Coherencias cognitivas vs matemáticas en el estudio del cambio

Se indaga en los desplazamientos entre herramientas de comunicación que ponen en juego profesores a la hora de comunicar qué y cómo cambia en una situación, en el marco de una línea de investigación en Pensamiento y Lenguaje Variacional (Proyecto Fondecyt Nº1030413 y Proyecto Diumce 06/07). Adscribimos a una mirada sistémica en la que entendemos a las matemáticas como una actividad humana en donde cobra vital importancia la persona haciendo matemáticas y no sólo el producto matemático. Por ello resulta relevante considerar -en la praxis educativa- las negociaciones y búsqueda de consenso entrelazadas éstas, con las acciones cognitivas de la persona al momento de enfrentarse a la solución de un problema. Asumimos una naturaleza de la noción de variación como red semántico operacional transversal, que imbrica distintos contenidos escolares de ciencia experimental y de matemática, particularmente aquellos de tiempo y velocidad. Entendemos al tiempo cotidiano formado por una red compleja de intencionalidades y coordinaciones que se estructuran a partir de las necesidades de coordinación con lo otro, con los otros y de las proyecciones intencionales hacia un futuro y un pasado, y, al tiempo matemático en su calidad de parámetro y figurado sobre la base de la metáfora de una distancia horizontal. A continuación se analizan, desde ese marco conceptual, las herramientas a que recurren profesores para comunicar cambios en una situación específica desarrollada en el marco las actividades del Proyecto de Investigación Las representaciones docentes del Cambio.

Funciones embotelladas

Esta es una propuesta didáctica que consta de una serie de actividades relacionadas con la representación gráfica de ciertas funciones y su vinculación con una representación en un contexto físico o icónico (dibujo de un recipiente). Las actividades son de dos tipos: Dadas las formas de los recipientes, bosquejar las gráficas correspondientes, teniendo en cuenta que la variable independiente es la altura del líquido y la variable dependiente es el área de la superficie del líquido (o bien el volumen del líquido dentro del recipiente); dadas las gráficas del área de la superficie del líquido versus altura, bosquejar los posibles recipientes correspondientes. Ambas actividades son diseñadas para propiciar el cambio de un sistema de representación a otro (Janvier, 1987; Duval, 1992, 1999; Hitt, 1992).

El concepto de límite como una aproximación óptima mediante la teoría APOE

El presente texto muestra una investigación que trabaja la enseñanza-aprendizaje de aspectos asociados al límite como aproximación optima, desde un análisis teórico (apoyado en APOE) que parte de una descomposición genética del objeto límite y brinda los primeros indicios de las construcciones mentales que poseen los estudiantes, luego se complementa con un parte de diseño e implementación de actividades en el aula con el ciclo de enseñanza ACE. Como la base es una investigación sobre la propia práctica del docente, se trata de un primer avance en este campo, lo que implica un estudio abierto a cualquier persona que requiera ampliarlo y/o complementarlo.

Tazas, cucharas y los vasos del Starbucks Coffee

Muchos son los líquidos (aceite, vinagre, leche, vino, licor...) y otros productos (sal, especies, arroz...) que son descritos en las recetas de cocina en relación al volumen. A veces se expresan dichos volúmenes en unidades precisas (litros, centilitros, mililitros...) pero en muchas ocasiones se presuponen las capacidades de determinados contenedores (cucharas, tazas, vasos...) para “aclarar” los volúmenes implicados. Cuando le recomiendan “ponga dos tazas de arroz por persona”, si usted no es del club de los iniciados, su estupor puede ser mayúsculo pues al abrir el armario de la cocina encontrará tazas de lo más diverso dispuestas a ser “la taza” recomendada.

Construyendo curvas con las manos

Toda persona que se dedica a enseñar sabe que la única manera de aprender algo es haciéndolo. Se aprende a montar en bicicleta montándola, como se aprende a escribir escribiendo; lo mismo ocurre con las matemáticas. No se trata de primero aprender matemáticas y luego ponerlas en práctica: se trata de aprender matemáticas practicándolas. Pero no es fácil encontrar un contexto en el que ejercitarnos en las matemáticas.

Historia de las matemáticas en el aula: experiencia desde un seminario permanente

En este articulo desarrollamos la experiencia de trabajo llevada a cabo por el Seminario Permanente «Historia de las Matemáticas», dependiente del CEP «Bajo Almanzora» de Cuevas del Almanzora (Almeria), durante el curso 1993/94.

Números insumisos. El ejército en el aula

En contra de lo que algunos creen, es posible abordar con éxito muchos problemas cotidianos de probabilidad, sin más instrumentos que una mente ordenada. A partir de un sencillo juego, intentaremos demostrar el mito de que el análisis del polémico sorteo de excedentes de cupo está vedado a cualquier persona que no sea de ciencias.

La matemática que protege de errores a los números de identificación

Con este material pretendemos divulgar la matemática implicada en los números de identificación tales como NIF, ISBN, EAN... La aritmética modular se utiliza para lijar el dígito de control, y algoritmos sencillos permiten al ordenador descubrir muchas falsificaciones o posibles errores en el número de identificación de la tarjeta, producto o persona. Los esquemas de codificación más usuales detectan todos los errores simples, esto es, cuando se confunde un dígito por otro pero, sin embargo, no descubren otros tipos de errores que, aunque son menos frecuentes, son posibles. El álgebra y la divisibilidad ayudan a elegir esquemas de codificación mas seguros.

Experiencia sobre la reforma de las enseñanzas medias en el CEI de Málaga

El C.E.I de Málaga se adhiere a la experimentación sobre la reforma de las enseñanza medias en el curso 84-85, cuando se inicia en la comunidad Andaluza y por tanto una año después que en territorio dependiente del M.E.C y otras comunidades autónomas, con competencias por lo que contábamos de partida con las programaciones propuestas por ellos, al menos como documento sobre el que empezar a discutir.

Generación y resolución de problemas: dos ejemplos

¿Bajo que condiciones una situación matemática es un problema para una persona? Tiene que interesarle y representar un reto, de forma que se sumerja en ella para intentar su resolución. Pero además, se detectan otras características en el proceso de generación y resolución de problemas: —Requiere un tiempo muy variable, imposible de predecir de antemano.— Lo que se busca suele ser bastante impreciso; las preguntas que perfilan un problema van surgiendo sincronizadas con las conjeturas y los resultados parciales o aproximados que se van encontrando. —Un problema puede abordarse con diferentes niveles de rigor y precisión. —La analogía es un recurso valioso, que puede guiar la búsqueda de soluciones.— Los medios disponibles (como una calculadora o un ordenador) abren nuevas vías de resolución y análisis que, de otro modo, estarían vedadas.

A case study of pre-midlife crisis: an extraordinary transformational episode in an ordinary life

This case study explored a single in-depth narrative of an episode of crisis. The participant, an English Jewish man in his late thirties (Guy), was selected using a ‘random purposeful’ design from a sample who had previously participated in a study on the experience of crisis in pre-midlife adulthood. From a subgroup of participants chosen for giving full accounts of both inner and outer dimensions of crisis, the individual was selected randomly. Data collection comprised two interviews followed by an email discussion. The crisis occurred in Guy’s late thirties, just before the midlife transition, and so can be considered a ‘pre-midlife’ crisis. It subsumed the period surrounding leaving a high-profile banking career and a dysfunctional marriage, and the ensuing attempts to rebuild life after this difficult and emotional period. Qualitative analysis found four trajectories of personal transformation over the course of the episode: Firstly there was a shift away from the use of a conventional persona to a more spontaneous and ‘authentic’ expression of self; secondly there was a move away from materialistic values toward relational values; thirdly a developing capacity to reflect on himself and his actions; fourthly an emerging feminine component of his personality. The case study portrays an extraordinary event in the life of an ordinary man approaching middle age. It illustrates the transformative nature of crisis in ordinary lives, the dramatic nature of narrative surrounding crisis, and also illustrates existing theory about the nature of adult crises.

What students can tell about lecturers when they are teaching: manifestations of confident and under-confident lecturers

Delivering a lecture requires confidence, a sound knowledge and well developed teaching skills (Cooper and Simonds, 2007, Quinn and Hughes, 2007). However, practitioners who are new to lecturing large groups in higher education may initially lack the confidence to do so which can manifest itself in their verbal and non-verbal cues and the fluency of their teaching skills. This results in the perception that students can identify the confident and non-confident teacher during a lecture (Street, 2007) and so potentially contributing to a lecturer’s level of anxiety prior to, and during, a lecture. Therefore, in the current educational climate of consumerisation, with the increased evaluation of teaching by students, having the ability to deliver high-quality, informed, and interesting lectures assumes greater significance for both lecturers and universities (Carr, 2007; Higher Education Founding Council 2008, Glass et al., 2006). This paper will present both the quantitative and qualitative data from a two-phase mixed method study with 75 nurse lecturers and 62 nursing students in one university in the United Kingdom. The study investigated the notion that lecturing has similarities to acting (Street, 2007). The findings presented here are concerned with how students perceived lecturers’ level of confidence and how lecturers believed they demonstrated confidence. In phase one a specifically designed questionnaire was distributed to both lecturers and students and a response rate of 91% (n=125) was achieved, while in phase two 12 in-depth semi-structured interviews were conducted with lecturers. Results suggested that students in a lecture could identify if the lecturer was confident or not by the way they performed a lecture. Students identified 57 manifestations of non-confidence and lecturers identified 85, while 57 manifestations of confidence were identified by students and 88 by lecturers. Overall, these fell into 12 main converse categories, ranging from body language to the use of space within the room. Both students and lecturers ranked body language, vocal qualities, delivery skills, involving the students and the ability to share knowledge as the most evident manifestations of confidence. Elements like good eye contact, smiling, speaking clearly and being fluent in the use of media recourses where all seen as manifestations confidence, conversely if these were poorly executed then a presentation of under confidence was evident. Furthermore, if the lecturer appeared enthusiastic it was clearly underpinned by the manifestation of a highly confidence lecturer who was secure in their knowledge base and teaching abilities: Some lecturers do appear enthusiastic but others don’t. I think the ones that do know what they are talking about, you can see it in their voice and in their lively body language. I think they are also good at involving the students even. I think the good ones are able to turn boring subjects into lively and interesting ones. (Student 50) Significantly more lecturers than students felt the lecturer should appear confident when lecturing. The lecturers stated it was particularly important to do so when they did not feel confident, because they were concerned with appearing capable. It seems that these students and lecturers perceived that expressive and apparently confident lecturers can make a positive impact on student groups in terms of involvement in lectures; the data also suggested the reverse, for the under confident lecturer. Findings from phase two indicated that these lecturers assumed a persona when lecturing, particularly, but not exclusively, when they were nervous. These lecturers went through a process of assuming and maintaining this persona before and during a lecture as a way of promoting their internal perceptions of confidence but also their outward manifestation of confidence. Although assuming a convincing persona may have a degree of deception about it, providing the knowledge communicated is accurate, the deception may aid rather than hinder learning, because enhances the delivery of a lecture. Therefore, the deception of acting a little more confidently than one feels might be justified when the lecturer knows the knowledge they are communicating is correct, unlike the Dr Fox Effect where the person delivering a lecture is an actor and does not know the subject in any detail or depth and where the deception to be justified (Naftulin, et al., 1973). In conclusion, these students and lecturers perceive that confident and enthusiastic lecturers communicate their passion for the subject in an interesting and meaningful manner through the use of their voice, body, space and interactions in such a way that shows confidence in their knowledge as well as their teaching abilities. If lecturers, therefore, can take a step back to consider how they deliver lectures in apparently confident ways this may increase their ability to engage their students and not only help them being perceived as good lecturers, but also contribute to the genuine act of education.

Museums as a factor for the social integration of art in the community. The experience of cultural volunteering by members of the senior community

After considering museums as cultural institutions responsible for preserving cultural memory and its evolution over time, this article describes the cultural practices within our society that are aimed at disseminating art and at reproducing and transmitting culture, history and identity. Further, it considers the key role that older people are steadily assuming in Spain’s ageing society. New social-empowerment activities based on volunteering by the elderly are linked to generativity because the individual and social groups acquire new skills through those activities, thereby strengthening a society for all ages. Never in the history of social work have so many older people been prepared to participate actively at the community level, and never has a social movement with these features gone so unnoticed by so many social agents.

Playback Theatre: the art of being oneself. A tool for empowerment and real change for individuals and communities

This article presents the application of a theatrical technique—Playback Theatre, which was developed in the United States during the 1970s—to social intervention, as a narrative and listening space that confers value and dignity upon the person and the unique and distinct individual experiences that facilitate their social and relational integration. This art of being oneself, as the author states, uses the oral tradition and spontaneous and creative communication of psychodrama and combines them with theatrical expression. This technique has been shown to be pertinent to both community social work and support groups for persons in problematic situations. The aim of this is to celebrate some specific moment of their lives, as individuals or as a community, and to define strategies for improving living conditions or resolving or alleviating conflicts. It is also used to assess the achievements of the proposed objectives, to strengthen the motivation to change and to transform existing relationships into collaborative ones. This is possible not only owing to the participation of persons, but also to the assumption of different roles that can permit the overcoming of certain traumatic events.In addition to support groups, it is used for the training and supervision of social work professionals. The theatrical technique in question allows them to assume roles as diverse as narrator, audience or actor, whether simultaneously or successively. Taking the role of «performer» or guide to the theatrical action requires prior preparation in order for the group of participants to be able to pool their individualities and their emotions and reflect on them. The participatory methodology that Playback Theatre proposes is important in community social work and is posed in a new and transformative key.

Intercultural competence in the area of drug dependencies

This article takes a multidimensional or biopsychosocial conception of drug dependency as its starting point. Within this analytical framework, we advocate making the intercultural dimension more visible, since it is essential for the design and implementation of integral intervention processes. We propose intercultural competence as a working model that can increase the capacities of institutions and professionals —a particularly important consideration in the case of social work— in order to effectively address the aforementioned cultural dimension. After an extensive review of the scientific literature, we have defined five processes that can contribute to strengthening an institution’s intercultural competence and four processes that can do the same for a professional’s intercultural competence. Though selected for application in the area of drug dependencies, all these processes can also prove useful in improving attention to any other kind of culturally diverse group or person.