Applications and modelling in mathematics teaching

The aim of this paper is a comprehensive presentation of some important basic and general aspects of the topic applications and modelling, with emphasis on the secondary school level. Owing to the review character of this paper, some overlap with the survey paper Blum and Niss (1989) for ICME-6 in Budapest is inevitable. The paper will consist of three parts. In part 1, I shall try to clarify some basic concepts and remind the reader of a few application and modelling examples suitable for teaching. In part 2, I shall formulate some general aims for mathematics instruction and, on that basis, summarise the most important arguments for and against applications and modelling in mathematics teaching. Finally, in part 3, I shall discuss some relevant instructional aspects resulting from the considerations in part 2.

Online Learning of Non-stationary Sequences

We consider an online learning scenario in which the learner can make predictions on the basis of a fixed set of experts. The performance of each expert may change over time in a manner unknown to the learner. We formulate a class of universal learning algorithms for this problem by expressing them as simple Bayesian algorithms operating on models analogous to Hidden Markov Models (HMMs). We derive a new performance bound for such algorithms which is considerably simpler than existing bounds. The bound provides the basis for learning the rate at which the identity of the optimal expert switches over time. We find an analytic expression for the a priori resolution at which we need to learn the rate parameter. We extend our scalar switching-rate result to models of the switching-rate that are governed by a matrix of parameters, i.e. arbitrary homogeneous HMMs. We apply and examine our algorithm in the context of the problem of energy management in wireless networks. We analyze the new results in the framework of Information Theory.

Teaching an Old Robot New Tricks: Learning Novel Tasks via Interaction with People and Things

As AI has begun to reach out beyond its symbolic, objectivist roots into the embodied, experientialist realm, many projects are exploring different aspects of creating machines which interact with and respond to the world as humans do. Techniques for visual processing, object recognition, emotional response, gesture production and recognition, etc., are necessary components of a complete humanoid robot. However, most projects invariably concentrate on developing a few of these individual components, neglecting the issue of how all of these pieces would eventually fit together. The focus of the work in this dissertation is on creating a framework into which such specific competencies can be embedded, in a way that they can interact with each other and build layers of new functionality. To be of any practical value, such a framework must satisfy the real-world constraints of functioning in real-time with noisy sensors and actuators. The humanoid robot Cog provides an unapologetically adequate platform from which to take on such a challenge. This work makes three contributions to embodied AI. First, it offers a general-purpose architecture for developing behavior-based systems distributed over networks of PC's. Second, it provides a motor-control system that simulates several biological features which impact the development of motor behavior. Third, it develops a framework for a system which enables a robot to learn new behaviors via interacting with itself and the outside world. A few basic functional modules are built into this framework, enough to demonstrate the robot learning some very simple behaviors taught by a human trainer. A primary motivation for this project is the notion that it is practically impossible to build an "intelligent" machine unless it is designed partly to build itself. This work is a proof-of-concept of such an approach to integrating multiple perceptual and motor systems into a complete learning agent.

People Recognition in Image Sequences by Supervised Learning

We describe a system that learns from examples to recognize people in images taken indoors. Images of people are represented by color-based and shape-based features. Recognition is carried out through combinations of Support Vector Machine classifiers (SVMs). Different types of multiclass strategies based on SVMs are explored and compared to k-Nearest Neighbors classifiers (kNNs). The system works in real time and shows high performance rates for people recognition throughout one day.

An Application of Augmented Reality (AR) in the Teaching of an Arc Welding Robot

Augmented Reality (AR) is an emerging technology that utilizes computer vision methods to overlay virtual objects onto the real world scene so as to make them appear to co-exist with the real objects. Its main objective is to enhance the user’s interaction with the real world by providing the right information needed to perform a certain task. Applications of this technology in manufacturing include maintenance, assembly and telerobotics. In this paper, we explore the potential of teaching a robot to perform an arc welding task in an AR environment. We present the motivation, features of a system using the popular ARToolkit package, and a discussion on the issues and implications of our research.

Alternative ways to estimate change points in multinomial sequences. An application to an authorship attribution problem

The statistical analysis of literary style is the part of stylometry that compares measurable characteristics in a text that are rarely controlled by the author, with those in other texts. When the goal is to settle authorship questions, these characteristics should relate to the author’s style and not to the genre, epoch or editor, and they should be such that their variation between authors is larger than the variation within comparable texts from the same author. For an overview of the literature on stylometry and some of the techniques involved, see for example Mosteller and Wallace (1964, 82), Herdan (1964), Morton (1978), Holmes (1985), Oakes (1998) or Lebart, Salem and Berry (1998). Tirant lo Blanc, a chivalry book, is the main work in catalan literature and it was hailed to be “the best book of its kind in the world” by Cervantes in Don Quixote. Considered by writters like Vargas Llosa or Damaso Alonso to be the first modern novel in Europe, it has been translated several times into Spanish, Italian and French, with modern English translations by Rosenthal (1996) and La Fontaine (1993). The main body of this book was written between 1460 and 1465, but it was not printed until 1490. There is an intense and long lasting debate around its authorship sprouting from its first edition, where its introduction states that the whole book is the work of Martorell (1413?-1468), while at the end it is stated that the last one fourth of the book is by Galba (?-1490), after the death of Martorell. Some of the authors that support the theory of single authorship are Riquer (1990), Chiner (1993) and Badia (1993), while some of those supporting the double authorship are Riquer (1947), Coromines (1956) and Ferrando (1995). For an overview of this debate, see Riquer (1990). Neither of the two candidate authors left any text comparable to the one under study, and therefore discriminant analysis can not be used to help classify chapters by author. By using sample texts encompassing about ten percent of the book, and looking at word length and at the use of 44 conjunctions, prepositions and articles, Ginebra and Cabos (1998) detect heterogeneities that might indicate the existence of two authors. By analyzing the diversity of the vocabulary, Riba and Ginebra (2000) estimates that stylistic boundary to be near chapter 383. Following the lead of the extensive literature, this paper looks into word length, the use of the most frequent words and into the use of vowels in each chapter of the book. Given that the features selected are categorical, that leads to three contingency tables of ordered rows and therefore to three sequences of multinomial observations. Section 2 explores these sequences graphically, observing a clear shift in their distribution. Section 3 describes the problem of the estimation of a suden change-point in those sequences, in the following sections we propose various ways to estimate change-points in multinomial sequences; the method in section 4 involves fitting models for polytomous data, the one in Section 5 fits gamma models onto the sequence of Chi-square distances between each row profiles and the average profile, the one in Section 6 fits models onto the sequence of values taken by the first component of the correspondence analysis as well as onto sequences of other summary measures like the average word length. In Section 7 we fit models onto the marginal binomial sequences to identify the features that distinguish the chapters before and after that boundary. Most methods rely heavily on the use of generalized linear models

The Personal tutorial guidance sessions in the framework of the teaching-learning field of the Bologna process: University of Minho (first cycle) courses students’ perceptions

The Bologna Process defends the adoption of a higher education in teaching-learning methodologies that – in contraposition to the previous model based on the transmission of knowledge, which for being essentially theoretical, gives the student a passive role in the knowledge construction process – allows a (pro) active, autonomous and practical learning, where the student acquires and develops his competences. The personal tutorial guidance sessions are included in the teaching contact hours. This abstract presents a study about the University of Minho (first cycle) Courses Students’ perceptions of the personal tutorial guidance sessions’ relevance in the scope of the learning-teaching process, so as to confirm if the implementation/implantation of the commonly called tutorial (type) education, as an approach to an active, autonomous and practical learning, is sensed by the learners themselves

Research and teaching: a holy or an unholy alliance?

Much of the self-image of the Western university hangs on the idea that research and teaching are intimately connected. The central axiom here is that research and teaching are mutually supportive of each other. An institution lacking such a set of relationships between research and teaching falls short of what it means to be a university. This set of beliefs raises certain questions: Is it the case that the presence of such a mutually supportive set of relationships between research and teaching is a necessary condition of the fulfilment of the idea of the university? (A conceptual question). And is it true that, in practice today, such a mutually supportive set of relationships between research and teaching characterises universities? (An empirical question). In my talk, I want to explore these matters in a critical vein. I shall suggest that: a) In practice today, such a mutually supportive set of relationships between research and teaching is in jeopardy. Far from supporting each other, very often research and teaching contend against each other. Research and teaching are becoming two separate ideologies, with their own interest structures. b) Historically, the supposed tight link between research and teaching is both of recent origin and far from universally achieved in universities. Institutional separateness between research and teaching is and has been evident, both across institutions and even across departments in the same institution. c) Conceptually, research and teaching are different activities: each is complex and neither is reducible to the other. In theory, therefore, research and teaching may be said to constitute a holy alliance but in practice, we see more of an unholy alliance. If, then, in an ideal world, a positive relationship between research and teaching is still a worthwhile goal, how might it be construed and worked for? Seeing research and teaching as two discrete and unified sets of activity is now inadequate. Much better is a construal of research and teaching as themselves complexes, as intermingling pools of activity helping to form the liquid university that is emerging today. On this view, research and teaching are fluid spaces, ever on the move, taking up new shapes, and themselves dividing and reforming, as the university reworks its own destiny in modern society. On such a perspective, working out a productive relationship between research and teaching is a complex project. This is an alliance that is neither holy nor unholy. It is an uneasy alliance, with temporary accommodations and continuous new possibilities

Recerca versus docència en una experiència d'internalització dels estudis de Geografia a la Universitat de Girona: The faces of landscape, Catalonia and North Karelia = Research versus teaching in one experience of internationalization of the Geography degree studies in the University of Girona: The faces of landscape, Catalonia and North Karelia

Un dels reptes cabdals de la Universitat és enllaçar l’experiència de recerca amb la docència, així com promoure la internacionalització dels estudis, especialment a escala europea, tenint present que ambdues poden actuar com a catalitzadores de la millora de la qualitat docent. Una de les fórmules d’internacionalització és la realització d’assignatures compartides entre universitats de diferents països, fet que suposa l’oportunitat d’implementar noves metodologies docents. En aquesta comunicació es presenta una experiència en aquesta línia desenvolupada entre la Universitat de Girona i la Universitat de Joensuu (Finlàndia) en el marc dels estudis de Geografia amb la realització de l’assignatura 'The faces of landscape: Catalonia and North Karelia'. Aquesta es desenvolupa al llarg de dues setmanes intensives, una en cadascuna de les Universitats. L’objectiu és presentar i analitzar diferents significats del concepte paisatge aportant també metodologies d’estudi tant dels aspectes físics i ecològics com culturals que s’hi poden vincular i que són les que empren els grups de recerca dels professors responsables de l’assignatura. Aquesta part teòrica es completa amb una presentació de les característiques i dinàmiques pròpies dels paisatges finlandesos i catalans i una sortida de camp. Per a la part pràctica es constitueixen grups d’estudi multinacionals que treballen a escala local algun dels aspectes en els dos països, es comparen i es realitza una presentació i defensa davant del conjunt d’estudiants i professorat. La llengua vehicular de l’assignatura és l’anglès

Aprender investigando. Una experiencia formativa en el ámbito de la enfermería = Research teaching processes used as a methodological strategy in the education of healthcare professionals

Este trabajo tiene como propósito presentar y valorar, desde la perspectiva del alumnado participante, un proyecto de investigación-formación puesto en marcha durante el curso 2003-2004 en la elaboración del trabajo de tesina, fin de carrera, en la Escuela de Enfermería de Vitoria, dentro del programa de Licenciatura Europea de Enfermería. Constituye el punto de partida de un proyecto a largo plazo, iniciado con la intención de desarrollar principios teóricos y procedimientos prácticos que nos permitan sistematizar procesos formativos que, centrados en la investigación, articulen la teoría y la práctica e integren una perspectiva comunicativa y cooperativa

English vocabulary teaching and learning strategies in Secondary Education

Resumen basado en el de la publicaci??n

Enseñar a aprender a pensar en los centros educativos, incluso en las actividades de evaluación.= Teaching to learn how to think at schools, even within assessment activities

El auténtico protagonismo de los centros educativos tiene que dirigirse a ayudar a pensar a sus alumnos y a enseñarlos a aprender, es decir, el docente tiene que enseñar estrategias de aprendizaje y debe promover el esfuerzo del estudiante para facilitar la construcción de esquemas y el aprendizaje permanente. El profesor debe utilizar cualquier situación de aprendizaje para enseñar dichas estrategias de aprendizaje, incluso en las situaciones de evaluación; por lo tanto, en este trabajo se sugiere que en las evaluaciones de los alumnos y alumnas se tenga en cuenta la metacognición como factor fundamental en el aprendizaje y la enseñanza

Towards Detecting Changes in Underwater Image Sequences

Detecting changes between images of the same scene taken at different times is of great interest for monitoring and understanding the environment. It is widely used for on-land application but suffers from different constraints. Unfortunately, Change detection algorithms require highly accurate geometric and photometric registration. This requirement has precluded their use in underwater imagery in the past. In this paper, the change detection techniques available nowadays for on-land application were analyzed and a method to automatically detect the changes in sequences of underwater images is proposed. Target application scenarios are habitat restoration sites, or area monitoring after sudden impacts from hurricanes or ship groundings. The method is based on the creation of a 3D terrain model from one image sequence over an area of interest. This model allows for synthesizing textured views that correspond to the same viewpoints of a second image sequence. The generated views are photometrically matched and corrected against the corresponding frames from the second sequence. Standard change detection techniques are then applied to find areas of difference. Additionally, the paper shows that it is possible to detect false positives, resulting from non-rigid objects, by applying the same change detection method to the first sequence exclusively. The developed method was able to correctly find the changes between two challenging sequences of images from a coral reef taken one year apart and acquired with two different cameras