Dialogical identities in students from cultural minorities or students categorised as presenting SEN: How do they shape learning, namely in mathematics?

Portuguese schools are multicultural. Diversity is their main characteristic. Portuguese policy documents assume inclusive principles (Ainscow & César, 2006). Students categorised as presenting Special Educational Needs (SEN) attend mainstream schools. Multiculturality and diversity are challenges to the educational system. We assume that teachers need to (re)construct the curricula, conceiving it as a mediating tool (César & Oliveira, 2005). Collaborative work facilitate students’ knowledge appropriation, the development of competencies (Elbers & de Haan, 2005), and the emergence of a learning community (Lave & Wenger, 1991). Students can be empowered and (re)construct their identities, including students whose voices are usually silenced. Identities are conceived as dialogical and conflictive (Hermans, 2001), particularly when the students’ cultures are far away from the school’s cultures, and transitions between them are difficult (César, 2003). These data are from the Interaction and Knowledge project whose main goal was to study and promote collaborative work in formal educational settings. It lasted 12 years, including classes all over the country (5th - 12th grades, 9/10 - 17/18 years old). It had two levels: (1) quasi experimental studies where different types of dyads were studied (César, 1994; Carvalho, 2001); (2) action-research studies based on interpretative/qualitative approaches, inspired in ethnographic methods; collaborative work was implemented during at least a school year (César & Santos, 2006). A ten years follow up was implemented. The cases in discussion were from two 9th grade classes, in two schools near Lisbon. Participant observation (different observers, including external evaluators; audio and/or videotaped), questionnaires, interviews, instruments inspired in projective tasks, students’ protocols and several documents were the data collecting instruments. The data analysis was a systematic and recurrent content analysis. The inductive categories and the interpretations that emerged were then discussed among the participants and by the project research group. The results illuminate that collaborative work and being part of a learning community can be powerful tools that allow students to (re)construct their identities, namely their identity as (mathematics) students. Collaborative work empowered students and had an impact in their life paths even many years after leaving the project. The participants’ accounts illuminate the role of teachers’ practices in their identities, as well as the conflicts these students had to face, namely the ones related to their cultures and to the experiences related to their categorisation as presenting SEN. Learning how to deal with these conflicts is an essential step to school achievement and to avoid exclusion

Isoperimetric and stable sets for log-concave perturbations of Gaussian measures

Let $\Omega$ be an open half-space or slab in $\mathbb{R}^{n+1}$ endowed with a perturbation of the Gaussian measure of the form $f(p):=\exp(\omega(p)-c|p|^2)$, where $c>0$ and $\omega$ is a smooth concave function depending only on the signed distance from the linear hyperplane parallel to $\partial\Omega$. In this work we follow a variational approach to show that half-spaces perpendicular to $\partial\Omega$ uniquely minimize the weighted perimeter in $\Omega$ among sets enclosing the same weighted volume. The main ingredient of the proof is the characterization of half-spaces parallel or perpendicular to $\partial\Omega$ as the unique stable sets with small singular set and null weighted capacity. Our methods also apply for $\Omega=\mathbb{R}^{n+1}$, which produces in particular the classification of stable sets in Gauss space and a new proof of the Gaussian isoperimetric inequality. Finally, we use optimal transport to study the weighted minimizers when the perturbation term $\omega$ is concave and possibly non-smooth.Comment: final version, to appear in Analysis and Geometry in Metric Space

Small firms, borrowing constraints, and reputation

This paper presents a simple model relating firm age with firm size and access to credit markets. Lending to new firms is risky because lenders have had no time to accumulate observations about them. As a result, interest rates are high and loans are small for entering firms. As firms need credit to operate, credit markets impose a limit on the scale of operation of new firms. Reputation building by the firms allows markets to overcome these difficulties over time. Large firms face lower interest rates than small firms, and credit markets fluctuations are shown to have different effects on firms of different size