Representing addition and subtraction : learning the formal conventions

The study was designed to test the effects of a structured intervention in teaching children to represent addition and subtraction. In a post-test only control group design, 90 five-year-olds experienced the intervention entitled Bi-directional Translation whilst 90 control subjects experienced typical teaching. Post-intervention testing showed some significant differences between the two groups both in terms of being able to effect the addition and subtraction operations and in being able to determine which operation was appropriate. The results suggest that, contrary to historical practices, children's exploration of real world situations should precede practice in arithmetical symbol manipulation

Changing classroom culture, curricula, and instruction for proof and proving: how amenable to scaling up, practicable for curricular integration, and capable of producing long-lasting effects are current interventions?

This paper is a commentary on the classroom interventions on the teaching and learning of proof reported in the seven empirical papers in this special issue. The seven papers show potential to enhance student learning in an area of mathematics that is not only notoriously difficult for students to learn and for teachers to teach, but also critically important to knowing and doing mathematics. Although the seven papers, and the intervention studies they report, vary in many ways—student population, content domain, goals and duration of the intervention, and theoretical perspectives, to name a few—they all provide valuable insight into ways in which classroom experiences might be designed to positively influence students’ learning to prove. In our commentary, we highlight the contributions and promise of the interventions in terms of whether and how they present capacity to change the classroom culture, the curriculum, or instruction. In doing so, we distinguish between works that aim to enhance students’ preparedness for, and competence in, proof and proving and works that explicitly foster appreciation for the need and importance of proof and proving. Finally, we also discuss briefly the interventions along three dimensions: how amenable to scaling up, how practicable for curricular integration, and how capable of producing long-lasting effects these interventions are

Chicken CRTAM Binds Nectin-Like 2 Ligand and Is Upregulated on CD8⁺ αβ and γδ T Lymphocytes with Different Kinetics

During a search for immunomodulatory receptors in the chicken genome, we identified a previously cloned chicken sequence as CRTAM homologue by its overall identity and several conserved sequence features. For further characterization, we generated a CRTAM specific mab. No staining was detectable in freshly isolated cell preparations from thymus, bursa, caecal tonsils, spleen, blood and intestine. Activation of splenocytes with recombinant IL-2 increased rapid CRTAM expression within a 2 h period on about 30% of the cells. These CRTAM+ cells were identified as CD8+ γδ T lymphocytes. In contrast, CRTAM expression could not be stimulated on PBL with IL-2, even within a 48 h stimulation period. As a second means of activation, T cell receptor (TCR) crosslinking using an anti-αβ-TCR induced CRTAM on both PBL and splenocytes. While CRTAM expression was again rapidly upregulated on splenocytes within 2 h, it took 48 h to reach maximum levels of CRTAM expression in PBL. Strikingly, albeit the stimulation of splenocytes was performed with anti-αβ-TCR, CRTAM expression after 2 h was mainly restricted to CD8+ γδ T lymphocytes, however, the longer anti-TCR stimulation of peripheral blood lymphocytes (PBL) resulted in CRTAM expression on αβ T lymphocytes. In order to characterize the potential ligand we cloned and expressed chicken Necl-2, a member of the nectin and nectin-like family which is highly homologous to its mammalian counterpart. Three independent assays including a reporter assay, staining with a CRTAM-Ig fusion protein and a cell conjugate assay confirmed the interaction of CRTAM with Necl-2 which could also be blocked by a soluble CRTAM-Ig fusion protein or a CRTAM specific mab. These results suggest that chicken CRTAM represents an early activation antigen on CD8+ T cells which binds to Necl-2 and is upregulated with distinct kinetics on αβ versus γδ T lymphocytes

Teachers and didacticians: key stakeholders in the processes of developing mathematics teaching

This paper sets the scene for a special issue of ZDM-The International Journal on Mathematics Education-by tracing key elements of the fields of teacher and didactician/teacher-educator learning related to the development of opportunities for learners of mathematics in classrooms. It starts from the perspective that joint activity of these two groups (teachers and didacticians), in creation of classroom mathematics, leads to learning for both. We trace development through key areas of research, looking at forms of knowledge of teachers and didacticians in mathematics; ways in which teachers or didacticians in mathematics develop their professional knowledge and skill; and the use of theoretical perspectives relating to studying these areas of development. Reflective practice emerges as a principal goal for effective development and is linked to teachers' and didacticians' engagement with inquiry and research. While neither reflection nor inquiry are developmental panaceas, we see collaborative critical inquiry between teachers and didacticians emerging as a significant force for teaching development. We include a summary of the papers of the special issue which offer a state of the art perspective on developmental practice. © 2014 FIZ Karlsruhe

Terminal amino acid sequences and proteolytic cleavage sites of mouse mammary tumor virus env gene products.

The mature envelope glycoproteins of mouse mammary tumor virus (gp52 and gp36) were isolated by reversed-phase high-pressure liquid chromatography. The N-terminal amino acid sequence of gp36 was determined for 28 residues. The C-terminal amino acid sequences of gp52 and gp36 were determined by carboxypeptidase digestion. The N-terminal amino acid sequence of gp52 has been reported previously (L. O. Arthur et al., J. Virol. 41:414-422, 1982). These data were aligned with the predicted amino acid sequence of the env gene product obtained by translation of the DNA sequence (S. M. S. Redmond and C. Dickson, Eur. Mol. Biol. Org. J. 2:125-131, 1983). The amino acid sequences of the mature viral proteins were in agreement with the predicted amino acid sequence of the env gene product over the regions of alignment. This alignment showed the sites of proteolytic cleavages of the env gene product leading to the mature viral envelope glycoproteins. The N-terminal amino acid sequence of gp52 starts at residue 99 of the predicted structure indicating proteolytic cleavage of a signal peptide. A dipeptide (Lys-Arg) is excised between the C-terminus of gp52 and the N-terminus of gp36. The C-terminal amino acid sequence of gp36 is identical to the sequence predicted by the codons immediately preceding the termination codon for the env gene product. The data show that there is no proteolytic processing at the C-terminal of the murine mammary tumor virus env gene product and that the env gene coding region extends into the long terminal repeat

Commentary on cognitive and non-cognitive factors in a vertical perspective: the case of percentages

In this contribution we deal with the interplay between cognitive and non-cognitive factors (including linguistic ones) in the resolution of mathematics word problems in the transition between secondary to tertiary level. We consider the topic of percentages, which is proposed by the Italian National Guidelines as a learning goal already at the end of primary school but also has proved to be one of the most problematic even at undergraduate level. We analyse data from standardized tests carried out at the beginning of some Italian scientific undergraduate courses (cognitive assessment tests for freshmen at STEM studies). This topic is relevant also because it highlights how different factors (cognitive, non-cognitive, linguistic) affect students\u2019 performance