Discussing a teacher MKT and its role on teacher practice when exploring data analysis

This article considers teacher knowledge in managing mathematically critical situations and the role of what can be termed a mathematical summary in the analysis of a teaching episode, viewed from the perspective of Mathematical Knowledge for Teaching (MKT). The analysis is based on an episode of content review, from a perspective which aims to understand the teacher’s logic rather than merely identify gaps in their knowledge. We discuss the importance of approaching mathematically critical situations in order to contribute to eradicating mathematical innumeracy (statistics) and to promote a kind of practice which is “mathematically demanding” as well as “pedagogically exciting”

Assessing welfare impacts of some debt-consolidation episodes in the European Union

This paper aims at characterizing debt consolidation processes put forward by some European countries in order to assess welfare and, in particular, the inequality effects involved. For that we built a general equilibrium heterogeneous-agent model capable of exploring the relationship between fiscal policy variables and the endogenous crosssection distribution of income and wealth. Results show that, with the exception of the Belgian case, all consolidation strategies entail positive welfare gains. The transition costs affect all episodes and are determinant in sorting among the welfareenhancing strategies. Our results confirm the superiority of the adjustments based on unproductive expenditures over those based on tax increases or social transfer reductions. Finally, all strategies involve lower welfare inequality costs.fiscal consolidation dynamics, European Union, heterogeneous agent model, inequality, welfare.

Welfare-improving Government Behaviour and Inequality - Inspection Using a Heterogeneous-agent Model

Governments behavior is expected to be non-neutral in terms of impacts on both welfare and inequality. In spite of their multivariate form, a tentative assessment of such inequality impacts can be provided by using a general equilibrium model with heterogeneous-agents and where wealth and income distribution is determined endogenously. Using a model capable of exploring the relationship between fiscal policy variables and the endogenous cross-section distribution of income, wealth, consumption and leisure, this paper produces a welfare and inequality analysis of several equilibriums resulting from different combinations of debt levels and of government budget variables. Moreover, such assessment is based on the empirical reality of the EU countries.government budget composition and debt, heterogeneous agent model, idiosyncratic shock, inequality, welfare.

Dirac points merging and wandering in a model Chern insulator

We present a model for a Chern insulator on the square lattice with complex first and second neighbor hoppings and a sublattice potential which displays an unexpectedly rich physics. Similarly to the celebrated Haldane model, the proposed Chern insulator has two topologically non-trivial phases with Chern numbers $\pm1$. As a distinctive feature of the present model, phase transitions are associated to Dirac points that can move, merge and split in momentum space, at odds with Haldane's Chern insulator where Dirac points are bound to the corners of the hexagonal Brillouin zone. Additionally, the obtained phase diagram reveals a peculiar phase transition line between two distinct topological phases, in contrast to the Haldane model where such transition is reduced to a point with zero sublattice potential. The model is amenable to be simulated in optical lattices, facilitating the study of phase transitions between two distinct topological phases and the experimental analysis of Dirac points merging and wandering

CONVERSION to ORGANIC FARMING in MAINLAND PORTUGAL

The objectives of the research were: i) to assess the in-conversion period as a barrier impeding farms conversion to organic; ii) to assess the potential of conversion-grade markets in removing this barrier; iii) to identify other barriers (drives) along the food chain impeding (easing) farms conversion in mainland Portugal. Results show that the in-conversion period is not the major barrier to conversion nor is a good idea the set-up of conversion grade markets to help Portuguese farms’ conversion. Conversion feasibility depends of the organic market premium prices, in intensive farms, and of the CAP organic agri-environmental area payments, in extensive farms.organic farming, conversion, conversion grade markets, market premium prices, CAP payments.

The Impacts of Structural Changes in the Labor Market: a Comparative Statics Analysis Using Heterogeneous-agent Framework

In this paper we aim at analyzing the impacts on welfare and wealth and consumption distribution across different labor market structural features. In particular, we pursue a steady-state analysis to assess the impacts of unit vacancy costs, unemployment replacement ratio or the job destruction rate, when they are changed in order to promote a given reduction in the unemployment rate. We combine a labor market search and matching framework with unions, based on Mortensen and Pissarides (1994) with a heterogeneous-agent framework close to Imrohoroglu (1989) in a closed economy model. Such approach enables the joint assessment of macroeconomic welfare and inequality together with implications derived from institutional changes in labor market. Moreover, the transition matrix between worker's states is endogenous, fully derived from labor market conditions. Using feasible calibration to the Euro Area, we conclude that different institutional changes to promote unemployment reduction have non-neutral and differentiated effects on welfare and inequality. While changing unit vacancy costs and job destruction can be ranked, changes in the unemployment benefit replacement ration involve a trade-off between gains in welfare and in consumption/income distribution.Labor market institutions, search and matching models, heterogeneous-agent models, welfare and inequality.

Conhecimento e desenvolvimento profissional do professor. Analisando a prática de Maria, uma professora do 1.º Ciclo

Como qualquer profissional, cumpre-nos, no papel de formadores, o dever de procurar, a cada momento, uma melhoria da nossa atuação e da formação que facultamos. Enquanto formador de professores, esta assunção foi um dos motivos que conduziu à elaboração de uma investigação centrada no desenvolvimento profissional do professor focando, em particular, algumas das dimensões que considero centrais no seu conhecimento profissional (crenças, objetivos, conhecimentos – mathematical knowledge for teaching – e tipos de comunicação matemática promovidos), tendo para isso sido desenvolvidos dois modelos de análise complementares (Modelo Cognitivo e de Representação do Desenvolvimento Profissional – MRDP). Neste texto, a partir da análise da prática, analisam-se e discutem-se as “evoluções” das relações entre as dimensões em análise, recorrendo aos dois modelos. Inicio com algumas considerações sobre cada uma das dimensões em análise e, com recurso a um exemplo da prática, ilustro a aplicação do MRDP. A utilização destes modelos permite obter uma mais ampla compreensão da prática, dos fatores que a influenciam e como a influenciam, revelando-se o MRDP um potente instrumento que permite uma mais clara representação visual das alterações e persistências que se verificam na prática ao longo do tempo, sendo estas (in)alterações encaradas em termos da reflexividade do professor sobre a sua prática. Um outro aspeto relevante relacionase com as potencialidades do recurso a ambos os modelos para a/na formação de professores e o papel que podem assumir nela