Reviving Pólya's “Look Back” in a Singapore school

This study is based on the stance that Pólya's “Look Back,” though understudied, remains relevant to Mathematics curricula that place emphasis on problem solving. Although the Singapore Mathematics curriculum adopts the goal of teaching Look Back, research about how it is carried out in actual classroom practice is rare. In our project, we focus on a redesign of a teacher development programme that is targeted to help teachers realize Pólya's original vision of Look Back in the classroom. We report the cases of two teachers who have participated in the teacher development programme: their thinking about Look Back (through interview records) and their interpretation of Look Back in their classroom practice (through video records). By bringing these two spheres of data together, we discuss their degree of ‘buy-in’ to Look Back in the overall problem solving enterprise.     

(+)‐(2R,3S)‐3‐Bromo‐2‐chloro‐N,N‐diiso­propyl‐3‐phenyl­propan­amide and (+)‐(2R,3S)‐3‐bromo‐2‐chloro‐N‐(4‐nitro­phenyl)‐3‐phenyl­propan­amide

The stereochemistries at positions 2 and 3 of the title compounds, C₁₅H₂₁BrClNO, (I), and C₁₅H₁₂BrClN₂O₃, (II), have been confirmed by X‐ray structural analysis. The halogen atoms adopt an antiperiplanar arrangement in each case.     

Synthesis and characterization of chemically anchored adenosine with PHEMA grafted gold nanoparticles

The synthesis of chemically anchored adenosine with biocompatible poly(2-hydroxylethyl methacrylate) grafted gold nanoparticles (Ado-i-PHEMA-g-AuNPs) was realized by employing a simple strategy. Disulfide-containing poly(2-hydroxylethyl methacrylate) (DT-PHEMA) was initially synthesized by atom transfer radical polymerization (ATRP). The formation of DT-PHEMA was confirmed by ¹H-NMR and FT-IR. The molecular weight and molecular weight distribution were found to be 9.6 kg/mol and 1.40 from GPC analysis. DT-PHEMA was subsequently used for the synthesis of PHEMA-g-AuNPs by a grafting to protocol. The grafting of DT-PHEMA on the surface of AuNPs was confirmed by FT-IR, TGA, XPS, and EDX analyses. The particle size of the PHEMA-g-AuNPs was found to be ca. 5.0 nm from HR-TEM analysis. Boronic acid was used for functionalization of PHEMA-g-AuNPs, which was then subjected for covalent immobilization with adenosine via strong interaction between free hydroxyl groups of adenosine and boronic acid. Characterization and properties of the Ado-i-PHEMA-g-AuNPs were investigated by taking advantage from FT-IR, XPS, EDX, and UV-visible spectroscopy. The Ado-i-PHEMA-g-AuNPs nanocomposite exhibits a surface plasmon resonance peak at 586 nm which is red shifted from AuNPs (521 nm), indicating significant changes of surface property upon PHEMA-adenosine immobilization onto the surface of AuNPs.     

Synthesis and characterization of poly(1,4‐bis((E)‐2‐(3‐dodecylthiophen‐2‐yl)vinyl)benzene) derivatives

New amorphous semiconducting copolymers, poly(9,9‐dialkylfluorene)‐alt‐(3‐dodecylthienyl‐divinylbenzene‐3‐dodecylthienyl) derivatives (PEFTVB and POFTVB), were designed, synthesized, and characterized. The structure of copolymers was confirmed by H NMR, IR, and elemental analysis. The copolymers showed very good solubility in organic solvents and high thermal stability with high T_g of 178–185 °C. The weight average molecular weight was found to be 107,900 with polydispersity of 3.14 for PEFTVB and 76,700 with that of 3.31 for POFTVB. UV–vis absorption studies showed the maximum absorption at 428 nm (in solution) and 435 nm (in film) for PEFTVB and at 430 nm (in solution) and 436 nm (in film) for POFTVB. Photoluminescence studies showed the emission at 498 nm (in solution) and 557 nm (in film) for PEFTVB and at 498 nm (in solution) and 536 nm (in film) for POFTVB. The solution‐processed thin‐film transistors showed the carrier mobility of 2 × 10^?4 cm² V^?1 s^?1 for PEFTVB‐based devices and 2 × 10^?5 cm² V^?1 s^?1 for POFTVB‐based devices. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 3942–3949, 2010     

Solvent‐dependent formation of inclusion complexes between methylated cyclodextrins and biodegradable polymers

The inclusion complexes (ICs) of unmodified natural and methylated α‐cyclodextrins (CDs) with biodegradable polymers, polyethylene glycol and poly(ε‐caprolactone), were prepared by two methods, that is, the one using water and the other using chloroform as the solvent for the respective CDs. The ICs obtained were characterized by IR, WAXD, DSC, and ¹³C CP/MAS NMR. It was found that the possibility and the phenomena of IC formation could be varied with the degree of methyl substitution of CD as well as the type of solvents used. Methylated α‐CDs showed the prominent characteristics of IC formation with polymers in the case where chloroform was used than in the case where water was used as the solvent for CDs, while vice versa in the case of native α‐CD. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 879–891, 2008     

Morphological changes during heating in poly(L‐lactic acid)/poly(butylene succinate) blend systems as studied by synchrotron X‐ray scattering

Blends of poly(L ‐lactic acid) (PLA) and poly(butylene succinate) (PBS) were prepared in various compositions via melt mixing, and the morphological changes were investigated with differential scanning calorimetry and synchrotron wide‐angle and small‐angle X‐ray scattering techniques at a heating rate of 10 °C/min. Differential scanning calorimetry thermograms of PLA/PBS blends showed two distinct melting peaks over the entire composition range. The exothermal peak for PLA shifted significantly to a lower temperature and overlapped with that of PBS around 100 °C. A depression of the melting point of the PLA component via blending was observed. The synchrotron wide‐angle X‐ray scattering during heating revealed that there was no cocrystallization or crystal modification via blending. The synchrotron small‐angle X‐ray scattering data showed that well‐defined double‐scattering peaks (or peaks with a clear scattering shoulder) appeared during crystallization, indicating that this system possessed dual lamellar stacks. These peaks were deconvoluted into two components with a peak separation computer program, and then the morphological parameters of each component were obtained by means of the correlation function. The long period and average lamellar thickness of the two components before melting decreased with an increasing content of the other polymer component. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1931–1939, 2002     

Catalytic Stereoinversion of L‐Alanine to Deuterated D‐Alanine

A combination of an achiral pyridoxal analogue and a chiral base has been developed for catalytic deuteration of L ‐alanine with inversion of stereochemistry to give deuterated D ‐alanine under mild conditions (neutral pD and 25 °C) without the use of any protecting groups. This system can also be used for catalytic deuteration of D ‐alanine with retention of stereochemistry to give deuterated D ‐alanine. Thus a racemic mixture of alanine can be catalytically deuterated to give an enantiomeric excess of deuterated D ‐alanine. While catalytic deracemization of alanine is forbidden by the second law of thermodynamics, this system can be used for catalytic deracemization of alanine with deuteration. Such green and biomimetic approach to catalytic stereocontrol provides insights into efficient amino acid transformations.