Teachers' beliefs on teacher training contents and related characteristics of implementation—the example of introducing the topic study method in mathematics classrooms

So-called “bottom-up” strategies for implementation based on mathematics teachers' own developmental activities are considered to be a powerful approach when encouraging teachers to introduce alternative instructional practices. For evaluational research of in-service teacher training programs using “bottom-up” implementation strategies, the way how teachers implement contents of the teacher training is at the centre of interest. As the teachers' active role in the implementation process is necessary, their individual beliefs on the contents of the teacher training and their expectancies might influence the teachers' implementational activities. These beliefs can be considered as components of professional knowledge and pedagogical contents knowledge (Shulman, 1986) in particular. For this reason, the study focuses on the development of beliefs on contents of a teacher training program throughout the training on the one hand and relationships with characteristics of implementation on the other hand. We consider the example of introducing a student-centred learning environment, the so-called topic study method, in the teachers' classrooms. The results indicate that there are interdependencies between beliefs on the teacher training contents and characteristics of implementation.     

The structures of German mathematics textbooks

From a socio-cultural perspective it is argued that the modality of artefacts has, structuring effects on the activities in which the artefact is involved. The mathematics textbook is an artefact that has a major influence on the activity of learning mathematics. Against this setting, the structures of the units in German mathematics textbooks for different grades and ability levels have been analysed. Firstly, the different structural elements have been examined with regard to: characteristics in terms of content; linguistic characteristics; visual characteristics; their pedagogical functions within the learning process; and situative conditions. Secondly, the orders of the structural elements within the units of the different textbooks have been compared. The findings reveal that the structure of the units is very similar in different mathematics textbooks. The units are not only composed of analogous structural elements, but these elements are also arranged in almost the same sequence. In order to develop a deeper understanding of these findings the structure of the units has been compared to the influential learning theories of J. F. Herbart and H. Roth. On this basis it is argued that the structure of the units seems to reflect the phases of idealised learning processes in general. The issue is raised if this is an appropriate structure in order to provide opportunities to learn mathematics.     

Manifolds with almost nonnegative curvature operator and principal bundles

We study closed manifolds with almost nonnegative curvature operator (ANCO) and derive necessary and/or sufficient conditions for the total spaces of principal bundles over (A)NCO manifolds to admit ANCO connection metrics. In particular, we provide first examples of closed simply connected ANCO manifolds which do not admit metrics with nonnegative curvature operator.     

A deflated conjugate gradient method for multiple right hand sides and multiple shifts

We consider the task of computing solutions of linear systems that only differ by a shift with the identity matrix as well as linear systems with several different right-hand sides. In the past, Krylov subspace methods have been developed which exploit either the need for solutions to multiple right-hand sides (e.g. deflation type methods and block methods) or multiple shifts (e.g. shifted CG) with some success. In this paper we present a block Krylov subspace method which, based on a block Lanczos process, exploits both features—shifts and multiple right-hand sides—at once. Such situations arise, for example, in lattice quantum chromodynamics (QCD) simulations within the Rational Hybrid Monte Carlo (RHMC) algorithm. We present numerical evidence that our method is superior compared to applying other iterative methods to each of the systems individually as well as, in typical situations, to shifted or block Krylov subspace methods.     

The NiII,HgII and CuII complexes of 12‐membered‐ring mixed‐donor macrocycles

The structures of di­aqua(1,7‐dioxa‐4‐thia‐10‐aza­cyclo­do­decane)­nickel dinitrate, [Ni(C₈H₁₇NO₂S)(H₂O)₂](NO₃)₂, (I), bis­(nitrato‐O,O′)(1,4,7‐trioxa‐10‐aza­cyclo­do­decane)­mercury, [Hg(NO₃)₂(C₈H₁₇NO₃)], (II), and aqua­(nitrato‐O)(1‐oxa‐4,7,10‐tri­aza­cyclo­do­decane)copper nitrate, [Cu(NO₃)(C₈H₁₉N₃O)(H₂O)]NO₃, (III), reveal each macrocycle binding in a tetradentate manner. The conformations of the ligands in (I) and (III) are the same and distinct from that identified for (II). These differences are in agreement with molecular‐mechanics predictions of ligand conformation as a function of metal‐ion size.     

Secondary bonding interactions in biomimetic [2Fe-2S] clusters

A series of synthetic [2Fe-2S] complexes with terminal thiophenolate ligands and tethered ether or thioether moieties has been prepared and investigated in order to provide models for the potential interaction of additional donor atoms with the Fe atoms in biological [2Fe-2S] clusters. X-ray crystal structures have been determined for six new complexes that feature appended Et (1(C)), OMe (1(O)), or SMe (1(S)) groups, or with a methylene group (2(C) ), an ether-O (2(O)), or an thioether-S (2(S)) linking two aryl groups. The latter two systems provide a constrained chelate arrangement that induces secondary bonding interactions with the ether-O and thioether-S, which is confirmed by density functional theory (DFT) calculations that also reveal significant spin density on those fifth donor atoms. Structural consequences of the secondary bonding interactions are analyzed in detail, and effects on the spectroscopic and electronic properties are probed by UV-vis, M?ssbauer, and (1)H NMR spectroscopy, as well by SQUID measurements and cyclic voltammetry. The potential relevance of the findings for biological [2Fe-2S] sites is considered.     

P-hydrogen-substituted 1,3,2-diazaphospholenes: molecular hydrides

P-Hydrogen-substituted 1,3,2-diazaphospholenes 1 were prepared by an improved procedure from diazadienes and were characterized by spectroscopy and in one case by X-ray diffraction. A unique hydride-type reactivity of the P-H bonds was documented by extensive reactivity studies. Aldehydes and ketones were readily reduced to diazaphospholene derivatives of the corresponding alcohols, with alkyl-substituted ketones being converted at much lower rates than aldehydes or diaryl ketones. Reactions with the tetrachlorides of group 14 elements proceeded via hydride/chloride metathesis to give either partially chlorinated derivatives EH(n)Cl(4-n) (n = 0-3 for E = C, Si) or HCl and phosphenium salts 16c[ECl3] (for E = Ge, Sn) which were characterized by spectroscopic and X-ray diffraction studies. Tin dichloride was readily reduced to the element. Reactions of 1c with the P-chloro-diazaphospholene 3c and the salt 16c[OTf] allowed the first experimental detection of intermolecular exchange of a hydride, rather than a proton, between phosphine derivatives. Computational studies indicated that the hydride transfer between 1c and the cation 16c involves a transient H-bridged species with bonding properties similar to those of B2H7-. The preference for the formation of these bridged intermediates over P-P bonded phosphenium-phosphine adducts is attributed to the low electrophilicity of the diazaphospholenium cations and characterizes a novel reaction mode for phosphenium ions.     

Phase behavior and viscoelastic properties of entangled block copolymer gels

Triblock copolymers in midblock‐selective solvents can form physical gels. However, at low triblock contents (near the percolation threshold), the bridging of chains between micelles can lead to macrophase separation. Adding a styrene–isoprene diblock to a styrene–isoprene–styrene triblock copolymer in squalane can eliminate macrophase separation, yielding a wide range of stable, single‐phase gels with a disordered arrangement of micelles. The plateau modulus of these triblock gels scales with the 2.2 power of polymer content, indicating the importance of entanglements in dictating the modulus. Comparing gels made from the midblock‐saturated derivative of the same polymer [styrene‐(ethylene‐alt‐propylene)‐styrene] in squalane reveals that the modulus differences in the gels are a direct consequence of the difference in the entanglement molecular weight of the midblock homopolymer in bulk. Finally, the broad relaxation spectrum of these triblocks is well‐described by a recent theory for the dynamics of entangled star polymers, with the breadth of the relaxation spectrum dictated by the number of entanglements per midblock in the gel. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2183–2197, 2001     

Binding of β-lactam antibiotics to a bioinspired dizinc complex reminiscent of the active site of metallo-β-lactamases

Metallo-β-lactamases (mβls) cause bacterial resistance toward a broad spectrum of β-lactam antibiotics by catalyzing the hydrolytic cleavage of the four-membered β-lactam ring, thus inactivating the drug. Minutiae of the mechanism of these enzymes are still not well understood, and reports about binding studies of the substrates to the enzymes as well as to synthetic model systems are rare. Here we report a new pyrazolate-based bioinspired dizinc complex (1) reminiscent of the active site of binuclear mβls. Since 1 does not mediate hydrolytic degradation of β-lactams, the binding of a series of common β-lactam antibiotics (benzylpenicillin, cephalotin, 6-aminopenicillanic acid, ampicillin) as well as the inhibitor sulbactam and the simplest β-lactam, 2-azetidinone, to the dizinc core of 1 could now be studied in detail by NMR and IR spectroscopy as well as mass spectrometry. X-ray crystallographic information was obtained for 1 and its complexes with 2-azetidinone (2) and sulbactam (3); the latter represents the first structurally characterized dizinc complex with a bound β-lactam drug. While 2-azetidinone was found deprotonated and bridging in the clamp of the two zinc ions in 2, in 3 and all other cases the substrates preferentially bind via their carboxylate group within the bimetallic pocket. The relevance of this binding mode for mβls and consequences for the design of functional model systems are discussed.