Navigating Schooled Numeracies: Explanations for Low Achievement,in Mathematics of UK Children From Low SES Background

The intention of the research reported here was to seek explanations for low achievement in school mathematics, as conventionally assessed, that derive from broad understandings of mathematics as social. Such a broad social perspective can provide explanations for low achievement, which could lead to different understandings and hence to different teaching approaches. This study centered on 5- to 8-year-old children from a White working-class area in England. Data were collected during visits to the children in school, in their homes, and in the broader community over a 3-year period. Parents, teachers, and other professionals in the broad school context were interviewed, and data were also collected from school documents and policy statements. Interpretations of these data in terms of ways of understanding children's achievements in school mathematics are put forward. The potential effects of these factors on low schooled numeracy attainment are discussed, together with some possible strategic implications for practice and policy.     

Novel route to synthesis of allyl starch and biodegradable hydrogel by copolymerizing allyl‐modified starch with methacrylic acid and acrylamide

Maize starch was modified by allyl chloride adopting an interfacial reaction technique with cetyltrimethyl ammonium bromide as a phase‐transfer catalyst and pyridine as an acid acceptor. The degree of substitution was determined from an increasing carbon content of the modified starch. The percentage of carbon and hydrogen of the allyl‐modified starch was estimated by elemental analysis (C, H, and N), and the product characterization was done through ¹H NMR and ¹³C NMR analyses. The allyl‐modified starch was then copolymerized with methacrylic acid and a combination of methacrylic acid and acrylamide at 50 and 70 °C with potassium persulfate as an initiator. The copolymer thus formed swelled in distilled water after neutralization with sodium carbonate. The percentage of absorption capacity of the hydrogels was determined with distilled water and 0.9% NaCl solution. The highest percentage of absorption, 6500%, was achieved for the developed hydrogel containing allyl starch and acrylic monomer in a 1.7:1 w/w ratio and acrylic monomer, namely, methacrylic acid and acrylamide in a 3.2:1 w/w ratio. The study on biodegradability of the developed hydrogel showed that the hydrogel is degradable in the presence of diastase (amylase). © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1650–1658, 2003     

Minimal regular polygons serving as universal covers in R 2

A universal cover is a set K with the property that each set of unit diameter is a subset of a congruent copy of K. It is shown that the smallest regular n-gon, for fixed n 4, which serves as an universal cover in R ² is the smallest regular n-gon covering a Reuleaux triangle of unit width.     

The robinson annulation of some medium ring size 2-hydroxymethylenecyclanones

The adducts formed from methyl vinyl ketone and the 2-hydromethylene derivatives of cyclooctane and cyclodecanone can be cyclised to spiroketones containing the same number of C atoms. The spiroketone from cyclooctanone possesses a single UV maximum at 227 nm; the cyclodecanone compound has a further absorption at ca 246 nm. The constitution and stereochemistry of the ketols produced from the adducts under mild cyclising conditions have been investigated.     

Sign changes in the prime number theorem

The Ramanujan Journal - Let V(T) denote the number of sign changes in $$\psi (x) - x$$ for $$x\in [1, T]$$ . We show that $$\liminf _{T\rightarrow \infty } V(T)/\log T\ge \gamma _{1}/\pi +...     

The entropy of small clusters of atoms using an Einstein model

We present a generalized Einstein model for calculating thermodynamic properties of small clusters of atoms and demonstrate its validity by comparing its predictions with Burton's exact calculations. The simplicity of the method enables one to easily compute thermodynamic quantities for many systems beyond those previously considered.     

Potassium carbonate,a support for the green synthesis of azoles and diazines

A novel potassium carbonate mediated synthesis of 2‐amino‐1,3‐thia/oxa zoles, 2‐amino‐1,3,4‐thia/oxa diazines and 2‐hydrazino‐1,3,4‐thiadiazines has been described here. The use of K₂CO₃ allows for an aqueous workup thereby eliminating the organic solvent from both the reaction step and post reaction stage, without compromising the yield and reaction time.     

Magnetically aligned phospholipid bilayers with large q ratios stabilize magnetic alignment with high order in the gel and L(alpha) phases

The magnetic alignment behavior ofbicelles (magnetically alignable phospholipid bilayered membranes) as a function of the q ratio (1,2-dihexanoyl-sn-glycerol phosphatidylcholine/1,2-dimyristoyl-sn-glycerol phosphatidylcholine mole ratio) and temperature was studied by spin-labeled X-band electron paramagnetic resonance (EPR) spectroscopy and solid-state 2H and 31P NMR spectroscopy. Well-aligned bicelle samples were obtained at 45 degrees C for q ratios between 2.5 and 9.5 in both the EPR and NMR spectroscopic studies. The molecular order of the system, S(mol), increased as the q ratio increased and as the temperature decreased. For higher q ratios (> or = 5.5), bicelles maintained magnetic alignment when cooled below the main phase transition temperature (approximately 30 degrees C when in the presence of lanthanide cations), which is the first time, to our knowledge, that bicelles were magnetically aligned in the gel phase. For the 9.5 q ratio sample at 25 degrees C, S(mol) was calculated to be 0.83 (from 2H NMR spectra, utilizing the isotopic label perdeuterated 1,2-dimyristoyl-sn-glycerol phosphatidylcholine) and 0.911 (from EPR spectra utilizing the spin probe 3beta-doxyl-5alpha-cholestane). The molecular ordering of the high q ratio bicelles is comparable to literature values of S(mol) for both multilamellar vesicles and macroscopically aligned phospholipid bilayers on glass plates. The order parameter S(bicelle) revealed that the greatest degree of bicelle alignment was found at higher temperatures and larger q ratios (S(bicelle) = -0.92 for q ratio 8.5 at 50 degrees C).     

Facile route to 3,5-disubstituted morpholines: enantioselective synthesis of O-protected trans-3,5-bis(hydroxymethyl)morpholines

[reaction: see text] (3R,5R)-1 R1 & R2 = TBDPS, (3S,5R)-2 R1 = Bn,R2 = TBDPS, (3S,5S)-3 R2 & R2 = Bn. trans-3,5-Bis(benzyl/tert-butyldiphenylsilyloxymethyl)morpholines, promising candidates for the C(2)-symmetric class of chiral reagents, were prepared with excellent optical purity. A key step in the synthesis is the coupling of a serinol derivative with 2,3-O-isopropylideneglycerol triflate or its equivalent. This methodology was extended to the synthesis of chiral trans-3-(benzyloxymethyl)-5-(tert-butyldiphenylsilyloxymethyl)morpholine, a potentially useful chiral building block.     

Synthesis and S-methylation of 2-thioxopyrido[3′,2′:4,5]thieno[3,2-d]-pyrimidin-4(3H)-ones with and without a phase transfer catalyst

A number of 2-thioxopyrido[3′,2′:4,5]thieno[3,2-H]pyrimdin-4(3H-ones (5) have been synthesized by cyclocondensation of 2-carbethoxy-3-amino-4-phenyl-6-substituted-thieno[2,3-b]pyridines (3) with various isothiocyanates. Compounds 5 were S-methylated routinely and the reactions compared under solid-liquid phase transfer conditions to obtain 2-methylthiopyrido[3′,2′:4,5]thieno[3,2-d]pyrimidin-4(3H)-^ones (6). The new triheterocyclic pyridothienopyrimidines were prepared with the objective to study their pharmacological properties.