Estudiamos las concepciones de alumnos universitarios sobre el infinito matemático, mediante un cuestionario escrito individual. Los participantes fueron 120 estudiantes ingresantes y avanzados de distintas carreras
146Educación MatEMática, vol. 28, núM. 3, diciEMbrE dE 2016 más compleja, la infinitista, sólo fue explicitada por estudiantes universitarios, según dos enfoques: pensar la cardinalidad de los conjuntos infinitos como una única cantidad infinita, o concebir distintos cardinales infinitos, este último expresado sólo por estudiantes avanzados de matemática.Palabras clave: conjuntos numéricos, infinito cardinal, educación secundaria, estudiantes universitarios.Abstract: We studied how students with different mathematical background conceive infinite cardinality of number sets. We analyzed a task in which high school and college students were requested to compare infinite number sets. Students were classified according to their ideas on infinity. Using this classification together with the students' level of math education, we performed a correspondence factorial analysis. A gradient was found in the depth of students' ideas. At one end we found what we called horror infiniti, based students propensity avoid infinity and instead construe it as something undefined. These views were associated with students with less mathematical education. In an intermediate zone, the finitist conception was placed. It was the most frequent way of thinking among the participants of the study, with three versions: tacitly infinitist, explicitly finitist, or taking the integers as model of inclusion. At the other end, the infinitist conception was placed. It was present among students with college mathematical education, according to two types: thinking of the cardinality of number sets as a unique infinite quantity; or conceiving different infinite cardinals. The latter was found only in advanced mathematics students.
Drawing on a mixed-methods cross-cultural study undertaken in five locations in Argentina, Denmark, Hong Kong, England and the United States in 2018, this paper explores how children (aged five and seven) conceive of playfulness. Following a card-sorting task, 387 children selected familiar activities that they felt were most representative of play and not-play and explained their reasons. The children's justifications were fully transcribed, and five corpora were created (one per site). Lexicometry was applied, generating sets of the characteristic responses per age in each site. In-depth qualitative interpretation of these modal responses revealed nine dimensions across play and not-play: pleasure, social context, materials, movement, agency, risk, goal, time and focus. Commonalities revealed that children's ideas around play are not aligned with specific activities but with the sense of agency in a secure physical and social context when carrying out an activity experienced as an end in itself. Implications for playful pedagogies highlight the need to open up play with opportunities for children's choice and initiative, confident exploration and immersion in the activities in which they participate. RESUMENA partir de un estudio multicultural de métodos mixtos realizado en 2018 en cinco localidades de Argentina, Dinamarca, Hong Kong, Reino Unido y Estados Unidos, en este artículo se exploran las concepciones acerca de la actividad lúdica de niños de cinco y siete años. Tras una tarea de clasificación de tarjetas, 387 niñas y niños seleccionaron aquellas actividades familiares que consideraban más representativas de juego y aquellas más ajenas al juego y explicaron sus razones. Se realizó una transcripción completa de sus justificaciones y se crearon cinco corpus (uno ARTICLE HISTORY
El presente trabajo está enmarcado en el proyecto de investigación: Lademostración en geometría en la formación de profesores, que con el objetivogeneral de estudiar el proceso de aprendizaje de la demostración en geometría deestudiantes de Profesorado de Matemática, se propone en particular indagaracerca de las concepciones de estos estudiantes sobre la demostraciónmatemática.Reportamos aquí el análisis de una entrevista realizada a estos estudiantes con elfin de obtener indicios de sus concepciones sobre el aprendizaje de lademostración y las posibles relaciones de estas ideas con las pruebas que estosestudiantes producen frente a un problema de demostrar. Encontramosprincipalmente las siguientes tres ideas: se aprende a demostrar estudiandológica; a demostrar se aprende demostrando y se aprende de entenderdemostraciones bien presentadas; relacionadas con estudiantes que producenpruebas ingenuas; de ejemplo genérico-crucial y formales respectivamente.
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