Providing Job Embedded Professional Learning for Mathematics Specialists

We know that if professional learning opportunities are to be meaningful and create long-lasting and systemic change, they must be ongoing and job-embedded. One of the most beneficial aspects of having mathematics specialists in schools is that they can provide job-embedded professional learning directly to teachers. Perhaps due to the strong impact mathematics specialists have on teaching and learning, we may overlook the need to provide professional learning to support the growth of mathematics specialists themselves. Just as we provide coaching to teachers to affect their professional growth, we must identify similar opportunities to affect the growth of mathematics specialists. This paper will identify the purposes of these opportunities to include supporting growth in content knowledge, pedagogical expertise, coaching skills, and professionalism and leadership. We recognize that sustained efforts must be undertaken to see significant growth in these areas. Through interviews with individuals from Virginia school divisions and professional organizations, we identify models that can be replicated to provide the recommended professional learning for mathematics specialists

A simple, integrative assay to quantify nutritional quality of browses for herbivores

Many regard the concentrations of nitrogen (N), tannins and plant cell wall constituents (fibre) as key indicators of food quality and habitat suitability for browsing herbivores; yet there is no method for measuring their combined effects. We have developed a simple in vitro assay for measuring the effects of tannins and fibre on N availability in browse. We determined the effects of tannins by measuring the polyethylene glycol (PEG)-binding capacity (PEG-BC) of Eucalyptus leaf samples, followed by a two-stage in vitro digestion with pepsin and cellulase to determine the digestibility of dry matter and N. There was a significant relationship between concentrations of digestible N and the PEG-BC of the leaves. Furthermore, adding PEG significantly improved the digestibility of N. Our results concur with in vivo observations from several mammalian species. This suggests that our method is effective for measuring the nutritional quality of browse and the benefits of adding PEG, providing some index of the detrimental effects of tannins. We further simplified the assay by removing the PEG step, allowing us to quickly analyse samples in bulk. Nevertheless, this simplified method is still not practical for analysing the many samples necessary to compare the nutritional values of different tracts of forest. We used near-infrared reflectance spectroscopy to produce calibration equations and predicted total and digestible N in 322 trees at eleven sites. Both within and between sites, we found a wide variation in concentrations of digestible N but a much lower variation in total N, with either no relationship or poor relationships between the two measures. This confirms the variability in the nutritional quality of eucalypt forests, which may explain the distribution and abundance of mammalian herbivores. Thus, our assay provides a useful tool for understanding how food resources influence herbivore populations at different scales

Food for folivores: nutritional explanations linking diets to population density

Ecologists want to explain why populations of animals are not evenly distributed across landscapes and often turn to nutritional explanations. In seeking to link population attributes with food quality, they often contrast nutritionally positive traits, such as the concentration of nitrogen, against negative ones, such as fibre concentration, by using a ratio of these traits. This specific ratio has attracted attention because it sometimes correlates with the biomass of colobine primates across sites in Asia and Africa. Although empirically successful, we have identified problems with the ratio that may explain why it fails under some conditions to predict colobine biomass. First, available nitrogen, rather than total nitrogen, is nutritionally important, while the presence of tannins is the major factor reducing the availability of nitrogen in browse plant species. Second, tannin complexes inflate measures of fibre. Finally, simple ratios may be unsound statistically because they implicitly assume isometric relationships between variables. We used data on the chemical composition of plants from three continents to examine the relationships between the concentrations of nitrogen, available nitrogen, fibre and tannins in foliage and to evaluate the nitrogen to fibre ratio. Our results suggest that the ratio of the concentration of nitrogen to fibre in leaves does sometimes closely correlate with the concentration of available nitrogen. However, the ratio may give misleading results when leaves contain high concentrations of tannins. The concentration of available nitrogen, which incorporates measures of total nitrogen, dry matter digestibility and tannins, should give a better indication of the nutritional value of leaves for herbivorous mammals that can readily be extrapolated to habitats