Primary school teacher’s noticing of students’ mathematical thinking in problem solving

Professional noticing of students’ mathematical thinking in problem solving involves the identification of noteworthy mathematical ideas of students’ mathematical thinking and its interpretation to make decisions in the teaching of mathematics. The goal of this study is to begin to characterize pre-service primary school teachers’ noticing of students’ mathematical thinking when students solve tasks that involve proportional and non-proportional reasoning. From the analysis of how pre-service primary school teachers notice students’ mathematical thinking, we have identified an initial framework with four levels of development. This framework indicates a possible trajectory in the development of primary teachers’ professional noticing.

The "other" cities: urban planning and architecture for tourism: the case of the Spanish Mediterranean (1945-1975)

There we analyce the first touristic nucleus arouse in the Spanish Mediterranean coast between World War II and the Petroleum Crisis (1945-75). Special attention is payed to the characteristics of these new villages: the relation of their urban frame with nature -original or artificial- and the lack of industry. We make a distintion of three types: cluster nucleus (La Manga and El Saler), tridimentional urbanism (Playa de San Juan y Urbanova) and extreme typologies (Campoamor and Benidorm). With them the cities for vacations are discovered, mainly for second home purpouse (vacation home/holiday home). The panorama after the current crisis is a lineal chain of small urban settlements on the coast. Finally, Finally, we can see how these "secondary cities" without industry and specialized in leisure, are developing to our days until become new cities of services, doubling the existing ones; now they are "the other cities".