Cálculo mental e a produção do conhecimento matemático

This text presents the research developed with students of the 5th year of elementary school at a public school in the city of Taubaté-SP, involved in solving problems involving the Mental Calculation. The read authors show that the Mental Calculation is relevant for the production of mathematical knowledge as it favors the autonomy of students, making it the most critical. Official documents that guide educational practices, such as the Parâmetros Curriculares Nacionais also emphasize that working with mental arithmetic should be encouraged as it has the potential to encourage the production of mathematical knowledge by the student. In this research work Completion of course the tasks proposed to students, who constituted the fieldwork to production data, were designed, developed and analyzed in a phenomenological approach. The intention, the research was to understand the perception of students in the face of situations that encourage them to implement appropriate technical and mental calculation procedures. We analyze how students express and realize the strategies for mental calculation in the search for solution to problem situations

Cálculo mental e a produção do conhecimento matemático

This text presents the research developed with students of the 5th year of elementary school at a public school in the city of Taubaté-SP, involved in solving problems involving the Mental Calculation. The read authors show that the Mental Calculation is relevant for the production of mathematical knowledge as it favors the autonomy of students, making it the most critical. Official documents that guide educational practices, such as the Parâmetros Curriculares Nacionais also emphasize that working with mental arithmetic should be encouraged as it has the potential to encourage the production of mathematical knowledge by the student. In this research work Completion of course the tasks proposed to students, who constituted the fieldwork to production data, were designed, developed and analyzed in a phenomenological approach. The intention, the research was to understand the perception of students in the face of situations that encourage them to implement appropriate technical and mental calculation procedures. We analyze how students express and realize the strategies for mental calculation in the search for solution to problem situations

Aritmética de la escalera : una lección de cálculo mental sobre un modelo imaginado para alumnos de 9 a 10 años.

Se describe un ejemplo de clase activa de cálculo mental, experimentado con alumnos de 9 y 10 años del Instituto de San Isidro de Madrid, que utiliza como material una escalera imaginaria, y que permite la introducción heurística de gran número de conceptos, tanto aritméticos como geométricos.

Aritmética de la escalera : una lección de cálculo mental sobre un modelo imaginado, para alumnos de nueve a diez años.

Se reproduce una experiencia didáctica llevada a cabo en un aula de matemáticas en la que un profesor juega con los alumnos, sin ellos darse cuenta, desarrollando un ejercicio de cálculo mental en el que el alumnado pone a prueba sus conocimientos de aritmética y algebra, haciendo sumas, restas, multiplicaciones y divisiones sencillas a grandes velocidades e incluso, desarrollando conciencia plena sobre los números enteros y sus subdivisiones. Con este ejercicio el maestro pretendía demostrar la importancia del dominio del cálculo mental en la enseñanza primaria, para poder seguir desarrollándolo y mejorándolo en la enseñanza secundaria y posteriormente, en el Bachillerato.

Nombres signats. Càlcul mental. Normes per recollir informació. 'Números con signos. Cálculo mental. Normas para recoger información'.

Crédito de matemáticas para Educación Secundaria Obligatoria. El tema del crédito es los números e isometrías. Se trabaja el planteamiento y el cálculo de expresiones aritméticas y algebraicas, y el uso de recursos para afrontar situaciones problemáticas en clase. Está dividido en dos partes temáticas: una es una revisión del sistema de numeración decimal, y la otra se dedica a la medida y la geometría, revisa y amplia conceptos elementales y trabaja los movimientos rígidos aplicados a figuras planas. Estas dos partes deben ser trabajadas conjuntamente en el crédito. Se ofrece una primera parte de guía didáctica para el profesor y una segunda de material de soporte.

Càlcul amb fraccions : la proporcionalitat aritmètica. Interés en la presentació acurada de tota mena de treballs. 'Cálculo con fracciones : la proporcionalidad aritmética. Interés en la presentación detallada de todo tipo de trabajos'.

Crédito del módulo 5 del área de Matemáticas. El núcleo central lo constituye la proporcionalidad, en sus vertientes aritmética y gráfica. Hace un repaso de las fracciones e inicia el estudio de las funciones. Incluye ejercicios de cálculo mental. Propone una serie de actividades de aprendizaje y de evaluación.

El papel de la memoria de trabajo en el cálculo mental un cuarto de siglo después de Hitch.

Resumen tomado de la revista

Del cálculo mental.

Manual dirigido a educadores de estudiantes ciegos o con deficiencia visual de Primaria y Secundaria. La finalidad es aportar un material que contribuya a desarrollar en estos alumnos destrezas de cálculo de manera autónoma, es decir, prescindiendo de la escritura, la calculadora o cualquier instrumental específico de cálculo aritmético. Se recopilan y clasifican técnicas y estrategias aplicables con cada una de las operaciones aritméticas. En la parte didáctica, se proponen una serie de ejercicios graduados según criterios de destrezas-objetivo por operaciones, niveles educativos y dominios numéricos. Por último, se presentan algunas sugerencias para el diseño de situaciones dinámicas a modo lúdico.

Dificultades en el aprendizaje de la aritmética : un análisis desde los modelos cronométricos.

Resumen basado en el del autor. Resumen en castellano e inglés

Neurolinguistic contributions to understanding the bilingual mental lexicon

Introduction Many bilinguals will have had the experience of unintentionally reading something in a language other than the intended one (e.g. MUG to mean mosquito in Dutch rather than a receptacle for a hot drink, as one of the possible intended English meanings), of finding themselves blocked on a word for which many alternatives suggest themselves (but, somewhat annoyingly, not in the right language), of their accent changing when stressed or tired and, occasionally, of starting to speak in a language that is not understood by those around them. These instances where lexical access appears compromised and control over language behavior is reduced hint at the intricate structure of the bilingual lexical architecture and the complexity of the processes by which knowledge is accessed and retrieved. While bilinguals might tend to blame word finding and other language problems on their bilinguality, these difficulties per se are not unique to the bilingual population. However, what is unique, and yet far more common than is appreciated by monolinguals, is the cognitive architecture that subserves bilingual language processing. With bilingualism (and multilingualism) the rule rather than the exception (Grosjean, 1982), this architecture may well be the default structure of the language processing system. As such, it is critical that we understand more fully not only how the processing of more than one language is subserved by the brain, but also how this understanding furthers our knowledge of the cognitive architecture that encapsulates the bilingual mental lexicon. The neurolinguistic approach to bilingualism focuses on determining the manner in which the two (or more) languages are stored in the brain and how they are differentially (or similarly) processed. The underlying assumption is that the acquisition of more than one language requires at the very least a change to or expansion of the existing lexicon, if not the formation of language-specific components, and this is likely to manifest in some way at the physiological level. There are many sources of information, ranging from data on bilingual aphasic patients (Paradis, 1977, 1985, 1997) to lateralization (Vaid, 1983; see Hull & Vaid, 2006, for a review), recordings of event-related potentials (ERPs) (e.g. Ardal et al., 1990; Phillips et al., 2006), and positron emission tomography (PET) and functional magnetic resonance imaging (fMRI) studies of neurologically intact bilinguals (see Indefrey, 2006; Vaid & Hull, 2002, for reviews). Following the consideration of methodological issues and interpretative limitations that characterize these approaches, the chapter focuses on how the application of these approaches has furthered our understanding of (1) selectivity of bilingual lexical access, (2) distinctions between word types in the bilingual lexicon and (3) control processes that enable language selection.

Is there something quantum-like about the human mental lexicon?

Following an early claim by Nelson & McEvoy suggesting that word associations can display `spooky action at a distance behaviour', a serious investigation of the potentially quantum nature of such associations is currently underway. In this paper quantum theory is proposed as a framework suitable for modelling the mental lexicon, specifically the results obtained from both intralist and extralist word association experiments. Some initial models exploring this hypothesis are discussed, and they appear to be capable of substantial agreement with pre-existing experimental data. The paper concludes with a discussion of some experiments that will be performed in order to test these models.