Flexible autonomy: an online approach to developing mathematics subject knowledge for teachers

This paper uses an adaptation of Brookfield’s (2017) lenses to critically reflect upon a Subject Knowledge Enhancement Course designed and taught by the authors. Learning occurs through a synthesis of asynchronous engagement with online e-learning modules, weekly synchronous tutorials and self-reflection following formative and summative assessment opportunities. Interrogating the course design, learner feedback and observation, and tutor pedagogic choices through connectivist and social constructivist learning theory, the paper concludes that the common perceived learning gains occur through the flexibility in learning, and the supported autonomy that learners are given. Further developments in our offer should therefore aim to improve these opportunities for learners where possible

Forest Conversion and Degradation in Papua New Guinea 1972-2002

Quantifying forest change in the tropics is important because of the role these forests play in the conservation of biodiversity and the global carbon cycle. One of the world's largest remaining areas of tropical forest is located in Papua New Guinea. Here we show that change in its extent and condition has occurred to a greater extent than previously recorded. We assessed deforestation and forest degradation in Papua New Guinea by comparing a land-cover map from 1972 with a land-cover map created from nationwide high-resolution satellite imagery recorded since 2002. In 2002 there were 28,251,967 ha of tropical rain forest. Between 1972 and 2002, a net 15 percent of Papua New Guinea's tropical forests were cleared and 8.8 percent were degraded through logging. The drivers of forest change have been concentrated within the accessible forest estate where a net 36 percent were degraded or deforested through both forestry and nonforestry processes. Since 1972, 13 percent of upper montane forests have also been lost. We estimate that over the period 1990–2002, overall rates of change generally increased and varied between 0.8 and 1.8 percent/yr, while rates in commercially accessible forest have been far higher—having varied between 1.1 and 3.4 percent/yr. These rates are far higher than those reported by the FAO over the same period. We conclude that rapid and substantial forest change has occurred in Papua New Guinea, with the major drivers being logging in the lowland forests and subsistence agriculture throughout the country with comparatively minor contributions from forest fires, plantation establishment, and mining

Distributed branch points and the shape of elastic surfaces with constant negative curvature

We develop a theory for distributed branch points and investigate their role in determining the shape and influencing the mechanics of thin hyperbolic objects. We show that branch points are the natural topological defects in hyperbolic sheets, they carry a topological index which gives them a degree of robustness, and they can influence the overall morphology of a hyperbolic surface without concentrating energy. We develop a discrete differential geometric (DDG) approach to study the deformations of hyperbolic objects with distributed branch points. We present evidence that the maximum curvature of surfaces with geodesic radius $R$ containing branch points grow sub-exponentially, $O(e^{c\sqrt{R}})$ in contrast to the exponential growth $O(e^{c' R})$ for surfaces without branch points. We argue that, to optimize norms of the curvature, i.e. the bending energy, distributed branch points are energetically preferred in sufficiently large pseudospherical surfaces. Further, they are distributed so that they lead to fractal-like recursive buckling patterns.Comment: 59 pages, 20 figures. Major revisions including new proofs with weakened hypotheses, expanded discussion and additional references. Some images are not at their original resolution to keep them at a reasonable size. Comments are very welcome and much appreciate

Heat engines and heat pumps in a hydrostatic atmosphere: How surface pressure and temperature constrain wind power output and circulation cell size

The kinetic energy budget of the atmosphere's meridional circulation cells is analytically assessed. In the upper atmosphere kinetic energy generation grows with increasing surface temperature difference \$\Delta T_s\$ between the cold and warm ends of a circulation cell; in the lower atmosphere it declines. A requirement that kinetic energy generation is positive in the lower atmosphere limits the poleward cell extension \$L\$ of Hadley cells via a relationship between \$\Delta T_s\$ and surface pressure difference \$\Delta p_s\$: an upper limit exists when \$\Delta p_s\$ does not grow with increasing \$\Delta T_s\$. This pattern is demonstrated here using monthly data from MERRA re-analysis. Kinetic energy generation along air streamlines in the boundary layer does not exceed \$40\$~J~mol\$^{-1}\$; it declines with growing \$L\$ and reaches zero for the largest observed \$L\$ at 2~km height. The limited meridional cell size necessitates the appearance of heat pumps -- circulation cells with negative work output where the low-level air moves towards colder areas. These cells consume the positive work output of the heat engines -- cells where the low-level air moves towards the warmer areas -- and can in theory drive the global efficiency of atmospheric circulation down to zero. Relative contributions of \$\Delta p_s\$ and \$\Delta T_s\$ to kinetic energy generation are evaluated: \$\Delta T_s\$ dominates in the upper atmosphere, while \$\Delta p_s\$ dominates in the lower. Analysis and empirical evidence indicate that the net kinetic power output on Earth is dominated by surface pressure gradients, with minor net kinetic energy generation in the upper atmosphere. The role of condensation in generating surface pressure gradients is discussed.Comment: 26 pages, 9 figures, 2 tables; re-organized presentation, more discussion and a new figure (Fig. 4) added; in Fig. 3 the previously invisible dots (observations) can now be see

On estimating tropical forest carbon dynamics in Papua New Guinea

One of the few initiatives to address ongoing global warming that did not completely stall at the UNFCCC climate change negotiations was the reduction emissions from deforestation and forest degradation (REDD). REDD has a focus on the forests of the tropics. Unfortunately forest mensuration in most tropical countries has been inadequate to accurately determine forest carbon stocks, much less the effects of land use and changes in land use on them (Houghton et al. 2009; Bryan et al. 2010a). Whilst tropical logging is known to be widespread, the exact areas of tropical forest subject to logging have not been accurately mapped (Asner et al. 2009) or mapped with sufficient regularity to provide adequate data on the areas subject to this activity. Biomass losses due to logging have usually been derived from limited plot data, or derived via various models from estimates of regional biomass and timber extraction volumes (Houghton et al. 2009) and thus encapsulate considerable uncertainty. For these reasons the carbon impact of tropical logging remains an open question, and one that needs to be closed before any international institutional arrangement considers promoting forms of timber extraction as a tool for controlling carbon emissions. Here, we examine the current state of forest carbon research in Papua New Guinea (PNG) to illustrate the problems that can arise by developing forest management policy prematurely from incomplete forest research

Nature's forms are frilly, flexible, and functional

A ubiquitous motif in nature is the self-similar hierarchical buckling of a thin lamina near its margins. This is seen in leaves, flowers, fungi, corals and marine invertebrates. We investigate this morphology from the perspective of non-Euclidean plate theory. We identify a novel type of defect, a branch-point of the normal map, that allows for the generation of such complex wrinkling patterns in thin elastic hyperbolic surfaces, even in the absence of stretching. We argue that branch points are the natural defects in hyperbolic sheets, they carry a topological charge which gives them a degree of robustness, and they can influence the overall morphology of a hyperbolic surface without concentrating elastic energy. We develop a theory for branch points and investigate their role in determining the mechanical response of hyperbolic sheets to weak external forces. We also develop a discrete differential geometric (DDG) framework for applications to the continuum mechanics of hyperbolic elastic sheets.Comment: 35 pages, 26 figure

Extreme Differences in Forest Degradation in Borneo: Comparing Practices in Sarawak, Sabah, and Brunei

The Malaysian states of Sabah and Sarawak are global hotspots of forest loss and degradation due to timber and oil palm industries; however, the rates and patterns of change have remained poorly measured by conventional field or satellite approaches. Using 30 m resolution optical imagery acquired since 1990, forest cover and logging roads were mapped throughout Malaysian Borneo and Brunei using the Carnegie Landsat Analysis System. We uncovered ∼364,000 km of roads constructed through the forests of this region. We estimated that in 2009 there were at most 45,400 km(2) of intact forest ecosystems in Malaysian Borneo and Brunei. Critically, we found that nearly 80% of the land surface of Sabah and Sarawak was impacted by previously undocumented, high-impact logging or clearing operations from 1990 to 2009. This contrasted strongly with neighbouring Brunei, where 54% of the land area remained covered by unlogged forest. Overall, only 8% and 3% of land area in Sabah and Sarawak, respectively, was covered by intact forests under designated protected areas. Our assessment shows that very few forest ecosystems remain intact in Sabah or Sarawak, but that Brunei, by largely excluding industrial logging from its borders, has been comparatively successful in protecting its forests.CLASlite is made possible by the Gordon and Betty Moore Foundation, the John D. and Catherine T. MacArthur Foundation, and the Grantham Foundation for the Protection of the Environment. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Accumulation of Microbial Biomass within Particulate Organic Matter of Aging Golf Greens

Microbial biomass (MB) is a key variable controlling soil organic matter dynamics in soil. Currently, there is little information on the amount and significance of MB in highly managed golf greens. Our objective was to determine the amount and distribution of MB within soil structural components of golf greens and its relationship to the location of organic substrates. During 1996, 47 greens were sampled from 12 golf courses within Nebraska (USA). Microbial biomass, determined as extractable lipid phosphate on field-moist soils, increased linearly with age of green (Y = 19.39 + 3.54x; r2 = 0.87, P = 0.001). In 1997 and 1999, selected greens were resampled and separated into mineral fraction (MF) and particulate organic matter (POM) fraction using a sodium metatungstate (NMT; r = 2.3 g cm-3). Then, POM was separated into light (L-POM) and heavy (H-POM) fractions using NMT (r = 2.0 g cm-3). Amount of MB of whole soil and POM was linearly related to green age (r2 = 0.76 and 0.68, respectively). Amount of MB in MF was not related to green age. The portion of total soil MB associated with POM increased significantly from 25.6% for an 8-yr-old green to 77.8% for a 28-yr-old green. Carbon in fulvic acid and humic acid increased with green age from 0.5 to 1.7 and 0.6 to 2.6 g kg-1 soil, respectively. As humus is a relatively stable form of soil organic matter, we hypothesized that humus accumulation within POM renders both POM and associated MB more resistant to degradation; thus, they accumulate

Nonsymbiotic hemoglobins in rice are synthesized during germination and in differentiating cell types

Nonsymbiotic hemoglobins (ns-Hbs) previously have been found in monocots and dicots; however, very little is known about the tissue and cell type localization as well as the physiological function(s) of these oxygen-binding proteins. We report the immunodetection and immunolocalization of ns-Hbs in rice (Oryza sativa L.) by Western blotting and in situ confocal laser scanning techniques. Ns-Hbs were detected in soluble extracts of different tissues from the developing rice seedling by immunoblotting. Levels of ns-Hbs increased in the germinating seed for the first six days following imbibition and remained relatively constant thereafter. In contrast, ns-Hb levels decreased during leaf maturation. Roots and mesocotyls contained detectable, but low levels of ns-Hbs. Split-seed experiments revealed that ns-Hbs are synthesized de novo during seed germination and are expressed in the absence of any signal originating from the embryo. Immunolocalization of ns-Hbs by con- focal microscopy indicated the presence of ns-Hbs primarily in differentiated and differentiating cell types of the developing seedling, such as the aleurone, scutellum, root cap cells, sclerenchyma, and tracheary elements. To our knowledge, this is the first report of the specific cellular localization of these proteins during seedling development

Nonsymbiotic hemoglobins in rice are synthesized during germination and in differentiating cell types

Nonsymbiotic hemoglobins (ns-Hbs) previously have been found in monocots and dicots; however, very little is known about the tissue and cell type localization as well as the physiological function(s) of these oxygen-binding proteins. We report the immunodetection and immunolocalization of ns-Hbs in rice (Oryza sativa L.) by Western blotting and in situ confocal laser scanning techniques. Ns-Hbs were detected in soluble extracts of different tissues from the developing rice seedling by immunoblotting. Levels of ns-Hbs increased in the germinating seed for the first six days following imbibition and remained relatively constant thereafter. In contrast, ns-Hb levels decreased during leaf maturation. Roots and mesocotyls contained detectable, but low levels of ns-Hbs. Split-seed experiments revealed that ns-Hbs are synthesized de novo during seed germination and are expressed in the absence of any signal originating from the embryo. Immunolocalization of ns-Hbs by con- focal microscopy indicated the presence of ns-Hbs primarily in differentiated and differentiating cell types of the developing seedling, such as the aleurone, scutellum, root cap cells, sclerenchyma, and tracheary elements. To our knowledge, this is the first report of the specific cellular localization of these proteins during seedling development