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.

An evolutive approach for the delineation of local labour markets

This paper presents a new approach to the delineation of local labour markets based on evolutionary computation. The main objective is the regionalisation of a given territory into functional regions based on commuting flows. According to the relevant literature, such regions are defined so that (a) their boundaries are rarely crossed in daily journeys to work, and (b) a high degree of intra-area movement exists. This proposal merges municipalities into functional regions by maximizing a fitness function that measures aggregate intra-region interaction under constraints of inter-region separation and minimum size. Real results are presented based on the latest database from the Census of Population in the Region of Valencia. Comparison between the results obtained through the official method which currently is most widely used (that of British Travel-to-Work Areas) and those from our approach is also presented, showing important improvements in terms of both the number of different market areas identified that meet the statistical criteria and the degree of aggregate intra-market interaction.

Enseñando a programar: un camino directo para desarrollar el pensamiento computacional

Está ampliamente aceptado que es fundamental desarrollar la habilidad de resolver problemas. El pensamiento computacional se basa en resolver problemas haciendo uso de conceptos fundamentales de la informática. Nada mejor para desarrollar la habilidad de resolver problemas usando conceptos informáticos que una asignatura de introducción a la programación. Este trabajo presenta nuestras reflexiones acerca de cómo iniciar a un estudiante en el campo de la programación de computadores. El trabajo no detalla los contenidos a impartir, sino que se centra en aspectos metodológicos, con la inclusión de experiencias y ejemplos concretos, a la vez que generales, extensibles a cualquier enseñanza de programación. En general, aunque se van desarrollado lenguajes cada vez más cercanos al lenguaje humano, la programación de ordenadores utilizando lenguajes formales no es una materia intuitiva y de fácil comprensión por parte de los estudiantes. A la persona que ya sabe programar le parece una tarea sencilla, pero al neófito no. Es más, dominar el arte de la programación es complejo. Por esta razón es indispensable utilizar todas las técnicas y herramientas posibles que faciliten dicha labor.