História da matemática e teatro nas aulas sobre Teorema de Tales: um script proposto

This study will present the results of an investigation of how the history of mathematics and theater can contribute to the construction of mathematical knowledge of students in the 9th year of elementary school, through the experience, preparation and execution of a play, beyond presentation of the script. This brings a historical approach, defining space and time of events, putting the reader and viewer to do the route in the biography of Thales of Miletus (624-546 a.C), creating situations that led to the study and discussion of the content related to the episode possible to measure the height of the pyramid Khufu and the Theorem of Thales. That said, the pedagogical proposal implemented in this work was based on theoretical and methodological assumptions of the History of Mathematics and Theatre, drawing upon authors such as Mendes (2006), Miguel (1993), Gutierre (2010), Desgrandes (2011), Cabral (2012). Regarding the methodological procedures used qualitative research because it responds to particular issues, analyzing and interpreting the data generated in the research field. As methodological tools we have used participant observation, the questionnaire given to the students, field diary and dissertativos texts produced by students. The processing and analysis of data collected through the questionnaires were organized, classified and quantified in tables and graphs for easy viewing, interpretation, understanding and analysis of data. Data analysis corroborated our hypothesis and contributed to improving the use and display of the play as a motivating activity in mathematics classrooms. Thus, we consider that the script developed, ie the educational product proposed will bring significant contributions to the teaching of Mathematics in Primary Education

Teorema de Tales e suas aplicações

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES

Actividad interdisciplinar de Ciencias Naturales y Matemáticas en la Casa de Campo.

Se describe una actividad interdisciplinar, de Matemáticas y Ciencias Naturales, realizada en la Casa de Campo de Madrid. Se trata de conocer los árboles de la familia de las quercinias y averiguar la altura de algunos ejemplares y su adaptación a distintas zonas de España, utilizando herramientas matemáticas. Los objetivos son clasificar e identificar animales y plantas con ayuda de guías sencillas, valorando el beneficio que aportan a los seres humanos; aplicar el Teorema de Tales; y determinar medidas en figuras geométricas a partir de las medidas de otras semejantes. En cuanto a la metodología, dos días antes de comenzar la actividad, se pide a los alumnos que estudien, en cualquier guía de identificación de árboles, las especies que se encuentran en el recorrido para que sepan reconocerlas. El itinerario comienza en la estación de metro de Batán y discurre por la carretera que lleva al Parque de Atracciones y a la Venta de Batán; se visita la Encina de la Venta del Batán y la Glorieta de la Encina del Trillo; y se termina en el Centro de Información de la Casa de Campo.

Teoría de la semejanza : cursillo de Matemáticas para auxiliares.

Partiendo de la observación de la naturaleza, podemos atribuir a toda figura rígida diferentes posiciones, ligada cada una de ella a instantes diferentes; cada par de estas posiciones nos marcan un movimiento seguido por la figura. En realidad prescindiremos de todo tiempo para llegar a la noción general de movimiento inicial y final. Entonces tenemos un conjunto de pares ordenados (F, Fï) (F posición inicial y Fï posición final) de tal forma que a todo punto A de F le podemos hacer corresponder A de Fï siendo uno el homólogo de otro, su movimiento y su identidad. A partir de aquí desarrollaremos al teoría de la semejanza en un triángulo siguiendo el teorema de Tales de la homotecia. De gran importancia en matemáticas. Todo ello, hay que interpretarlo con la prudencia, pues no olvidemos que aún siguiendo las directrices de muchos matemáticos que consideran a la geometría como el estudio del grupo de los movimientos, no se trata de desterrar los clásicos métodos euclídeos, que al fin han sido la base de nuestros conocimientos geométricos.

Deducciones del teorema de Pitágoras a lo largo de la historia como recurso didáctico en el proceso de enseñanza-aprendizaje de la matemática

Las deducciones que a lo largo de la historia se han realizado en torno al teorema de Pitágoras pueden ayudar en el proceso de enseñanza-aprendizaje que realmente necesitan nuestros estudiantes, con el fin de que comprendan los conceptos a través de la reconstrucción de un método, de tal manera que no mecanicen reglas sino mas bien se logre aumentar y relacionar los conceptos adquiridos previamente de tal manera que se logre una mejor comprensión. Usaremos el enfoque histórico como una propuesta metodológica que actué como motivación para el alumno, ya que por medio de ella el estudiante descubrirá como generar los conceptos a través de métodos que aprenderá en clase. Discutiremos los conceptos y propiedades fundamentales de magnitudes, tales como la longitud y el área de figuras geométricas dadas en una y dos dimensiones, repasaremos los conceptos del producto notable del cuadrado de la suma de dos cantidades desde el punto de vista geométrico lo cual nos ayudara a inducir la demostración del teorema de Pitágoras a través de triángulos rectángulos notables e isósceles rectángulos, tomando en consideración el área de los cuadrados que se encuentra en los lados de dichos triángulos. Esto nos ayudara a recalcar la generalización del teorema de Pitágoras a través de figuras regulares. Las deducciones se harán pasando de la rama de la matemática llamada Algebra, conjugándola o dándole soporte con otra que muestra la forma estructural, como lo es la Geometría.

Deducciones del Teorema de Pitágoras a lo largo de la historia como recurso didáctico en el proceso enseñanza-aprendizaje de la matemática

Las deducciones que a lo largo de la historia se han realizado en torno al Teorema de Pitágoras pueden ayudar en el proceso de enseñanza-aprendizaje que realmente necesitan nuestros estudiantes, con el fin de que comprendan los conceptos a través de la reconstrucción de un método, de tal manera que no mecanicen reglas sino mas bien se logre aumentar y relacionar los conceptos adquiridos previamente de tal manera que se logre una mejor comprensión. Usaremos el enfoque histórico como una propuesta metodológica que actué como motivación para el alumno, ya que por medio de ella el estudiante descubrirá como generar los conceptos a través de métodos que aprenderá en clase. Discutiremos los conceptos y propiedades fundamentales de magnitudes, tales como la longitud y el área de figuras geométricas dadas en una y dos dimensiones, repasaremos los conceptos del producto notable del cuadrado de la suma de dos cantidades desde el punto de vista geométrico lo cual nos ayudara a inducir la demostración del Teorema de Pitágoras a través de triángulos rectángulos notables e isósceles rectángulos, tomando en consideración el área de los cuadrados que se encuentra en los lados de dichos triángulos. Esto nos ayudara a recalcar la generalización del Teorema de Pitágoras a través de figuras regulares. Las deducciones se harán pasando de la rama de la matemática llamada Álgebra, conjugándola o dándole soporte con otra que muestra la forma estructural, como lo es la Geometría.

Traveller’s Tales : The Expatriate English Language Teacher in the New Global Culture

Most of the research into ELT has focused on its linguistic and methodological aspects, which are based on Western scientific traditions. The contributions and experiences of English language teachers themselves, especially their work in overseas contexts, have frequently been overlooked. This volume aims to document the complexity of ELT as ‘work’ in new global economic and cultural conditions, and to explore how this complexity is realised in the everyday experiences of ELT teachers. The development of ELT from the colonial experience to its current status as a global commodity is explored; ELT is then situated in the discourses of globalisation, specifically within Appadurai’s theorisation of global flows of people, images, ideas, technology and money, or scapes. Within this framework, narratives are constructed from the experiences of Native-speaking English teachers. These reveal much about the personal, pedagogical and cultural dimensions of ELT work in non-Centre countries, and will contribute to a greater understanding of the intercultural dimensions of ELT for all those who work in it, and in related educational fields.

Traveller’s Tales : ELT teachers in a globalising world

This chapter summarizes a quasi-ethnographic case study of the lives and work of nine native-speaking English language teachers who have lived and worked outside their countries of origin for extended periods. The study aimed to document the complexity of ELT as ‘work’ in new global economic and cultural conditions, and to explore how this complexity is realised in the everyday experiences of ELT teachers.

Telling tales, shaping stories : the creative practitioner and the artful life story

Norman K. Denzin (1989) claims that the central assumption of the biographical method—that a life can be captured and represented in a text—is open to question. This paper explores Denzin’s statement by documenting the role of creative writers in re-presenting oral histories in two case studies from Queensland, Australia. The first, The Queensland Business Leaders Hall of Fame, was a commercial research project commissioned by the State Library of Queensland (SLQ) in 2009, and involved semi-formal qualitative interviews and digital stories. The second is an on-going practice-led PhD project, The Artful Life: Oral History and Fiction, which investigates the fictionalisation of oral histories. Both projects enter into a dialogue around the re-presentation of oral and life histories, with attention given to the critical scholarship and creative practice in the process. Creative writers represent a life having particular preoccupations with techniques that more closely align with fiction than non-fiction (Hirsch and Dixon 2008). In this context, oral history resources are viewed not so much as repositories of historical facts, but as ambiguous and fluid narrative sources. The comparison of the two case studies also demonstrates that the aims of a particular project dictate the nature of the re-presentation, revealing that writing about another’s life is a complex act of artful ‘shaping’. Alistair Thomson (2007) notes the growing interdisciplinary nature of oral history scholarship since the 1980s; oral histories are used increasingly in art-based contexts to produce diverse cultural artefacts, such as digital stories and works of fiction, which are very different from traditional histories. What are the methodological implications of such projects? This paper will draw on self-reflexive practice to explore this question.

Anthony Browne and the cultural capital of classic fairy tales

Prolific British author/illustrator Anthony Browne both participates in the classic fairy-tale tradition and appropriates its cultural capital, ultimately undertaking a process of self-canonisation alongside the dissemination of fairy tales. In reading Browne’s Hansel and Gretel (1981), The Tunnel (1989) and Into the Forest (2004), a trajectory emerges that moves from broadly intertextual to more exclusively self-referential modes of representation which reward readers of “Anthony Browne”, rather than readers of “fairy tales”. All three books depict ‘babes in the woods’ stories wherein child characters must negotiate some form of threat outside the home in order to return home safely. Thus, they represent childhood agency. However, these visions of agency are ultimately subordinated to logics of capital, which means that child readers of Browne’s fairy-tale books are overtly invited to identify with children who act, but are interpellated as privileged if they ‘know’. Bourdieu’s model of ‘cultural capital’ offers a lens for considering Browne’s production of ‘value’ for his own works within a broader cultural landscape which privileges literary fairy tales as a register of juvenile cultural competency. If cultural capital can be formulated most simply as the symbolic exchange value of approved modes of knowing and being, it is clearly helpful when trying to unpack logics of meaning within heavily intertextual or citational texts. It is also helpful thinking about what kinds of stories we as a culture choose to disseminate, choose to privilege, or choose to suppress. Zipes notes of fairy tales that, “the genre itself becomes a kind of institute that is involved in the socialization and acculturation of readers” (22). He elaborates that, “We initiate readers and expect them to learn the fairy-tale code as part of our responsibility in the civilizing process” (Zipes 29), so it is little wonder that Tatar describes fairy tales as “a vital part of our cultural capital” (xix). Although Browne is clearly interested in literary fairy tales, the most obvious strategies of self-canonisation take place in Browne’s work not in words but in pictures: hidden in plain sight, as illustration becomes self-reflexive citation.

The tales we tell : exploring the legal stories of Queensland women who kill

The bulk of the homicide research to date has focused on male offending, with little consideration given to women's offending and in particular, their constructions within the courtroom following a homicide-related charge. This thesis examines, in detail, nineteen homicide cases finalised in the Queensland Supreme Courts between 01/01/1997 and 31/12/2002, in order to document and discuss the various legal stories available to women who kill. Predominantly, two “stock stories” are available within the court. The first, presented by the defence, offers the accused woman a victimised position to occupy. Evidence of victimisation is made available through previous abuse, expert testimony from psychologists and psychiatrists, challenges to her mental health, or appeals to her emotional nature. The second stock story, presented by the prosecution, positions the accused woman as angry, full of revenge, calculating and self serving. Such a script is usually supported by witnesses, police evidence, and family members. This thesis examines these competing and contradictory scripts using thematic discourse analysis to examine the court transcripts in detail. It argues that the "truth" of the fatal incident is based on one of these two prevailing scripts. This research destabilises the dominant script of violent female offending in the feminist literature. Most research to date has focussed on explaining the circumstances in which women kill, concentrating attention on the victimisation of the violent offending woman and negating or de-prioritising any volition on her part. By analysing all transcripts of women whose trials were held within the specified period, this research is able to demonstrate the stories used to describe their complex offending, and draw attention to the anger and intent that can occur alongside the victimisation.

Pinteresque puppets and masters weave dark tales of a dystopic world

A HARBINGER is a messenger, foreshadowing what is to come. This adult fairytale, told with a cast of human actors and 22 puppets, foretells the story of a little girl found in the shadows of countless books in the library of a character known as the Old Man.