Interactive Curriculum Based on Models of Mind & Brain

What does it mean for curriculum to be interactive? It encourages student engagement and active participation in both individual and group work. It offers teachers a coherent set of materials to choose from that can enhance their classes. It is the product of on-going development and continuous improvement based on research and feedback from the field. This paper will introduce work in progress from the Center for Excellence in Education, Science, and Technology (CELEST), an NSF Science of Learning Center. Among its many goals, CELEST is developing a unique educational curriculum, an interactive curriculum based upon models of mind and brain. Teachers, administrators, and governments are naturally concerned with how students learn. Students are greatly concerned about how minds work, including how to learn. CELEST aims to introduce curricula that not only meet current U.S. standards in mathematics, science, and psychology but also influence plans to improve those standards. Software and support materials are in development and available at http://cns.bu.edu/celest/private/. Interested parties are invited to contact the author for access.

Foundations of stochastic geometry and theory of random sets

The first section of this chapter starts with the Buffon problem, which is one of the oldest in stochastic geometry, and then continues with the definition of measures on the space of lines. The second section defines random closed sets and related measurability issues, explains how to characterize distributions of random closed sets by means of capacity functionals and introduces the concept of a selection. Based on this concept, the third section starts with the definition of the expectation and proves its convexifying effect that is related to the Lyapunov theorem for ranges of vector-valued measures. Finally, the strong law of large numbers for Minkowski sums of random sets is proved and the corresponding limit theorem is formulated. The chapter is concluded by a discussion of the union-scheme for random closed sets and a characterization of the corresponding stable laws.

Gender Stereotypes and Gendered Vocational Aspirations among Secondary School Students

Research Topic/Aim: Horizontal gender inequalities appear to be rather stable, with girls more often choosing ‘female' service professions, and boys choosing career paths related to science, technology, engineering or mathematics, since measures to bring more women into typical ‘male' jobs and more men into typical ‘female' jobs did not turn out to be sustainable. This paper focuses on gender stereotypes, namely non-egalitarian patriarchal gender-role orientations and gender associations of the school subjects German and mathematics. Dealing with and abolishing such gender stereotypes may be key strategy to reach sustainability regarding more equal vocational choices. Thus, gender stereotypes will be theorised and empirically analysed as a major predictor of gender-typical vocational perspectives considering interest in these school subjects as a mediating factor. Furthermore, we focus on structural patriarchy as a root of gender-role orientations, and teacher gender regarding its impact on gendered images of subjects. Theoretical and methodology framework: Our analyses of gender segregation in vocational aspirations and vocational choice center on Gottfredson's (2002; Gottfredson and Becker, 1981) Theory of Circumscription, Compromise and Self-Creation. One of the main assumptions of this theory is that people associate jobs with particular sexes and those jobs that do not fit particular gender roles are not considered. Empirical analyses are based on survey data of eighth-graders in the Swiss canton of Bern (N = 672). Structural Equation Models (SEM) for male and female students are estimated. Conclusions/Findings: Results reveal different patterns for boys and girls; for boys, gender-typical (male) vocational perspective could be explained via gender role orientations, interest in mathematics and gender associations of the school subjects, for girls, the factors under consideration could be empirically linked to ‘atypical vocational perspective'. Relevance to Nordic educational research: The study focuses on gender relations in society and how they are reproduced. Gender segregation in vocational choice and at the labour market is a universal issue - affecting both egalitarian and non-egalitarian gender regimes in similar ways. Although in general Northern countries appear to be more equal regarding gender inequality, gender segregation is rather persistent (Jarman, Blackburn and Brooks, 2012) and therefore remains a relevant topic.

How need for cognition affects the processing of achievement-related information

The present article analyzed, how need for cognition (NFC) influences the formation of performance expectancies. When processing information, individuals with lower NFC often rely on salient information and shortcuts compared to individuals higher in NFC. We assume that these preferences of processing will also make individuals low in NFC more responsive to salient achievement-related cues because the processing of salient cues is cognitively less demanding than the processing of non-salient cues. Therefore, individuals lower in NFC should tend to draw wider ranging inferences from salient achievement-related information. In a sample of N = 197 secondary school students, achievement-related feedback (grade on an English examination) affected changes in expectancies in non-corresponding academic subjects (e.g., expectation of final grade in mathematics or history) when NFC was lower, whereas for students with higher NFC, changes in expectancies in non-corresponding academic subjects were not affected.

Rasmussen's spectral sequences and the \germslN-concordance invariants

Combining known spectral sequences with a new spectral sequence relating reduced and unreduced slN-homology yields a relations hip between the Homflypt-homology of a knot and its slN-concordance invariants. As an application, some of the slN-concordance invariants are shown to be linearly independent.

Orchestrating Whole Group Discourse to Mediate Mathematical Meaning

The most common pattern of classroom discourse follows a three-part exchange of teacher initiation, student response, and teacher evaluation or follow-up (IRE/IRF) (Cazden, 2001). Although sometimes described as encouraging illusory understanding (Lemke, 1990), triadic exchanges can mediate meaning (Nassaji & Wells, 2000). This paper focuses on one case from a study of discursive practices of seven middle grades teachers identified for their expertise in mathematics instruction. The central result of the study was the development of a model to explain how teachers use discourse to mediate mathematical meaning in whole group instruction. Drawing on the model for analysis, thick descriptions of one teacher’s skillful orchestration of triadic exchanges that enhance student understanding of mathematics are presented.

On the Density and the Volume Density Property

This article gives a short introduction into the notions of density property (DP) and volume density property (VDP). Moreover we develop an effective criterion of verifying whether a given X has VDP. As an application of this method we give a new proof of the basic fact that the product of two Stein manifolds with VDP admits VDP.

Descripción, comparación y ejemplos de uso de las funciones de la toolbox de procesado digital de imágenes de MATLAB®

Matlab, uno de los paquetes de software matemático más utilizados actualmente en el mundo de la docencia y de la investigación, dispone de entre sus muchas herramientas una específica para el procesado digital de imágenes. Esta toolbox de procesado digital de imágenes está formada por un conjunto de funciones adicionales que amplían la capacidad del entorno numérico de Matlab y permiten realizar un gran número de operaciones de procesado digital de imágenes directamente a través del programa principal. Sin embargo, pese a que MATLAB cuenta con un buen apartado de ayuda tanto online como dentro del propio programa principal, la bibliografía disponible en castellano es muy limitada y en el caso particular de la toolbox de procesado digital de imágenes es prácticamente nula y altamente especializada, lo que requiere que los usuarios tengan una sólida formación en matemáticas y en procesado digital de imágenes. Partiendo de una labor de análisis de todas las funciones y posibilidades disponibles en la herramienta del programa, el proyecto clasificará, resumirá y explicará cada una de ellas a nivel de usuario, definiendo todas las variables de entrada y salida posibles, describiendo las tareas más habituales en las que se emplea cada función, comparando resultados y proporcionando ejemplos aclaratorios que ayuden a entender su uso y aplicación. Además, se introducirá al lector en el uso general de Matlab explicando las operaciones esenciales del programa, y se aclararán los conceptos más avanzados de la toolbox para que no sea necesaria una extensa formación previa. De este modo, cualquier alumno o profesor que se quiera iniciar en el procesado digital de imágenes con Matlab dispondrá de un documento que le servirá tanto para consultar y entender el funcionamiento de cualquier función de la toolbox como para implementar las operaciones más recurrentes dentro del procesado digital de imágenes. Matlab, one of the most used numerical computing environments in the world of research and teaching, has among its many tools a specific one for digital image processing. This digital image processing toolbox consists of a set of additional functions that extend the power of the digital environment of Matlab and allow to execute a large number of operations of digital image processing directly through the main program. However, despite the fact that MATLAB has a good help section both online and within the main program, the available bibliography is very limited in Castilian and is negligible and highly specialized in the particular case of the image processing toolbox, being necessary a strong background in mathematics and digital image processing. Starting from an analysis of all the available functions and possibilities in the program tool, the document will classify, summarize and explain each function at user level, defining all input and output variables possible, describing common tasks in which each feature is used, comparing results and providing illustrative examples to help understand its use and application. In addition, the reader will be introduced in the general use of Matlab explaining the essential operations within the program and clarifying the most advanced concepts of the toolbox so that an extensive prior formation will not be necessary. Thus, any student or teacher who wants to start digital image processing with Matlab will have a document that will serve to check and understand the operation of any function of the toolbox and also to implement the most recurrent operations in digital image processing.

Could it be possible to replace DERIVE with MAXIMA?

In recent years, a considerable number of teachers in Spain have been using DERIVE to teach math subjects in High Schools and Universities. This software has been used by the authors of this work as a support tool in Mathematics courses for Engineering. Since Texas Instruments does not support DERIVE, we were faced with finding an alternative software product, and considering the possibility of using a public-domain software such as MAXIMA. Here we make a comparative study of DERIVE and MAXIMA as support tools for a Calculus course for first year Engineering students.

Después de Einstein: una arquitectura para una teoría

En 1905, aparecen en la revista "Annalen der physik" tres artículos que revolucionarán las ciencias físicas y pondrán en jaque los asentados conceptos newtonianos de Espacio y Tiempo. La formulación de la Teoría de la Relatividad por Albert Einstein pone en crisis el valor absoluto de estos conceptos, y permite proponer nuevas reflexiones a propósito de su concepción dentro del campo de la física. Esta revolución ¿podría extrapolarse al campo de la arquitectura, donde Espacio y Tiempo tienen un papel protagonista? Hay que entender la complejidad del hecho arquitectónico y las innumerables variables que participan de su definición. Se estudia en esta Tesis Doctoral un aspecto muy concreto: cómo un paradigma (la Teoría de la Relatividad) puede intervenir y modificar, o no, la Arquitectura. Se plantea para ello ir al origen; desentrañar el momento de interacción entre la Teoría de la Relatividad y la Teoría de la Arquitectura, que permita determinar si aquella influyó sobre ésta en los escritos teóricos de las vanguardias aplicados a la Arquitectura. “Después de Einstein. Una arquitectura para una teoría” buscará los puntos de conexión de la Teoría de la Relatividad con la teoría arquitectónica de las vanguardias de principio del siglo XX, su influencia, la contaminación entre una y otra, con posibles resultados arquitectónicos a partir de esta interacción, capaz de definir nuevos argumentos formales para un nuevo lenguaje enArquitectura. Annalen der physik Después de Einstein. Una arquitectura para una teoría Para ello la Tesis se estructura en cuatro capítulos. El primero expone el ámbito geográfico y cronológico donde se desarrolla la Teoría de la Relatividad con la repercusión teórica que tiene para el arte, en función de una nueva definición de espacio vinculado al tiempo, como evento que se desarrolla en un ámbito cuatridimensional; la indeterminación de las medidas de espacio y de las medidas de tiempo, y la importancia de entender la materia como energía. El segundo capítulo estudia los movimientos de vanguardia coetáneos a la eclosión de la Relatividad, enmarcados en su ámbito geográfico más próximo. El cubismo se muestra como movimiento que participa ocasionalmente de las matemáticas y la geometría, bajo el influjo del científico Henri Poincaré y las geometrías no euclidianas. El futurismo indaga en los avances de la ciencia desde una cierta lejanía, cierta falta de rigor o profundidad científica para extraer las leyes de su nuevo idealismo plástico constructivo, definiendo e interpretando su Universo a partir de los avances de la ciencia, en respuesta a la crisis del espacio y del tiempo newtonianos. El lenguaje científico se encuentra presente en conceptos como "simultaneidad" (Boccioni), "expansión esférica de la luz en el espacio" (Severini y Carrá), "cuatridimensionalidad", "espacio-tiempo", "aire-luz-fuerza", "materia y energía" que paralelamente conforman el cuerpo operacional de la teoría de Einstein. Si bien no es posible atribuir a la Teoría de la Relatividad un papel protagonista como referente para el pensamiento artístico, en 1936, con la aparición del manifiesto Dimensionista, se atribuyen explícitamente a las teorías de Einstein las nuevas ideas de espacio-tiempo del espíritu europeo seguido por cubistas y futuristas. El tercer capítulo describe cómo la Teoría de la Relatividad llegó a ser fuente de inspiración para la Teoría de la Arquitectura. Estructurado en tres subcapítulos, se estudia el autor principal que aportó para la Arquitectura conceptos e ideas extrapoladas de la Teoría de la Relatividad después de su estudio e interpretación (Van Doesburg), dónde se produjeron las influencias y puntos de contacto (Lissitzky, Eggeling, Moholy-Nagy) y cómo fueron difundidas a través de la arquitectura (Einsteinturm de Mendelsohn) y de las revistas especializadas. El cuarto capítulo extrae las conclusiones del estudio realizado en esta Tesis, que bien pudiera resumir MoholyNagy en su texto "Vision inmotion" (1946) al comentar: "Ya que el "espacio-tiempo" puede ser un término engañoso, tiene que hacerse especialmente hincapié en que los problemas de espacio-tiempo en el arte no están necesariamente basados en la Teoría de la Relatividad de Einstein. Esto no tiene intención de descartar la relevancia de su teoría para las artes. Pero los artistas y los laicos rara vez tienen el conocimiento matemático para visualizar en fórmulas científicas las analogías con su propio trabajo. La terminología de Einstein del "espacio-tiempo" y la "relatividad" ha sido absorbida por nuestro lenguaje diario." ABSTRACT. "AFTER EINSTEIN:ANARCHITECTUREFORATHEORY." In 1905, three articles were published in the journal "Annalen der Physik ". They revolutionized physical sciences and threw into crisis the newtonian concepts of Space and Time. The formulation of the Theory of Relativity by Albert Einstein put a strain on the absolute value of these concepts, and proposed new reflections about them in the field of Physics. Could this revolution be extrapolated to the field of Architecture, where Space and Time have a main role? It is necessary to understand the complexity of architecture and the countless variables involved in its definition. For this reason, in this PhD. Thesis, we study a specific aspect: how a paradigm (Theory of Relativity) can intervene and modify -or not- Architecture. It is proposed to go back to the origin; to unravel the moment in which the interaction between the Theory of Relativity and the Theory of Architecture takes place, to determine whether the Theory of Relativity influenced on the theoretical avant-garde writings applied to Architecture. "After Einstein.An architecture for a theory " will search the connection points between the Theory of Relativity and architectural avant-garde theory of the early twentieth century, the influence and contamination between them, giving rise to new architectures that define new formal arguments for a new architectural language. Annalen der Physik This thesis is divided into four chapters. The first one describes the geographical and chronological scope in which the Theory of Relativity is developed showing its theoretical implications in the field of art, according to a new definition of Space linked to Time, as an event that takes place in a fourdimensional space; the indetermination of the measurement of space and time, and the importance of understanding "matter" as "energy". The second chapter examines the avant-garde movements contemporary to the theory of relativity. Cubism is shown as an artist movement that occasionally participates in mathematics and geometry, under the influence of Henri Poincaré and non-Euclidean geometries. Futurism explores the advances of science at a certain distance, with lack of scientific rigor to extract the laws of their new plastic constructive idealism. Scientific language is present in concepts like "simultaneity" (Boccioni), "expanding light in space" (Severini and Carra), "four-dimensional space", "space-time", "light-air-force," "matter and energy" similar to the operational concepts of Einstein´s theory. While it is not possible to attribute a leading role to the Theory of Relativity, as a benchmark for artistic laws, in 1936, with the publication of the Dimensionist manifest, the new ideas of space-time followed by cubist and futurist were attributed to the Einstein's theory. The third chapter describes how the Theory of Relativity became an inspiration for the architectural theory. Structured into three subsections, we study the main author who studied the theory of relativity and ,as a consequence, contributed with some concepts and ideas to the theory of architecture (Van Doesburg), where influences and contact points took place (Lissitzky, Eggeling, Moholy-Nagy) and how were disseminated throughArchitecture (Einsteinturm, by Mendelsohn) and journals. The fourth chapter draws the conclusions of this PhD. Thesis, which could be well summarized by Moholy Nagy in his text "Vision in Motion" (1946): vi Since "space-time" can be a misleading term, it especially has to be emphasized that the space-time problems in the arts are not necessarily based upon Einstein´s Theory of Relativity. This is not meant to discount the relevance of his theory to the arts. But artists and laymen seldom have the mathematical knowledge to visualize in scientific formulae the analogies to their own work. Einstein's terminology of "space-time" and "relativity" has been absorbed by our daily language.

Aprendizaje multimedia en inglés: Análisis de circuitos

Este proyecto tiene como objetivo facilitar el aprendizaje multimedia en inglés de los conceptos básicos relacionados con el análisis de circuitos para los alumnos de grado de la nuestra escuela, en especial para los de nuevo ingreso. El aprendizaje será realizado directamente en inglés, cumpliendo así el doble objetivo: por un lado el de abordar unos conceptos nuevos para el alumno de ingeniería y, además, el poder hacerlo en inglés, lo que le servirá para llegar a mejorar su nivel de competencia en la lengua extranjera, o al menos mantenerlo. El proyecto realizado tiene varios apartados. En primer lugar, un apartado didáctico en el que se exponen los conceptos básicos sobre el análisis de circuitos que se quieren explicar, siempre orientados al aprendizaje de inglés. Para abordar estos nuevos temas de un modo didáctico y que incite al autoaprendizaje, se recurrirá a la tecnología y por medio de vídeos e imágenes y actividades didácticas multimedia se podrá afrontar la asignatura con facilidad e interés para captar los conceptos en una lengua extranjera. Se han diseñado actividades para la práctica de: la audición, con dictado y asociación de sonidos con palabras; de la comprensión lectora y adquisición de vocabulario, con ejercicios de rellenar huecos y emparejar definiciones. Las actividades se han adaptado a la plataforma Moodle para obtener la retroalimentación de los alumnos, si se desea. El apartado de aprendizaje se complementará con un glosario específico y alfabéticamente ordenado donde también dispondremos de la transcripción fonética de cada una de las palabras incluidas en el mismo. Para llegar a conseguir el objetivo didáctico se ha diseñado un sitio web capaz de albergar todo el contenido anterior. Abstract The main objective of this Project has been to facilitate a multimedia resource for learning in English the basic concepts related to circuit analysis. The final product is directly addressed to the undergraduate students at a Telecommunications School, the EUITT from Universidad Politécnica de Madrid. Learning technical notions directly in English serves the students to reach the double purpose of not only acquiring a number of new concepts but also improving their proficiency in the foreign language or keeping up with their level of English through their studies. The project has several sections. There is a didactic section which explains the basic concepts using videos and images in order to approach the subject with ease and interest. This part is supplemented with a glossary in alphabetic order provided with the phonetics of the English words and some multimedia exercises for practicing different skills mainly listening, reading, and using technical vocabulary in English. All these activities have been adapted to the platform Moodle so that the students results can be assessed, if convenient. On the other hand, the practical implementation of the Project has consisted of designing a website capable of including all of the points mentioned above.

Autonomous Acquisition of Natural Situated Communication

An important part of human intelligence, both historically and operationally, is our ability to communicate. We learn how to communicate, and maintain our communicative skills, in a society of communicators – a highly effective way to reach and maintain proficiency in this complex skill. Principles that might allow artificial agents to learn language this way are in completely known at present – the multi-dimensional nature of socio-communicative skills are beyond every machine learning framework so far proposed. Our work begins to address the challenge of proposing a way for observation-based machine learning of natural language and communication. Our framework can learn complex communicative skills with minimal up-front knowledge. The system learns by incrementally producing predictive models of causal relationships in observed data, guided by goal-inference and reasoning using forward-inverse models. We present results from two experiments where our S1 agent learns human communication by observing two humans interacting in a realtime TV-style interview, using multimodal communicative gesture and situated language to talk about recycling of various materials and objects. S1 can learn multimodal complex language and multimodal communicative acts, a vocabulary of 100 words forming natural sentences with relatively complex sentence structure, including manual deictic reference and anaphora. S1 is seeded only with high-level information about goals of the interviewer and interviewee, and a small ontology; no grammar or other information is provided to S1 a priori. The agent learns the pragmatics, semantics, and syntax of complex utterances spoken and gestures from scratch, by observing the humans compare and contrast the cost and pollution related to recycling aluminum cans, glass bottles, newspaper, plastic, and wood. After 20 hours of observation S1 can perform an unscripted TV interview with a human, in the same style, without making mistakes.

Riskmática: Una tecnología educativa desarrollada con Unity

Historically, teachers have always searched for a connection with their students to make education interesting and a vital experience. In the 19th century, pedagogue Johann Heinrich Pestalozzi taught children how to sum using wood blocks. His successors have followed his legacy and today they use a wide variety of media, including board games, in order to reach out to their students. These methods are denominated educational technologies, which are defined as the study and ethical practice of facilitating learning and improving performance by creating, using, and managing appropriate technological processes and resources. With the advent of the information technologies, teachers have at their disposal new media with which they can increase the interest of their students. This technologic revolution is changing the present educational model. The objective of this dissertation is to develop an educational videogame in order to help students learn mathematics. To reach this goal, the videogame has been developed with the game engine Unity as the main tool. Additionally, agile software development methodologies as well as other software engineering techniques have also been used. The result is Riskmatica, an educational videogame based on geographical domination in which knowledge is the best weapon. The players must conquer enemy teritories answering correctly a mathecatical question. Moreover the videogame has the functionality required to configure a new game and input new questions. To conclude, this project has created an educational technology which greatly appeals to students and that can be used by the educators to improve their lessons in mathematics.---RESUMEN---A lo largo de la historia, los educadores siempre han buscado conectar con los alumnos para poder captar su interés y hacer que la educación se convierta en una experiencia vital. El pedagogo Johann Heinrich Pestalozzi conseguía esto en el siglo XIX, enseñando a niños a contar con bloques de madera. Sus sucesores han seguido su legado y hoy en día utilizan variedad de medios con los que motivar a sus alumnos, en algunos casos los juegos de mesa. Estos métodos son denominados tecnologías educativas, que se definen como los estudios y prácticas éticas que facilitan y mejoran la enseñanza, mediante la creación, el uso y el empleo de procesos y recursos tecnológicos. Con el advenimiento de las tecnologías de la información, los educadores tienen a su disposición un nuevo medio con el que llegar al alumnado. Esta revolución tecnológica está cambiando el modelo educativo actual. El objetivo de este proyecto es el de crear un videojuego educativo que ayude a los alumnos a estudiar matemáticas. Para lograrlo se ha utilizado el popular motor de videojuego Unity como herramienta principal. También se han empleado metodologías ágiles de desarrollo además de otras técnicas de ingeniería del software. El resultado es Riskmática, un videojuego educativo de dominación geográfica en el que el arma más eficaz es el conocimiento. Los jugadores deberán conquistar territorios a sus adversarios mediante la respuesta de preguntas de carácter matemático. Además el videojuego cuenta con la funcionalidad necesaria para configurar una partida e introducir nuevas preguntas. Como conlusión, este proyecto ha logrado crear una tecnología educativa muy atractiva para los alumnos con la que los profesores pueden mejorar la enseñanza de las matemáticas.

A avaliação formativa por meio do feedback escrito no processo de ensino-aprendizagem de alunos de 2.º ciclo em matemática

Relatório final apresentado para a obtenção do grau de mestre em Ensino do 1.º ciclo e do 2.º ciclo do ensino básico