Feedback-related Brain Potential Activity Complies with Basic Assumptions of Associative Learning Theory

Feedback-related negativity (FRN) is an ERP component that distinguishes positive from negative feedback. FRN has been hypothesized to be the product of an error signal that may be used to adjust future behavior. In addition, associative learning models assume that the trial-to-trial learning of cueoutcome mappings involves the minimization of an error term. This study evaluated whether FRN is a possible electrophysiological correlate of this error term in a predictive learning task where human subjects were asked to learn different cueoutcome relationships. Specifically, we evaluated the sensitivity of the FRN to the course of learning when different stimuli interact or compete to become a predictor of certain outcomes. Importantly, some of these cues were blocked by more informative or predictive cues (i.e., the blocking effect). Interestingly, the present results show that both learning and blocking affect the amplitude of the FRN component. Furthermore, independent analyses of positive and negative feedback event-related signals showed that the learning effect was restricted to the ERP component elicited by positive feedback. The blocking test showed differences in the FRN magnitude between a predictive and a blocked cue. Overall, the present results show that ERPs that are related to feedback processing correspond to the main predictions of associative learning models. ■

Una Aproximació a la construcció significativa del coneixement matemàtic a l'ESO

This study displays and analyzes the contents of the Mathematics subject in ESO’s second cycle from a constructivist perspective. This analysis has been carried out by contrasting two groups of participants (control group and experimental group). These groups were formed by a sample of 240 students between the ages of 14 and 16 from four different educational centres of the Osona area. Research – Action methodology has been employed, combining quantitative techniques (statistical study with the SPSS package) with qualitative analysis (transcriptions of interviews and discussion group). This study has been carried out after years of classroom observation, reflection and action. The theoretical framework employed is a cognitive one, based on Ausubel’s Significative Learning Theory. Quantitative analysis shows how the researcher’s design improves, on the one hand, the students’ academic motivation and, on the other hand, their comprehensive memory, enabling them to achieve a more significant learning of the subjects’ contents. Furthermore, our analysis shows that the proposed method is more comprehensive than those employed by teachers collaborating with control groups. The main aim of the qualitative analysis is that of identifying the elements which configure the programme and contribute to an improvement of the aspects mentioned above. The key elements here are: co-operation as the basis of group dynamics; the employment, in some cases, of easily handled materials; the type of interaction between teacher and students, where, through open discussion, students are lead by teaching staff towards the course objectives; induction, that is, deducing formulae by initially using examples which are close to the students’ knowledge and experience or taken from everyday life (what we could call “down-top” mathematics). We should add here that the qualitative analysis does not only corroborate the results obtained by quantitative techniques, but also displays an increase of motivation in teaching staff. Teachers did show a positive attitude and welcomed the use and development of these materials in the next academic year. Finally, we discuss possible directions for further research.

Algebraic properties of isochronous centers of polynomial quadratic-like Hamiltonian systems

Projecte de recerca elaborat a partir d’una estada a la School of Mathematics and Statistics de la University of Plymouth, United Kingdom, entre abril juliol del 2007.Aquesta investigació és encara oberta i la memòria que presento constitueix un informe de la recerca que estem duent a terme actualment. En aquesta nota estudiem els centres isòcrons dels sistemes Hamiltonians analítics, parant especial atenció en el cas polinomial. Ens centrem en els anomenats quadratic-like Hamiltonian systems. Diverses propietats dels centres isòcrons d'aquest tipus de sistemes van ser donades a [A. Cima, F. Mañosas and J. Villadelprat, Isochronicity for several classes of Hamiltonian systems, J. Di®erential Equations 157 (1999) 373{413]. Aquell article estava centrat principalment en el cas en que A; B i C fossin funcions analítiques. El nostre objectiu amb l'estudi que estem duent a terme és investigar el cas en el que aquestes funcions són polinomis. En aquesta nota formulem una conjectura concreta sobre les propietats algebraiques que venen forçades per la isocronia del centre i provem alguns resultats parcials.

The effects of teacher talk on students’ oral productions

The present study is a brief personal enquiry into the teaching and learning of EFL in the classroom with an orientation to action and personal professional development. It focuses on teacher talk, making special emphasis on questions, as well as on students’ resulting oral productions. The research contains samples of empirical data, which include their interpretations in the light of relevant research literature, and a more personal overall reflection of the teaching practice. Both the analysis and the reflections derive to a large extent from the self-observation paper 1 (SO1) and the Practicum portfolio (PP) developed within the TED Masters Degree practicum stages

A teaching/learning support tool for introductory programming courses

In This work we present a Web-based tool developed with the aim of reinforcing teaching and learning of introductory programming courses. This tool provides support for teaching and learning. From the teacher's perspective the system introduces important gains with respect to the classical teaching methodology. It reinforces lecture and laboratory sessions, makes it possible to give personalized attention to the student, assesses the degree of participation of the students and most importantly, performs a continuous assessment of the student's progress. From the student's perspective it provides a learning framework, consisting in a help environment and a correction environment, which facilitates their personal work. With this tool students are more motivated to do programming

The interactional space in CLIL (Content and Language Integrated Learning) and EFL (English as a Foreign Language) classrooms

Aquest estudi pretén investigar els intercanvis verbals mestre/a – aprenent(s) en dos contextos d'instrucció diferents: classes amb un enfocament AICLE (Aprenentatge Integrat de Continguts Curriculars i Llengua Estrangera) on s’aprenen continguts no lingüístics a través de l’anglès, per una banda, i classes 'tradicionals' d'anglès com a llengua estrangera, on l’anglès és alhora objecte d’estudi i vehicle de comunicació, per una altra banda. Més concretament, les preguntes que formula el/la mestre/a, la producció oral dels aprenents i el 'feedback' del/de la mestre/a en els episodis d’atenció a la forma s’han estudiat a la llum de les principals teories provinents del camp de l’Adquisició de Segones Llengües (SLA) per tal de demostrar el seu paper en l’aprenentatge de l’anglès. El corpus de dades prové de l’enregistrament de 7 sessions AICLE i d'11 sessions EFL enregistrades en format àudio i vídeo en dos centres públics d’Educació Primària (EP) de Catalunya. A cadascuna de les escoles, el/la mateix/a mestre/a és l’encarregat/da dels dos tipus d’instrucció amb el mateix grup d’aprenents (10-11 anys d’edat), fet que permet eliminar variables individuals com l'aptitud dels aprenents o l'estil del/de la mestre/a.Els resultats mostren un cert nombre de similituds discursives entre AICLE i EFL donat que ambdós enfocaments tenen lloc en el context-classe amb unes característiques ben definides. Tal com apunta la recerca realitzada en aquest camp, la instrucció AICLE reuneix un seguit de condicions idònies per un major desenvolupament dels nivells de llengua anglesa més enllà de les classes ‘tradicionals’ d’anglès. Malgrat això, aquest estudi sembla indicar que el potencial d'AICLE pel que fa a facilitar una exposició rica a l’anglès i una producció oral significativa no s’explota degudament. En aquest sentit, els resultats d’aquest estudi poden contribuir a la formació dels futurs professors d'AICLE si es busca l’assoliment d’una complementarietat d’ambdós contextos amb l’objectiu últim de millorar els nivells de domini de la llengua anglesa.

Resolució de problemes i mètode de raonament en l'educació matemàtica

Des del principi dels temps històrics, la Matemàtica s'ha generat en totes les civilitzacions sobre la base de la resolució de problemes pràctics.Tanmateix, a partir del període grec la Història ens mostra la necessitat de fer un pas més endavant: l'evolució històrica de la Matemàtica situa els mètodes de raonament com a eix central de la recerca en Matemàtica. A partir d'una ullada als objectius i mètodes de treball d'alguns autors cabdals en la Història dels conceptes matemàtics postulem l'aprenentatge de les formes de raonament matemàtic com l'objectiu central de l'educació matemàtica, i la resolució de problemes com el mitjà més eficient per a coronar aquest objectiu.English version.From the beginning of the historical times, mathematics has been generated in all the civilizations on the base of the resolution of practical problems. Nevertheless, from the greek period History shows us the necessity to take one more step: the historical evolution of mathematics locates the methods of reasoning as the central axis of the research in mathematics. Glancing over the objectives and methods of work used bysome fundamental authors in the History of the mathematical concepts we postulated the learning of the forms of mathematical reasoning like the central objective of the mathematical education, and the resolution of problems as the most efficient way to carry out this objective.

On a series of Goldbach and Euler

Theorem 1 of Euler s paper of 1737 'Variae Observationes Circa Series Infinitas', states the astonishing result that the series of all unit fractions whose denominators are perfect powers of integers minus unity has sum one. Euler attributes the Theorem to Goldbach. The proof is one of those examples of misuse of divergent series to obtain correct results so frequent during the seventeenth and eighteenth centuries. We examine this proof closelyand, with the help of some insight provided by a modern (and completely dierent) proof of the Goldbach-Euler Theorem, we present a rational reconstruction in terms which could be considered rigorous by modern Weierstrassian standards. At the same time, with a few ideas borrowed from nonstandard analysis we see how the same reconstruction can be also be considered rigorous by modern Robinsonian standards. This last approach, though, is completely in tune with Goldbach and Euler s proof. We hope to convince the reader then how, a few simple ideas from nonstandard analysis, vindicate Euler's work.

Mathematics in Catalonia: 1996-2002

The aim of this article is to present the main conclusions of the Report on research in Catalonia for the area of mathematics**. The report was prepared by Joaquim Bruna, Marta Sanz, Joan de Solà-Morales and the author of this text, and published by the Institute for Catalan Studies in 1998. In the report, scientific activity in the area of mathematics was measured essentially by examining two parameters: papers published in specialised journals and doctoral theses read. It should be recognised that a considerable amount of activity in the field of mathematics consists of applying existing knowledge to the resolution of practical technological problems that arise in particular companies. This kind of scientific activity was not measured in any way in the report due to the difficulty of obtaining objective data. This article is divided into the following sections: human resources, scientific production, funding, research publications, research centres, and conclusions.

The Arts (Music, Arts&Crafts and Drama) as a procedure for learning pre-school content: Grupo Edebé Project

There is nothing as amazing and fascinating as children learning process. Between 0 and 6 years old, a child brain develops in a waythat will never be repeated. At this age, children are eager to discover and they have great potential of active and affective life.Because of this, their learning capacity in this period is incalculable. (Jordan-Decarbo y Nelson, 2002; Wild, 1999).Pre-school Education is a unique and special stage, with self identity, which aims are:attending children as a whole,motivate them to learn,give them an affective and stable environment in which they can grow up and get to be balanced and confident people and inwhich they can relate to others, learn, enjoy and be happy.Arts, Music, Visual Arts and Drama (Gardner, 1994) can provide a framework of special, even unique, personal expression.With the aim of introducing qualitative improvements in the education of children and to ensure their emotional wellbeing, and havingnoticed that teachers had important needs and concerns as regards to diversity in their student groups, we developed a programbased on the detection of needs and concerns explained by professionals in education.This program of Grupo edebé, object of our research, is a multicultural, interdisciplinary and globalizing project the aims of which are:developing children's talent and personality,keeping their imagination and creativity and using these as a learning resource,promoting reasoning, favouring expression and communication,providing children with the tools to manage their emotions,and especially, introducing Arts as a procedure to increase learning.We wanted to start the research by studying the impact (Brice, 2003) that this last point had on the learning of five-year-old childrenschooled in multicultural environments.Therefore, the main goal of the research was the assessment of the implementation of a child education programme attending todiversity in a population of five-year-old children, specifically in the practice of procedures based on the use of Arts (music, arts andcrafts and theatre) as a vehicle or procedure for learning contents in Pre-school stage.Because children emotional welfare was a subject of our concern, and bearing in mind that the affective aspects are of vitalimportance for learning and child development (Parke and Gauvain, 2009), Grupo Edebé has also evaluated the starting, evolving andfinal impact in five-year-old children given that they finish Pre-school education at that age.

Diversitat cultural i matemàtiques

En aquesta recerca es presenten els resultats i les conclusions d’unes entrevistes realitzades a pares i mares d’alumnes de quart de primària de diferents orígens culturals, amb l’objectiu de descobrir el valor que cada família dóna a les matemàtiques, d’observar amb quines dificultats es troben els pares i mares quan han d’ajudar als seus fills i filles a fer els deures de matemàtiques, a més d’esbrinar quins recursos i/o estratègies tenen per ajudar-los. Per altra banda, també es vol saber si les experiències que tenen els adults en relació amb les matemàtiques afecta a l’ensenyament-aprenentatge dels seus fills i filles.

Symmetries of the free Schrödinger equation in the non-commutative plane

We study all the symmetries of the free Schr odinger equation in the non-commu- tative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetries could be useful for constructing non-relativistic interacting higher spin theories. A finite-dimensional subalgebra is given by the Schröodinger algebra which, besides the Galilei generators, contains also the dilatation and the expansion. We consider the quantization of the symmetry generators in both the reduced and extended phase spaces, and discuss the relation between both approaches.

Symmetries of the free Schrödinger equation in the non-commutative plane

We study all the symmetries of the free Schrödinger equation in the non-commu- tative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetries could be useful for constructing non-relativistic interacting higher spin theories. A finite-dimensional subalgebra is given by the Schröodinger algebra which, besides the Galilei generators, contains also the dilatation and the expansion. We consider the quantization of the symmetry generators in both the reduced and extended phase spaces, and discuss the relation between both approaches.

Teaching fundamentals of computing theory: a constructivist approach

A Fundamentals of Computing Theory course involves different topics that are core to the Computer Science curricula and whose level of abstraction makes them difficult both to teach and to learn. Such difficulty stems from the complexity of the abstract notions involved and the required mathematical background. Surveys conducted among our students showed that many of them were applying some theoretical concepts mechanically rather than developing significant learning. This paper shows a number of didactic strategies that we introduced in the Fundamentals of Computing Theory curricula to cope with the above problem. The proposed strategies were based on a stronger use of technology and a constructivist approach. The final goal was to promote more significant learning of the course topics.

Method development for the simultaneous determination of methylmercury and inorganic mercury in seafood

This paper reports the method development for the simultaneous determination of methylmercury MeHgþ) and inorganic mercury (iHg) species in seafood samples. The study focused on the extraction and quantification of MeHgþ (the most toxic species) by liquid chromatography coupled to on-line UV irradiation and cold vapour atomic fluorescence spectroscopy (LC-UV-CV-AFS), using HCl 4 mol/L as the extractant agent. Accuracy of the method has been verified by analysing three certified reference materials and different spiked samples. The values found for total Hg and MeHgþ for the CRMs did not differ significantly from certified values at a 95% confidence level, and recoveries between 85% and 97% for MeHgþ, based on spikes, were achieved. The detection limits (LODs) obtained were 0.001 mg Hg/kg for total mercury, 0.0003 mg Hg/kg for MeHgþ and 0.0004 mg Hg/kg for iHg. The quantification limits (LOQs) established were 0.003 mg Hg/kg for total mercury, 0.0010 mg Hg/kg for MeHgþ and 0.0012 mg Hg/kg for iHg. Precision for each mercury species was established, being 12% in terms of RSD in all cases. Finally, the developed method was applied to 24 seafood samples from different origins and total mercury contents. The concentrations for Total Hg, MeHg and iHg ranged from 0.07 to 2.33, 0.003-2.23 and 0.006-0.085 mg Hg/kg, respectively. The established analytical method allows to obtain results for mercury speciation in less than 1 one hour including both, sample pretreatment and measuring step.