The transition to secondary school geometry: Can there be a "chain of school mathematics"?

Students mainly perceive the transition to secondary school as an opportunity to start their school career anew. Reality often proves them wrong, especially in the case of mathematics. In our paper, we briefly discuss children's transition to secondary school as both an opportunity and a problem, with reference to the Greek context. In discussions about the transition to secondary school and its effect on the teaching and learning of mathematics, primary and secondary school teachers in Greece often depict school mathematics as a "chain" of concepts and procedures. With this metaphor as our reference point, we discuss how ideologies about the teaching of mathematics are enacted in both school levels. We will base our discussion on the analysis of extracts taken from dialogues in primary and secondary school mathematics classrooms in Greece. In our analysis, we employ a Peircean view of semiotics in an attempt to conceptualize students' rushed introduction to rigor in justifying mathematical statements in secondary school. These extracts are part of a longitudinal study that aimed, on the one hand, to pinpoint discontinuities and continuities in the teaching of geometry between primary and secondary schools and, on the other, to investigate whether a set of curriculum material that we designed could serve as a link in the teaching of geometry between the two school levels. © 2007 Springer Science+Business Media B.V

Rapid screening of in cellulo grown protein crystals via a small-angle X-ray scattering/X-ray powder diffraction synergistic approach

Crystallization of recombinant proteins in living cells is an exciting new approach for structural biology that provides an alternative to the time-consuming optimization of protein purification and extensive crystal screening steps. Exploiting the potential of this approach requires a more detailed understanding of the cellular processes involved and versatile screening strategies for crystals in a cell culture. Particularly if the target protein forms crystalline structures of unknown morphology only in a small fraction of cells, their detection by applying standard visualization techniques can be time consuming and difficult owing to the environmental challenges imposed by the living cells. In this study, a high-brilliance and low-background bioSAXS beamline is employed for rapid and sensitive detection of protein microcrystals grown within insect cells. On the basis of the presence of Bragg peaks in the recorded small-angle X-ray scattering profiles, it is possible to assess within seconds whether a cell culture contains microcrystals, even in a small percentage of cells. Since such information cannot be obtained by other established detection methods in this time frame, this screening approach has the potential to overcome one of the bottlenecks of intracellular crystal detection. Moreover, the association of the Bragg peak positions in the scattering curves with the unit-cell composition of the protein crystals raises the possibility of investigating the impact of environmental conditions on the crystal structure of the intracellular protein crystals. This information provides valuable insights helping to further understand the in cellulo crystallization process