Teachers in transition: Moving towards CAS-supported classrooms

In the near future many teachers may be required to incorporate CAS into their teaching practices. Based on classroom observations and interviews over two years, this paper reports how two teachers made the transition from using graphics calculators to CAS calculators while teaching differential calculus to upper secondary school students. Both teachers taught with CAS in ways that were consistent with their beliefs about learning and teaching. Over two years, the teachers' teaching approaches and purpose for use of technology were stable and seemed to be underpinned by their beliefs about learning. In contrast, both teachers made changes to the content they taught (and thus what they used technology for) in response to new institutional knowledge. Content choice seemed to be underpinned by the teachers' purpose for teaching. Other influences impacted on what the teachers taught and how they taught it: the teachers' content knowledge, their pedagogical content knowledge, and the lack of legitimacy of CAS as a tool for learning and during examinations in the trial school and wider educational community. The extent of differences noted between the responses of just two teachers indicates that there will be many responses to using CAS in classrooms, as teachers aim to achieve different learning goals and interpret their responsibilities to students in different ways.     

A Framework for Monitoring Progress and Planning Teaching Towards the Effective Use of Computer Algebra Systems

This article suggests a framework to organise a cluster of variables that are associated with students' effective use of computer algebra systems (CAS) in mathematics learning. Based on a review of the literature and from the authors' own teaching experience, the framework identifies the main characteristics of students' interactions with CAS technology and how these may be used to monitor students' developing use of CAS; from this, the framework may be used to plan teaching in order to gain greater benefit from the availability of CAS. Four case studies describing students' development over a semester are reported. These demonstrate a variety of combinations of technical competencies and personal attributes. They indicate the importance of both the technical and personal aspects but suggest that negative attitudes rather than technical difficulties can limit the effective use of CAS. Finally practical suggestions are given for teaching strategies which may promote effective use of CAS.This revised version was published online in September 2005 with corrections to the Cover Date.     

The practical synthesis of a novel and highly potent analogue of bryostatin

Macrocycle 1 is a new highly potent analogue of bryostatin 1, a promising anti-cancer agent currently in human clinical trials. In vitro, 1 displays picomolar affinity for PKC and exhibits over 100-fold greater potency than bryostatin 1 when tested against various human cancer cell lines. Macrocycle 1 can be generated in clinically required amounts by chemical synthesis in only 19 steps (LLS) and represents a new clinical lead for the treatment of cancer.     

Aspects of stereochemistry—I Properties and reactions of some diols

The extent of intramolecular hydrogen-bonding, as determined by infra-red spectroscopy in the hydroxyl stretching region, in certain vicinal diols of cyclohexane, cyclopentane, tetrahydropyran and tetrahydrofuran and in related compounds provides evidence for the stabilities of different conformations. In certain compounds these stabilities can be affected by hydrogen bonding from a substituent hydroxyl group to a ring oxygen. Additional evidence is provided in the case of the tetrahydropyran diols by [M]_D values. The rate of reaction of the vicinal diols of these cyclic systems with glycol splitting reagents, and their zone electrophoretic mobility in an alkaline borate buffer is influenced by the presence of a ring oxygen.     

Crystal and molecular structure, and P N.M.R. characteristics of di-μ-chlorodi(propionyl)bis(dimethylphenylphosphine)diplatinum(III). Trans-influence of ligands in binuclear complexes

The known complex, $\text{trans}$-(η-C₅H₅)₂Rh₂(CO)₂(CF₃C₂CF₃) is formed in high yield from (η-C₅H₅)Rh(CO)₂ and CF₃FCCF₃ at 100°. The less stable $\text{cis}$-isomer of the complex is obtained in low yield from the same reaction. The infrared, ¹H, ¹⁹F and ¹³C NMR spectra of the two isomers are compared. The $\text{trans}$-isomer undergoes CO scrambling in solution at room temperature, and the variable temperature ¹³C NMR spectra are consistent with a pairwise bridge opening and closing mechanism. The mechanism is extended to account for the isomerization of $\text{cis}$ to $\text{trans}$ isomer, whihc has a half-life of 12 h at room temperature. The ¹³C spectrum indicates that the $\text{cis}$-isomer is static in solution at room temperature. The $\text{trans}$-isomer is reversibly protonated by protonic acids, and BF₄^? and PF₆^? salts of the protonated species can be isolated. The spectroscopic properties of these salts are consistent with protonation at one of the alkynyl-carbons, but it is not possible to distinguish between two alternative structures for the complex cation.Treatment of (η-C₅H₅)₂Rh₂(CO)₂(CF₃C₂CF₃) with (η-C₅H₅)Rh(CO)₂ gives the trinuclear complex (η-C₅H₅)₃Rh₃(CO)(CF₃C₂CF₃) in 80% yield. The analogoug but-2-yne complex is formed from (η-C₅H₅)₃Rh₃(CO)₃ and MeCCMe. The infrared, ¹H, ¹⁹F and ¹³C NMR spectra indicate that the hexafluorobut-2-yne complex exists in two different structural arrangements in solution. One has an edge bridging, and the other a face bridging carbonyl. The proportion of the isomers is affected by the solvent polarity. The spectra of the but-2-yne complex indicate it is fluxional at room temperature, and has a face bridging structure in solution regardless of the polarity of the solvent. Reversible protonation of the hexafluorobut-2-yne complex occurs in protonic acids, and the salt [(η-C₅H₅)₃Rh₃(CO)(CF₃C₂CF₃)H]⁺[BF₄]^?,H₂O can be isolated. The spectroscopic properties of this complex are consistent with a structure incorporating an edge-bridging carbonyl, and probably, an edge-bridging hydride ligand.     

Asymmetric enamide hydrogenation in the synthesis of N-acetylcolchinol: a key intermediate for ZD6126

A synthesis of N-acetylcolchinol, a key intermediate in the synthesis of ZD6126, was developed. The enantiodifferentiating step required the catalytic asymmetric hydrogenation of an enamide. After screening a range of metal and ligand combinations it was found that (S,S)-ⁱPr-FerroTANE Ru(methallyl)₂ and [(S,S)-^tBuFerroTANE Rh(COD)]BF₄ gave both high enantioselectivity (>90% ee) and high catalyst utility (molar S/C = 1000).     

Supersilylating agents from chlorosilanes

The addition of R₃SiCl to B(OTf)₃ gives “supersilylating agents” formulated as R₃SiB(OTf)₃Cl. The catalytic properties of these species are similar to those of the previously-described (but less accessible) R₃SiB(OTf)₄.     

Samarium(II)-mediated reactions of gamma,delta-unsaturated ketones. Cyclization and fragmentation processes

[reaction: see text] On treatment with samarium(II) iodide, gamma,delta-unsaturated ketones undergo very different processes depending upon the nature of the reaction conditions. Employing samarium(II) iodide and MeOH, functionalized syn-cyclopentanol products are obtained stereoselectively. Mechanistic studies suggest that this cyclization occurs via a sequential reduction/intramolecular aldol reaction. With samarium(II) iodide and HMPA, products of a 4-exo-trig cyclization and of an interesting fragmentation reaction are observed.     

Structure of a styrylbenzoselenazole platinum(II) complex: [NEt4][Pt(nsbse)Br3]

Tetraethylammonium tribromo[2-(2-chloro-5-nitrostyryl)benzoselenazole] platinate (II), [(C₂H₅)₄N][PtBr₃(C₁₅H₉ClN₂O₂Se)], is monoclinic, in space groupP2₁/c, witha=9.496(2),b=20.321(7),c=15.166(3)Å,=100.18(1)°,V=2880(2)ų,M _r =928.72,Z=4,D _x =2.141 g cm^–3, (MoK)=0.71073 Å,=104.1 cm^–1,F(000)=1752,T=298 K. The structure was solved by direct methods and refined toR=0.032 for 2626 unique observed reflections withI>3(I). The [Pt(nsbse)Br₃)] unit has square-planar geometry about the Pt atom, with the nsbse coordinated to the Pt through the N of the selenazole ring. The ligand molecule is non-planar, with a dihedral angle of 61.6(2)° between the benzoselenazole and phenyl rings. The dihedral angles between the PtBr₃ plane and the benzoselenazole and phenyl planes are 105.2(1) and 80.7(1)°, respectively.