Beyond mathematical content knowledge: A mathematician's knowledge needed for teaching an inquiry-oriented differential equations course

In this research report we examine knowledge other than content knowledge needed by a mathematician in his first use of an inquiry-oriented curriculum for teaching an undergraduate course in differential equations. Collaboratively, the mathematician and two mathematics education researchers identified the challenges faced by the mathematician as he began to adopt reform-minded teaching practices. Our analysis reveals that responding to those challenges entailed formulating and addressing particular instructional goals, previously unfamiliar to the instructor. From a cognitive analytical perspective, we argue that the instructor's knowledge — or lack of knowledge — influenced his ability to set and accomplish his instructional goals as he planned for, reflected on, and enacted instruction. By studying the teaching practices of a professional mathematician, we identify forms of knowledge apart from mathematical content knowledge that are essential to reform-oriented teaching, and we highlight how knowledge acquired through more traditional instructional practices may fail to support research-based forms of student-centered teaching.     

Molecular Recognition by Zn(II)-Capped Dynamic Foldamers

Two α-aminoisobutyric acid (Aib) foldamers bearing Zn(II)-chelating N-termini have been synthesized and compared with a reported Aib foldamer that has a bis(quinolinyl)/mono(pyridyl) cap (BQPA group). Replacement of the quinolinyl arms of the BQPA-capped foldamer with pyridyl gave a BPPA-capped foldamer, then further replacement of the linking pyridyl with a 1,2,3-triazole gave a BPTA-capped foldamer. Their ability to relay chiral information from carboxylate bound to Zn(II) at the N-terminus to a glycinamide-based NMR reporter of conformational preference at the C-terminus was measured. The importance of the quinolinyl arms became readily apparent, as the foldamers with pyridyl arms were unable to report on the presence of chiral carboxylate in acetonitrile. Low solubility, X-ray crystallography and ¹H NMR spectroscopy suggested that interfoldamer interactions inhibited carboxylate binding. However changing solvent to methanol revealed that the end-to-end relay of chiral information could be observed for the Zn(II) complex of the BPTA-capped foldamer at low temperature.     

Clemmensen Reductions Using Ultrasonic Irradiation

A variety of ketones have been reduced to the corresponding methylene compounds using amalgamated zinc and conducting the reaction in an ultrasonic laboratory cleaner.     

(1R,5S)-(+)-Nopinone of High Enantiomeric Purity

Commercial β-pinene of 87% ee can be upgraded to the 98plus;% ee level by simple treatment with silver perchlorate. A solid complex is obtained whose formation is more rapid when two like enantiomers are involved. Simple dissolution of this precipitate in water releases the enantioenriched hydrocarbon from which (+)-nopinone of high enantiomeric purity is obtained via ozonolysis.     

Picosecond water dynamics adjacent to charged paramagnetic ions measured by magnetic relaxation dispersion

Measurements of water-proton spin-lattice relaxation rate constants as a function of magnetic field strength [magnetic relaxation dispersion (MRD)] in aqueous solutions of paramagnetic solutes reveal a peak in the MRD profile. These previously unobserved peaks require that the time correlation functions describing the water-proton-electron dipolar coupling have a periodic contribution. In aqueous solutions of iron(III) ion the peak corresponds to a frequency of 8.7 cm-1, which the authors ascribe to the motion of water participating in the second coordination sphere of the triply charged solute ion. Similar peaks of weaker intensity in the same time range are observed for aqueous solutions of chromium(III) chloride as well as for ion pairs formed by ammonium ion with trioxalatochromate(III) ion. The widths of the dispersion peaks are consistent with a lifetime for the periodic motion in the range of 5 ps or longer.     

Biomimetic mineralisation of polymeric scaffolds using a combined soaking and Kitano approach

Chitosan hydrogels are of considerable interest in synthetic biomimetic mineralisation strategies due to their favourable characteristics such as the presentation of a large surface area for crystal nucleation within a structured yet responsive scaffold. Chitosan hydrogels were prepared and subsequently calcium carbonate mineralisation was initiated using a method which combines alternate soaking of the films with precursor solutions followed by treatment with Kitano solution. This combined approach allows for increased extent of mineralisation, inducement of mineralisation uniformly throughout the hydrogel rather than only at the peripheral surface and ready scalability and shape manipulation. The base synthetic system is readily modified through the introduction of additives that manipulate the nucleation and growth of the calcium carbonate. Addition of poly(acrylic acid) inhibits nucleation and induces tangential crystal growth along the internal and external interfaces of the hydrogel. The resulting composite is comprised of stacked overlapping plates of calcium carbonate intercalated with carbohydrate. The method is applicable in combination with a variety of hydrogels including macroporous chitosan, chitosan-alginate bilayers and pure alginate hydrogels. The composite materials were analysed by SEM, XRD, microRaman spectroscopy and mechanical strength testing.     

Evaluation of Anthocyanin Content,Antioxidant Potential and Antimicrobial Activity of Black,Purple and Blue Colored Wheat Flour and Wheat-Grass Juice against Common Human Pathogens

The present study aimed to analyze the antioxidant and antimicrobial activity of anthocyanins extracted from colored wheat flour and wheat-grass juice against human pathogens. The total anthocyanin content and antioxidant potential in colored wheat flour and wheat-grass juice extracts were significantly higher than white flour and wheat-grass juice extracts. Ultra-performance liquid chromatography showed the maximum number of anthocyanin peaks in black wheat, with delphinidin-3-o-galactoside chloride, delphinidin-3-o-glucoside chloride, and cyanindin-3-o-glucoside chloride as the major contributors. Among flour extracts, maximum zones of inhibition against Staphylococcus aureus (MTCC 1934), Pseudomonas aeruginosa (MTCC 1434), Escherichia coli, and Candida albicans (MTCC 227) were produced by black flour extract, having the highest anthocyanin content. It exhibited a minimum microbicidal concentration (MMC) of 200 mg/mL against E. coli and C. albicans; and 100 and 150 mg/mL against S. aureus and P. aeruginosa, respectively. Black and purple flour extracts exhibited a minimum inhibitory concentration (MIC) of 50 mg/mL against S. aureus and P. aeruginosa. White flour extracts did not show MMC against E. coli and C. albicans. Among wheat-grass juice extracts, black wheat-grass was most effective and showed an MIC of 100–150 mg/mL against all pathogens. It exhibited an MMC of 200 mg/mL against S. aureus and P. aeruginosa. Hence, anthocyanin-rich colored wheat could be of nutraceutical importance.