“Can you help me count these pennies?”: Surfacing preschoolers’ understandings of counting

ABSTRACT

Capturing the breadth and variety of children’s understanding is critical if studies of children’s mathematical thinking are to inform policy and practice in early childhood education. This article presents an investigation of young children’s counting. Detailed coding and analyses of assessment interviews with 476 preschoolers revealed understandings that would be overlooked by solely assessing the accuracy of their responses. In particular, many children demonstrated understandings of counting principles on a challenging task that were not captured by other, simpler tasks. We conclude that common approaches to capturing young children’s mathematical understanding are likely underestimating their capabilities. This study contributes to researchers’ understanding of what making sense of counting looks and sounds like for preschool age children (3–5 years), the development and relations among counting principles (one-to-one, cardinal, and patterns of the number sequence), and the affordances of challenging, open-ended tasks. We close by considering the implications of recognizing and building from what children know and can do for researchers, practitioners, and policymakers.     

Direct density determination of low- and high-density glassy polyamorphs following a liquid–liquid phase transition in Y2O3–Al2O3 supercooled liquids

Evidence has been presented for a density-driven phase transition occurring between supercooled liquids in the system Y₂O₃–Al₂O₃. The high- and low-density liquids were quenched to metastably coexisting glasses. Chemical analysis showed the compositions of the two glasses to be identical, and it was inferred that they differed in their densities and entropies. The entropy difference has been verified by calorimetry. Here, we confirm that the chemical compositions of the glassy materials derived from the high- and low-temperature liquids are identical. We present a direct density determination of the two glasses using sink-float techniques. The measured densities are 3.72(3) g/cm³ for the glass derived from the high-temperature liquid (i.e., the high-density amorphous or HDA polyamorph), and 3.58(1) g/cm³ for the low-temperature (low-density, LDA) polyamorph.     

Enhanced hydrogen storage in Ni/Ce composite oxides

The properties of dried (but not calcined) coprecipitated nickel ceria systems have been investigated in terms of their hydrogen emission characteristics following activation in hydrogen. XRD and BET data obtained on the powders show similarities to calcined ceria but it is likely that the majority of the material produced by the coprecipitation process is largely of an amorphous nature. XPS data indicate very little nickel is present on the outermost surface of the particles. Nevertheless, the thermal analytical techniques (TGA, DSC and TPD-MS) indicate that the hydrogen has access to the catalyst present and the nickel is able to generate hydrogen species capable of interacting with the support. Both unactivated and activated materials show two hydrogen emission features, viz. low temperature and high temperature emissions (LTE and HTE, respectively) over the temperature range 50 and 500 degrees C. A clear effect of hydrogen interaction with the material is that the activated sample not only emits much more hydrogen than the corresponding unactivated one but also at lower temperatures. H(2) dissociation occurs on the reduced catalyst surface and the spillover mechanism transfers this active hydrogen into the ceria, possibly via the formation and migration of OH(-) species. The amount of hydrogen obtained (~0.24 wt%) is approximately 10x higher than those observed for calcined materials and would suggest that the amorphous phase plays a critical role in this process. The affiliated emissions of CO and CO(2) with that of the HTE hydrogen (and consumption of water) strongly suggests a proportion of the hydrogen emission at this point arises from the water gas shift type reaction. It has not been possible from the present data to delineate between the various hydrogen storage mechanisms reported for ceria.     

Structural studies and polymorphism in amorphous solids and liquids at high pressure

When amorphous materials are compressed their structures are expected to change in response to densification. In some cases, the changes in amorphous structure can be discontinuous and they can even have the character of first-order phase transitions. This is a phenomenon referred to as polyamorphism. Most evidence for polyamorphic transitions between low and high density liquids or analogous transformations between amorphous forms of the same substance to date has been indirect and based on the changes in thermodynamic and other structure-related properties with pressure. Recent studies using advanced X-ray and neutron scattering methods combined with molecular dynamics simulations are now revealing the details of structural changes in polyamorphic systems as a function of pressure. Various "two state" or "two species" models are used to understand the anomalous densification behaviour of liquids with melting curve maxima or regions of negative melting slope. Thermodynamic analysis of the two state model leads to the possibility of low- to high-density liquid transitions caused by differences in bulk thermodynamic properties between different amorphous forms and on the degree of cooperativity between low- and high-density structural configurations. The potential occurrence of first-order transitions between supercooled liquids is identified as a critical-like phenomenon. In this tutorial review we discuss the background to polyamorphism, incorporating the experimental observations, simulation studies and the two-state models. We also describe work carried on several systems that are considered to be polyamorphic.     

Influence of acute hyperglycemia on otoacoustic emissions and the medial olivocochlear reflex

Stimulus-frequency (SF) otoacoustic emission (OAE) amplitude and the amplitude of medial olivocochlear (MOC) inhibition of SF OAEs for ipsilateral, contralateral and bilateral MOC reflex elicitors were recorded in six subjects with type 2 diabetes during a glucose tolerance test (GTT). Five of the six subjects were tested twice for a total of 11 trials and three subjects were tested in a control experiment. During the GTT experiment, the subjects' blood glucose was elevated from a euglycemic level below 150 mg/dL to a hyperglycemic level above 160 mg/dL following the consumption of a bolus of 80 g of sugar. A subset of three subjects were tested in a control experiment during which SF OAE and MOC reflex measurements were made while blood sugar levels remained constant within the euglycemic region. Mean SF OAE amplitudes were elevated following glucose consumption. A statistically significant increase in MOC inhibition amplitude was observed during elevated sugar levels for the 11 GTT trials. Maximum inhibition occurred about an hour after glucose consumption when blood glucose levels peaked. Results indicate that acute hyperglycemia influences efferent control of the cochlea in people with type 2 diabetes.     

Tackling the chemical diversity of microbial nonulosonic acids – a universal large-scale survey approach

Nonulosonic acids, commonly referred to as sialic acids, are a highly important group of nine-carbon sugars common to all domains of life. They all share biosynthetic and structural features, but otherwise display a remarkable chemical diversity. In humans, sialic acids cover all cells which makes them important for processes such as cellular protection, immunity and brain development. On the other hand, sialic acids and other nonulosonic acids have been associated with pathological processes including cancer and viral infections. In prokaryotes, nonulosonic acids are commonly associated with pathogens, which developed through molecular mimicry a strategy to circumvent the host''s immune response. However, the remarkably large chemical diversity of prokaryotic nonulosonic acids challenges their discovery, and research on molecular characteristics essential for medical applications are often not feasible. Here, we demonstrate a novel, universal large-scale discovery approach that tackles the unmapped diversity of prokaryotic nonulosonic acids. Thereby, we utilize selective chemical labelling combined with a newly established mass spectrometric all-ion-reaction scanning approach to identify nonulosonic acids and other ulosonic acid-like sugars. In doing so, we provide a first molecular-level comparative study on the frequency and diversity across different phyla. We not only illustrate their surprisingly wide-spread occurrence in non-pathogenic species, but also provide evidence of potential higher carbon variants. Many biomedical studies rely on synthetic routes for sialic acids, which are highly demanding and often of low product yields. Our approach enables large-scale exploration for alternative sources of these highly important compounds.

A novel large-scale survey approach for microbial nonulosonic acids (sialic acids) including a first molecular level comparative study is presented.     

Arabinose utilization by xylose-fermenting yeasts and fungi

Various wild-type yeasts and fungi were screened to evaluate their ability to fermentl-arabinose under oxygen-limited conditions when grown in defined minimal media containing mixtures ofl-ara-binose,d-xylose, andd-glucose. Although all of the yeasts and some of the fungi consumed arabinose, arabinose was not fermented to ethanol by any of the strains tested. Arabitol was the only major product other than cell mass formed froml-arabinose; yeasts converted arabinose to arabitol at high yield. The inability to fermentl-arabinose appears to be a consequence of inefficient or incomplete assimilation pathways for this pentose sugar.     

Influence of operating conditions and vessel size on oxygen transfer during cellulase production

The production of low-cost cellulase enzyme is a key step in the development of an enzymatic-based process for conversion of lignocellulosic biomass to ethanol. Although abundant information is available on cellulase production, little of this work has examined oxygen transfer. We investigated oxygen transfer during the growth of Trichoderma reesei, a cellulase-producing microorganism, on soluble and insoluble substrates in vessel sizes from 7 to 9000 L. Oxygen uptake rates and volumetric mass transfer coefficients (k _La) were determined using mass spectroscopy to measure off gas composition. Experimentally measured k _La values were found to compare favorably with a k _La correlation available in the literature for a non-Newtonian fermentation broth during the period of heavy cell growth.     

The structures and vibrational spectra of crystals and glasses in the silica-alumina system

Solar furnace melting and fast-quench techniques have been used to prepare SiO₂Al₂O₃ glasses to high alumina content (near 60 mol% Al₂O₃), which have been studied by Raman spectroscopy. These spectra may not be simply interpreted. The structures of crystalline compounds in the SiO₂Al₂O₃ system are discussed in relation to their vibrational spectra. On the basis of this discussion and other considerations, a structural model for the silica-alumina glass system is proposed, which is consistent with the stable or metastable immiscibility suggested along this join. The essential features of this model include a modified silica structure at low alumina content, and “structure-broken” regions at high alumina compositions, with silicon in tetrahedral coordination, but aluminium assuming a variety of bonding geometries. These are proposed to include aluminate tetrahedra with higher polymerization than simple corner-sharing, and less well-defined polyhedra of higher average coordination number.