This paper presents the model, The Mathematics Teacher's Specialised Knowledge (MTSK). It acknowledges earlier contributions to understanding and structuring teachers' knowledge, in particular, the special debt owed to Shulman's notion of pedagogical content knowledge and to Ball and collaborators' Mathematical Knowledge for Teaching (MKT) influential for the specialised nature of one of its sub-domains. Our research with teachers has led us to explore the characteristics of MKT and to refine the descriptors relating to its sub-domains, a task which has underlined the difficulty involved in unambiguously delimiting the boundaries which separate these. As a result, and taking into consideration a broader view of the specialised nature of the teacher's mathematical knowledge, we propose a framework which, whilst respecting the major domains of Content Knowledge and Pedagogical Content Knowledge, regards the specialisation in respect of mathematical knowledge as a property which is inherent to the model and extends across all sub-domains.

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The role of biotic interactions including vertebrate predation and interspecific competition was studied among members of a semiarid small mammal assemblage in a long-term field manipulation in north central Chile. Fences and netting selectively excluded mammalian and avian predators, and a putative rodent competitor, the degu ( Octodon de gus), from large, replicated grids. Small mammal populations were censused monthly over >4 yr, and effects of predator and degu exclusions on numbers and survival of small mammals were assessed with repeated measures ANOVAs. Marginally significant predator exclusion effects were detected on 0. degus, and highly significant year X predation interactions in both wet and dry seasons; degu survival (= persistence) was also significantly longer on exclusion grids. Predation had significant effects on numbers of Phyllotis darwini, and a significant month X predator interaction existed in the wet season; survival was also significantly higher on predator exclusion grids. There was a marginally significant year X competitor interaction in the dry season for this species. Akodon olivaceus had significant month X predator and month X competitor interactions in the wet season only; survival was significantly longer on degu exclusion grids. An irruptive species, Oligoryzomys longicaudatus, showed no significant predator or competitor effects in 1991-1992; however, survival was significantly longer on predator + competitor exclusion (vs. control) grids.An uncommon species, Abrothrix longipilis, had marginally nonsignificant time X competitor interactions but no treatment differences in survival. Finally, a second uncommon rodent, Abrocoma bennetti (not analyzed numerically) had significantly longer survival on predator exclusion grids with degus. Degus and P. darwini were significantly overrepresented (relative to availability) in diets of culpeo foxes (Pseudalopex culpaeus) and three nocturnal owls, respectively, whereas A. bennetti was significantly overrepresented in predator diets generally. Vertebrate predation has pervasive effects on some species that, however, may be related to their intrinsic demographic characteristics. Competition may be mediated by subtle behavioral interactions among assemblage members. Long-term studies are necessary to elucidate the role of biotic and abiotic factors in semiarid environments.

We monitored the cover and seed bank response of shrubs, perennial herbs, and ephemeral plants to experimental exclusion of both the principal rodent herbivore, Octodon degus, and its vertebrate predators from 1989 to 1994 in a semiarid Chilean mediterranean site. Although both richness and species composition of the plant community at the study site were largely determined by abiotic factors (mainly rainfall and soil nutrients), predator and herbivore exclusion had significant effects on the relative abundance of several plant species. Experimental exclusion of herbivores was associated with increased cover of some shrubs and a perennial grass, and decreased cover and seed densities of several ephemerals, especially those exotic or restricted to areas underneath shrubs. Herbivores apparently reduced shrubs through browsing and indirectly affected herb cover and seed densities by opening up areas under shrubs and/or modifying physical and chemical conditions of the soil. Plant responses to predator exclusion were less clear. Nevertheless, higher cover of some shrubs and ephemerals in the presence of predators suggests tritrophic effects through changes in small mammal densities and/or foraging behavior.