author(s):  
Liliana Patricia Ospina Marulanda ◽  
César Augusto Delgado García
Keyword(s):  
Learning Outcomes ◽  
Preliminary Analysis ◽  
Summative Assessment ◽  
Assessment Practices ◽  
Anthropological Theory ◽  
Learning Content ◽  
Assessment Of Learning ◽  
Operational Learning ◽  
Made In ◽  
Anthropological Theory Of Didactics

AbstractWe present progress made in doctoral thesis «Configuration of the assessment practices of mathematics teachers at university». Preliminary analysis shows the predominance of «summative assessment» of learning, content-centered, aside from the teaching and study activities, producing poor operative learning outcomes. This didactic phenomenon entails the problem of establishing the conditions and constraints that hinder the development of a more functional kind of assessment that mediates these activities and obtain more operational learning. Finally, we construct the concept of assessment of mediated interactivity as a contribution to the design and management of didactic and mathematical praxeology.ResumenPresentamos los avances de la tesis doctoral: «Configuración de las prácticas evaluativas de los profesores de matemáticas en la universidad». Los análisis preliminares ponen de manifiesto el predominio de la «evaluación sumativa», centrada en contenidos, al margen de las actividades de enseñar y estudiar, produciendo aprendizajes poco operativos. Este fenómeno didáctico conduce a plantear el problema de establecer las condiciones y restricciones que dificultan o impiden el desarrollo de una evaluación más funcional, que medie en dichas actividades y logre aprendizajes más operativos. Finalmente, construimos el concepto de evaluación de la interactividad mediada como aporte al diseño de praxeologías didácticas y matemáticas.

scholarly journals Reference epistemological model: what form and function in school institutions?Modelo epistemológico de referencia: ¿qué forma y función en las instituciones escolares?

2020 ◽  
Vol 22 (4) ◽  
pp. 240-249
Author(s):  
Ignasi Florensa ◽  
Marianna Bosch ◽  
Josep Gascon
Keyword(s):  
Teacher Education ◽  
Reference Model ◽  
Form And Function ◽  
Anthropological Theory ◽  
Partial Representation ◽  
Epistemological Model ◽  
And Function ◽  
Education Courses ◽  
Anthropological Theory Of Didactics

ResumenMuchos problemas docentes están relacionados con la ausencia, en las instituciones escolares, de herramientas epistemológicas para diseñar, gestionar y evaluar procesos de estudio. Proponemos incluir entre dichas herramientas los mapas de cuestiones y respuestas que constituyen una representación parcial del modelo epistemológico de referencia. En este artículo resumimos las conclusiones de cuatro estudios experimentales que incluyen formación del profesorado y recorridos de estudio e investigación. Los resultados muestran las potencialidades de los mapas de cuestiones y respuestas y las nuevas cuestiones que se abren.Palabras clave: Teoría antropológica de la didáctica, Modelo epistemológica de referencia.AbstractMany teaching problems are related with the lack in the school institutions of epistemological tools to design, manage and evaluate study processes. We propose to include within these tools the question-answer maps as a partial representation of the reference epistemological models. In this paper we summarize the conclusions of four experiences including teacher education courses and study and research paths. The results show the potentialities of question – answer maps and new open questions.Keywords: Anthropological Theory of Didactics, Epistemological Reference Model

scholarly journals Praxéologies du professeur : analyse comparative de manuels scolaires dans l'enseignement des équations polynomiales du premier degréTeacher's Praxeologies: Comparative Analysis of the Textbook in Teaching First-Degree Polynomial Equations

2020 ◽  
Vol 22 (4) ◽  
pp. 224-231
Author(s):  
Edelweis Jose Tavares Barbosa ◽  
Anna Paula de Avelar Brito Lima
Keyword(s):  
Polynomial Equation ◽  
Classroom Teachers ◽  
Polynomial Equations ◽  
Degree Polynomial ◽  
Mots Clés ◽  
Anthropological Theory ◽  
The Common ◽  
Analyse Comparative ◽  
Théorie Anthropologique Du Didactique ◽  
Anthropological Theory Of Didactics

RésuméLe but de cet article est d'analyser, de manière comparative, les livres didactiques et les praxéologies mises en place par les enseignants dans leur pratique pédagogique, concernant l'enseignement des équations polynomiales du premier degré. Cette étude est faite dans le cadre de la théorie anthropologique du didactique (TAD) proposée par Yves Chevallard et ses collaborateurs (1999, 2002, 2009, 2010). La méthodologie est basée sur une approche ethnographique qualitative, dans laquelle les organisations mathématiques et didactiques de trois enseignants sont analysées en les comparant à celles des livres de référence. Les résultats indiquent qu'il existe une certaine conformité entre les praxéologies à enseigner, proposées par les auteurs des manuels scolaires et les praxéologies effectivement enseignées par les professeurs en classe. Les enseignants sont les organisateurs des tâches, des techniques et de la technologie de complexité croissante (FONSECA, 2004) qui sont rendus routinières ou problématiques en classe. La résolution d’une équation polynomiale du premier degré du type ax+b=c a été le point commun des trois professeurs, bien que deux des trois enseignants aient aussi travaillé des équations du type a1x+b1=a2x+b2.Mots-clés : Livres didactiques, Équations polynomiales du premier degré, Théorie Anthropologique du didactique.AbstractThe aim of this article was to analyze, comparatively, praxeologies in didactic books and praxeologies carried out by the teacher, concerning the teaching of polynomial equations of the first degree. This study is done within the framework of the Anthropological Theory of Didactics (ATD), proposed by Yves Chevallard and his collaborators (1999, 2002, 2009, 2010). The methodology consists of a qualitative ethnographic approach, in which the mathematical and didactic organizations of three teachers were compared with those of their reference books. The results indicate that there is some conformity between the praxeologies to be taught, proposed by the authors of the textbooks, and the praxeologies effectively taught by the teachers in the classroom. Teachers are the organizers of tasks, techniques, and technology of increasing complexity (FONSECA, 2004) that are made routine or problematic in the classroom. The resolution of a first-degree polynomial equation of the type ax+b=c was the common point among the three teachers, although two of the three teachers also worked on equations of the type a1x+b1=a2x+b2.Keywords: Didactic books, Polynomial equations of the first degree, Anthropological theory of didactics.

scholarly journals Research and study paths at the university: a praxeological model of reference related to costs calculationParcours de recherche et d'études à l'université: un modèle praxéologique de référence lié au calcul des coûts

2020 ◽  
Vol 22 (4) ◽  
pp. 563-578
Author(s):  
Diana Patricia Salgado ◽  
María Rita Otero ◽  
Verónica Parra
Keyword(s):  
Teaching Mathematics ◽  
Mots Clés ◽  
Anthropological Theory ◽  
Study Programme ◽  
The University ◽  
Théorie Anthropologique Du Didactique ◽  
Anthropological Theory Of Didactics ◽  
Course Of Study

AbstractThis work fits within a wider research whose general objective is teaching mathematics to non-mathematicians at the university, taking central assumptions of the Anthropological Theory of Didactics. This work proposes a praxeological model of reference related to a micro-entrepreneurship costs calculation. The generative question How to calculate micro-entrepreneurship costs? links mathematical and economic praxeologies. This model allows to go through a part of the study programme of a university calculus course.Keywords: Anthropological theory of the didactic; Course of study and research; Praxeological Reference Model.RésuméCe travail fait partie d’une recherche plus large dont l’objectif général est l’enseignement des mathématiques pour non-mathématiciens à l’université dans le cadre de la Théorie Anthropologique du Didactique. On propose un modèle praxéologique de référence sur le calcul de coûts d’une micro-entreprise. La question génératrice est Comment calculer les coûts dans une micro-entreprise? Elle associe plusieurs organisations mathématiques et économiques. Ce modèle permet de couvrir une partie du programme d’études d’un cours de Calcul du niveau universitaire. Mots-clés : Théorie anthropologique de la didactique, Parcours d'étude et de recherche, Modèle de référence praxéologique.

scholarly journals Relação Institucional Pessoal do Professor em sala de aula sob a ótica da Teoria Antropológica do Didático Personal institutional relationship of the teacher in the classroom from the perspective of the anthropological theory of didactics

2019 ◽  
Vol 20 (3) ◽  
Author(s):  
Edelweis Jose Tavares Barbosa ◽  
Anna Paula Avelar Brito Lima
Keyword(s):  
Personal Relationships ◽  
Polynomial Equations ◽  
Reference Book ◽  
Teaching Process ◽  
Doctoral Research ◽  
Anthropological Theory ◽  
Ethnographic Approach ◽  
Relationship Of ◽  
Anthropological Theory Of Didactics

Esse artigo apresenta os resultados de parte de uma pesquisa de doutorado cujo objetivo foi investigar as relações institucionais e pessoais de três professores em comparação com às praxeologias materializadas por esses professores em ação na sala de aula com o saber relativo as equações polinomiais do primeiro grau. A realização deste estudo está fundamentada na ótica da Teoria Antropológica do Didático (TAD). A metodologia se constituiu em uma abordagem qualitativa de cunho etnográfico. Os resultados indicam que os três professores, em parte, balizaram suas aulas nas sequências sugeridas pelos autores dos livros didáticos. Embora que, mesmo o professor escolhendo o livro de referência, vimos que ele faz adaptações no processo de ensino em sua sala de aula. <br>This article presents the results of part of a doctoral research whose objective was to investigate the institutional and personal relationships of three teachers in comparison to the praxeology materialized by these teachers in action in the classroom with the knowledge relative to the polynomial equations of the first degree. The accomplishment of this study is based on the perspective of the Anthropological Didactic Theory (ATD). The methodology was based on a qualitative ethnographic approach. The results indicate that the three teachers, in part, used their classes in the sequences suggested by the authors of the textbooks. Although that same teacher choosing the reference book, we saw that he makes adaptations in the teaching process in his classroom.

scholarly journals Paradigmas didácticos y reforma curricular: el caso de la teoría antropológica de lo didácticoDidactic paradigms and curricular reform: the case of the anthropological theory of the didactic

2020 ◽  
Vol 22 (4) ◽  
pp. 423-437
Author(s):  
Josep Gascón Pérez ◽  
Pedro Nicolás
Keyword(s):  
Curriculum Reform ◽  
Curricular Reform ◽  
Anthropological Theory ◽  
The World ◽  
Epistemological Model ◽  
Anthropological Theory Of Didactics

ResumenCaracterizamos un paradigma didáctico, sustentado en cierto modelo epistemológico de los conocimientos que están en juego, mediante tres elementos concurrentes: los fenómenos a los que responde; los fines que propugna, que son los que determinan la dirección del cambio que persigue; y los medios que propone para alcanzar dichos fines. Como medios para evitar las consecuencias del fenómeno global del «monumentalismo», la teoría antropológica de lo didáctico propone ciertas organizaciones didácticas (tanto a nivel pedagógico y disciplinar como en las diferentes áreas y sectores de la matemática escolar) compatibles con los paradigmas fundados en la indagación. Esta estrategia constituye una forma de avanzar hacia el paradigma del cuestionamiento del mundo y plantea una propuesta de cambio curricular.Palabras-clave: Paradigmas didácticos, Reforma curricular, Teoría antropológica de lo didáctico.Abstract.We characterize a didactic paradigm, based on a given epistemological model concerning the knowledge at stake, according to three concurrent elements: the phenomena to which this paradigm reacts; the proposed ends, which determine the direction of the pursued change; and the means offered to reach these ends. As means to overcome some consequences of the global phenomenon called “monumentalism”, the Anthropological Theory of the Didactic offers certain didactic organizations (living at the pedagogical and disciplinary level, area or sector of the scholar mathematics) compatible with inquiry-based paradigms. This strategy is a way to advance towards the paradigm of questioning the world and it sets out a curriculum shift.Keywords: Didactic paradigms, Curriculum reform, Anthropological theory of didactics.

Sign in / Sign up

Export Citation Format

Share Document