Using Learning Trajectories for Teacher Learning to Structure Professional Development

As a result of the increased focus on data literacy and data science across the world, there has been a large demand for professional development in statistics. However, exactly how these professional development opportunities should be structured remains an open question. The purpose of this paper is to describe the first iteration of a design experiment involving Project-SET (www.project-set.com) professional development program. Project-SET provided professional development to enhance teachers’ understanding of statistics concepts. The project constructed two learning trajectories for teacher learning and subsequently used the learning trajectories to structure the professional development curriculum. The main goal of this paper is to illustrate how the utilization of the teacher-learning trajectories to structure the professional development allowed participating teachers to develop several aspects of Statistics Knowledge for Teaching (Groth, 2013).     

Experimental and Computational Studies of the Molybdenum‐Flanking Arene Interaction in Quadruply Bonded Dimolybdenum Complexes with Terphenyl Ligands

To clarify the nature of the Mo?C_arene interaction in terphenyl complexes with quadruple Mo?Mo bonds, ether adducts of composition [Mo₂(Ar′)(I)(O₂CR)₂(OEt₂)] have been prepared and characterized (Ar′=Ar^Xyl₂, R=Me; Ar′=ArMes₂, R=Me; Ar′=Ar^Xyl2, R=CF₃) (Mes=mesityl; Xyl=2,6‐Me₂C₆H₃, from now on xylyl) and their reactivity toward different neutral Lewis bases investigated. PMe₃, P(OMe)₃ and PiPr₃ were chosen as P‐donors and the reactivity studies complemented with the use of the C‐donors CNXyl and CN₂C₂Me₄ (1,3,4,5‐tetramethylimidazol‐2‐ylidene). New compounds of general formula [Mo₂(Ar′)(I)(O₂CR)₂( L )] were obtained, except for the imidazol‐2‐ylidene ligand that yielded a salt‐like compound of composition [Mo₂(Ar^Xyl2)(O₂CMe)₂(CN₂C₂Me₄)₂]I. The Mo?C_arene interaction in these complexes has been analyzed with the aid of X‐ray data and computational studies. This interaction compensates the coordinative and electronic unsaturation of one of the Mo atoms in the above complexes, but it seems to be weak in terms of sharing of electron density between the Mo and C_arene atoms and appears to have no appreciable effect in the length of the Mo?Mo, Mo?X, and Mo? L bonds present in these molecules.     

Highly Homogeneous Stereocontrolled Construction of Quaternary Hydroxyesters by Addition of Dimethylzinc to α‐Ketoesters Promoted by Chiral Perhydrobenzoxazines and B(OEt)3

A highly efficient enantioselective addition of Me₂Zn to α‐ketoesters, assisted by a chiral perhydro‐1,3‐benzoxazine ligand, is described. This novel catalytic system offers homogeneous elevated enantioselectivities in the preparation of α‐hydroxyesters that bear a quaternary stereocenter, with a minor dependence on electronic and steric effects when aromatic, heteroaromatic, or aliphatic α‐ketoesters are employed. The catalyst can be recovered and reused without loss of activity.     

Reductive Ring Opening of Ephedrine and Pseudo-Ephedrine-Derived Oxazolidinium Methiodides by Sodium Borohydride. A Direct Access to New Chiral Amine-Borane Adducts

Sodiun borohydride reacts with oxazolidinium methiodides derived from ephedrine and pseudoephedrine, in ethereal solvents, cleaving regioselectively the C-N bond of the ring and leading, in good yields, to chiral amine-borane adducts of know absolute configuration. The ¹HNMR data allow to predict the most stable conformation.     

Experimental and Theoretical Studies on Arene‐Bridged Metal–Metal‐Bonded Dimolybdenum Complexes

The bis(hydride) dimolybdenum complex, [Mo₂(H)₂{HC(N‐2,6‐iPr₂C₆H₃)₂}₂(thf)₂], 2 , which possesses a quadruply bonded Mo₂^II core, undergoes light‐induced (365 nm) reductive elimination of H₂ and arene coordination in benzene and toluene solutions, with formation of the Mo^I₂ complexes [Mo₂{HC(N‐2,6‐iPr₂C₆H₃)₂}₂(arene)], 3?C₆H₆ and 3?C₆H₅Me , respectively. The analogous C₆H₅OMe, p‐C₆H₄Me₂, C₆H₅F, and p‐C₆H₄F₂ derivatives have also been prepared by thermal or photochemical methods, which nevertheless employ different Mo₂ complex precursors. X‐ray crystallography and solution NMR studies demonstrate that the molecule of the arene bridges the molybdenum atoms of the Mo^I₂ core, coordinating to each in an η² fashion. In solution, the arene rotates fast on the NMR timescale around the Mo₂‐arene axis. For the substituted aromatic hydrocarbons, the NMR data are consistent with the existence of a major rotamer in which the metal atoms are coordinated to the more electron‐rich C?C bonds.     

Novel spiro and fused heterocycles from the allylation of indigo

The allylation of indigo results in the one-step synthesis of two unique complex heterocyclic systems: a spiroindoline-pyridoindolone arising from the addition of three allyl moieties and a fused pyridoindolo-azepinoindolone generated from the addition and subsequent cyclisation of two allyl moieties. The structures of these novel heterocycles are assigned unambiguously using extensive NMR experiments and by X-ray crystallographic analysis. The distribution of the products is influenced by the use of thermal versus microwave heating.     

Synthetic,Mechanistic, and Theoretical Studies on the Generation of Iridium Hydride Alkylidene and Iridium Hydride Alkene Isomers

Experimental and theoretical studies on equilibria between iridium hydride alkylidene structures, [(Tp^Me2)Ir(H){?C(CH₂R)ArO }] (Tp^Me2=hydrotris(3,5‐dimethylpyrazolyl)borate; R=H, Me; Ar=substituted C₆H₄ group), and their corresponding hydride olefin isomers, [(Tp^Me2)Ir(H){R(H)C? C(H)OAr}], have been carried out. Compounds of these types are obtained either by reaction of the unsaturated fragment [(Tp^Me2)Ir(C₆H₅)₂] with o‐C₆H₄(OH)CH₂R, or with the substituted anisoles 2,6‐Me₂C₆H₃OMe, 2,4,6‐Me₃C₆H₂OMe, and 4‐Br‐2,6‐Me₂C₆H₂OMe. The reactions with the substituted anisoles require not only multiple C? H bond activation but also cleavage of the Me? OAr bond and the reversible formation of a C? C bond (as revealed by ¹³C labeling studies). Equilibria between the two tautomeric structures of these complexes were achieved by prolonged heating at temperatures between 100 and 140 °C, with interconversion of isomeric complexes requiring inversion of the metal configuration, as well as the expected migratory insertion and hydrogen‐elimination reactions. This proposal is supported by a detailed computational exploration of the mechanism at the quantum mechanics (QM) level in the real system. For all compounds investigated, the equilibria favor the alkylidene structure over the olefinic isomer by a factor of between approximately 1 and 25. Calculations demonstrate that the main reason for this preference is the strong Ir–carbene interactions in the carbene isomers, rather than steric destabilization of the olefinic tautomers.