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

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

Methodological Considerations in the Analysis of Classroom Interaction in Community College Trigonometry

We report analyses of classroom interaction in trigonometry classes taught at an American community college focusing on two dimensions: the mathematical novelty of questions that instructors and students ask and the interactional moves that the instructors use to encourage student involvement in the lesson. The analyzed lessons were particularly challenging because existing frameworks that analyze classrooms did not account for the cases in which the delivery mode was lecture. We discuss the analytical strategies we used and show data to illustrate how they help us in capturing the complexity of classroom interaction and differences between instructors when lecture is the primary mode of instructional delivery. We conclude with suggestions for further work.National Science Foundation CAREER award DRL-0745474 to the first authorPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/96961/1/Mesa_Lande_MetConsClassInt_DEEPBLUE.pd