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.

Evolution, gene regulation and functional analysis of BMP2 in fish

Bone morphogenetic proteins (BMPs) are multifunctional growth factors belonging to the transforming growth factor β (TGFβ) superfamily with a central role in bone formation and mineralization. BMP2, a founding member of this family, has demonstrated remarkable osteogenic properties and is clinically used to promote bone repair and fracture healing. Lack of basic data on factors regulating BMP2 expression and activity have hampered a better understanding of its role in bone formation and bone-related diseases. The objective of this work was to collect new functional data and determine spatiotemporal expression patterns in a fish system aiming towards a better understanding of BMP2 function and regulation. Transcriptional and post-transcriptional regulation of gilthead seabream BMP2 gene was inferred from luciferase reporter systems. Several bone- and cartilage-related transcription factors (e.g. RUNX3, MEF2c, SOX9 and ETS1) were found to regulate BMP2 transcription, while microRNA 20a was shown to affect stability of the BMP2 transcript and thus the mineralogenic capacity of fish bone-derived host cells. The regulation of BMP2 activity through an interaction with the matrix Gla protein (MGP) was investigated in vitro using BMP responsive elements (BRE) coupled to luciferase reporter gene. Although we demonstrated the functionality of the experimental system in a fish cell line and the activation of BMP signaling pathway by seabream BMP2, no conclusive evidence could be collected on a possible interaction beween MGP and BMP2. The evolutionary relationship among the members of BMP2/4/16 subfamily was inferred from taxonomic and phylogenetic analyses. BMP16 diverged prior to BMP2 and BMP4 and should be the result of an ancient genome duplication that occurred early in vertebrate evolution. Structural and functional data suggested that all three proteins are effectors of the BMP signaling pathway, but expression data revealed different spatiotemporal patterns in teleost fish suggesting distinct mechanisms of regulation. In this work, through the collection of novel data, we provide additional insight into the regulation, the structure and the phylogenetic relationship of BMP2 and its closely related family members.