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

Geographic variation in social organization of Galápagos mockingbirds: ecological correlates of group territoriality and cooperative breeding

To investigate ecological influences on cooperative social organization, I studied the four allopatric species of mockingbirds ( Nesomimus spp.) endemic to the Galápagos archipelago on four islands. On three small, low and arid islands (Genovesa, Champion and Española), mockingbird territories filled all terrestrial habitat, mean group size varied from 4.5 to 14.2 adults, maximum group size ranged from seven to 24 birds, and 70–100% of groups contained more than two birds. San Cristóbal is larger and higher, and it supports a broader range of habitats. At one highland and two coastal sites on this island, mockingbirds did not hold territories in all available habitats, group size averaged 2.2 adults, only 25% of groups were larger than two, and none included more than three adults. Adults dispersed into vacant habitat to establish new territories only on San Cristóbal. Helping behavior has not yet been observed on San Cristóbal, but it occurs on the other three islands. These results support the hypothesis that social groups and cooperative breeding are maintained where limited availability of preferred habitat constrains dispersal. The mechanism relaxing habitat saturation on San Cristóbal, however, remains undetermined. Predation by introduced rats and cats may reduce survival and indirectly reduce group size; these predators are absent from Genovesa, Champion and Española. Differences in food supplies could also affect interand intra-island variation in population density. Variation in social organization among arid coastal sites on the four islands, and similarity between climatically different sites on San Cristóbal, suggest that climatic conditions are less important as determinants of dispersal and breeding. Skews in adult sex ratios also fail to account for inter-island variation in sociality. Although they live in a climatically variable environment, territorial behavior and the physical limits of suitable habitat have an overriding influence on cooperative social organization in Galápagos mockingbirds.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46894/1/265_2004_Article_BF00302932.pd

An experimental study of unsteady natural convection in a reservoir model subject to periodic thermal forcing using combined PIV and PIT

The present experimental investigation is concerned with the transient flow response in a reservoir model to periodic heating and cooling at the water surface. The experiment reveals a stable stratification of the water body during the heating phase and an unsteady mixing flow in the reservoir during the cooling phase. It is shown that thermal instabilities play an important role in breaking up the residual circulation and initiating a reverse flow circulation in deep waters after the switch of thermal forcing from heating to cooling. Moreover, the heating from the water surface results in a stable large-scale convective roll that is clearly observed in the experiment. The present flow visualization is carried out with the application of thermo-chromic liquid crystals. Quantitative temperature and velocity fields are extracted using Particle Image Thermometry and Particle Image Velocimetry techniques. Understanding of the flow mechanisms pertinent to this problem is important for predicting the transport of nutrients and pollutants across reservoirs

Cooperative Didactic Engineering

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