RESUMEN
The nature of the area of mathematical competitions as a design science is considered, historical roots of mathematical problem-solving competitions are traced, the complementary aspects of mathematics as theory building and as problem solving are touched upon in relation to the practice of competitions. Two historical figures, Euler and Erdos, emerge, and the appropriateness of many of Euler's mathematical ventures are seen as role models for competition mathematics as first put into practice in mathematical competitions towards the end of the nineteenth century. Distinctions and definitions are made, a venture into identifying competition syllabi and the principal types of reasoning employed in solving competition problems is explored, and a description of the many different types of competitions is considered. Interaction between the field of mathematics itself and problem-solving competitions is briefly explored, as are the possibilities that open when competitions and their access to huge amounts of data, both national and international, are taken into account in research belonging to mathematics education. Finally, the range of topics addressed in this special issue of ZDM is covered, along with some possible conclusions relating to the components of the overview.
RESUMEN
Esta investigación consiste en el diseño, ejecución y evaluación de un programa de intervención psicoeducativa basado en imágenes, aplicado a nueve niños con Trastorno Generalizado del Desarrollo (TGD) de tipo autista, cuyas edades fluctuaban entre los 3 y 8 años de edad en Temuco. El programa se enfocó para activar el desarrollo de las dimensiones de anticipación y flexibilidad en niños con TGD. Con el propósito de determinar el perfil de desarrollo inicial de los participantes, se les aplicó el Inventario de Desarrollo de Espectro Autista IDEA. Una vez ejecutado el programa se les evaluó nuevamente con el mismo instrumento, evidenciándose diferencias significativas en las dimensiones de anticipación t = 0,039 (P<0.05), complementariamente se encontraron resultados no esperados, en la escala de trastorno de desarrollo social t = 0,040 (P<0.05). No hubo evidencias significativas en la dimensión de sentido de actividad propia, obteniéndose un resultado de t = 0, 57 (P>0, 05). Los resultados reflejan la efectividad de la aplicación del programa de intervención con imágenes cuyo propósito es aportar a la sistematización del trabajo con niños que padecen algún trastorno generalizado del desarrollo.
This investigation is about the design, execution and evaluation of a psycho-educative intervention program based on the use of images, tested on nine children with autistic type of Pervasive Developmental Disorder (PDD) from 3 to 8 years old in Temuco, Chile. This program was implemented to activate de development in the anticipation and flexibility dimensions en children with PDD. In order to determine the initial participants profile, the autism spectrum disorders development inventory IDEA was applied. After the program was finished, this instrument was also used, showing significant differences in the anticipation dimension with t = 0,039 (P<0.05). As a non expected result in the social development dimension there was found that t = 0,040 (P<0.05). There was no significant change in the own activity self perception dimension, obtaining a t = 0, 57 (P>0, 05). These results show the effectiveness of the image based intervention program applied which purpose is to make a contribution to systematize the work with children suffering some Pervasive Developmental Disorder.