Accessing prospective early years’ teachers’ knowledge on fractions in order to design tasks for developing teachers’ MKT

Fractions is perhaps one of the most complex and difficult topics pupils explore in the early years of schooling. Difficulties in learning this topic may have its genesis in the fact that fractions comprise a multifaceted construct (Kieren, 1995) or can be conceived as being grounded in the instructional approaches employed to teach fractions (Behr, Harel, Post & Lesh, 1993). Thus, students’ limited understanding might be related to how their teachers understand and interpret fractions — it’s thus related with teachers’ knowledge and practice. Although there is a generalized agreement on teachers’ role on/for students learning, most research on fractions focus on students, leaving aside teachers’ role (and their knowledge on the topic). Thus, teachers’ training has in certain respects been left behind. We still know little about how teachers’ knowledge on fractions influences students’ broader view of mathematics, and its connection and evolution within and along schooling. Aimed at conceptualize ways of improving teachers’ knowledge, training and practices, it’s of fundamental importance to access the areas of knowledge (here conceived as mathematical knowledge for teaching (MKT) (Ball, Thames & Phelps, 2008) in which (prospective) teachers are more deficitaries.

Using data envelopment analysis to assess the efficiency of social security systems: the case of income protection in old age

As the number of pensioners in Europe rises relative to the number of people in employment, the gap between the contributions and the benefit levels increases, and consequently ensuring adequate pensions on a sustainable basis has become a major challenge. This study aims to explore the potential of using the Data Envelopment Analysis (DEA) technique in order to access the efficiency of the income protection in old age, one of the most important branches of Social Security. To this effect, we collected data from the 27 European Union Member States regarding this branch. Our results show important differences among the Member States and stress the importance of identifying best practices to achieve more adequate, sustainable and modernised pension systems. Our results also highlight the importance of using DEA as a decision support tool for policy makers.