How much time do students have to think about teacher questions? An investigation of the quick succession of teacher questions and student responses in the German mathematics classroom

Several studies have shown that the style of the German mathematics classroom at secondary level is mostly based on the so called “fragend-entwickelnde” teaching style which means developing the lesson content by a teacher directed sequence of teacher questions and student responses. In this article we describe a study on the time the students have for thinking about a teacher question in the public classroom interaction. Our investigation is based on a reanalyasis of 22 geometry lessons from grade 8 classes which mainly deal with a challenging proving content. The results show that the average time between a teacher question and a student response is 2.5 seconds. There are no remarkable differences between different phases of the lessons like comparing homework, repetition of content or working on new content. Moreover, for 75% of the teacher questions the first student was called to answer within a three second time interval.     

Synthesis and characterization of novel amino cellulose esters

The homogeneous conversion of cellulose dissolved in N-methyl-2-pyrrolidone/LiCl and 1-N-butyl-3-methylimidazolium chloride with N-methyl-2-pyrrolidone, ε-caprolactam, N-methyl-ε-caprolactam, and N-methyl-2-piperidone in the presence of p-toluenesulphonic acid chloride was studied. Depending on the reaction conditions, novel cellulose esters with degree of substitution (DS) values ranging from 0.12 to 1.17 could be prepared. The structure of the amino group containing cellulose esters was elucidated by elemental analysis, FTIR- and NMR spectroscopy. NMR spectroscopy revealed an almost complete esterification of position 6 of the anhydroglucose unit at DS of 1. The conversion can be conducted between room temperature and 40 °C, while side-reactions became predominant at 60 °C. Starting with DS of 0.24, the samples were soluble both in water and dimethyl sulphoxide. The derivatives described are capable of forming polyelectrolyte complexes. The samples were stable at room temperature in aqueous solution at pH 2 and 7. Lower viscosities were found for samples with higher DS in aqueous solution at comparable molar mass.     

Stable cellulose nanospheres for cellular uptake

Pure, perfectly spherical cellulose nanoparticles with sizes of ≈80-260 nm can be prepared by dialysis starting from trimethylsilylcellulose (TMSC). The aqueous suspensions obtained are storable for several months. Subsequent covalent labeling of the cellulose nanoparticles with FITC has no influence on particle size, shape, and stability. The particles can be sterilized and suspended in biological media without structural changes. Incorporation of FITC-labeled cellulose nanoparticles into living human fibroblasts is studied using confocal LSM. In contrast to cellulose nanocrystals, fast cellular uptake is found for the nanospheres without transfection reagents or attachment of a receptor molecule. This suggests an influence of the geometry of biocompatible nanomaterials on endocytosis.     

Semi-synthetic polysaccharide sulfates as anticoagulant coatings for PET, 1--cellulose sulfate

In the present study, blood-compatible PET surfaces were prepared by coating with anticoagulant cellulose sulfates that were synthesized homogeneously in ionic liquids. The adsorption behavior of polysaccharides on PET films was investigated using QCM-D. It was demonstrated that pre-coating with different amino-group-containing polysaccharides improves the affinity toward cellulose sulfate. Moreover, the effect of different degrees of sulfation on the adsorption process was evaluated. Based on these results, several layer-by-layer coated PET foils were prepared that showed significantly improved blood compatibility compared to the initial untreated material.     

The lattice discrepancy of certain three-dimensional bodies

Based on a very precise approximation to the lattice discrepancy of a Lamé disc, an asymptotic formula is established for the number of lattice points in the three-dimensional body $$|u_1|^{mk}+\left(|u_2|^k+|u_3|^k\right)^{m}\le x^{mk},$$ for large real x and fixed reals m, k. Particular attention is paid to the boundary points of Gaussian curvature zero.     

Structure–Function Relationships of New Lipids Designed for DNA Transfection

Cationic liposome/DNA complexes can be used as nonviral vectors for direct delivery of DNA‐based biopharmaceuticals to damaged cells and tissues. To obtain more effective and safer liposome‐based gene transfection systems, two cationic lipids with identical head groups but different chain structures are investigated with respect to their in vitro gene‐transfer activity, their cell‐damaging characteristics, and their physicochemical properties. The gene‐transfer activities of the two lipids are very different. Differential scanning calorimetry and synchrotron small‐ and wide‐angle X‐ray scattering give valuable structural insight. A subgel‐like structure with high packing density and high phase‐transition temperature from gel to liquid‐crystalline state are found for lipid 7 (N′‐2‐[(2,6‐diamino‐1‐oxohexyl)amino]ethyl‐2,N‐bis(hexadecyl)propanediamide) containing two saturated chains. Additionally, an ordered head‐group lattice based on formation of a hydrogen‐bond network is present. In contrast, lipid 8 (N′‐2‐[(2,6‐diamino‐1‐oxohexyl)amino]ethyl‐2‐hexadecyl‐N‐[(9Z)‐octadec‐9‐enyl]propanediamide) with one unsaturated and one saturated chain shows a lower phase‐transition temperature and a reduced packing density. These properties enhance incorporation of the helper lipid cholesterol needed for gene transfection. Both lipids, either pure or in mixtures with cholesterol, form lamellar phases, which are preserved after addition of DNA. However, the system separates into phases containing DNA and phases without DNA. On increasing the temperature, DNA is released and only a lipid phase without intercalated DNA strands is observed. The conversion temperatures are very different in the two systems studied. The important parameter seems to be the charge density of the lipid membranes, which is a result of different solubility of cholesterol in the two lipid membranes. Therefore, different binding affinities of the DNA to the lipid mixtures are achieved.