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.

Organisational structure, communication and group ethics

This paper investigates experimentally how organisational decision processes affect the moral motivations of actors inside a firm that must forego profits to reduce harming a third party. In a "vertical" treatment, one insider unilaterally sets the harm-reduction strategy; the other can only accept or quit. In a "horizontal" treatment, the insiders decide by consensus. Our 2-by-2 design also controls for communication effects. In our data, communication makes vertical firms more ethical; voice appears to mitigate "responsibility-alleviation" in that subordinates with voice feel responsible for what their firms do. Vertical firms are then more ethical than the horizontal firms for which our bargaining data reveal a dynamic form of responsibility-alleviation and our chat data indicate a strong "insider-outsider" effect.

Minimal lenght elements of Thompson's groups F(p)

We describe a method for determining the minimal length of elements in the generalized Thompson's groups F(p). We compute the length of an element by constructing a tree pair diagram for the element, classifying the nodes of the tree and summing associated weights from the pairs of node classifications. We use this method to effectively find minimal length representatives of an element.

Contraction groups in complete Kac-Moody groups

Let G be an abstract Kac-Moody group over a finite field and G the closure of the image of G in the automorphism group of its positive building. We show that if the Dynkin diagram associated to G is irreducible and neither of spherical nor of affine type, then the contraction groups of elements in G which are not topologically periodic are not closed. (In those groups there always exist elements which are not topologically periodic.)

Itinerari d'educació ambiental: petjades a Comes de Rubió

El Parc Natural de l’Alt Pirineu (PNAP) va ser creat l’any 2003. A causa de la seva recent creació, manca el desenvolupament de moltes de les seves àrees. Actualment, el parc està creant una xarxa d’itineraris d’Educació Ambiental (EA). Per aquesta raó, és interessant dedicar aquest treball al disseny d’un itinerari d’EA a la zona de Comes de Rubió, situada dins l’àmbit territorial del PNAP. L’objectiu principal del present projecte és l’elaboració d’aquest itinerari amb els recursos necessaris per tal que sigui implementable d’una manera immediata. Per tal d’analitzar la viabilitat de l’itinerari s’ha aplicat el protocol de valoració dissenyat pel grup Edukamb. La puntuació que s’ha obtingut ha estat 61 sobre 100, fet que indica que l’itinerari és viable tot i que compta amb algunes mancances. S’ha constatat que les condicions de l’itinerari són idònies per poder ser visitat pel públic en general, entre altres coses per la forma circular de l’itinerari, per tenir 3 km de recorregut i per disposar d’una gran varietat d’aspectes d’interès. En el disseny de l’itinerari s’ha definit el recorregut, s’han determinat els elements d’interès, s’han proposat 5 parades, s’han dissenyat els materials pedagògics, s’ha definit la situació de la senyalització i s’han proposat correccions per a les mancances detectades en el protocol, entre altres, una millora en l’accessibilitat al punt d’inici i la construcció de passeres en els punts potencialment erosionables. Les principals pautes a seguir a l’hora d’elaborar el material pedagògic han estat la integració de l’aspecte social amb el natural i la promoció de la sensibilització envers el medi ambient.

Inter-group conflict and intra-group punishment in an experimental contest game

We study how conflict in a contest game is influenced by rival parties being groups and by group members being able to punish each other. Our main motivation stems from the analysis of socio-political conflict. The relevant theoretical prediction in our setting is that conflict expenditures are independent of group size and independent of whether punishment is available or not. We find, first, that our results contradict the independence of group-size prediction: conflict expenditures of groups are substantially larger than those of individuals, and both are substantially above equilibrium. Towards the end of the experiment material losses in groups are 257% of the predicted level. There is, however, substantial heterogeneity in the investment behaviour of individual group members. Second, allowing group members to punish each other after individual contributions to the contest effort are revealed leads to even larger conflict expenditures. Now material losses are 869% of the equilibrium level and there is much less heterogeneity in individual group members' investments. These results contrast strongly with those from public goods experiments where punishment enhances efficiency and leads to higher material payoffs.

The Measurement of social polarization in a multi-group context

Polarization indices presented up to now have only focused their attention on the distribution of income/wealth. However, in many circumstances income is not the only relevant dimension that might be the cause of social conflict, so it is very important to have a social polarization index able to cope with alternative dimensions. In this paper we present an axiomatic characterization of one of such indices: it has been obtained as an extension of the (income) polarization measure introduced in Duclos, Esteban and Ray (2004) to a wider domain. It turns out that the axiomatic structure introduced in that paper alone is not appropriate to obtain a fully satisfactory characterization of our measure, so additional axioms are proposed. As a byproduct, we present an alternative axiomatization of the aforementioned income polarization measure.

Tree automorphisms and quasi-isometries of Thompson's group F

We prove that automorphisms of the infinite binary rooted tree T2 do not yield quasi-isometries of Thompson's group F, except for the map which reverses orientation on the unit interval, a natural outer automorphism of F. This map, together with the identity map, forms a subgroup of Aut(T2) consisting of 2-adic automorphisms, following standard terminology used in the study of branch groups. However, for more general p, we show that the analgous groups of p-adic tree automorphisms do not give rise to quasiisometries of F(p).

Individual versus group strategy-proofness: when do they coincide?

A social choice function is group strategy-proof on a domain if no group of agents can manipulate its final outcome to their own benefit by declaring false preferences on that domain. Group strategy-proofness is a very attractive requirement of incentive compatibility. But in many cases it is hard or impossible to find nontrivial social choice functions satisfying even the weakest condition of individual strategy-proofness. However, there are a number of economically significant domains where interesting rules satisfying individual strategy-proofness can be defined, and for some of them, all these rules turn out to also satisfy the stronger requirement of group strategy-proofness. This is the case, for example, when preferences are single-peaked or single-dipped. In other cases, this equivalence does not hold. We provide sufficient conditions defining domains of preferences guaranteeing that individual and group strategy-proofness are equivalent for all rules defined on the

The loop group and the cobar construction

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

Singular integrals on Ahlfors-David regular subsets of the Heisenberg group

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

Itinerari d'educació ambiental i sensorial de Sant Pere del Burgal

El Parc Natural de l’Alt Pirineu (PNAP) va ser creat l’any 2003. Actualment, el parc està desenvolupant una xarxa d’itineraris d’Educació Ambiental (EA). L’Ecomuseu de la Vall d’Àneu (EVA) ofereix rutes guiades al sender del Monestir de Sant Pere del Burgal, ja senyalitzat i equipat pel PNAP, en estar inscrit al seu àmbit territorial. Es tracta d’un sender de fàcil accés i recorregut, molt ample al primer tram tot oferint una gran varietat d’aspectes d’interès. L’objectiu principal del present projecte és plantejar un itinerari d’EA sensorial adaptat als col·lectius amb mobilitat reduïda i persones invidents. Amb aquesta finalitat es desenvolupen continguts i materials didàctics i es determinen les accions que els articularan. En un primer moment s'ha analitzat la viabilitat de l’itinerari aplicant el protocol de valoració dissenyat pel grup Edukamb. La puntuació obtinguda és de 74 punts sobre 100, corroborant la idoneïtat del seu recorregut pels visitants. En el disseny de l’itinerari, s’han determinat els elements i processos d’interès a l’entorn, s’han proposat quatre parades sensorials i una pasarel·la de fusta al primer tram i quatre parades de component antropològica i la instal·lació d’una corda perimetral al segon tram. Finalment també, la instal·lació de maquetes tridimensionals tàctils, una descriptiva dels aspectes i les parades de l’itinerari a l’inici del camí i una arquitectònica de l’entorn del monestir en arrivar al mateix. S’han proposat millores en la senyalització present, alternatives i complements al material pedagògic considerat al projecte i el disseny de protocols de valoració per itineraris adaptats a tot tipus de col·lectius.