El aprendizaje reflexivo en la formación inicial del profesorado: un modelo para aprender a enseñar matemáticas = Reflective learning in the early formation of teachers: a model to learn to teach maths

In this study we analize the application of the reflective learning during initial formation mathematics teachers. This model is based on the sociocultural theories of the human learning and assumes that the interaction and the contrast make possible the coconstruction and the active reconstruction of knowledge.In order to make the study, it was left from a sample of 29 teaching students. The qualitative analysis allowed to identify factors that facilitate the incorporation of the reflective learning in university teaching, as well as the degree of effectiveness of this model to learn to teach mathematics

Capital formation in machinery in Latin America, 1890-1930

Investment in machinery is a key aspect in the analysis of long-term economic growth during the era of the spread of industrialisation. But, historiography has only revealed what the pace of capital accumulation was in a few Latin American economies. This article offers continuous (annual) and consistent series on the magnitude of this investment in all of the Latin American countries for the period at the height of the first globalisation, 1890-1930. The paper gives special attention to comparative analysis, showing the differences that exist at the heart of the Latin American community, in the levels of capital formation in machinery as well as in the national development of this over time. The differences in the levels appear very indicative of the unequal degree of development reached by these economies. This article puts to test the hypothesis of intraregional divergence, obtaining the tentative result that there was divergence until 1913, but that there was convergence from 1914-1930.

An experience beyond continuous assessment activities: virtual tour to the medieval medicinal plant garden of the Pedralbes monastery

[eng] The group of teaching innovation in the area of Botany (GIBAF), University of Barcelona (UB), is raised each year to design new accreditation activities under continuous evaluation framework. We present the experience carried out during the academic year 2008-09 in the course of Pharmaceutical Botany. The aim has been to involve students for a semester in the authorship of a tutored project immediately useful and of easy permanence, beyond its assessment proving usefulness. The Medicinal Plants Garden of the Monastery of Pedralbes has been used as a resource and a collaboration agreement has been signed between the UB faculty and the Institute of Culture of Barcelona. The students have developed the work using the Moodle platform CampusvirtualUB into five stages which included preparation of files by students that have been modified in some steps following the various feedbacks from teachers. At the beginning of the activity, students were provided with a complete schedule of activities, the schedule for its implementation, and a total of 18 forced-use library resources. Finally, through Google sites, a website has been implemented, allowing for a virtual tour of the garden, documenting by referenced literature 50 medicinal plants for their nomenclature, botanical description, distribution, uses historical, current and future) and toxicity. The result of the activity was presented at a public ceremony in the Monastery of Pedralbes and is available at: http://sites.google.com/site/jardimedievalpedralbes/ [spa] El grupo de innovación docente integrado por profesores del área de Botánica (GIBAF) de la Universidad de Barcelona (UB) se plantea cada curso el diseño de nuevas actividades acreditativas en el marco de la evaluación continuada. Se presenta la experiencia llevada a cabo durante el curso 2008-09 en la asignatura Botánica Farmacéutica. El objetivo ha sido implicar durante un semestre a los estudiantes en la autoría de un proyecto tutorizado de inmediata utilidad y clara perdurabilidad, más allá de su utilidad acreditativa. Como recurso se ha utilizado el Jardín de Plantas Medicinales del Monasterio de Pedralbes y se ha firmado un convenio de colaboración docente entre la UB y el Instituto de Cultura de Barcelona. Los estudiantes han realizado el trabajo utilizando la plataforma Moodle del Campus virtual de la UB en cinco etapas que han incluido la confección de unas fichas que se han ido modificando en función de las diversas retroacciones de los profesores. Al inicio de la actividad, se facilitó a los estudiantes el cronograma completo de la actividad, la pauta para su realización, así como un total de 18 recursos bibliográficos de uso obligado. Finalmente, a través de GoogleSites, se ha realizado una web que permite realizar un paseo virtual por el jardín, documentando de forma referenciada para las 50 plantas medicinales su nomenclatura, descripción botánica, distribución, usos (históricos, actuales y futuros) y toxicidad. El resultado de la actividad fue presentado en un acto público en el Monasterio de Pedralbes y puede consultarse en: http://sites.google.com/site/jardimedievalpedralbes/

Some remarks on the class of continuous (Semi-) strictcly quasiconvex functions

Vegeu el resum a l'inici del document del fitxer adjunt

Clarke critical values of subanalytic Lipschitz continuous functions

We prove that any subanalytic locally Lipschitz function has the Sard property. Such functions are typically nonsmooth and their lack of regularity necessitates the choice of some generalized notion of gradient and of critical point. In our framework these notions are defined in terms of the Clarke and of the convex-stable subdifferentials. The main result of this note asserts that for any subanalytic locally Lipschitz function the set of its Clarke critical values is locally finite. The proof relies on Pawlucki's extension of the Puiseuxlemma. In the last section we give an example of a continuous subanalytic function which is not constant on a segment of "broadly critical" points, that is, points for which we can find arbitrarily short convex combinations of gradients at nearby points.

Forecasting volatility using a continuous time model

This paper evaluates the forecasting performance of a continuous stochastic volatility model with two factors of volatility (SV2F) and compares it to those of GARCH and ARFIMA models. The empirical results show that the volatility forecasting ability of the SV2F model is better than that of the GARCH and ARFIMA models, especially when volatility seems to change pattern. We use ex-post volatility as a proxy of the realized volatility obtained from intraday data and the forecasts from the SV2F are calculated using the reprojection technique proposed by Gallant and Tauchen (1998).

Coalition formation in a contest game with three heterogeneous players

We analyze the incentives for cooperation of three players differing in their efficiency of effort in a contest game. We concentrate on the non-cooperative bargaining foundation of coalition formation, and therefore, we adopt a two-stage model. In the first stage, individuals form coalitions following a bargaining protocol similar to the one proposed by Gul (1989). Afterwards, coalitions play the contest game of Esteban and Ray (1999) within the resulting coalition structure of the first stage. We find that the grand coalition forms whenever the distribution of the bargaining power in the coalition formation game is equal to the distribution of the relative efficiency of effort. Finally, we use the case of equal bargaining power for all individuals to show that other types of coalition structures may be observed as well.

When does universal peace prevail? Secession and group formation in rent seeking contests and policy conflicts

This paper analyzes secession and group formation in a general model of contest inspired by Esteban and Ray (1999). This model encompasses as special cases rent seeking contests and policy conflicts, where agents lobby over the choice of a policy in a one-dimensional policy space. We show that in both models the grand coalition is the efficient coalition structure and agents are always better off in the grand coalition than in a symmetric coalition structure. Individual agents (in the rent seeking contest) and extremists (in the policy conflict) only have an incentive to secede when they anticipate that their secession will not be followed by additional secessions. Incentives to secede are lower when agents cooperate inside groups. The grand coalition emerges as the unique subgame perfect equilibrium outcome of a sequential game of coalition formation in rent seeking contests.

The possibility for continuous growth with exhaustible resources: unknowingly an agreement has been reached, but it may not be correct

It is the size of the elasticity of substitution that has been the central issue in the long debate over the possibility of continuous growth in the presence of exhaustible resources. This paper reviews the debate and comes to the surprising conclusion that , unnoticed by the pessimists, the optimist position has gradually evolved so that it now approximates that of the pessimists. The paper also summarises some preliminary work by the author that indicates that this common position may not be correct

Sequential formation of coalitions through bilateral agreements

We study a sequential protocol of endogenous coalition formation based on a process of bilateral agreements among the players. We apply the game to a Cournot environment with linear demand and constant average costs. We show that the final outcome of any Subgame Perfect Equilibrium of the game is the grand coalition, provided the initial number of firms is high enough and they are sufficiently patient.

Unemployment and wage formation in a growth model with public capital

We study the relation between public capital, employment and growth under different assumptions concerning wage formation. We show that public capital increases economic growth, and that, if there is wage inertia, employment positively depends on both economic growth and public capital.

Consumption externalities, habit formation, and equilibrium efficiency

We analyze the welfare properties of the competitive equilibrium in a capital accumulation model where individual preferences are subjected to both habit formation and consumption spillovers. We also discuss how consumption externalities and habits interact to generate an inefficient dynamic equilibrium. Finally, we characterize optimal tax policies aimed to restore efficient decentralized paths.

Growth, habit formation, and catching-up\ with the Joneses

When habits are introduced multiplicatively in a capital accumulation model, the consumers' objective function might fail to be concave. In this paper we provide conditions aimed at guaranteeing the existence of interior solutions to the consumers' problem. We also characterize the equilibrium path of two growth models with multiplicative habits: the internal habit formation model, where individual habits coincide with own past consumption, and the external habit formation (or catching-up with the Joneses) model, where habits arise from the average past consumption in the economy. We show that the introduction of external habits makes the equilibrium path inefficient during the transition towards the balanced growth path. We characterize in this context the optimal tax policy.

Income taxation with habit formation and consumption externalities

We analyze the dynamic behavior and the welfare properties of the equilibrium path of a growth model where both habits and consumption externalities affect the utility of consumers. We discuss the effects of flat rate income taxes and characterize the optimal income taxation policy. We show that, when consumption externalities and habit adjusted consumption are not perfect substitutes, a counter-cyclical income tax rate allows the competitive equilibrium to replicate the efficient path. Our analysis highlights the crucial role played by complementarities between externalities and habits in order to generate an inefficient dynamic equilibrium.